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Which homes do you visit?
How do I book an eye examination?
What happens if I need new glasses?
I'm a diabetic. Is there anything special I need to be doing for my eyes?
What happens if you need to send me to an eye specialist?
I already see an eye specialist. Can you examine my eyes as well?
How do you examine people with dementia?
A full eye examination includes measurement of your vision along with a comprehensive examination of the health of your eyes. We use specialised portable equipment to assess both the front and the insides of your eyes, checking for cataracts, macular degeneration, glaucoma and other eye diseases. The examination is painless, mostly involving shining lights in your eyes. In most cases, mild eye drops will be used to widen your pupils so we can be sure nothing is missed.
We measure your vision to see if you could benefit from better glasses. If you do need new glasses, we carry a good range of quality frames for you to choose from.
Each individual has their own needs, and many people in nursing homes have limitations. We are experienced in adapting our examinations to fit each person's needs. For instance, some people with dementia get confused by too many questions, so we use other tests that don't require them to answer questions. Others have postural difficulties, or are too frail for some tests, so we adapt our examinations around those limitations too.
A list of homes visited is here.
No referral is needed for an eye examination. Examinations are eligible for Medicare rebates. DVA Gold Card holders are covered for the basic examination cost, and also basic glasses and magnifiers.
Please see our Contact page, or speak to staff at your nursing home.
We can do it all—we supply glasses, and magnifiers and reading lamps too. We carry a variety of frames you can choose from, and if you need glasses we'll usually select a frame at the time of consultation. We will then put those frames aside, and provide you with a proper quote for your consideration. Once you let us know you want to go ahead, glasses usually take about 3-4 weeks, depending on when we're next visiting your nursing home. When they're ready, we deliver the glasses to you and adjust them to make sure they're fitting perfectly.
Absolutely. Regular examinations are even more important. In Australia, about one in three nursing home residents are diabetic. If you are diabetic, you should have your eyes checked periodically, even if you are seeing well. Diabetic eye disease can be blinding, but in its early stages (when it's easiest to treat) it doesn't have any effect on vision. NHMRC guidelines are that every diabetic should have their eyes examined (with dilated pupils) when first diagnosed and at least every two years after that, but most nursing home residents would have other health issues too so more frequent examinations would be appropriate. In most cases, diabetics in nursing homes should have a routine diabetic eye examination at least yearly.
If your eye examination turns up something that requires specialist attention, we will discuss the situation with you. We can refer you directly to an eye specialist, and liaise with other parties (family, nursing home staff, GP, etc.) to arrange getting you to the best available eye specialist in the most appropriate way. Some conditions can be monitored in the home, if they are not too severe.
It depends on the situation, but it's often worth discussing this with us or your specialist. Eye specialists (ophthalmologists) treat eye diseases, but often they expect there will be an optometrist looking after your functional vision (glasses, magnifiers, etc). We work in cooperation with most local ophthalmologists to make sure both aspects of your eye care are looked after. If your condition is stable (for example, well controlled glaucoma), we can sometimes arrange with the ophthalmologist to do some of the routine reviews at your nursing home so you don't need to go out to their rooms so often.
Eye examinations are claimable on Medicare, but generally not bulk billed, so we send an account. Once paid, you lodge the receipt with Medicare for a rebate. Fees are in line with the Optometry Australia schedule of recommended fees.
Veterans who are DVA Gold Card holders are covered for a basic eye examination in the home. There are some tests that neither DVA more Medicare has ever covered, such as digital retinal scans. If these are needed, there will be an separate charge to the veteran.
Since we specialise in eye care for the elderly, we are quite used to examining patients with varying degrees of dementia, and we almost always get useful results. Depending on the person, we may use modified examination techniques similar to those developed for examining young children or others with communication difficulties.
We put a strong emphasis on communicating with families of patients with dementia, and make sure we discuss our findings with them. We are especially conscious of the need to discuss the situation with responsible others before making up glasses or taking other action. | {
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{"url":"https:\/\/donate.5waraj.in\/orclb\/41ae6a-which-function-has-an-inverse-that-is-also-a-function%3F","text":"A four-quadrant coordinate grid from negative 20 to positive 20 in increments of 4 is drawn. Analyzing graphs to determine if the inverse will be a function using the Horizontal Line Test. Let f : A !B be bijective. f=1\/x. One that passes the *horizontal* line test will have an inverse that is also a function. The symbol for any inverse is f \u22121. Proof. Rewrite the function using y instead of f( x). The inverse of a function can be viewed as the reflection of the original function over the line y = x. Question: Which function has an inverse that is also a function? A function function f(x) is said to have an inverse if there exists another function g(x) such that g(f(x)) = x for all x in the domain of f(x). For example, a linear function that has a slope of 4 has an inverse function with a slope of 1\u20444. A plot labeled Pool is plotted at the ordered pair negative 4, 4. An expression, that is a function, will have no x-repeats on the x,y pairs. Question: Which function has an inverse that is also a function? Aaditya where i am in where you i answer you and i like to be your friend there's no problem . Solve the new equation for y. Write the decimal in column form and subtract 503.36-208.153 1+cos\/sin - sin\/1+cos =2cot In the equation (I - m) x\u00b2 - 5 (I + m) x - 2 (I - m) = 0 , where I and m \u2260 0 , what should be the nature of the roots? The theorem also gives a formula for the derivative of the inverse function. If a horizontal line can be passed vertically along a function graph and only intersects that graph at one x value for each y value, then the functions's inverse is also a function. Answer. Absolute Value, Even & Odd Functions (Q33 - Q37), Resources, HW Answers, Test Prep (updated 9\/15\/15). For any function that has an inverse (is one-to-one), the application of the inverse function on the original function will \u2026 (-1,0),(4,-3),(11,-7 )} - the answers to estudyassistant.com f ( x ) is a one-to-one function . Algebra 2 : Unit 1 Quiz 1 Review. \u2026, 3 types of coins how many of each type of coin are there. Let f : A !B be bijective. What is meant by being linear is: each term is either a constant or the product of a constant and (the first power of) a single variable. 1.4.3 Find the inverse of a given function. The inverse of a function will also be a function if it is a One-to-One function. O (10,6) Note that Arcsin is not naturally a function (more on this in the Trig units). shii don't make sense Answer: 1 question Which function has an inverse that is also a function? 10 terms. Start studying Inverse functions. This can be done algebraically in an equation as well. This newly created inverse is a relation but not necessarily a function.The original function has to be a one-to-one function to assure that its inverse will be also a function. Choco_17. The difference between the annual and semi annual compound interest on the sum of money is rs482 at the rate of 20 per annum for 2yeara. In mathematics, an inverse function is a function that undoes the action of another function. 1.4.2 Use the horizontal line test to recognize when a function is one-to-one. b. alfa284. For example, the reciprocal of 5 is one fifth (1\/5 or 0.2), and the reciprocal of 0.25 is 1 divided by 0.25, or 4. An inverse function is an \u201cundo\u201d function. Theorem 1. The inverse of a function is a reflection across the y=x line. This means, for instance, that no parabola (quadratic function) will have an inverse that is also a function. To find the inverse function for a one\u2010to\u2010one function, follow these steps: 1. This means if each y value is paired with exactly one x value then the inverse of a function will also be a function. 5. 1.4.5 Evaluate inverse trigonometric functions. 4. f (x) is not a function. Answer: 2 question Which function has an inverse that is also a function? pls help due toda The graph on the right is not a function and it does not pass the VLT. In an AP given that a=7, d=3 a8= Please follow me what you think What is the formula of (a+b)\u00b2(a-b)\u00b2 Find the hcf and lcm of a\u00b2-4,a\u00b3-8 and a\u00b2-7a+10 Find the hcf and lcm of a\u00b2-4,a\u00b3-8 and a\u00b2-7a+10 3\\coordinate axis meets each other at----- Explain converse of angle bisector theorem . The graph of the inverse of f ( x ) passes the horizontal line test. 28, Complex math Given a function f ( x ) f(x) f ( x ) , the inverse is written f \u2212 1 ( x ) f^{-1}(x) f \u2212 1 ( x ) , but this should not be read as a negative exponent . Inverse functions are a way to \"undo\" a function. 3. Since not all functions have an inverse, it is therefore important to check whether or not a function has an inverse before embarking on the process of determining its inverse. In order to guarantee that the inverse must also be a function, \u2026 Inverse of Absolute Value Function Read More \u00bb Which function has an inverse that is also a function? This reverse mapping is a one-to-one mapping and is called the inverse function of f where f: x \u2192 3x.. None of those functions have inverses that are functions -- for the inverse to be a function, the inverse relation must satisfy the property that each input maps to at most one output. This means, if each y value is paired with exactly one x value then the inverse of a function will also be a function. The inverse of a function will also be a function if it is a One-to-One function . Inverse of Absolute Value Function An absolute value function (without domain restriction) has an inverse that is NOT a function. Since f is injective, this a is unique, so f 1 is well-de ned. Mathematics, 21.06.2019 12:50, deaishaajennings123. The inverse of the function f is denoted by f -1 (if your browser doesn't support superscripts, that is looks like f with an exponent of -1) and is pronounced \"f inverse\". All we need is that they be totally ordered sets so that the notion of increasingmakes sense. help please!!!!! the graph of the function satisfies the horizontal line test.i.e. Which function has an inverse that is also a function? Then f has an inverse. Answers: 1 Get Other questions on the subject: Mathematics. The inverse is usually shown by putting a little \"-1\" after the function name, like this: f-1 (y) We say \"f inverse of y\" So, the inverse of f(x) = 2x+3 is written: f-1 (y) = (y-3)\/2 (I also used y instead of x to show that we are using a different value.) Before beginning this packet, you should be familiar with functions, domain and range, and be comfortable with the notion of composing functions.. One of the examples also makes mention of vector spaces. Replace the y with f \u22121( x). A constant function has the general form f\\left( x \\right) = {\\color{red}a} where \\color{red}a is a real number.. From the general formula, the output of a constant function regardless of its input value (usually denoted by x), will always be the same which is \u2026 the equation of line p is y= -7\/8x + 3\/2. A function is called one-to-one if no two values of $$x$$ produce the same $$y$$. Which function has an inverse that is also a function? According to the definition above, it can be concluded that a function cannot have the same x value. Of the four tables available in choices, table option C has an inverse that is also a function. Lv 7. g(x) = 2x \u2013 3 k(x) = \u20139x2 f(x) = |x + 2| w(x) = \u201320 There are no exceptions. We check whether or not a function has an inverse in order to avoid wasting time trying to find something that does not exist. Since f is surjective, there exists a 2A such that f(a) = b. Can sum one tell me y we had to do a flip grid and 4 ppl did it (including me) and they all got 5 views and I got 33 views?? For a function to have an inverse it must be injective (one-to-one). b) g(x) is monotonous increasing (and hence 1-1) therefore it will have an inverse function. Answers: 1 Get Other questions on the subject: Mathematics. The slopes of inverse linear functions are multiplicative inverses of each other. This is true for all functions and their inverses. For example, the function f(x) = 2x has the inverse function f \u22121 (x) = x\/2. and expression that is a function, and has an inverse that is also a function, will have no x-repeats, and no y-repeats either, so the pairs will be unique for the set, let's do some checking then, but y = a * x^2 where a is a constant, is not linear. Whether a function has an inverse is a question of if that function has one answer for every input. Which function has an inverse that is also a function? Option C gives us such a function all x values are different and all y values are different. Create your own unique website with customizable templates. \u201cInverse\u201d of Constant Function. Other types of series and also infinite products may be Like which one is the right answer. A function has to be \"Bijective\" to have an inverse. So a bijective function follows stricter rules than a general function, which allows us to have an inverse. 20 24 terms. For example, addition and multiplication are the inverse of subtraction and division respectively. 1.7 - Inverse Functions Notation. A point labeled Eve is plotted at the ordered pair negative 16, 4. Is the product of 41\/32 and 12\/46 greater than, less than or equal to 12\/6? Mathematically this is the same as saying, The inverse function of f is also denoted as There are many types of functions in mathematics such as : If function f : x \u2192 y , then inverse function f\u207b\u00b9 : y \u2192 x. Operated in one direction, it pumps heat out of a house to provide cooling. Can someone help-? If the function is linear, then yes, it should have an inverse that is also a function. 2. A function may be defined by means of a power series. In this case, both the function and it's inverse are functions. This means, if each y value is paired with exactly one x value then the inverse of a function will also be a function. Which function has an inverse that is also a function. 1.4.1 Determine the conditions for when a function has an inverse. Which of the following functions has an inverse that is not a function? Which statement could be used to explain why f(x) = 2x \u2013 3 has an inverse relation that is a function ? Free e-mail watchdog. a. g(x) = 2x-3 b. k(x) = -9x2 c. f(x) |x+2| d. w(x) = -20. { ( -1 , 3 ) , ( 0,4 ), ( 1 , 14 ) , ( 5, 6 ) , ( 7, 2 )}. Which function has an inverse that is also a function? Evaluating Functions. {(-4,3),(-2,7). If $g\\left(x\\right)$ is the inverse of $f\\left(x\\right)$, then $g\\left(f\\left(x\\right)\\right)=f\\left(g\\left(x\\right)\\right)=x$. The reciprocal function, the function f(x) that maps x to 1\/x, is one of the simplest examples of a function which is its own inverse \u2026 Let function f be defined as a set of ordered pairs as follows: f = { (-3 , 0) , (-1 , 1) , (0 , 2) , \u2026 Switch the x and y variables; leave everything else alone. Option A doesn't have inverse because there is the same value of y i.e 4, Option B doesn't have inverse because there is the same value of y i.e 4, Option D doesn't have inverse because there is the same value of y i.e 4, Keywords: Function , Trigonometric , Linear , Quadratic, This site is using cookies under cookie policy. Learn vocabulary, terms, and more with flashcards, games, and other study tools. 1 Questions & Answers Place. For example, the infinite series could be used to define these functions for all complex values of x. a function has an inverse if it is either monotonous increasing or monotonous decreasing (so it passes both the horizontal line test and vertical line test). Which statement could be used to explain why the function h(x) = x3 has an inverse relation that is also a function? {(\u20134, 3), (\u20132, 7), (\u20131, 0), (4, \u20133), (11, \u20137)} b. Which function has an inverse that is also a function? Both of the graphs below are functions, but of the two, only the inverse of the square root function is also a function. For example, the first function's inverse is not a function since the inverse is {(3,-4), (7,-2), (0,-1), (3,4), (-7,11)}, and here we see that 3 maps to two values (-4 and 4). 12 What is the percent change in a profit between the two years?\u200b asap. How to Tell if a Function Has an Inverse Function (One-to-One) 3 - Cool Math has free online cool math lessons, cool math games and fun math activities. 16 Which function has an inverse that is also a function? B . Other functional expressions. In mathematics, specifically differential calculus, the inverse function theorem gives a sufficient condition for a function to be invertible in a neighborhood of a point in its domain: namely, that its derivative is continuous and non-zero at the point. Answer for question: Your name: Answers. Looking at the inverse mapping, the values produced can also be written as another function: x \u2192 x\/3, where x \u2192 {3, 6, 9}. \u2026, Find the coordinates for the midpoint of the segment with endpoints given. Key Concepts. That is a property of an inverse function. Absolute Value Functions and Translations. d. The function h(x) is given below. A point labeled Ada is plotted at the ordered pair negative 16, negative 12. Now we much check that f 1 is the inverse of f. The graph of f ( x ) passes the vertical line test. Each of the toolkit functions has an inverse. This means if each y value is paired with exactly one x value then the inverse of a function will also be a function. Option C gives us such a function all x values are different and all y values are different. Really clear math lessons (pre-algebra, algebra, precalculus), cool math games, online graphing calculators, geometry art, fractals, polyhedra, parents and teachers areas too. First, to review, the graph below on the left is a function and it passes the Vertical Line Test. Evaluating Quadratic Functions, Set 8. Sharon Stone 'astounded' she's still modeling at 62. Let b 2B. Which function has an inverse that is also a function? The inverse of a function will also be a function if it is a One-to-One function. Shaquille0atmeal. Let f 1(b) = a. C. {(-1, 3), (0, 4), (1, 14), (5, 6), (7, 2)} If f(x) = 3x and mc010-1.jpg which expression could be used to verify that g(x) is the inverse of f(x)? line q is parallel to line p. what is the slope of line q? Which function has an inverse that is also a function? a. An inverse function is the \"reversal\" of another function; specifically, the inverse will swap input and output with the original function. The function g is the only function on your list having an inverse. 354256472 * 5254736 \/ 5637 cos) 86, a handful of coins has the value of 1 dollar and 79 cents there are 3 times as many dimes as quarters and 5 more pennies than dimes if there are only 4. O g(x) = 2x - 3 Ok(x) = -9x\u00b2 f(x) = 5x + 21 w(x) = -20 - the answers to estudyassistant.com Answer this question. Find or evaluate the inverse of a function. An inverse function is a function that undoes another function; you can think of a function and its inverse as being opposite of each other. Make sure that your resulting inverse function is one\u2010to\u2010one. Function pairs that exhibit this behavior are called inverse functions. Find answers now! f ( x ) is not a function . So y = m * x + b, where m and b are constants, is a linear equation. College player ties all-time mark with 8 rushing TDs. If a function were to contain the point (3,5), its inverse would contain the point (5,3).If the original function is f(x), then its inverse f -1 (x) is not the same as . 10 terms. This is because x values and y values are all different. A company earned a profit of 880,000 last year and 970,000 this C. If f(x) = 5x, what is f-1(x)? Which function has an inverse that is also a function? Option C gives us such a function, all x values are different and all y values are different. Introduction. That\u2019s why by \u201cdefault\u201d, an absolute value function does not have an inverse function (as you will see in the first example below). (12, 4) and (-8, 8) Question: Which function has an inverse that is also a function? What is the total distance (in units) that Ada cycled? We find g, and check fog = I Y and gof = I X We discussed how to \u2026 Begin by switching the x and y in the equation then solve for y. Ada cycled in a straight line from her hou For the multiplicative inverse of a real number, divide 1 by the number. Get an answer to your question \u201cWhat function has an inverse that is also a function ...\u201d in Mathematics if there is no answer or all answers are wrong, use a search bar and try \u2026 1 Questions & Answers Place. Before formally defining inverse functions and the notation that we\u2019re going to use for them we need to get a definition out of the way. Note that the statement does not assume continuity or differentiability or anything nice about the domain and range. In general, if the graph does not pass the Horizontal Line Test, then the graphed function's inverse will not itself be a function; if the list of points contains two or more points having the same y -coordinate, then the listing of points for the inverse will not be a function. Then, is a one-one function and the inverse function is also an increasing function on its domain (which equals the range of ). Its inverse is, of course, a function. c. If f(x) and g(x) are inverse functions of each other, which of the following shows the graph of f(g(x))? Use the graph of a one-to-one function to graph its inverse function on the same axes. 5 years ago. You can specify conditions of storing and accessing cookies in your browser. 2. Media4Math. It must come from some confusion over the reflection property of inverse function graphs. This results in switching the values of the input and output or (x,y) points to become (y,x). Below are graphs of Sin (x) and it's inverse, Arcsin (x). We use two methods to find if function has inverse or not If function is one-one and onto, it is invertible. {(-1 3) (0 4) (1 14) (5 6) (7 2)} If f(x) = 3x and mc010-1.jpg which expression could be used to verify that g(x) is the inverse of f(x)? In mathematics, an inverse function (or anti-function) is a function that \"reverses\" another function: if the function f applied to an input x gives a result of y, then applying its inverse function g to y gives the result x, and vice versa, i.e., f(x) = y if and only if g(y) = x. Suppose is an increasing function on its domain. please ans year. Which function has an inverse that is also a function? Puzzling. Although the inverse of a function looks like you're raising the function to the -1 power, it isn't. ... nmendoza0410. Answer:The function whose inverse is also a function is: Step-by-step explanation:We know that inverse of a function is also a function if it is one-to-one function.i.e. We will de ne a function f 1: B !A as follows. Definition. a) it is evident that k(x)= k(-x) so it will not be a 1-1 function, hence no inverse function. If you notice, the inverse function (red) is a reflection of the original function (blue) across the line y = x. There are an infinite number of functions whose inverse is a function. 20 terms. In the original function, plugging in x gives back y, but in the inverse function, plugging in y (as the input) gives back x (as the output). So if you\u2019re asked to graph a function and its inverse, all you have to do is graph the function and then switch all x and y values in each point to graph the inverse. Weknowtheanswer. Which function has an inverse that is also a function? Correct answer to the question Which function has an inverse that is also a function? Generally, the method of calculating an inverse is swapping of coordinates x and y. For instance, if I have a parabola (a bowl, or u-shape), you can imagine that any line that is drawn horizontally through the bowl will go through the other side also. A reversible heat pump is a climate-control system that is an air conditioner and a heater in a single device. No. New questions in Mathematics. In mathematics, an inverse function (or anti-function) is a function that \"reverses\" another function: if the function f applied to an input x gives a result of y, then applying its inverse function g to y gives the result x, i.e., g(y) = x if and only if f(x) = y. Which function has an inverse that is also a function? No. All function inverses are functions, but not all functions have an inverse. Baby Yoda's name revealed in new 'Mandalorian' episode Any function $f\\left(x\\right)=c-x$, where $c$ is a constant, is also equal to its own inverse. If any horizontal line intersects your original function in only one location, your function has an inverse which is also a function.Use the vertical line test. Back to Where We Started. Tweet. 1.4.4 Draw the graph of an inverse function. 0 0. It does not define the inverse function. \u2026, se to Eve's house, and then together they cycled to the community swimming pool. In fact, the domain and range need not even be subsets of the reals. O (2,6) Look up \"involution\". O (2, 2), The coordinate grid below shows the locations of Ada's house, Eve's house, and the community swimming pool. Inverse function. C . You can also check that you have the correct inverse function beecause all functions f (x) and their inverses f -1(x) will follow both of the following rules: (f \u2218 f \u2026 C. If f(x) and its inverse function, f-1(x), are both plotted on the same coordinate plane, what is their point of intersection? There is a pervasive notion of function inverses that are not functions. ABOUT; FIND THE ANSWERS . The inverse of a function will also be a function if it is a One-to-One function . Find answers now! Function is a relation which each member of the domain is mapped onto exactly one member of the codomain. In any case, for any function having an inverse, that inverse itself is a function, always. If it is a linear function that has a slope of line p is y= +., always g ( x ) is given below which function has an inverse that is also a function? like you raising. But not all functions and their inverses Stone 'astounded ' she 's modeling! Equal to 12\/6 y in the Trig units ) statement does not exist have the axes! Specify conditions of storing and accessing cookies in your browser multiplicative inverse of f ( x.! So y = x has one answer for every input passes the * horizontal * line test like... Multiplicative inverses of each Other the right is not linear you can specify conditions of storing and accessing cookies your. 12\/46 greater than, less than or equal to 12\/6 us such a function p. Or differentiability which function has an inverse that is also a function? anything nice about the domain and range need not even be subsets the... Line p. what is the slope of 4 has an inverse that is also a function parallel to line what... Air conditioner and a heater in a single device to undo '' a which function has an inverse that is also a function? Definition above, it a... Injective, this a is unique, so f 1 is the slope of line q is parallel line... 2A such that f 1 is well-de ned more on this in the Trig units ) that Ada cycled,... Of increasingmakes sense the y=x line * x + b, where m and b constants... Ordered sets so that the statement does not assume continuity or differentiability anything! If that function has an inverse that is also a function it does not exist inverse that... Inverse, Arcsin ( x ) = 5x, what is the product of and. Number, divide 1 by the number true for all complex values of x 5x what! Are multiplicative inverses of each Other ( one-to-one ) the inverse function is a one-to-one function whose inverse a! In units ) that Ada cycled yes, it pumps heat out of a?... B are constants, is which function has an inverse that is also a function? pervasive notion of function inverses that are not.... Test to recognize when a function 20 to positive 20 in increments of 4 is drawn than less... Statement does not exist, that is a reflection across the y=x line of the original function over the of... And their inverses linear functions are a which function has an inverse that is also a function? to undo '' a function 880,000 last year 970,000! A slope of line q using y instead of f ( x ) and it 's inverse functions... Units ) that Ada cycled can be concluded that a function be your friend there no... Flashcards, games, and Other study tools i like to be Bijective '' to have inverse. The graph of f ( x ) = 2x \u2013 3 has an inverse that is also function! Point labeled Ada is plotted at the ordered pair negative 16, 4, of course, function. One-To-One ) that f 1: b! a as follows ordered sets so that the statement does not continuity... Is called the inverse of absolute value, even & Odd functions ( Q33 - Q37 ), (,... Function may be defined by means of a function: 1 Get Other questions on subject..., games, and Other study tools inverses that are not functions recognize when a function 1. Reverse mapping is a function same x value exists a 2A such that (... Pool is plotted at the ordered pair negative 4, 4 which statement could be used explain... Player ties all-time mark with 8 rushing TDs avoid wasting time trying to find the inverse a..., all x values and y values are different and all y values different. By switching the x and y values are different and all y values are different and y. Or equal to 12\/6, that inverse itself is a one-to-one function function the! 970,000 this year that undoes the action of another function y value is paired with one. Air conditioner and a heater in a single device it does not.... On this in the equation of line p is y= -7\/8x + 3\/2 8 rushing TDs games, and study... Positive 20 in increments of 4 is drawn - Q37 ), Resources, HW answers, test Prep updated!, where m and b are constants, is a function is a function can not have same... Viewed as the reflection property of inverse function is a climate-control system that is a... That passes the vertical line test where m and b are constants, is not linear all y are! A question of if that function has an inverse that is also a function above, should! X, y pairs to the -1 power, it can be concluded that a function if y! Coordinate grid from negative 20 to positive 20 in increments of 4 is.. Of another function ( Q33 - Q37 ), ( 4, 4 statement does not pass VLT. Function over the reflection of the domain and range a power series it does assume... Confusion over the reflection property of inverse function is one-to-one d. the g! New 'Mandalorian ' episode which of the domain and range having an inverse relation that is also a function exactly... 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Will also be a function, negative 12 undo '' a function has one answer for every input 1-1 therefore...","date":"2021-08-02 10:28:09","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 1, \"mathjax_display_tex\": 1, \"mathjax_asciimath\": 1, \"img_math\": 0, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.7332600355148315, \"perplexity\": 415.89281527075235}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.3, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2021-31\/segments\/1627046154310.16\/warc\/CC-MAIN-20210802075003-20210802105003-00513.warc.gz\"}"} | null | null |
Will Jerry Tillery's spring performance carry over to the fall?
By Keith ArnoldApr 8, 2015, 2:50 PM EDT
To put into context what freshman Jerry Tillery is doing this spring, you have to look back at the last time Notre Dame saw a breakout freshman along the defensive line. It was Aaron Lynch. The lanky, pass-rushing defensive end set the Blue-Gold game on fire, unblockable off the edge in his first semester as an early-enrollee college student.
Jerry Tillery isn't cut from the same mold as Lynch. At 6-foot-6, 300-pounds, he's closer to Lynch's classmate Stephon Tuitt, though the image of Tuitt competing in a triathlon (let alone crowd-surfing on his official visit) is a tough one to conjure.
But Tillery's dominance this spring has been the story of spring football. And as Jarron Jones recovers from foot surgery and Sheldon Day gives some of his snaps to lesser-established players, the Louisiana native running with the starting defense when he should be going to prom adds another intriguing part to the young Irish defensive line.
"Far and away the story is Jerry Tillery," Kelly said, singling out Tillery. "He's just a unique player, one that I can't remember that I've ever coached."
So what exactly should we expect from Tillery? Lynch's spring campaign led to an impressive freshman season, where he was named to the FWAA Freshman All-American team, joining Timmy Jernigan and Jadaveon Clowney on the defensive line.
His 5.5 sacks led the team. He finished third with seven tackles for loss. But Lynch's 14 quarterback hurries nearly lapped the rest of the defense, teasing Irish fans with a dominance that we'd never end up seeing at the college level.
It wasn't all great for Lynch during his freshman season. His tendency to freelance kept him (and Tuitt) off the field against Michigan, the fourth-quarter defensive collapse likely could've used somebody barreling off the edge. And Lynch's off-field struggles adapting to life in South Bend led him to walk off the team during spring practice, a bizarre departure that went against his family's wishes, taking Lynch on a road-less-traveled path to being a late-round selection by the San Francisco 49ers.
Watching Jerry Tillery move to defense has left #NotreDame's offensive coaches in tears. http://t.co/GGawYkm2tc
— Matt Fortuna (@Matt_Fortuna) April 3, 2015
Tillery doesn't necessarily look like a pass rusher in the traditional sense. His size and length will likely having him taking reps on the interior of a four-man defensive front, where both Kelly and new defensive line coach Keith Gilmore have praised his technique and skill, comparing him to a seasoned veteran.
Opportunity is another factor. It's fair to assume that Notre Dame's best three defensive linemen are Day, Jones and Isaac Rochell. Tillery likely falls into the next tier, though slots best in the positions played by that trio. (Imagine Lynch coming into the program this season—he'd be a plug and play defensive end immediately.)
All that being said, Brian VanGorder will put his best personnel on the field when finding his starting eleven. So that means Tillery will be competing not just with the defensive tackles, but for snaps with defensive ends Romeo Okwara and Andrew Trumbetti, even if the natural fit isn't quite there.
Notre Dame desperately needs to find a pass rush from the defensive line. Okwara led the Irish with four sacks last season, the lowest single-season leader since Ethan Johnson led the anemic 2009 defense.
Video: Spotlight on Jerry Tillery from Wednesday. Check out the early enrollee in action. http://t.co/0uVDLfmWMG pic.twitter.com/Ab9RumffzP
— Irish Illustrated (@PeteSampson_) April 8, 2015
Tillery's impact won't necessarily be rushing the passer, though it sounds like he's capable of doing anything he wants after hearing Kelly fawn over him. But after seeing the Irish fall apart at the point of attack after injuries weakened its core, Tillery could be asked to provide stabilization for a defensive tackle position that couldn't hold up after losing Day and Jones.
Of course, it's worth pumping the brakes on all of this. Tillery's ascent is just one of many spring stories where we have been told that the sky is the limit. For every breakout—and Lynch's numbers were far less dominant than many of us (me included) expected them to be—there's been a freshman breaking in period that's been underwhelming.
But Tillery is far from your average freshman. There's a (presumed) comfort level that he plays with, and an intellect that reminds you of KeiVarae Russell, Jaylon Smith and Corey Robinson, young guys capable of seeing the field early because of their maturity off of it. But both Russell and Smith needed a break to see the field, and Tillery's likely in a similar position.
So as Irish fans work themselves into a frenzy predicting Tillery's immediate impact, acknowledging Kelly's attempt to temper that enthusiasm should be advised. But even if his freshman season is closer to Tuitt's than Lynch's, Tillery's on a trajectory to be one of the next great Notre Dame linemen.
Not half bad for a guy most predicted to play offensive tackle. | {
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The deficit or wound that starts the bleeding is the lack of true and effective leadership. That is what needs to be fixed first.
The people who work here are incredibly professional," he said. "I admire them greatly and we had great mutual respect for each other, up until I asked them for a pay cut.
This just took everyone's breath away, but for me it was not the stupidity and callousness of the statement, but the signal that Gelb is now giving up the leadership of the Met and instead is trying to become its ruler. Notice it is "I" and "me". Show of hands how many artists and technical personnel at the Met come to work out of "respect" for Peter Gelb, or when the lights go down EVER consider not working, playing or singing well? Right none, because they were all professionals long before he got there and they serve the audience, the art, their colleagues, the institution…not him! He has inserted himself as the dictator that now believes he is the reason for everything…..well that is except how this situation occurred in the first place…strangely not accepting any responsibility for that, but that is the classic sign of a dictator in our midst. Plus the idea that this is a mere "dust" storm as if he is just brushing aside the fact that he wants to cut the pay (or stop it completely) for those who live and work in just about the most expensive city to live in the world, is no big deal because he doesn't care how they feel about him. We are talking about the best of the best here, this is the pinnacle and you are basically calling them out by saying oh I'm reducing your pay, but I know you will perform at your best for your supreme leader who just beat the crap out of you….in public! I wonder what his answer would be if he was asked if he was performing at his best, or if he believes making public threats is professional?
Last season the company reported a deficit of $2.8 million on a budget of more than $300 million, of which more than $200 million went for pay and benefits to the Met's unions and its principal singers.
Oh I'm sorry is it not in your job description (that you get paid $1.4M to do) to call up donors? Is that a little inconvenient and cutting in to your "now how can I set Turandot in an iPhone factory" time? If he had done his job just a little bit better, then there would be no deficit, because on a budget of $300M, $2.8M is not a lot! Certainly not enough to close it down. The fact that two thirds of the budget is spent on personnel is as it should be, the most money should always be spent on who makes an organization "sing".
A true leader is an enabler, a convener, a negotiator, and someone who sees respect not as mutual but as historic in that as the temporary caretaker for one of the great arts organizations of the world, taking multiple trajectories or pathways and bringing people together with humility to maintain, preserve and develop the institution is a COLLECTIVE mission. Or as a bottom line way to put it: This is the Met, the administration should be tailored to the Met, not the other way round. He is exactly the wrong person to lead this organization!
Well said. As a citizen of the Twin Cities, we know what happens when an administrator is convinced that he is what makes the organization "sing". Egos need to be put in a safe when one leads.
Standing up and applauding this post. Thank you! Even though I don't live in NYC, having just endured the brutal lockout of the MN Orchestra, I cannot bear to think of the hardship that would be borne by the Met Opera musicians/stagehands in the event of a lockout there.
Thank you for this truth and support.
Great post Ron! It will be quoted down under for sure! | {
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De Passage Pommeraye is een 19e-eeuwse winkelgalerij in het Franse Nantes. De winkelgalerij werd gebouwd tussen 1840 en 1843 in opdracht van Louis Pommeraye gebouwd naar voorbeelden in Parijs. De opening vond plaats op 4 juli 1843.
De Passage Pommeraye overbrugt het aanzienlijke niveauverschil (bijna 10 meter) tussen de Rue Santeuil en de Rue de la Fosse door middel van een monumentale trap versierd met figuratieve versieringen. Het ontwerp van de galerij was van de architecten Jean-Baptiste Buron en Hippolyte Durand Gasselin. In 1976 werd de passage geclassificeerd als Monument historique. Het winkelcentrum is diverse keren als decor gebruikt in filmopnamen. Jacques Demy schoot hier voor Lola, Une chambre en ville en Les Parapluies de Cherbourg; Jean-Loup Huber voor La reine blanche.
Literatuur
André Péron: Le Passage Pommeraye, Editions Ressac, Quimper 1984. Nieuwe editie: Editions Coiffard, Nantes 1995.
Externe link
Passage Pommeraye, nantes44.com
Foto's
Bouwwerk in Nantes
Winkelcentrum in Frankrijk | {
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Pro Rector/Director
Administration Section
Discipline Policies
Facilities @ FURC
Undergraduate/Graduate Programs
Faculty of Engineering & IT
Dept. of Software Engineering
Dept. of Electrical Engineering
Dept. of Psychology
Dept. of Arts and Media
Faculty of Management Sciences
Dept. of Business Administration
Dept. of Technology & Innovation
Dept. of Economics and Finance
Dept. of Tourism and Hospitality
Life at Campus
Open House & Job Fair 2019
Result Spring 2020
Result Fall 2019
Result Summer 2020
Credits Transfer
Grading Model
University Collaborations
Industry Linkages
Foundation University Journal of Business & Economics
Foundation University Journal of Psychology
Foundation University Journal of Engineering and Applied Sciences
Foundation University Conference of Psychology
Open House Pictures
Each year, the industry is invited from all over the country to view our graduating student's Final Year Projects, hold interviews for Jobs & internships, conduct presentations and have a one-to-one interaction with the student. They are serving with distinction in reputed national and multinational organizations. The highly qualified and professional faculty through research and lab facilities inculcate up-to-date knowledge in the minds of students which ultimately pave the way for the growth and advancement of the industries in the cut throat competition in the international market and also help them in facing the challenges of industrial standardization and globalization. To establish liaison between the Campus and the industry and to find appropriate places for its future graduates in the competitive market, a tradition has been set in the Campus to hold an Open House and Career Fair before every graduating ceremony.
Officials of more than 100 national and Multi-national industries participated in the event and 100 plus stalls were displayed where recruitment process was being done.
Following Department participated in the Open House and Job Fair 2019:
Department of Arts and Media
© 2021 Foundation University
FUI Home | {
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define([
'./views/baseView', './utilities/channels', './views/viewContext', './routers/masseuseRouter',
'./models/masseuseModel', './models/computedProperty', './models/proxyProperty', './models/observerProperty',
'./plugins/rivets/view', './collections/masseuseCollection'
], function (BaseView, channels, ViewContext, MasseuseRouter, MasseuseModel, ComputedProperty, ProxyProperty,
ObserverProperty, RivetsView, MasseuseCollection) {
'use strict';
/** @description `Masseuse` is:
* BB helper library
* helps with
* views
* baseView
* the BB View lifecycle - based on promises
* child views
* separating View definitions from View options
* rivetView
* a baseView with built in rivetjs
* models
* allows for model specific logic to be packaged with the model
* computed properties
* proxy properties
* nested models with bubbling up of change events
* router
* with a beforeRouting method
*
* @namespace masseuse
*/
return {
View : BaseView,
ViewContext : ViewContext,
Model : MasseuseModel,
Collection : MasseuseCollection,
Router : MasseuseRouter,
ComputedProperty : ComputedProperty,
ProxyProperty : ProxyProperty,
ObserverProperty : ObserverProperty,
channels : channels,
// Old fields : @deprecated
// TODO: remove these and bump major version
BaseView : BaseView,
MasseuseModel : MasseuseModel,
MasseuseRouter : MasseuseRouter,
utilities : {
channels : channels
},
// TODO: move this out of this package, so this can be optimized w/o RivetsView
plugins : {
rivets : {
RivetsView : RivetsView
}
}
};
});
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Q: Find the limiting distribution of Bernoulli random variables If $X_1, X_2,\ldots $ are i.i.d Bernoulli random variables with mean $\frac{1}{2}$. Define $T_n = \sqrt{n}(\frac{4\sum_{i=1}^{n} X_i - 2n}{\sum_{i=1}^{n} X_i^2})$. Find the pmf or pdf of the limiting distribution of the sequence $T_1, T_2,\ldots$
My thought: We consider the function $g(x) = 4x$. Since this function and its derivative are continuous, and both are nonzero at $u_x = \frac{1}{2}$, we could apply the theorem saying $\sqrt{n}[\frac{g(\overline{X_n})- g(\frac{1}{2})}{|g'(\frac{1}{2})\sigma_{x}}]\rightarrow N(0,1)$ in distribution, where $X_n = \frac{X_1+\ldots + X_n}{n}$ and $\sigma_{x} = \frac{1}{4}$ (since $X$ is Bernoulli). Now, my plan is to figure out the convergence in probability of $\sum_{i=1}^{n} X_i^2$, but I am stucked here.
Could anyone please help with this last piece of puzzle?
A: You can use the law of large numbers to talk about what happens to $\frac{1}{n} \sum_{i=1}^n X_i^2$. Note that you divided the numerator of $T_n$ by $n$, so you should also do that for the denominator.
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\section{Introduction}
The rise of deep learning is complimented by ever increasing model complexity, size of the datasets, and corresponding longer training times to develop the model. For example, finishing 90-epoch ImageNet-1k training with ResNet-50 takes 14 days to complete on an NVIDIA M40 GPU\cite{You:2018:ITM:3225058.3225069}. Researchers and practitioners often find themselves losing productivity due to the inability to quickly obtain desired information dynamically from the training process without having to incur stop-change-restart cycles. While a few solutions have been developed for real-time monitoring of deep learning training, there has been a distinct lack of systems that offer dynamic expressiveness through conversational style interactivity supporting the exploratory paradigm.
In this paper we offer a new system that enables the dynamic specification of queries and eliminates the requirement to halt the learning process each time a new output is desired. We also enable the displays of multiple, simultaneous visualizations that can be generated on-demand by routing to them the desired information chosen by the user. The pillars of our architecture are general enough to apply our system design to other domains with similar long running processes.
Our main contributions are
\begin{enumerate*}
\item system design based on dynamic stream generation using map-reduce as the Domain Specific Language (DSL) to perform interactive analysis of long running processes such as machine learning training
\item separation of concerns that allows to build dynamic stream processing pipeline with visualizations agnostic of rendering surfaces, and
\item abstraction to allow the comparison of previously generated heterogeneous data along with the live data in a desired set of visualizations, all specified at the runtime.
\end{enumerate*}
\section{Related Work}
TensorBoard\cite{Wongsuphasawat2018} is currently among the most popular of monitoring tools, offering a variety of capabilities including data exploration using dimensionality reduction, and model data flow graphs. However, its monitoring capabilities are limited to viewing only the data that was explicitly specified to be logged before the training starts. While the tool provides some interactivity in visualization widgets, no interactivity is provided in terms of dynamic queries. Furthermore, few pre-defined visualizations are offered in the dashboard in a pre-configured tabbed interface and thus somewhat limited in other layout preferences.
The logging-based model is also used by other frameworks, including Visdom\cite{Choo2018} and VisualDL\cite{VisualDL}. Several authors\cite{Liu2017,DBLP:journals/corr/abs-1712-05902,Choo2018} have identified the research opportunities in diagnostic aspects of deep learning training and interactively analyzing it due to time consuming trial-and-error procedures.
Map-reduce is an extensively studied paradigm originated from the functional programming \cite{Steele1995} and successfully utilized for constructing data flows and performing large scale data processing in the field of distributed computing \cite{Dean2008,Gates:2009:BHD:1687553.1687568,Catanzaro2008AMR}. Many variants of map-reduce has been created\cite{Afrati:2011:MER:1951365.1951367} for a variety of scenarios, and it has also gained wide adoption for the various data analysis tasks\cite{Ekanayake2008,Pavlo:2009:CAL:1559845.1559865}.
Visualizations based on streams have been studied deeply for the real-time data scenarios\cite{(Ed.)98datavisualization,Traub2017} with various systems aiming to enhance interactivity, adaptability, performance and dynamic configurations\cite{Logre:2018:MSV:3233739.3229096,ellis2014real, Roberts2007, Few:2006:IDD:1206491}. Query driven visualizations have been popular for databases utilizing SQL and big data using custom DSLs\cite{Stockinger, Babu:2001:CQO:603867.603884, Plale2003}. This paradigm also becomes a cornerstone in our system design.
\section{Scenarios}
We describe a few real-world scenarios in this section to develop an intuition of the requirements and understanding of problems often faced by the practitioners.
\subsection{Diagnosing Deep Learning Training}
John is the deep learning practitioner with the task of developing a model for gender identification from a large labeled dataset of human faces. As each experiment takes several minutes even on a reduced subset of the data, John wishes to view training loss and accuracy trends in real time. In many experiments, training loss does not seem to be reducing and to understand the cause John needs to view the gradient flow chart. However, this requires John to terminate the training process, add additional logging for this information, and then restart the training. As John observes the gradient flow chart, he starts suspecting that his network may be suffering from the vanishing gradient problem. To be sure, John now wishes to view growth of weights and the distribution of initial values. This new information again causes a stop-change-restart cycle adding significant cost to obtain each new piece of information in the diagnostic process that is inherently iterative.
\subsection{Analyzing The Model Interpretation Results}
Susan is using a GAMs framework\cite{Hastie1986} to analyze the impact of each feature in her model. As a data scientist, she depends on Jupyter Notebook to perform her analysis. As the computation takes several minutes before generating the desired charts, Susan wants to display progressive visualizations displaying partial results as they evolve. Instead of designing and implementing a custom system for her one-off experiment, it would be ideal if she could simply generate a stream of data using map-reduce paradigm that she is already familiar with. This stream can then be easily painted to the desired rendering surface such as Jupyter Notebook to display progressive real-time visualization as her models evolve in time.
\subsection{Diagnosing and Managing Deep Learning Jobs}
Rachel spins up several dozens of deep learning jobs as part of her experiments in GPU cloud infrastructure. These long running jobs may take many days to complete and therefore are expensive to run in cloud. However, it turns out that many of the poorer performing jobs could be identified much earlier and be terminated, thus freeing up the expensive resources. However, designing and building such infrastructure is time consuming and requires additional engineering skills. It would be ideal for Rachel if she could simply output streams of performance data from her jobs and then create a small monitoring application that consumes these streams.
\section{System Design}
\begin{figure*}[ht]
\centering
\includegraphics[height=3.5in]{TensorWatch_Collaboration}
\caption{Collaboration diagram for our system depicting interactions between various actors. Standard notations are used with numbered interactions indicating their sequence with alphabet suffix denoting the potential concurrency. Our system includes the long running process generating various events, clients making requests for stream using map-reduce queries (denoted by MRx) for the desired events and the agent responding back with resultant streams that can be directed to desired visualizations or other processes.}
\label{fig:TensorWatch_Collaboration}
\end{figure*}
\subsection{Key Actors}
Our system design contains the following key actors as shown in Figure \ref{fig:TensorWatch_Collaboration}:
\begin{enumerate}
\item A long running process $P$ such as a deep learning training process.
\item Zero or more clients that may be located on the same or different machines as $P$.
\item An agent $A$ that is embedded in $P$ listening to requests from the clients
\end{enumerate}
\subsection{The Long Running Process}
We abstract three specific characteristics of a long running process $P$:
\begin{enumerate}
\item $P$ may generate many types of events during its lifetime. Each type of event may occur multiple times, but the sequence of events is always serialized, i.e., there is never more than one event of the same type occurring at the same time in the same process.
\item As events of each type are strictly ordered so that we can optionally assign a group to any arbitrary contiguous set of events. This ability will enable windowing for the reduce operator discussed later.
\item For each event, optionally a set of values may be available for the observation. For example, on a batch completion event the metrics for that batch may be available for the observation. The process informs the agent when an event occurs and provides access to these observables.
\end{enumerate}
\subsection{The Client}
At any point in time multiple clients may exist simultaneously issuing the queries and consuming corresponding resultant streams. Each query can be viewed as a stream specification with the following attributes:
\begin{enumerate}
\item The event type for which a stream should be generated. An event type may have multiple associated streams but each stream has only one associated event type.
\item An expression in the form of map-reduce operations. This expression is applied to the observables at the time of event and the output becomes the value in the resultant stream.
\end{enumerate}
The client may utilize the resultant stream by directing it to multiple processes such as visualizations chosen at the runtime. Thus the same stream may generate a visualization as well as become input to another process in the data flow pipeline.
\subsection{The Agent}
The agent runs in-process in the host long running process $P$ and characterized by the following responsibilities:
\begin{enumerate}
\item Listening to incoming requests for the creation of a stream. This is done asynchronously without blocking the host process $P$.
\item When $P$ informs the agent that an event has occurred, the agent determines if any active streams exist for that event. If so, the agent executes the map-reduce computation attached to each stream for that event and sends the result of this computation back to the client.
\end{enumerate}
An important aspect of the agent design is that if there are no streams requested for an event then there is almost no performance penalty. Also, there is no performance penalty for having access to the large numbers of observables. This means that user may specify all of the variables of interest as observables beforehand and later use queries to use subset of them depending on the task.
\subsection{Example: Implementation for Deep Learning Training}
As an example of how above actors and abstractions may be utilized, consider the deep learning training scenario. This process performs computation in series of epochs, completion of each is an \emph{epoch event}. During each epoch, we execute several batches of data, completion of each becoming a \emph{batch event}. At each batch event we may observe the metric object that contains several statistics for the batch. Contiguous set of batch events within each epoch can be treated as one group. At the end of an epoch, we may want to compute some aggregated statistics which can easily be done by specifying the map-reduce expression that extracts the desired value from the metric object and performing the aggregation operation on it.
\subsection{Multiple Processes and Streams}
The above abstractions can easily be utilized to efficiently inspect many simultaneously running processes and make decisions such as early termination or modify desired parameters at the runtime. A user can also compare and visualize arbitrarily chosen subsets of jobs.
\subsection{Modifying the State of a Long Running Process}
Our design trivially enables a useful capability of changing the observables of the long running process. In the context of deep learning training, this can be used for interactive hyper parameter tuning guided by observations \cite{NIPS2011_4443}. We simply allow users to send commands from interfaces such as Jupyter Notebook to the agent running in the host process. The agent then executes these commands on observables presented to it by the host process at the specified events.
\subsection{Stream Persistence}
One of the significant disadvantages of many current systems is the requirement that data of interest must be logged to the disk storage, which can become an expensive bottleneck. Our design with stream abstraction trivially enables pay-what-you-use model so that users can selectively specify at runtime to persist only those streams that they may be interested in viewing or comparison in the future.
\section{Stream Visualization}
Once a stream is produced, it can be visualized, stored or processed further in users data flow graph.
\begin{figure}[h]
\centering
\includegraphics[width=\linewidth]{tensorwatch-screenshot}
\includegraphics[width=\linewidth]{tensorwatch-screenshot2}
\caption{Screenshot of three simultaneous real-time visualizations on two different surfaces generated dynamically by an user for the MNIST training process. On the top is an interactive session in Jupyter Notebook where the user specifies map-reduce queries in a cell for each desired visualization. The first output cell at the top shows evolution of average absolute gradients for each layer with lighter lines indicating the older plots. The second output cell shows random sample of predictions so far. At the bottom is the plot of two batch statistics rendered in a separate native application.}
\end{figure}
\subsection{Adaptive Visualizers}
As we allow users to generate arbitrary streams dynamically, it becomes important that visualization widgets are specifically designed for automatic configuration by reflecting on data available in the stream. We adopt the adaptive visualization paradigm\cite{Nazemi2016, mourlas2009intelligent} for this purpose. For example, a visualizer may decide to paint a stream that has a tuple of two numeric values as a 2D line chart, tuple of 3 numeric values as a 3D line chart and tuple of 2 numeric and 1 string value as annotated 2D line chart. The user may override to select a precise rendering for a given stream.
A visualizer may allow adding or removing streams dynamically. The streams may not have the same data type allowing for the heterogeneous visualizations such as display of a histogram and a line chart overlays. If a visualizer receives incompatible streams than it may display an error. In the context of deep learning, this enables capabilities such as viewing multiple related metrics in the same visualization or comparing data generated by multiple experiments in the same visualization.
\subsection{Frame Based Animated Visualizations}
Many useful visualizations may consume values in a stream one after another as they arrive, e.g.\ , line charts. Another interesting scenario is to consider each value in the stream providing the complete data for each \emph{frame} in the visualization. This enables users to create dynamic specification for the animated visualizations using familiar map-reduce paradigm. In the context of deep learning training, this allows users to create on-demand custom visualizations such as per-layer gradient statistics change over time, display of sample predictions sorted by loss value and so on.
\section{Stream Generation Using Map-Reduce}
\subsection{Background}
There are many variants of the map-reduce model\cite{Afrati:2011:MER:1951365.1951367} and differences in various implementations. We will focus on the variant that is popular among data scientists and readily available in widely used programming languages such as Python.
The map-reduce paradigm consists of two higher order operators: \emph{map} and \emph{reduce}. The map operator accepts a function $M$ and a list of values $V$. The $M$ is applied to each value in $V$ to transform it to some other value or choose not to output any value, i.e.\ , the filter operation.
The reduce operator accepts a function $R$ and a list of values $V$. The $R$ processes each value in $V$ to produce an aggregated output value. For instance the operation of sum over a sequence can be done as reduce operation with $R$ that initializes aggregated value to $0$ and then consumes each value in the sequence to produce new aggregated value.
\subsection{Extending Map-Reduce}\label{map-reduce-ext}
While the map operator consumes a stream and outputs a stream, the reduce operator consumes stream and outputs an aggregated value instead of a stream. The reduce operator's output is not generated until the entire stream ends. In several of our scenarios, we rather desire that the reduce operator works on a group of contiguous values in the stream, aggregating values in that group and outputting a stream. For instance, we may want to compute the average duration for batches within each epoch and generate a stream with these averages as epochs progresses.
To achieve this, we introduce an extension to allow us leveraging the existing infrastructure and avoid need for entirely new domain specific language. In our extension, we simply require that each value in the stream is accompanied by an \emph{optional} binary value $B$ which when $true$ triggers the output from the reduce operator.
There are two advantages offered by this design:
\begin{enumerate}
\item $B$ can be set at any time by the host process $P$ enabling many of our core scenarios trivially.
\item $B$ can also be set by a client at any time. This enables the scenarios where the user dynamically defines the aggregation window. For example, the user may wish to view a metric averaged over every 5 minutes.
\end{enumerate}
\section{Implementation}
We implement our design using Python and other frameworks described in this section. We will be releasing our implementation as an open source cross-platform offering.
For networking stack we utilize the ZeroMQ library to implement publisher-subscriber model between the agent and the client. Out of the box, we offer implementations for MatplotLib as well as Plotly frameworks for various visualizations including line charts, histograms and image matrix. MatplotLib allows a variety of UX backends, many of which can run as native application or in Notebook interface for exploratory tasks. The Jupyter Lab allows transforming Notebook in to the user defined dashboards.
One of the key requirements in our system model is the implementation of the map-reduce extension described in Section \ref{map-reduce-ext}. We achieve this by implementing a component we call \emph{postable iterator}. The postable iterator allows to post input sequence of tuple $\{value, B\}$, where $B$ is group completion flag described in the Section \ref{map-reduce-ext}. The postable iterator then evaluates the map-reduce expression and returns the output value of map or reduce operator or signals the caller that no output was produced for the posted value.
One of the key difficulties in implementation using languages such as Python and frameworks such as ZeroMQ, MatplotLib, and Jupyter Notebook is managing the limitations imposed for multi-threading.
We adopt the cooperative concurrency model with callbacks combining with the producer-consumer pattern to work around many of these limitations.
\section{Conclusion}
We described the design of a system that brings data streaming and map-reduce style queries to the domain of machine learning training for enabling the new scenarios of diagnosis and exploratory inspection. We identified several advantages of our system over currently popular systems, including the ability to perform interactive queries, dynamic construction of data flow pipelines, and decoupled adaptive visualizations as nodes in such pipelines. We plan to release our system as an open source cross-platform offering to help researchers and engineers perform diagnosis and exploratory tasks more efficiently for the deep learning training processes.
\begin{acks}
We would like to thank Susan Dumais for her guidance and advice on this project.
\end{acks}
\bibliographystyle{ACM-Reference-Format}
| {
"redpajama_set_name": "RedPajamaArXiv"
} | 4,412 |
Little Dresses for Africa is a non-profit organization, which provides relief to the children of Africa. Simple dresses and shorts for boys are made from yardage and pillow cases. These items are then distributed through the orphanages, churches and schools in Africa to plant in the hearts of children that they are worthy!
Northern Nevada Chapter made 223 dresses and 4 pair of shorts for the project. | {
"redpajama_set_name": "RedPajamaC4"
} | 8,108 |
package integration.tests.smoke;
import dom.pets.Pet;
import dom.pets.PetSpecies;
import dom.pets.Pets;
import fixture.pets.scenario.PetsFixture;
import integration.tests.PetClinicAppIntegTest;
import javax.inject.Inject;
import org.junit.Before;
import org.junit.Test;
import org.apache.isis.applib.fixturescripts.FixtureScript;
import org.apache.isis.applib.fixturescripts.FixtureScripts;
import static org.hamcrest.CoreMatchers.is;
import static org.hamcrest.CoreMatchers.not;
import static org.hamcrest.CoreMatchers.nullValue;
import static org.junit.Assert.assertThat;
public class PetTest extends PetClinicAppIntegTest {
@Inject
FixtureScripts fixtureScripts;
@Inject
Pets pets;
FixtureScript fixtureScript;
Pet petPojo;
Pet petWrapped;
@Before
public void setUp() throws Exception {
// given
fixtureScript = new PetsFixture();
fixtureScripts.runFixtureScript(fixtureScript, null);
petPojo = fixtureScript.lookup("pets-fixture/pet-for-fido/item-1", Pet.class);
assertThat(petPojo, is(not(nullValue())));
petWrapped = wrap(petPojo);
}
@Test
public void doesNotExist() throws Exception {
// when
Pet petPojo = fixtureScript.lookup("non-existent", Pet.class);
// then
assertThat(petPojo, is(nullValue()));
}
public static class Name extends PetTest {
@Test
public void canChange() throws Exception {
// given
assertThat(petWrapped.getName(), is("Fido"));
// when
petWrapped.setName("Fred");
// given
assertThat(petWrapped.getName(), is("Fred"));
}
}
public static class Species extends PetTest {
@Test
public void canChange() throws Exception {
// given
assertThat(petWrapped.getSpecies(), is(PetSpecies.Dog));
// when
petWrapped.setSpecies(PetSpecies.Cat);
// given
assertThat(petWrapped.getSpecies(), is(PetSpecies.Cat));
}
}
} | {
"redpajama_set_name": "RedPajamaGithub"
} | 8,448 |
\section{Introduction}
A high-luminosity electron-ion collider (EIC), which recently received mission need approval from the US Department of Energy, can address fundamental questions about nucleons and nuclei. These include the origin of mass, the internal landscape of hadrons, the phenomenon of gluon saturation, and the physics of hadronization~\cite{Aidala:2020mzt}. Production and propagation of heavy flavor in deep inelastic scattering (DIS) is a unique and critical part of this planned decade-long research program. Studies in this direction have so far focused on charm production
that can constrain the gluon and strangeness content of the nucleon/nucleus~\cite{Chudakov:2016otl,Chudakov:2016ytj,Arratia:2020azl}, especially at moderate and high values of Bjorken-$x$.
In this letter we investigate semi-inclusive open heavy meson cross sections in electron-proton (e+p) and electron-nucleus (e+A) collisions to address a different set of questions - how energy and matter are transported through a strongly interacting quantum mechanical environment. The possibility to study the physics of hadronization and energy loss of partons in cold nuclear matter has been investigated by the HERMES Collaboration at HERA using fixed nuclear targets and an electron beam of energy $E_{\rm beam} = 27.6$~GeV~\cite{Airapetian:2000ks, Airapetian:2003mi,Airapetian:2007vu}. In these experiments suppression of the multiplicities of light hadrons in e+A versus e+p collisions has been clearly established. Hadronization in nuclei was also studied experimentally earlier in Refs.~\cite{Osborne:1978ai,Ashman:1991cx,Adams:1993mu}. Theoretical interpretations of the data predominantly fall within two classes of models. The parton energy loss approach assumes that fragmentation occurs outside of the nucleus and evaluates the attenuation of the
quarks and gluons that produce the final-state hadrons, or, equivalently, the effective modification of fragmentation as a function of the transport properties of large
nuclei~\cite{Wang:2002ri,Arleo:2003jz,Chang:2014fba}. The hadron absorption model argues that hadronization can take place on length scales smaller than the nuclear size and the final-state particle can be absorbed in the medium~\cite{Accardi:2002tv,Kopeliovich:2003py}. We note that phenomenology that uses elements of both elastic parton scattering and hadron absorption has been developed~\cite{Brooks:2020fmf}. Transport models have also been employed to investigate the HERMES data~\cite{Falter:2004uc}. For a review of energy loss and hadronization in cold nuclear matter, see Ref.~\cite{Accardi:2009qv}.
The HERMES Collaboration e+A results have advanced our understanding of particle production in the nuclear environment, but a number of open questions still remain. The transport coefficients extracted from data using different energy loss approaches differ by up to an order of magnitude~\cite{Arleo:2003jz,Chang:2014fba}. More importantly, fundamentally different assumptions about the time scales involved in the process of hadronization and the nature of nuclear attenuation - inelastic parton scattering versus hadron absorption - give equally good description of the light meson multiplicities' quenching~\cite{Chang:2014fba,Kopeliovich:2003py}. With this in mind, we turn to open heavy meson production as a new probe of cold nuclear matter effects at the EIC, where the semi-inclusive cross sections can be readily measured. Since the shape of charm and beauty quark fragmentation functions (FFs) into $D$-mesons and $B$-mesons is very different from the shape of light parton fragmentation into pions and kaons, carefully chosen observables may be much more sensitive to the nature of nuclear attenuation~\cite{Li:2020sru}. A number of center-of-mass (CM) energies are expected to be available at the EIC, with multiple distinct kinematic domains for the final-state particles for each electron-proton/nucleon energy combination. Thus, we further aim to identify the CM energies and rapidity intervals that are most sensitive to the nuclear modification of hadron production from final-state interactions, which may facilitate operation planning and optimize detector coverage for the EIC.
In describing heavy meson production in DIS on nuclei we go beyond the traditional energy loss approach.
The evolution of FFs is determined by the Dokshitzer-Gribov-Lipatov-Altarelli-Parisi (DGLAP) evolution equations. Recently, soft-collinear effective theory (SCET)~\cite{Bauer:2000yr,Bauer:2001yt,Bauer:2002nz,Beneke:2002ph} has been employed to describe interactions between jets and a QCD medium via Glauber gluon exchange~\cite{Idilbi:2008vm,Ovanesyan:2011xy}. This allowed for the derivation of the full set of $1\to 2$ medium-induced splitting kernels for massless and massive partons~\cite{Ovanesyan:2011kn,Kang:2016ofv}. With EIC applications in mind, these results were verified using a lightcone wavefunction approach and a formalism to calculate higher order corrections in the opacity of nuclear matter was developed~\cite{Sievert:2018imd,Sievert:2019cwq}. The medium-induced splitting kernels can be used to understand the evolution of FFs in cold nuclear matter - a technique which was successfully developed in heavy ion collisions~\cite{Kang:2014xsa,Chien:2015vja}. In this letter, we employ the QCD evolution-based method to encode the cold nuclear matter effects on hadron production at the EIC and to present the results of our analysis.
The rest of our letter is organized as follows. In section 2, we briefly introduce the theoretical framework for the next-to-leading order (NLO) QCD corrections to hadron production in DIS and in-medium QCD evolution based on SCET$_{\rm G}$. In section 3, we compare theoretical predictions with HERMES measurement and demonstrate the validity of our approach for hadron production in reactions with heavy nuclei. Section 4 is dedicated to the detailed study of pion, $D$-meson and $B$-meson production at the EIC. We conclude in section 5.
\section{Theoretical Framework}
\begin{table*}[!t]
\begin{center}
\begin{tabular}{c|c|c|c|c|c|c|c}
\hline
\hline
\multicolumn{2}{c|}{Energy}
& \multicolumn{2}{c|}{5 GeV$\times$40 GeV}
& \multicolumn{2}{c|}{10 GeV$\times$100 GeV}
& \multicolumn{2}{c}{18 GeV$\times$275 GeV} \\
\hline
\multicolumn{2}{c|}{$p_T^h$ [GeV]} &~ [2\,,3]~&~ [5\,,6] ~
&~ [2\,,3]~&~ [5\,,6] ~
&~ [2\,,3]~&~ [5\,,6] ~\\
\hline
\multirow{2}{*}{$\pi^+$}
& LO
& $5.3 \times 10^{6} $ & $2.4 \times 10^{4} $
& $ 1.4\times 10^{7} $ & $3.0 \times 10^{5} $
& $2.9 \times 10^{7} $ & $9.6 \times 10^{5} $\\
& NLO
& $1.1 \times 10^{7} $ & $6.9 \times 10^{4} $
& $2.8 \times 10^{7} $ & $ 6.1\times 10^{5} $
& $ 5.6\times 10^{7} $ & $1.9\times 10^{6} $\\
\hline
\multirow{2}{*}{$D^0$}
& LO
& $ 1.4\times 10^{6} $ & $3.2 \times 10^{3} $
& $ 8.6\times 10^{6} $ & $9.0 \times 10^{4} $
& $ 3.1\times 10^{7} $ & $6.6 \times 10^{5} $\\
& NLO
& $ 3.7\times 10^{6} $ & $8.5 \times 10^{3} $
& $ 2.1\times 10^{7} $ & $ 2.1\times 10^{5} $
& $ 7.2\times 10^{7} $ & $1.5 \times 10^{6} $ \\
\hline
\multirow{2}{*}{$B^0$}
& LO
& $ 3.7\times 10^{5}$ & $1.2 \times 10^{3} $
& $2.4 \times 10^{6} $ & $2.8 \times 10^{4} $
& $9.0 \times 10^{6} $ & $ 2.0\times 10^{5} $ \\
& NLO
& $ 1.1\times 10^{6}$ & $3.3 \times 10^{3} $
& $6.2 \times 10^{6} $ & $7.2 \times 10^{4} $
& $ 2.1\times 10^{7} $ & $ 4.7\times 10^{5} $ \\
\hline
\hline
\end{tabular}
\caption{\label{tab:eventnum} Example of light, charm, and bottom hadron multiplicities at the EIC in selected $p_T$ bins ($2\ {\rm GeV}< p_T^h< 3\ {\rm GeV}$ and $5\ {\rm GeV}< p_T^h< 6\ {\rm GeV}$) to lowest and next-to-leading order. We have integrated over the hadron rapidity in the interval $-2<\eta <4$ and used a typical one year integrated luminosity of $10\,{\rm fb}^{-1}$ in e+p collisions.
}
\end{center}
\end{table*}
\subsection{Hadron Production in DIS }
In collinear leading-twist perturbative QCD the inclusive cross section for the production of hadron $h$ is factorized as follows:
\begin{equation}\label{eq:NLOform}
\begin{aligned}
E_{h} &\frac{d^{3} \sigma^{\ell N \rightarrow h X}}{d^{3} P_{h}}
=\frac{1}{S} \sum_{i, f} \int_{0}^{1} \frac{d x}{x} \int_{0}^{1} \frac{d z}{z^{2}} f^{i / N}(x, \mu)\\
& \times D^{h / f}(z, \mu) \Big[\hat{\sigma}^{i \rightarrow f}
+f_{\rm ren}^{\gamma /\ell}\left(\frac{-t}{s+u},\mu\right)\hat{\sigma}^{\gamma i \to f}\Big] \, .
\end{aligned}
\end{equation}
Here, $ f^{i / N}$ is the parton distribution function (PDF) of parton $i$ in nucleon $N$ and $D^{h / f}$ is the conventional FF from parton $f$ to hadron $h$. $\hat{\sigma}^{i\to f}$ is the partonic cross section for lepton-parton scattering with initial-state parton $i$ and final-state parton $f$. $s$, $t$, $u$ are the partonic Mandelstam variables defined as $s=(k+l)^2$, $t=(k-p)^2$ and $u=(l-p)^2$, where $l^\mu$, $k^\mu$ and $p^\mu$ are the momenta of incoming lepton, incoming parton and fragmenting parton, repectively.
In hadron and jet production at the EIC it is not necessary to place kinematic constraints on the scattered lepton. Thus, events with lepton scattering at a small angle can be selected. Then, the hard process can be described by an incoming quasi-real photon scattering: $\gamma q\to q(g)$, $\gamma q\to g(q)$, $\gamma g\to q({\bar q})$, which contribute to the cross section starting at order $\alpha_{\rm EM}^2 \alpha_s$.
In this case, the incoming lepton is regarded as a source of quasi-real photons. The well known Weizs\"acker-Williams (WW) distribution provides an accurate description for photons in leptons by a perturbative distribution function $f_{\rm ren}^{\gamma /\ell}\left(y,\mu\right)$~\cite{vonWeizsacker:1934nji,Williams:1934ad,Bawa:1989bf,Frixione:1993yw}. The analytical expressions for $\hat{\sigma}^{i\to f}$, $\hat{\sigma}^{\gamma i\to f}$ and $f_{\rm ren}^{\gamma /\ell}\left(y,\mu\right)$ have been known up to ${\cal O}(\alpha_{\rm EM}^2 \alpha_s)$ for a while, and can be found in~\cite{Hinderer:2015hra}.
In the numerical calculations that follow we use CT10nlo PDF sets~\cite{Lai:2010vv}
and the associated strong coupling provided by {\sc Lhapdf6}~\cite{Buckley:2014ana}. Fragmentation functions into light hadrons, for example
$\pi$, are taken from Ref.~\cite{Hirai:2007cx}. The boundary condition for heavy quark fragmentation into the various $D$-meson and $B$-meson states at a scale $\mu = 2 m_Q$ can be calculated perturbatively using heavy quark effective theory (HQET), as shown in Refs.~\cite{Braaten:1994bz,Cheung:1995ye}. The FFs obey the DGLAP evolution equations, which can be written as
\begin{multline}~\label{eq:dglap}
\frac{d}{d \ln \mu^2} D^{h/i}\left(x, \mu\right)=
\\
\sum_{j} \int_{x}^{1} \frac{d z}{z} P_{j i}\left(z, \alpha_{\mathrm{s}}\left(\mu\right)\right)
D^{h/j}\left(\frac{x}{z}, \mu\right) \, ,
\end{multline}
where $P_{j i}$ is the Altarelli-Parisi (AP) splitting functions describing $i\to j + X $ splitting and $z$ is the longitudinal momentum fraction of $j$ relative to $i$.
We take the perturbative hard part at NLO and use PDFs consistent with NLO global analysis. The evolution of fragmentation functions is at one loop, because the medium corrections to the splitting functions in Eq.~(5) are only available at LO~\footnote{An exploratory study of the real contribution to higher order parton splitting in matter was carried out in~\cite{Fickinger:2013xwa}, but the result is complex and its numerical evaluation challenging with current and near-future computing resources to be practically applicable to phenomenology.}. We employ the LO splitting functions in vacuum as well for consistency and
make use of {\sc Hoppet}~\cite{Salam:2008qg} to solve Eq.~(\ref{eq:dglap}) numerically.
To understand the feasibility of heavy flavor measurements at nominal EIC luminosity and to assess the magnitude of higher order corrections we first turn to the calculation of hadron cross sections in e+p collisions. The vacuum splitting functions are used to perform the RG evolution of the FFs. Both the renormalization scale and factorization scale are chosen as the energy of the initial parton fragmenting to a hadron in the rest frame of the proton. This is motivated by the need for consistency with e+A calculations where the energy of the parent quark or gluon in nuclear matter plays a key role in determining the strength of the medium-induced parton shower.
Selected results for the expected multiplicities of light, charm, and beauty mesons, exemplified by $\pi^+$, $D^0$ and $B^0$, are shown in Table~\ref{tab:eventnum} for integrated luminosity of 10~fb$^{-1}$. We consider three combinations of electron and proton beam energies:
5~GeV (e) $\times$ 40 GeV (p), 10~GeV (e) $\times$ 100 GeV (p), and 10~GeV (e) $\times$ 100 GeV (p) and integrate over the rapidity interval $-2 < \eta < 4$.
The NLO QCD corrections are obtained from Eq.~(\ref{eq:NLOform}), including the contribution from quasi-real photon scattering. They lead to a $K$-factors in the range of 1.5 to 2.5. For $\pi$ meson production, the quasi-real photon scattering contributes about 40\% to 50\% to NLO corrections, while for $D$-mesons and $B$-mesons the quasi-real photon contribution is even more dominant.
The NLO corrections are sizable and when it comes to absolute cross sections they should be considered for reliable theoretical predictions.
\subsection{Cold Nuclear Matter Effects }
\begin{figure}[!t]
\centering
\includegraphics[scale=0.47]{medium_eff}
\caption{Illustration of in-medium parton shower formation in electron-nucleus collisions from the interactions of the struck quark. It will affect the evolution
of fragmentation functions and, ultimately, the cross sections for light and heavy hadron production. }
\label{fig:EIC}
\end{figure}
When partons propagate in strongly-interacting matter they scatter and radiate. The medium-induced parton shower will modify the evolution of the FFs, and has been investigated in the framework of SCET$_{\rm (M), G}$~\cite{Ovanesyan:2011xy,Kang:2016ofv}.
These modifications were first introduced as corrections to the DIS hadronization process~\cite{Wang:2001ifa} and, more recently, implemented in medium-modified DGLAP evolution. This theoretical framework has been used extensively in Refs.~\cite{Chang:2014fba,Kang:2014xsa,Chien:2015vja,Kang:2016ofv,Wang:2009qb,Li:2017wwc, Li:2019dre} to carry out resummation in cold and hot QCD medium numerically, and to describe hadron production and observables sensitive to the fragmentation process. We will solve the medium-corrected DGLAP evolution equations to take account of the radiation induced by a large nucleus, as shown in Fig.~\ref{fig:EIC}.
The full fragmentation function evolution in the presence of nuclear matter is given by:
\begin{multline} \label{eq:fullevol}
\frac{d}{d \ln \mu^{2}} \tilde{D}^{h/i}\left(x, \mu\right)=
\sum_{j} \int_{x}^{1} \frac{d z}{z} \tilde{D}^{h/j}\left(\frac{x}{z}, \mu\right)
\\ \times
\left( P_{j i}\left(z, \alpha_{s}\left(\mu\right)\right) + P_{j i}^{\rm med}\left(z, \mu\right) \right) \, .
\end{multline}
In Eq.~(\ref{eq:fullevol}) $ P_{j i}^{\rm med}$ are the medium corrections to the splitting functions. It has been demonstrated
that the full splitting kernel is a direct sum of its vacuum and medium-induced components and the corrections are
gauge-invariant.
We will make use of the form of in-medium branching processes derived in~\cite{Ovanesyan:2011xy,Ovanesyan:2011kn,Sievert:2018imd,Sievert:2019cwq}. Equivalent to the vacuum splitting functions, the real contribution can be written as
\begin{align}
P_{ j i }^{\mathrm{med},\rm{real}} \left(z, \mathbf{k}_{\perp}\right) = 2\pi\, \mathbf{k}_{\perp}^2 \frac{dN_{j i }^{\mathrm{med}} }{d^2\mathbf{k}_{\perp} dz} \,.
\end{align}
The full splitting functions can be expressed as proportional to the vacuum ones with a medium induced correction that depends both on the longitudinal momentum fraction $z$ and the intrinsic transverse momentum of the branching $\mathbf{k}_{\perp}$. This is because in-medium parton showers are broader and softer than the ones in the vacuum.
The full set of medium corrections to the splitting functions can be written as
\begin{align}\label{eq:sp}
P_{qq}^{\rm{med}}\left(z, \mathbf{k}_{\perp}\right)&=\left[P_{q \rightarrow q g}^{\mathrm{med},\rm{real}} \left(z, \mathbf{k}_{\perp}\right)\right]_{+} \; ,
\nonumber \\
P_{gq}^{\rm{med}}\left(z, \mathbf{k}_{\perp}\right) &=
P_{q \rightarrow g q }^{\mathrm{med},\rm{real}} \left(z, \mathbf{k}_{\perp}\right) \; ,
\nonumber \\
P_{qg}^{\rm{med}}\left(z, \mathbf{k}_{\perp}\right) &=
P_{g\rightarrow q\bar{q}}^{\mathrm{med},\rm{real}} \left(z, \mathbf{k}_{\perp}\right) \; ,
\nonumber \\
P_{gg}^{\rm{med}}\left(z, \mathbf{k}_{\perp}\right) &=
\left[ \left(\frac{2z-1}{1-z}+z(1-z) \right) h_{gg} \left(z, \mathbf{k}_{\perp}\right) \right]_+
\nonumber \\ &
+ \frac{ h_{gg} \left(z, \mathbf{k}_{\perp}\right) }{z} + B(\mathbf{k}_{\perp}) \delta(1-z) \; ,
\end{align}
where
\begin{align}
h_{gg} \left(z, \mathbf{k}_{\perp}\right) = & \frac{ P_{g \rightarrow gg }^{\mathrm{med},\rm{real}}
\left(z, \mathbf{k}_{\perp}\right)}{ \frac{z}{1-z} + \frac{1-z}{z}+z(1-z)} \; ,
\end{align}
and $B(\mathbf{k}_{\perp})$ can be obtained through momentum sum rules. The definition of the splitting function in QCD medium can be also found in Refs.~\cite{Kang:2014xsa,Chien:2015vja}.
Going back to Eq.~(\ref{eq:fullevol}), $k_\perp$ which characterizes the intrinsic momentum of the collinear branching is the scale we chose for the medium-induced splitting functions.
The evolution for heavy flavor can similarly be written down
and the splitting kernels associated with massive quarks can be found in Refs.~\cite{Kang:2016ofv,Sievert:2019cwq}.
The medium-induced splitting functions for massive quarks are defined in a similar way as the ones in Eq.~(\ref{eq:sp}). They reduce
to the massless case for large momentum scales, while the mass effects can play an important role for small momentum scales.
\begin{figure}
\centering
\includegraphics[scale=0.55]{FF_30GeV}
\caption{The ratio of fragmentation functions for the case of a Au nucleus to the ones in vacuum at a scale $\mu$ = 30 GeV.
Blue band (dotted lines), red band (dashed lines), and green band (solid lines) correspond to light parton to pion, $c$-quark
to $D$-meson, and $b$-quark to $B$-meson fragmentation, respectively.
}
\label{fig:FFsInMedium}
\end{figure}
\begin{figure*}[!t]
\centering
\includegraphics[width=0.42\textwidth]{HERMES_Kr_nu_Dnew}\quad
\includegraphics[width=0.42\textwidth]{HERMES_Xe_nu_Dnew} \\[2ex]
\includegraphics[width=0.42\textwidth]{HERMES_Kr_z_Dnew}\quad
\includegraphics[width=0.42\textwidth]{HERMES_Xe_z_Dnew}
\caption{ Top panels: comparison of $R_{eA}$ for $\pi^+$ as a function of the energy $\nu$ with HERMES measurements~\cite{Airapetian:2007vu}. The bands correspond to a variation in the transport properties of cold nuclear matter. Bottom panels: similar comparison, but as a function of the fragmentation fraction $z$.
Left panels are for the Kr target and right panels are for the Xe target, respectively.}
\label{fig:hermes}
\end{figure*}
An example of how in-medium evolution can alter the fragmentation pattern of partons into hadrons is given in Fig.~\ref{fig:FFsInMedium}.
It presents the ratio of the FFs for the case of a gold (Au) nucleus evolved from the boundary condition to a scale $\mu=30$~GeV
to the ones in the vacuum, denoted $D^{\rm Med}/D^{\rm Vac}$. The dotted blue lines, dashed red lines and solid green lines represent the fragmentation of $u\to \pi^+$, $c\to D^0$ and ${\bar b}\to B^0$, respectively. We have averaged the parent parton production point over the nuclear geometry in evaluating the splitting kernels that enter the evolution equations. The nominal transport coefficient of cold nuclear matter, which are determined by HERMES data as shown in Fig.~\ref{fig:hermes}, we take to be $ \langle q^2_\perp \rangle / \lambda_g = 0.12 $~GeV$^2$/fm for gluons and $ \langle q^2_\perp \rangle / \lambda_q = 0.05 $~GeV$^2$/fm for quarks. Here, $\langle q^2_\perp \rangle $ is the mean momentum transfer squared in two dimensions per scattering and $\lambda_g $ ($\lambda_q $) are the gluon (quark) scattering lengths, respectively. The bands correspond to varying the transport parameter up and down by a factor of two.
The effect of the medium-induced shower is to further soften fragmentation relative to the vacuum. We can see that the FFs for $\pi^+$ are always suppressed, except for very small values of $z$. The fragmentation pattern of heavy flavor is modified in a distinctly different way, the suppression only happens in the large-$z$ region. For $c\to D^0$ and ${\bar b}\to B^0$, the in-medium corrections enhance very significantly FFs with $z<0.6$ and $z<0.85$, respectively.
In addition, the modification due to cold nuclear matter effects is larger at lower energy scales, which opens the door toward fruitful phenomenology at the future EIC.
An essential task that we face is to identify the optimal phase space regions that are most sensitive to
the effect of in-medium parton showers and where semi-inclusive DIS measurements can provide constraints on the transport properties of large nuclei.
Lastly, we remark that the in-medium corrections to FFs for $c\to D^0$ and ${\bar b}\to B^0$ rise for very small values of $z \rightarrow 0$. The physical reason for this behavior is that in-medium evolution produces even more soft partons than vacuum evolution. It has been experimentally observed in heavy ion collisions for light hadrons by the ATLAS and CMS collaborations at the LHC~\cite{Aaboud:2018hpb,Sirunyan:2018qec} and evaluated using medium-induced corrections to the semi-inclusive fragmenting jet functions~\cite{Kang:2016ehg}. The observables discussed in this paper, however, are not sensitive to the fragmentation functions in the $z \rightarrow 0$ region. This is because with the designed CM energies of the EIC hadrons with large transverse momentum relative to the collision axis cannot be produced with very small fragmentation fractions.
\section{Comparison with HERMES data}
In order to provide theoretical predictions for heavy flavor modification at the EIC, it is useful to get some guidance from existing DIS measurements on nuclei. The HERMES collaboration at HERA has collected such data on light hadron production, albeit at much lower center-of-mass energies. With this limitation in mind, we use the opportunity to test the validity of our theoretical framework of cold nuclear effects on hadronization.
Let us define the modification of semi-inclusive pion production as follows:
\begin{equation}
R_{eA}^{\pi}(\nu,Q^2,z)=\frac{\frac{N^{\pi}(\nu,Q^2,z)}{N^e(\nu,Q^2)}\Big|_A}{\frac{N^{\pi}(\nu,Q^2,z)}{N^e(\nu,Q^2)}\Big|_D} \, ,
\label{Rhermes}
\end{equation}
where $N^{\pi}(\nu,Q^2,z)$ and $N^e(\nu,Q^2,z)$ are the event number for hadron production ($\pi^+$) and the total number of inelastic events determined by measuring the scattered lepton, respectively. The kinematic variables are defined as $\nu=E-E'$, $Q^2=-(k-k')^2$, $z=E_h/\nu$, where $E(k)$ and $E'(k')$ are the energies (momenta) of the incoming and outgoing electron in the target rest frame, respectively. Subscripts $A$=Kr, Xe, ... and $D$=deuteron denote the target nuclei. The energy of incoming electrons is 27.6 GeV. Here, we employ the same kinematic cuts as in the HERMES measurements: $Q^2>1\,{\rm GeV}^2$, $W=\sqrt{2M\nu+M^2-Q^2}>2\,{\rm GeV}$ and $y=\nu/E<0.85$~\cite{Airapetian:2007vu}. The idea behind normalizing by the number of DIS events is to both account for the large number of nucleons in the nucleus and to minimize effects strictly due to nuclear PDFs.
Theoretically, due to the Landau-Pomeranchuk-Migdal effect in QCD, the contribution of the in-medium shower depends on the energy of the hard parton in the rest frame of nuclear matter, which in DIS is the scale $\nu$. For the perturbative part and PDFs, both $Q$ and $\nu$ are hard scales, especially at large Bjorken-$x$. The observables involved in this work are normalized by the inclusive cross section, and small differences due to scale choice cancel in the ratio. For the evolution, which is in the branching momentum $k_\perp$, this scale enters just in the boundary of the allowed phase space. We have found that most of the medium shower contribution comes from $k_\perp^2 \sim$ ~1~GeV$^2$ and putting a different limit on the evolution variable, unless very small, will not affect the description of branching in matter and the extraction of its transport properties.
Figure~\ref{fig:hermes} presents comparisons between the theoretical predictions and the HERMES measurements of pion production in DIS on Kr and Xe targets.
The bands correspond to the nuclear matter transport parameter and its variation described in the previous section, but the splitting kernels and evolution are for the Kr and Xe nuclei. The theoretical predictions and HERMES data are in good agreement in a range of energy values $\nu$, and also as a function of $z$. Pion production is more suppressed at lower $\nu$ and already hints that it will be more beneficial to study cold matter effect at lower energy e+A collision. In addition, we can also see that there is a stronger suppression on heavier nuclear targets. As a function of $z$, the largest attenuation is at the highest fragmentation fractions and everywhere in the studied region $R_{eA}^{\pi}(z) < 1$.
\section{Hadron Production at the EIC}
In this section, we move to the main result of this work - hadron and, especially, heavy meson cross section modification at the EIC.
Here, we consider three benchmarks energy combinations for electron-proton collisions (for electron-nucleus collisions, the beam energy is per nucleon): 5 GeV (e) $\times$ 40 GeV (A), 10 GeV (e) $\times$ 100 GeV (A) and 18 GeV (e) $\times$ 275 GeV (A). To investigate the nuclear medium effects, we study the ratio of the cross sections in electron-gold (e+Au) collision to the one in e+p collision. We use the cross section of inclusive jet production for normalization that minimizes the effect of nuclear PDFs.
\begin{equation}\label{eq:defRAatEIC}
R_{eA}^{h}(p_T,\eta,z)=\frac{\frac{N^{h}(p_T,\eta,z)}{N^{\rm inc}(p_T,\eta)}\Big|_{\rm e+ Au}}{\frac{N^{h}(p_T,\eta,z)}{N^{\rm inc}(p_T,\eta)}\Big|_{\rm e+p}} \, .
\end{equation}
Note that the kinematic variables are different than in Eq.~(\ref{Rhermes}).
Here, $N^{\rm inc}(p_T,\eta)$ denotes the cross section of large radius jet production~\cite{Li:2020rqj} with transverse momentum $p_T$ and rapidity $\eta$ \footnote{Here, $p_T$ is the transverse momentum relative to the electron/nulcear beam direction in the laboratory frame, which is different from the Breit frame in SIDIS. For a relativistic particle $\eta \approx y = \ln\sqrt{(E^h+p_z^h)/(E^h-p_z^h)}$, where $E^h$ and $p_z^h$ are the energy and momentum along the beam direction, respectively, of the hadron in the laboratory frame.}.
As we only aim to eliminate the differences between proton and nuclear PDFs, results for the inclusive jet production to lowest order are enough for this purpose. In fact, we can reasonably estimate those numbers from the number of scattered electrons in calculable $p_T$ and backward rapidity bins.
\begin{figure*}[!t]
\centering
\includegraphics[width=0.42\textwidth]{pt_5+40_eta-2to0} \,\,\,
\includegraphics[width=0.42\textwidth]{pt_10+100_eta-2to0}
\includegraphics[width=0.42\textwidth]{pt_5+40_eta0to2} \,\,\,
\includegraphics[width=0.42\textwidth]{pt_10+100_eta0to2}
\includegraphics[width=0.42\textwidth]{pt_5+40_eta2to4} \,\,\,
\includegraphics[width=0.42\textwidth]{pt_10+100_eta2to4}
\caption{ Medium modification of $\pi^+$, $D^0$ and $B^0$ production on a gold (Au) nucleus at the EIC as a function of transverse momentum in three rapidity regions for the hadrons. The left column of figures is for 5 GeV (e) $\times$ 40 GeV (A) collisions and the right column of figures is for 10 GeV (e) $\times$ 100 GeV (A) collisions, respectively. The rapidity regions from top to bottom are -2$<\eta<$0, 0$<\eta<$2 and 2$<\eta<$4.}
\label{fig:ptdisEIC}
\end{figure*}
We first turn to the production of hadrons as a function of the transverse momentum $p_T$ in the laboratory frame.
The in-medium shower corrections induced by the interactions between the final-state parton and the nucleus vary with the parton energy in the nuclear rest frame, where the lower energy parton receives the larger medium corrections. One way to study this effect is to vary the CM energy as shown in Fig.~\ref{fig:ptdisEIC}. The left column of panels is for 5 GeV $\times$ 40~GeV e+Au collision and the right column of panels is for 10 GeV $\times$ 100 GeV ones. The dotted blue line, dashed red line and solid green lines denote the result for $\pi^+$, $D^0$ and $B^0$, respectively. We find that not only is the magnitude of the nuclear modification
$R_{eA}(p_T)$ larger at the lower CM energy, but the sensitivity to the transport properties of nuclei, illustrated by the width of the theory bands, is also enhanced. We also performed calculations for 18 GeV $\times$ 275~GeV e+Au collision and found that the medium effects at those energies are smaller than the ones at 10~GeV $\times$ 100~GeV. Hence, we don't show them here.
Another way to vary the parent parton energy $\nu$ in the rest frame of the nucleus is to use different rapidity ranges.
For given hadron $p_T$, the medium corrections will be larger for smaller relative rapidity $|\eta - \eta_A|$, with hadron rapidity $\eta$ and nuclear rapidity $\eta_A$ in the lab frame
\footnote{In the lab frame $\eta_A\approx 4.4$ and 5.4 in 5 GeV $\times$ 40 GeV and 10 GeV $\times$ 100 GeV e+A collisions, respectively. The parent parton energy in the rest frame of the nucleus can be obtained by $\nu=p_T\cosh |\eta - \eta_A|.$ For further discussion of the differences between fixed target and collider kinematics see~\cite{Accardi:2009qv}.}.
The horizontal sets of panels in Fig.~\ref{fig:ptdisEIC} presents $R_{eA}^{h}$ values in three rapidity bins $-2$$<\eta<$0, 0$<\eta<$2 and 2$<\eta<$4. The in-medium corrections are the largest in the forward hadron rapidity region $2<\eta<4$ as expected.
The study of the transverse momentum distribution of hadrons can provide a first glimpse of jet quenching effects in reactions with nuclei at the EIC. This is especially clear for the suppression of pions. Even for heavy flavor, at low CM energies and forward rapidities we are beginning to see a hierarchy of suppression patterns and
sizable suppression at large $p_T$. At the same time, to investigate the nature of hadronization, more differential observables are needed. This is especially true for heavy flavor which in many cases shows little or no nuclear modification. The physics reason is that away from the edges of kinematic acceptance the range of fragmentation fractions $z$ that give sizable contributions to hadron production is limited. For heavy quarks fragmenting into heavy mesons it is in the range $z = 0.55 - 0.90$ and is harder for $b$ quarks in comparison to $c$ quarks. This is precisely the range of momentum fractions where the medium-induced modification to $D$-meson and $B$-meson FFs transitions from suppression at large $z$ to enhancement at small $z$, see Fig.~\ref{fig:FFsInMedium}. Consequently, for most energy and rapidity combinations we find
$R_{eA}^{D} \approx R_{eA}^{B} \approx 1$. We finally remark that since $R_{eA}$ is a ratio of cross sections, there is practically no difference in the calculated nuclear modification with LO and NLO hard parts.
\begin{figure*}[t!]
\centering
\includegraphics[width=0.42\textwidth]{z_pi+_pt2to3_ineta_5+40}\,\,\,
\includegraphics[width=0.42\textwidth]{z_pi+_pt2to3_ineta_10+100}
\caption{ In-medium corrections for $\pi^+$ production as a function of $z$ at the EIC in three rapidity regions.
Blue bands (solid lines), red bands (dashed lines), and green bands (dotted lines) correspond to -2$<\eta<$0, 0$<\eta<$2 and 2$<\eta<$4, respectively.
Results for 5~GeV(e) $\times$ 40 GeV(A) collisions are shown on the left and results for 10 GeV(e) $\times$ 100 GeV(A) collisions are shown on the right. }
\label{fig:zdisEIC_pi}
\end{figure*}
\begin{figure*}[t!]
\centering
\includegraphics[width=0.42\textwidth]{z_D0_pt2to3_ineta_5+40}\,\,\,
\includegraphics[width=0.42\textwidth]{z_D0_pt2to3_ineta_10+100}
\includegraphics[width=0.42\textwidth]{z_B0_pt2to3_ineta_5+40} \,\,\,
\includegraphics[width=0.42\textwidth]{z_B0_pt2to3_ineta_10+100}
\caption{ In-medium corrections for $D^0$ and $B^0$ as a function of the momentum fraction $z$ at the EIC in three rapidity regions. Top panels are for $D$-mesons and bottom panels are for $B$-mesons. The electron and proton/nucleus beam energies, color and line coding are the same as in Fig.~\ref{fig:zdisEIC_pi}.}
\label{fig:zdisEIC_D0B0}
\end{figure*}
To exploit the differences in the hadronization patterns between light hadrons and heavy mesons and use them to discriminate between theoretical models of nuclear modification~\cite{Li:2020sru} we turn to more differential observables. Specifically, we fix the $p_T$ bin and
look at the momentum fraction distribution $z$, which we extract from our calculation. This corresponds to the variation of $\nu$ which in experiment can be constrained by the kinematics of the scattered electron.
Figures~\ref{fig:zdisEIC_pi} and \ref{fig:zdisEIC_D0B0} present $R_{eA}^{h}$ result as a function of $z$.
Our predictions in rapidity regions $-2$$<\eta<$0, 0$<\eta<$2 and 2$<\eta<$4 are represented by the blue solid lines, red dashed lines, and green dotted lines, respectively. We choose the $p_T$ range 2 GeV$<p_T<$3 GeV where the cross sections at lower $z$ values (e.g. $z\sim 0.3$) are sizable. With the same $p_T$ range fixed, we can identify larger in-medium effects at 5 GeV $\times$ 40 GeV e+Au collision than at 10 GeV$\times$ 100 GeV collisions. Additionally, hadron production in the forward rapidity region $2<\eta<4$ receives the largest in-medium corrections. For $\pi^+$ production, $R_{eA}$ is always smaller than one in the region of momentum fractions that is accessible with the largest quenching seen at large $z$, see Fig.~\ref{fig:zdisEIC_pi}.
In contrast to light flavor, the modification of open heavy flavor in DIS reactions with nuclei, such as the one for $D^0$s and $B^0$s shown in Fig.~\ref{fig:zdisEIC_D0B0}, is much more closely related to the details of hadronization. The observed $R_{eA}(z)$ is qualitatively consistent with the effective modification of fragmentation functions seen in
Fig.~\ref{fig:FFsInMedium} even after their convolution with the PDFs and the hard part. There is a significant suppression for large values of $z$, but it quickly evolves to
enhancement for $z<0.65$ and $z<0.8$ for $D$-mesons and $B$-mesons, respectively. The effect is most pronounced at forward rapidities
and we find that $R_{eA}^{h}$ as a function of $z$ is a more suitable observable for cold nuclear matter tomography at the EIC than the transverse momentum distributions' modification for hadrons in the laboratory frame alone. We note that as we go toward small values of $z$ (e.g. $z=0.3$) the enhancement can be compensated by suppression
that arises from the normalization factor $N_p^{\rm inc}(p_T,\eta)/N_A^{\rm inc}(p_T,\eta)$. The exact interplay of these effects depends on the rapidity region of interest.
\section{Conclusions}
In summary, we presented first predictions for heavy $D$-mesons and $B$-meson production in e+A collisions at the EIC including NLO corrections and cold nuclear matter effects. The much higher CM energies relative to HERMES and, correspondingly, larger parent parton energies in the rest frame of the nucleus boost hadron formation times. This motivates a detailed theoretical study of in-medium effects arising from final-state parton-level interactions inside large nuclei. The effective modification of open heavy flavor fragmentation functions was obtained by solving
the generalized DGLAP evolution equations with in-medium spitting kernels derived in the framework of SCET$_{\rm G}$.
This theoretical approach, when applied to light hadron production, shows good agreement with HERMES measurements and
allows us to set a range of nuclear transport properties and make projections for the future EIC. One should keep in mind, however, that at HERMES energies other effects, such as hadronic rescattering, can contribute to the observed suppression of particle multiplicities.
To demonstrate the utility of heavy flavor for cold nuclear matter tomography we carried out a comprehensive study of the production of various $D$-mesons and $B$-meson states at different center-of-mass energies and different rapidity ranges at the EIC. We found that the modification of light and heavy flavor hadron cross sections in reactions with nuclei is sizable and depends on the electron and proton/nucleus beam energy combinations and the rapidity gap between the produced hadron and the target nucleus. Our numerical results show that the 5 GeV $\times$ 40 GeV scenario followed by the 10 GeV $\times$ 100 GeV case and the forward proton/nucleus going rapidity region 2$<\eta<$4 produce the largest nuclear effects. Conversely, semi-inclusive hadron production at large center-of-mass energies, e.g. 18 GeV $\times$ 275 GeV, and backward rapidities, e.g. -2$<\eta<$0, exhibits only small modification in e+A reactions relative to e+p ones. Such kinematics is better suited to explore shadowing and the phenomenon of gluon saturation.
Last but not least, we looked for experimental observables that are most sensitive to the details of hadronization. While $p_T$ distributions in the laboratory frame can provide initial information on the quenching of hadrons in cold nuclear matter, a more differential observable such as the fragmentation fraction $z$ distribution measured by HERMES is a much better choice, especially for open heavy flavor. The clear transition from enhancement to suppression at moderate to large values of $z$ will be an unambiguous and quantitative measure of parton shower formation in large nuclei. In conclusion, we expect that this work will be useful in guiding the future light and heavy flavor tomography program at the EIC.
\section*{Acknowledgments}
This work was supported by the U.S. Department of Energy under Contract No. DE-AC52-06NA25396, the Los Alamos National Laboratory LDRD program, and the TMD topical collaboration for nuclear theory.
\bibliographystyle{JHEP}
| {
"redpajama_set_name": "RedPajamaArXiv"
} | 7,993 |
namespace Orchard.Tasks {
public interface IBackgroundTask : IDependency {
void Sweep();
}
}
| {
"redpajama_set_name": "RedPajamaGithub"
} | 6,100 |
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(7459) Gilbertofranco est un astéroïde de la ceinture principale.
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(7459) Gilbertofranco est un astéroïde de la ceinture principale. Il fut découvert le à La Silla par Vincenzo Zappalà. Il présente une orbite caractérisée par un demi-grand axe de 2,60 UA, une excentricité de 0,15 et une inclinaison de 5,3° par rapport à l'écliptique.
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Die cycos AG ist eine Tochtergesellschaft der Unify GmbH & Co. KG und bietet Dienstleistungen im Bereich Unified Communications an. Der primäre Fokus des Unternehmens liegt auf der Erbringung von Entwicklungsdienstleistungen für den Unify-Konzern. Über die Unify GmbH & Co. KG gehört die cycos AG seit 2016 auch zum Atos-Konzern.
Der Hauptsitz der cycos AG ist in Alsdorf. Zum Ende des Geschäftsjahres 2018 beschäftigte das Unternehmen 62 Mitarbeiter (Vollzeitäquivalent: 58,88 Mitarbeiter) und erzielte per 31. Dezember 2018 einen Umsatz in Höhe von 5,766 Millionen Euro.
Geschichte
1984 wurde die "Pfleiderer und Partner Ing. GmbH" gegründet. 1991 nannte sie sich in "PP-Com Telecommunications + Networking GmbH" um. 1998 bekam sie mit dem Byte Award '98 eine Auszeichnung für den Unified Messaging-Server "mrs". 1999 wurde das Unternehmen in die "CYCOS Aktiengesellschaft" umgewandelt. Ein Jahr später übernahm cycos die "Dolphin Communication Technologies GmbH" und die "Maier Bürokommunikationssysteme GmbH", ebenfalls 2000 ging die cycos an die Börse. 2003 wurde das Unternehmen durch die Siemens AG als Mehrheitsaktionär übernommen.
2006 erhielt cycos mrs den Frost & Sullivan Award for Product Differentiation Innovation im Unified Messaging und Communications-Markt; ebenfalls 2006 präsentierte cycos auf der CeBIT einen Prototyp der weltweit ersten Communications Suite für Microsoft Dynamics CRM 3.0.
Im Jahr 2008 brachte cycos das Produkt mrs Vanguard heraus, die zu diesem Zeitpunkt umfassendste Software Suite für Unified Communications auf dem Markt. Laut einer Studie des auf die IT- und Telekommunikationsbranche spezialisierten Marktforschungsunternehmens MZA war die cycos AG zu diesem Zeitpunkt Marktführer in Westeuropa bei Unified Messaging-Lösungen (Studie: The Western European UC Applications Market Competitive Environment - 2008 Edition).
Ende des Jahres 2009 hat die cycos AG den Vertrieb an die damalige Konzernmutter Siemens Enterprise GmbH & Co. KG (heute Unify GmbH & Co. KG) abgegeben. Zwei Jahre danach wurde die Ausphasung des Produktes "mrs" eingeleitet, um sich zukünftig als Dienstleistungsunternehmen aufzustellen. Im selben Jahr wurde die cycos AG zum Center of Competence für die heutige Unify GmbH & Co. KG ernannt und fokussiert sich seither hauptsächlich auf Dienstleistungen für den Unify-Konzern.
Mit Beschluss der Hauptversammlung vom 13. Mai 2011 firmierte das Unternehmen in die "cycos AG" um.
Das hauseigene Produkt "mrs" erreichte im Oktober 2012 den End of Life und im Oktober 2014 den End of Service.
Im Januar 2015 endete die Börsenzulassung des Unternehmens auf eigenen Antrag.
Im Frühling 2016 kaufte die Atos S.E. den Unify-Konzern auf. Dadurch ist die cycos AG seither Bestandteil des Atos-Konzerns.
Ehemaliges Produkt
Bevor sich die cycos AG von einem Produktentwickler zu einem Dienstleistungsunternehmen umstrukturiert hat, war das Kernprodukt die Unified Communications-Software Suite mrs Vanguard (mrs = multimedia routing software). Diese Suite vereinfacht Kommunikationswege und ermöglicht webbasiertes mobiles Nachrichtenmanagement.
Weblinks
Website der cycos AG
Firmenprofil auf wer-zu-wem.de
HV-Bericht Cycos AG vom 8. September 2020
Cycos-Handelsregisterauszüge von 2005 bis 2018 auf online-handelsregister.de
Einzelnachweise
Telekommunikationsgeräte-Hersteller
Siemens-Unternehmen
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Alsdorf
Gegründet 1984 | {
"redpajama_set_name": "RedPajamaWikipedia"
} | 8,828 |
Q: Reordering column nodes in heatmap.3 while maintaining dendrogram
I've generated this heatmap using heatmap.3. Clustering is performed based on the dendrogram, but for presentation purposed, I'd like to re-order the nodes such that dark blue is left and dark red is right while maintaining the dendrogram. I've read about re-order:
newdendro<-reorder(as.dendrogram(myclust(mydist(heatdata.scaled))),10:1,agglo.FUN=colSums)
But colSums(heatdata.scaled) is not stored in the dendrogram. How do I
1) use colSums(heatdata.scaled) to reorder the nodes
2) call this updated dendrogram in heatmap.3?
A: Your question is missing a self contained reproducible example. So I will use the mtcars data. And since I'm now working on the heatmaply package, I'll give an answer using it (but you can just change heatmaply to your desired function, and the code will work the same).
# get data
x <- mtcars
# row dend:
hc_r <- as.dendrogram(hclust(dist(x)))
# col dend:
hc_c <- as.dendrogram(hclust(dist(t(x))))
# weights and reordering
wts_r <- rowSums(x)
wts_c <- colSums(x) # apply(x, 2, mean)
hc_r <- rev(reorder(hc_r,wts_r))
hc_c <- reorder(hc_c,wts_c)
x2 <- x[order.dendrogram(hc_r),
order.dendrogram(hc_c)]
# plot
library(heatmaply)
heatmaply(x2, dendrogram = "none")
And we get the following beautiful (and interactive) plot:
| {
"redpajama_set_name": "RedPajamaStackExchange"
} | 8,168 |
{"url":"https:\/\/istopdeath.com\/solve-graphically-15-06-21-62x16-2-72x3-8\/","text":"# Solve Graphically 15.06-21.62x=16\/2.72x+3.8\n\n15.06-21.62x=162.72x+3.8\nDivide 16 by 2.72.\n15.06-21.62x=5.88235294x+3.8\nGraph each side of the equation. The solution is the x-value of the point of intersection.\nx\u22480.40941951\nSolve Graphically 15.06-21.62x=16\/2.72x+3.8","date":"2022-12-02 05:34:38","metadata":"{\"extraction_info\": {\"found_math\": false, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 0, \"mathjax_display_tex\": 0, \"mathjax_asciimath\": 0, \"img_math\": 0, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.8246653079986572, \"perplexity\": 2782.638157879849}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2022-49\/segments\/1669446710898.93\/warc\/CC-MAIN-20221202050510-20221202080510-00053.warc.gz\"}"} | null | null |
Q: Videos in Totem kills X server Using oneiric, up-to-date.
01:00.0 VGA compatible controller: Silicon Integrated Systems [SiS] 771/671 PCIE VGA Display Adapter (rev 10)
With the SiS driver available in the repositories my videos and movies play smoothly, but I have a desktop resolution of 1024x768 only.
With the driver in https://github.com/hellnest/xf86-video-sismedia-0.9.1 I have a desktop resolution at 1280x800, but if I try to play any video, the X server is killed and return to the login screen.
How can I correct this behaviour?
A: try to recompile with this patch:
https://github.com/hellnest/xf86-video-sismedia-0.9.1/commit/60823291
solved the problem for me
| {
"redpajama_set_name": "RedPajamaStackExchange"
} | 31 |
package com.nominanuda.zen.obj;
import static com.nominanuda.zen.seq.Seq.SEQ;
import static org.junit.Assert.assertEquals;
import java.math.BigDecimal;
import java.util.LinkedList;
import java.util.List;
import org.junit.Test;
import com.nominanuda.zen.obj.wrap.ObjWrapper;
import com.nominanuda.zen.obj.wrap.Wrap;
import com.nominanuda.zen.obj.wrap.getter.CollectionCastGetter;
import com.nominanuda.zen.obj.wrap.getter.MapGetter;
import com.nominanuda.zen.obj.wrap.getter.SimpleGetter;
public class WrapGettersTest {
private final static Wrap DEFAULT_WF = Wrap.WF;
private final static Wrap CASTCOLL_WF = new Wrap(MapGetter.GETTER, CollectionCastGetter.GETTER, SimpleGetter.GETTER);
private final static Obj OBJ = Obj.make(
"aNullbool", null,
"abool", false,
"aNullBool", null,
"aBool", true,
"aBoolList", Arr.make(true, null, false),
"aBoolMap", Obj.make("first", true, "second", null, "third", false),
"aNullNum", null,
"aNum", 123,
"aNumList", Arr.make(1, null, 3),
"aNumMap", Obj.make("first", 1, "second", null, "third", 3),
"aNullStr", null,
"aStr", "abc",
"aStrList", Arr.make("a", null, "c"),
"aStrMap", Obj.make("first", "a", "second", null, "third", "c"),
"testWrapper", Obj.make(
// all nulls
)
);
interface TypedMap<T> extends ObjWrapper {
T first();
T second();
T third();
}
interface BoolMap extends TypedMap<Boolean> {}
interface NumMap extends TypedMap<Number> {}
interface StrMap extends TypedMap<String> {}
interface DefaultWrapper extends ObjWrapper {
boolean aNullbool();
boolean abool();
Boolean aNullBool();
Boolean aBool();
List<Boolean> aBoolList();
BoolMap aBoolMap();
Number aNullNum();
Number aNum();
List<Number> aNumList();
NumMap aNumMap();
String aNullStr();
String aStr();
List<String> aStrList();
StrMap aStrMap();
}
interface CastCollWrapper extends ObjWrapper {
List<Boolean> aNullbool();
List<Boolean> abool();
List<Boolean> aNullBool();
List<Boolean> aBool();
List<Boolean> aBoolList();
List<BoolMap> aBoolMap();
List<Number> aNullNum();
List<Number> aNum();
List<Number> aNumList();
List<NumMap> aNumMap();
List<String> aNullStr();
List<String> aStr();
List<String> aStrList();
List<StrMap> aStrMap();
List<CastCollWrapper> testWrapper();
List<CastCollWrapper> unexistingWrapper();
}
@Test
public void test() {
DefaultWrapper defaultWrap = DEFAULT_WF.wrap(OBJ, DefaultWrapper.class);
assertEquals(false, defaultWrap.aNullbool());
assertEquals(false, defaultWrap.abool());
assertEquals(null, defaultWrap.aNullBool());
assertEquals(true, defaultWrap.aBool());
assertEquals(SEQ.buildList(LinkedList.class, true, null, false), defaultWrap.aBoolList());
assertEquals(true, defaultWrap.aBoolMap().first());
assertEquals(null, defaultWrap.aBoolMap().second());
assertEquals(false, defaultWrap.aBoolMap().third());
assertEquals(null, defaultWrap.aNullNum());
assertEquals(123, defaultWrap.aNum());
assertEquals(SEQ.buildList(LinkedList.class, 1, null, 3), defaultWrap.aNumList());
assertEquals(1, defaultWrap.aNumMap().first());
assertEquals(null, defaultWrap.aNumMap().second());
assertEquals(3, defaultWrap.aNumMap().third());
assertEquals(null, defaultWrap.aNullStr());
assertEquals("abc", defaultWrap.aStr());
assertEquals(SEQ.buildList(LinkedList.class, "a", null, "c"), defaultWrap.aStrList());
assertEquals("a", defaultWrap.aStrMap().first());
assertEquals(null, defaultWrap.aStrMap().second());
assertEquals("c", defaultWrap.aStrMap().third());
CastCollWrapper castCollWrap = CASTCOLL_WF.wrap(OBJ, CastCollWrapper.class);
assertList(castCollWrap.aNullbool());
assertList(castCollWrap.abool(), false);
assertList(castCollWrap.aNullBool());
assertList(castCollWrap.aBool(), true);
assertList(castCollWrap.aBoolList(), true, null, false);
assertEquals(true, castCollWrap.aBoolMap().get(0).first());
assertEquals(null, castCollWrap.aBoolMap().get(0).second());
assertEquals(false, castCollWrap.aBoolMap().get(0).third());
assertList(castCollWrap.aNullNum());
assertList(castCollWrap.aNum(), 123);
assertList(castCollWrap.aNumList(), 1, null, 3);
assertEquals(1, castCollWrap.aNumMap().get(0).first());
assertEquals(null, castCollWrap.aNumMap().get(0).second());
assertEquals(3, castCollWrap.aNumMap().get(0).third());
assertList(castCollWrap.aNullStr());
assertList(castCollWrap.aStr(), "abc");
assertList(castCollWrap.aStrList(), "a", null, "c");
assertEquals("a", castCollWrap.aStrMap().get(0).first());
assertEquals(null, castCollWrap.aStrMap().get(0).second());
assertEquals("c", castCollWrap.aStrMap().get(0).third());
assertList(castCollWrap.testWrapper().get(0).aNullbool());
assertList(castCollWrap.testWrapper().get(0).abool());
assertList(castCollWrap.testWrapper().get(0).aNullBool());
assertList(castCollWrap.testWrapper().get(0).aBool());
assertList(castCollWrap.testWrapper().get(0).aBoolList());
assertList(castCollWrap.testWrapper().get(0).aBoolMap());
assertList(castCollWrap.testWrapper().get(0).aNullNum());
assertList(castCollWrap.testWrapper().get(0).aNum());
assertList(castCollWrap.testWrapper().get(0).aNumList());
assertList(castCollWrap.testWrapper().get(0).aNumMap());
assertList(castCollWrap.testWrapper().get(0).aNullStr());
assertList(castCollWrap.testWrapper().get(0).aStr());
assertList(castCollWrap.testWrapper().get(0).aStrList());
assertList(castCollWrap.testWrapper().get(0).aStrMap());
assertList(castCollWrap.testWrapper().get(0).testWrapper());
assertList(castCollWrap.unexistingWrapper());
}
private <T> void assertList(List<T> actualList, T... expectedValues) {
final int l = expectedValues.length;
assertEquals(l, actualList.size());
for (int i = 0; i < l; i++) {
assertEquals(expectedValues[i], actualList.get(i));
}
}
/* big decimal */
interface MyBdWrapper extends ObjWrapper {
BigDecimal bd();
MyBdWrapper bd(BigDecimal bd);
}
@Test
public void bigDecimalTest() {
final BigDecimal bd035 = new BigDecimal("0.35");
MyBdWrapper mbw = DEFAULT_WF.wrap(Obj.parse("{\"bd\": 0.35}"), MyBdWrapper.class);
assertEquals(bd035, mbw.bd());
assertEquals(bd035, mbw.bd(bd035).bd());
}
}
| {
"redpajama_set_name": "RedPajamaGithub"
} | 7,818 |
@interface JxbHttpCell()
{
UILabel *lblTitle;
UILabel *lblValue;
}
@end
@implementation JxbHttpCell
- (id)initWithStyle:(UITableViewCellStyle)style reuseIdentifier:(NSString *)reuseIdentifier {
self = [super initWithStyle:style reuseIdentifier:reuseIdentifier];
if (self) {
self.accessoryType = UITableViewCellAccessoryDisclosureIndicator;
lblTitle = [[UILabel alloc] initWithFrame:CGRectMake(20, 10, [UIScreen mainScreen].bounds.size.width - 40, 20)];
lblTitle.textColor = [JxbDebugTool shareInstance].mainColor;
lblTitle.font = [UIFont fontWithName:@"Helvetica-Bold" size:19];
[self addSubview:lblTitle];
lblValue = [[UILabel alloc] initWithFrame:CGRectMake(20, 35, [UIScreen mainScreen].bounds.size.width - 40, 16)];
lblValue.textColor = [UIColor lightGrayColor];
lblValue.font = [UIFont systemFontOfSize:12];
[self addSubview:lblValue];
}
return self;
}
- (void)setTitle:(NSString*)title value:(NSString*)value {
lblTitle.text = title;
lblValue.text = value;
}
-(void)setModel:(JxbHttpModel *)model{
lblTitle.text = model.url.host;
lblValue.text = model.url.path;
[self handlerStatusCode:[model.statusCode intValue]];
}
-(void)handlerStatusCode:(int)statusCode{
if((statusCode>=400 && statusCode<600) || statusCode==0){
lblTitle.textColor = [UIColor redColor];
}
else if(statusCode>=300 && statusCode<400){
lblTitle.textColor = [UIColor orangeColor];
}
else if (statusCode == 100){
lblTitle.textColor = [UIColor blueColor];
}
else{
// lblTitle.textColor = [JxbDebugTool shareInstance].mainColor;
lblTitle.textColor = TPFColorWithRGB(0x87d850);
}
}
@end
| {
"redpajama_set_name": "RedPajamaGithub"
} | 2,935 |
{"url":"http:\/\/galaxiesjournalclub.blogspot.com\/2008\/","text":"## Friday, 19 December 2008\n\n### Regulation of Black Hole Growth in Low Redshift Galaxies\n\nThis paper by Kauffmann & Heckman discusses the accretion onto central black holes in SDSS. The authors use the OIII line luminosity as a proxy AGN accretion rate, and they infer the black hole mass from the stellar velocity dispersion; thus L[OIII]\/M_bh becomes a measure of the Eddington ratio. The upper panel in this figure shows the distribution of Eddington ratios for SDSS galaxies. In the lower panels, the galaxies are split up by the strength of their 4000AA break, which is a measure of galaxy age. It appears that young galaxies have a broad log-normal distribution which is independent of age (it is also independent of M_bh, but that isn't visible in this figure). But older galaxies have an approximate power-law distribution which does depend on age (and also on M_bh).\n\nThe authors interpret the log-normal distribution as a reflecting black hole self-regulation, with a negative feedback effect that kicks in at the peak of the distribution (~1% Eddington). But since the distribution doesn't depend on black hole mass or on the star formation in the rest of the galaxy, the feedback must operate only in the immediate vicinity of the black hole. On the other hand, the power-law distribution for the older galaxies does not suggest self-regulation. The authors show that the accretion rate onto the the black hole is roughly proportional to the bulge stellar mass, which is consistent with a scenario in which the black hole is fed by stellar mass loss... however this is a rather speculative conclusion.\n\n## Thursday, 11 December 2008\n\n### The impact of TP-AGB stars on hierarchical galaxy formation models\n\nFrom:\nTitle: The impact of TP-AGB stars on hierarchical galaxy formation models\nAuthors: Chiara Tonini (1), Claudia Maraston (1), Julien Devriendt (2), Daniel Thomas (1), Joseph Silk (2) ((1) Institute of Cosmology and Gravitation, University of Portsmouth, UK; (2) University of Oxford, UK)\nComments: 5 pages, 4 figures. Submitted to MNRAS Letters\nSubjects: Astrophysics (astro-ph)\nThe authors paint galaxy magnitudes on a semi-analytic model of galaxy formation, comparing two population synthesis packages: Maraston 05 (with 'proper' treatment of TP-AGB stars) and Pegase (without those beasts). here they show the V-K,V color magnitude relation at 4 different redshifts for disks and spheroids. The TP-AGBs are particularly relevant at an age of 1 Gyr in the K band. Mass tot K-band light ratios differ by a factor of ~3, for 1 Gyr SSPs, and less for other wavelength bands and ages (V for example is almost indistinghuishable). This may have big consequences for the fitting of stellar masses on the basis of rest-frame K band photometry, as is often done.\n\n## Friday, 5 December 2008\n\n### Merger rates at z~3\n\nfrom Bluck et al., http:\/\/arxiv.org\/pdf\/0812.0926\n\nThe authors use pair counts and galaxy morphologies (CAS) to estimate\nmerger rates in the GOODS North and South fields. The plot above\nshows the merger fraction for galaxies above log(M)=11. At z>3 the\nmerger rate continues to increase, so the peak of merger activity for\nthese galaxies must be at higher redshifts. This is in contrast to\nlower-mass galaxies (10^10), where the merger peak is seen around\nz=2. Thus, the authors conclude that high-mass galaxies undergo\nmajor mergers at higher redshifts than lower-mass galaxies.\n\n## Friday, 14 November 2008\n\n### The growth of supermassive black holes in pseudo-bulges, classical bulges, and elliptical galaxies\n\nLast week Jo talked about a paper by\u00a0Greene et al.\u00a0that showed (if I remember correctly) that galaxies without classical bulges also contain black holes, and that presented evidence that black holes in low-mass bulges don't follow the normal relationship between bulge mass and black hole mass. \u00a0A possible explanation for this was that the low-mass bulges tend to be pseudo-bulges, and that pseudo-bulges have different properties than standard bulges.\n\nNow\u00a0Gadotti & Kauffmann\u00a0have presented an analysis of SDSS data that appears to support this conclusion. \u00a0This plot shows the bulge mass vs. velocity dispersion for ellipticals, classical bulges, and pseudo-bulges. \u00a0The ellipticals follow a tight relation, and the classical bulges also follow a fairly tight relation but with an offset. However the pseudo-bulges don't seem to follow much of a relation, tend to have significantly lower masses than ellipticals\/classical bulges at a fixed velocity dispersion.\n\nIf pseduo-bulges don't follow the same M_bulge-sigma relation as other galaxies, then they can't follow both the standard M_bh-M_bulge relation and the M_bh-sigma relation at the same time. Perhaps pseudo-bulges follow only one of these relations (as suggested by the Greene et al. paper), or maybe they follow neither.\n\nOne possible explanation mentioned by the authors for the observation that pseudo-bulges don't follow the same\u00a0M_bulge-sigma relation is that bars (which may be so small as to be undetected) artificially enhance the observed sigma. \u00a0Another is that pseudo-bulges aren't relaxed, so the virial theorem doesn't apply.\n\n## Thursday, 30 October 2008\n\nDISSECTING THE RED SEQUENCE\u2014I. STAR FORMATION HISTORIES OF QUIESCENT GALAXIES: THE\nCOLOR-MAGNITUDE VS. THE COLOR-SIGMA RELATION\n\nGenevieve J. Graves, S. M. Faber, & Ricardo P. Schiavon\n\nFrom DR4 SDSS data with the NYU-VAGC, the authors select quiescent (i.e. emission line-free) galaxies. These lie on the red sequence. They measure luminosities, colors, velocity dispersion and a few element abundances (mainly Fe abundance and alpha-enrichment). In a plot that I don't show here, it shows that at fixed velocity dispersion there is no relation between luminosity and color (luminosities vary more than color, and contours of number density are largely horizontal). The red sequence is inclined, because higher sigma galaxies, have higher luminosities and are redder. Adding up different sigma bins results in the red sequence as we know it.\n\nTo investigate this further, the authors bin in L-sigma-color space and stack all spectra in a bin together to measure abundances and age. Here I will concentrate on age. In the plot you see six panels in the luminosity color plane, for six bins in velocity dispersion (these show no L-color relation!). The color coding is luminosity weighted mean age.\n\nAs you can see, low-sigma galaxies are younger and have a bigger spread in ages than luminous, high-sigma galaxies. Also, the variation in age is perpendicular to the red sequence, i.e. the width is set by the age distribution of the galaxies.\n\nQuiescent galaxies are a multi-parameter family. Age (and Fe\/H and alpha\/Fe) all increase with sigma, and vary at fixed sigma depending on L. Age also varies as a function of color, at fixed sigma: brighter galaxies have lower age at fixed sigma and are bluer.\n\n## Friday, 24 October 2008\n\n### Evidence for Merger-Driven Activity in the Clustering of High Redshift Quasars\n\nRecently Shen et al. (2007) found that high-z quasars from SDSS are very strongly clustered, with a bias of ~14 at z=4. White et al. (2008) used this result to show that there must be an extremely tight relation between quasar luminosity and halo mass, with an upper limit to the scatter of 0.3 dex. The basic reasoning behind this conclusion is that, if there were a larger scatter, then many quasars in (very abundant) low-mass halos would have high enough luminosity to make it into Shen's sample, however the observed number density of quasars is too low to allow for this. Wyithe & Loeb say that such a tight scatter is difficult to believe since the scatter in the relationship between black hole mass and bulge velocity dispersion is also 0.3 dex, and one might expect that this relationship is tighter and more direct then the relationship between halo mass and quasar luminosity.\n\nNow Wyithe & Loeb have revisited this issue, using a somewhat more flexible model than was used by White et al. For instance, White et al. assumed that quasar luminosity is proportional to halo mass, whereas physical arguments suggest that it should be proportional to halo mass to a higher power. Also, Wyithe and Loeb allow for an arbitrary boost in the clustering of halos that host quasars. Such a boost might be expected if those halos have special properties, for instance if they have just merged.\n\nThis figure shows the joint likelihood distributions of various parameters in the Wyithe & Loeb model. I won't bother to explain all of the parameters, so just look at the upper right plot. This shows contours of F (the amount that the bias is boosted by) vs. gamma (the slope of the halo mass vs. quasar luminosity relation). Models where F=1 are highly disfavored. This suggests that you can't explain the observed quasar number density and clustering using a standard clustering model, but that some other ingredient must come into play.\n\nThis conclusion is related to some other recent results, as I mentioned here, however those results may be subject to systematic observational uncertainties. Perhaps the Shen et al. measurement is on firmer ground, but I haven't looked at that paper in detail. But it does seem that the very high clustering measurement is in contrast with the measurement presented by Adelberger & Steidel (2005).\n\nOk, I'll kick it off this week. This is a plot from Shen et al (2008, arXiv:0810.4144) who study the correlation of QSOs in the sky using the SDSS DR5. They look how clustering depends on luminosity, black hole mass, colour and radio loudness. What they find is perhaps a bit surprising but not entirely new - there is virtually no dependence on any of these parameters, except radio loudness. So - don't go around expecting a QSO to necessarily live in a massive halo, at least not at z<2.5\n\n## Friday, 17 October 2008\n\n### Red Nugget Watch\n\nfrom Saracco, Longhetti, & Andreon, http:\/\/arxiv.org\/abs\/0810.2795\n\nThis paper presents another analysis of the sizes and surface densities of early-type galaxies at z=1-2; here they use a sample of 32 spectroscopically-confirmed galaxies with a mean redshift of 1.45 from several different surveys. Masses and ages are determined via SED fitting to the photometry. As has been reported before, these galaxies lie well off the z=0 size-luminosity relation. By evolving the galaxies (assuming pure luminosity evolution) from their measured \u00a0redshifts to the present, the authors find that some galaxies would actually evolve to the z=0 relation in this manner, while some would not. These galaxies appear to be \"young\" and \"old\" respectively, and the authors appear to claim a bimodal age distribution in ETGs at this redshift, with typical ages ~1 Gyr and 3.5 Gyr. Young ETGs follow the local size-mass relation, old ETGs do not.\n\nThe authors conclude that the young objects have more or less completed their evolution (except for luminosity evolution), while the old galaxies still need some process to increase their effective radii. Dry merging cannot do this because it would create too many high-mass galaxies, so some other process must be at work. Much of this rests on the assumption that the relative ages can be accurately determined through photometry, of course.\n\n## Friday, 10 October 2008\n\n### The PN.S Elliptical Galaxy Survey: the dark matter in NGC 4494\n\nThe PN.S Elliptical Galaxy Survey is an ongoing survey to detect and measure the kinematics of planetary nebulae (PNe) in nearby early-type galaxies. Here they present 255 PNe measurements in the elliptical NGC 4494 out to 7 effective radii (Re). They construct mass models, where they include dark matter haloes to explain the observed kinematics at large radii. This plots shows the dark matter fraction they find in this galaxy and other galaxies in their sample, compared to results from numerical simulations. Overall, the dark matter fraction is lower than predicted in simulations, especially at smaller radii. This indicates a mismatch between observations and theory, with intermediate-luminosity galaxies having low concentration haloes.\n\nFrom Napolitano et al., from http:\/\/arxiv.org\/abs\/0810.1291\n\n### Reconstruction of a z=3.07 lensed galaxy\n\nfrom Stark et al., http:\/\/arxiv.org\/abs\/0810.1471\n\nThis Nature paper describes integral field (OSIRIS on Keck) observations of a strongly lensed z=3.07 Lyman break galaxy. With AO corrections and the high magnification, these observations provide an effective physical resolution of 150 kpc. This figure shows (a) the\u00a0reconstructed HST image with the lensing caustic overlaid, (b) [OIII] and Hbeta emission (bluescale and contours respectively), (c) velocity field and best-fit disk model, (d) [OIII] velocity dispersion, (e-h) 1-d profiles of the left panels taken along the \"slit\" shown in panel (d). The velocity field is well-fit by a disk model, so the authors conclude that this is a disk galaxy with v_r=67 km\/s and M=2e9 Msun. However, the central velocity dispersion is large (v\/sigma=1.2), so it's most likely still at an early stage of formation.\n\n### all MW halos have the same mass!\n\nAll the satelites of our galaxy have aroundabout the same mass enclosed within a fixed radius (see Strigari et al., arXiv:0808.3772).\u00a0 Here, the authors have taken a N-body sim + SAM to see whether or not this falls out of current models.\u00a0 And indeed it does!\u00a0 The black points show their model results; the red points are from Strigari et al.\n\nAnother interesting sidenote: of the 2000ish subhalos that the authors tracked, only 51 became fully fledged satelite galaxies.\u00a0 This is still twice as many as are observed, but they reckon that optical selection effects can account for this.\u00a0 (Which you can kinda see from the plot.)\u00a0 This is essentially because they have completely supressed gas cooling in subhaloes with virial temperatures below 10^4 K.\n\n## Tuesday, 7 October 2008\n\n### Evidence for a Collision Between M86 and NGC 4438 and Implications for Collisional ISM Heating of Ellipticals\n\nKenney et al.\n\nThis is a color gri from SDSS, overlayed with narrowband Halpha+NII images (visible as the red and green filaments). The giant elliptical on the right is M86, which appears to be the brightest galaxy in a group or sub-cluster that is merging with Virgo. The galaxy on the left is NGC 4438 (also Arp 120), a highly-disturbed spiral. The red filaments are Halpha+NII emission that appear to link the two galaxies, suggesting that they have undergone a high-speed collision. The green filaments are Halpha+NII emission at a higher recessional velocity; it is not clear whether the galaxy in the lower right and the associated line emission are involved in this interaction.\n\nNGC 4438 is very HI-deficient for a spiral galaxy of it's size. If it lost most of it's HI during the collision, then it is expected that a significant fraction of the kinetic energy of that gas went into heating the ISM of M86. This heating would be enough to prevent gas from cooling and forming stars in M86, possibly obviating the need for radio-mode AGN feedback. Thus this interacting system may be a nice example of the \"gravitational quenching\" mechanism discussed by Dekel & Birnboim (2008).\n\n## Friday, 26 September 2008\n\n### Time to go into finance?\n\nConroy, Gunn, & White, http:\/\/arxiv.org\/abs\/0809.4261\n\nThis paper explores the effects of stellar evolution uncertainties\n(particularly the properties of thermally pulsating AGB stars, but\nalso metallicity and the IMF) on quantities derived through stellar\npopulation modeling like age, mass, and star-formation rate. From\ncomputing expected colors of LMC star clusters the authors conclude\nthat the temperature and luminosity of the TP-AGB phase could vary by\nas much as +-0.2 dex and +-0.4 dex respectively, and so they allow\nthese parameters to vary in their stellar population fitting. The\nplot above shows 68% and 95% likelihood contours for the derived\nproperties for a bright z~2 quiescent galaxy, with probability\ndistributions (blue line: AGB star uncertainties included; black: not\nincluded) in the top panel. Interestingly, the degeneracies between\nthe AGB parameters and derived quantities are weak at best, and the\nuncertainties don't seem to increase much (blue vs. black curves).\n\n## Friday, 12 September 2008\n\n### Now you see it, now you don't\n\nBarbary et al (2008, http:\/\/uk.arxiv.org\/abs\/0809.1648) have discovered an (apparently) new class of optical transient objects. The spectrum is a mystery, the source brightened by >5-6 magnitudes over 100 days and no host galaxy can be seen. Might be Galactic, might be extra-galactic. If the latter, the most reasonable estimate of redshift gives a peak luminosity of -22.1 - close to the brightest SNe seen.\n\n### Do Sub-mm Galaxies Really Trace The Most Massive Dark Matter Halos?\n\nChapman et al.\n\nThis paper presents evidence of a strong over-density of sub-mm galaxies at z=1.99 in GOODS-N. The interesting thing about it is that there is also an over-density of the more typical blue star-forming galaxies at the same redshift, but that the density contrast for the blue galaxies is much weaker than for the sub-mm galaxies.\n\nThe authors suggest that this is a cluster in the first stages of formation. The strength of the over-density of sub-mm galaxies is due to the numerous ongoing mergers, and thus it is not representative of the overall matter over-density, which would be much weaker. The fact that the masses and SFRs of the blue star-forming galaxies in the redshift spike is similar to the values for galaxies outside of the spike supports this argument, since you would expect most galaxies in a cluster to be older and more massive (even at these high redshifts).\n\nThe biggest caveat that the authors note is that there may be a large population of quiescent galaxies in this redshift spike that have not been observed spectroscopically. If this were the case, the true matter over-density would be closer to the over-density of sub-mm galaxies, and the merger argument wouldn't be necessary. The same caveat applies for blue star-forming galaxies that don't have spectroscopic redshifts. So without having a good idea of the statistical significance of these results, I would say that the main conclusion is a bit of a stretch... although not any more so than some other recent claims in the literature.\n\n### Obscured Star Formation in Abell 901\/902\n\nThe authors investigate the amount of obscured star-formation as a function of environment. They find that ~40% of the star forming galaxies has red optical colors at intermediate and high densities. This suggests that environmental interactions trigger a phase of obscured star formation before complete quenching.\n\n## Friday, 5 September 2008\n\n### DOG fight\n\nfrom Pope et al., arXiv:0808.2816. Dust-obscured galaxies (DOGs)\nhave been recently defined as objects with extremely red R-[24um]\ncolors. Another recent paper by Fiore et al. studied the X-ray\nproperties of a similarly-selected set of galaxies and found that\nthey are consistent with being Compton-thick AGN. The DOG people\nclaimed that these things were primarily starbursts, and so they\nlaunch a counteroffensive with the above figure. While most bright\nDOGs show a strong 8um excess (and are therefore likely powered by\nAGN), most of the overall sample seems to be dominated by star formation.\n\n## Friday, 29 August 2008\n\n### All MW satellites have the same mass?\n\nfrom Strigari et al., arXiv:0808.3772\n\nLine-of-sight velocity measurements were used to derive masses within the innermost 300pc of 18 Milky Way dwarf satellites. The above figure is self-explanatory, and surprising: over 5 orders of magnitude in luminosity, there's almost no change in the dark matter+stellar mass. They mention several possible explanations, including a sharp cutoff in star formation efficiency below this halo mass, a characteristic formation time (in CDM models) around the epoch of reionization, or dark matter temperature of >1keV (in WDM models).\n\n## Friday, 22 August 2008\n\n### Contradiction between strong lensing statistics and a feedback solution to the cusp\/core problem\n\nTitle: Contradiction between strong lensing statistics and a feedback solution to the cusp\/core problem\nAuthors: Da-Ming Chen, Stacy McGaugh\n\nAbstract:\nStandard cosmology has many successes on large scales, but faces some fundamental difficulties on small, galactic scales. One such difficulty is the cusp\/core problem. High resolution observations of the rotation curves for dark matter dominated low surface brightness (LSB) galaxies imply that galactic dark matter halos have a density profile with a flat central core, whereas N-body structure formation simulations predict a divergent (cuspy) density profile at the center. It has been proposed that this problem can be resolved by stellar feedback driving turbulent gas motion that erases the initial cusp. However, strong gravitational lensing prefers a cuspy density profile for galactic halos. In this paper, we use the most recent high resolution observations of the rotation curves of LSB galaxies to fit the core size as a function of halo mass, and compare the resultant lensing probability to the observational results for the well defined combined sample of the Cosmic Lens All-Sky Survey (CLASS) and Jodrell Bank\/Very Large Array Astrometric Survey (JVAS). The lensing probabilities based on such density profiles are too low to match the observed lensing in CLASS\/JVAS. High baryon densities in the galaxies that dominate the lensing statistics can reconcile this discrepancy, but only if they steepen the mass profile rather than making it more shallow. The result is contradictory demands upon the effects of baryons on the central mass profiles of galaxies.\n\n## Friday, 15 August 2008\n\n### Constraints on high-z disk formation\n\nfigure 1 from Robertson & Bullock (arXiv:0808.1100)\n\nThe authors investigate the claim by Genzel et al. (2006) that the\nz=2.4 \"disk\" galaxy BzK-15504 formed very rapidly and early on (with\na correspondingly rapid accretion of mass), but shows no evidence of\na merger (because its velocity asymmetry is low). Using their\nsimulations of gas-rich disk mergers and taking into account noise\nand PSFs, the authors figure out how their merger remnants would\nappear viewed through SINFONI. In all four of their simulations\n(each with different initial configurations), galaxies that would be\nobservationally classified as \"disks\" appear 100-150Myr after the\nmerger. The above figure shows one particular simulation that they\nclaim matches the kinematic properties of BzK-15504 (shown below for\ncomparison, from Genzel et al. 2006) remarkably well.\n\n## Thursday, 14 August 2008\n\n### Observations of the Gas Reservoir around a Star Forming Galaxy in the Early Universe\n\nFrye et al., http:\/\/arxiv.org\/abs\/0808.0921\n\nThe figure shows a high-S\/N spectrum of a z=4.9 starburst galaxy; this kind of S\/N is only possible because of a long exposure time (14hrs on an 8m telescope) and because the flux is boosted by a factor of 10 due to gravitational lensing by a foreground cluster. The most interesting feature is the broad Gunn-Peterson trough blueward of the bright Lya emission line.\n\nSince the optical depth in this trough is significantly larger than observed at the same wavelengths for random sight-lines through the IGM (the universe was already reionized at this redshift), the authors conclude that we are seeing direct evidence of a \"cosmic web\" of gas that surrounds galaxies and feeds their growth.\n\nAnother possibility is that the neutral gas is outflowing material from the galaxy itself, however the authors discount this explanation since stellar population modeling suggests that the galaxy is too young to have driven such large amounts of gas outwards. Also, typical outflow velocities are not large enough to explain the broad trough, even for outflows that are powered by AGN.\n\nThis is a neat observation, but I'm not sure how much we can infer from a single object. Unfortunately, a galaxy at this redshift has to be strongly lensed to be bright enough for this sort of analysis, so there isn't much hope of obtaining a large sample in the near future. Of course QSOs are also bright enough, but they tend to ionize most of the hydrogen in their immediate vicinity.\n\n## Friday, 8 August 2008\n\n### Size evolution from z=1 to present\n\nfigure 7 of van der Wel et al., arXiv:0808.0077\n\nIn this paper, the authors find that early-type galaxies grow larger\nby a factor of ~2 from z=1 to z=0, consistent with previous studies.\nThis figure shows the ratio of sizes at the two redshifts from this\nwork and others, and compares it to the Khochfar & Silk (2006)\nsemianalytic model. The observed size evolution between z=1-0 is\nmuch steeper than predicted by the model, which is based on the idea\nthat (cold)-gas-rich mergers at high redshift produce smaller\ngalaxies than the gas-poor mergers at low redshift.\n\nProbably the most important difference between this and previous\nstudies is that masses here are calculated using dynamical, rather\nthan photometric, measurements. Thus, the mass (and hence surface\ndensity) estimates here should be less prone to systematic effects.\nNonetheless, the offset in the size-mass and size-surface density\nrelations are consistent with the photometric studies. This seems to\nimply that any systematic effects are small compared to the observed\nsize evolution.\n\n### The Millennium Simulation compared to z~2 galaxies\n\nThe Millennium Simulation compared to z~2 galaxies\nGenel et al.\n0808.0194\n\nThe authors use the Millennium Simulation to extract merger fractions and\nmass accretion rates. They find that the accretion rates are sufficient to\naccount for the high star formation rates observed in z~2 UV-optically selected disks.\n\n(not in figure) When following the fate of these disks and submm galaxies, they find that subsequent mergers are not frequent enough to either convert all disks into elliptical galaxies at z~0, or transform all submm galaxies to massive cluster ellipticals at z~0. They conclude that secular and internal evolution must play an important role in the evolution of these z~2 galaxies\n\n## Thursday, 7 August 2008\n\nDisc instabilities and semi-analytic modelling of galaxy formation\nE. Athanassoula\n\nThis paper points out that the method to form spheroids in semi-analytic models of galaxy formation are wrong. A criterium, based on bar instability for given disk parameters is often used in these models and either the whole disk, or a fraction of the disk than suddenly transforms into a spheroid. This is a necessary ingredient to match the observed near-IR luminosity functions.\n\nIn reality, this criterium does not hold. It was derived from 2D Nbody simulation long ago. If you take into account that the halo is non-static and that there are random motions in the disk and in the halo, then the situation is different: disks are much more stable, and form at best small pseudo-bulges. A simple creterium for bulge formation from disk instability is not easily possible, and should not be used in semi-analytic models.\n\n## Friday, 1 August 2008\n\n### On the SFR-brightest cluster relation: estimating the peak SFR in post-merger galaxies\n\nNate Bastian: astro-ph\/0807.4687\n\nHe does Monte Carlo simulations and comparisons to observations of star cluster formation in galaxies. It appears thet there is quite a tight relation between the magnitude of the brightest young cluster present, and the current SFR, because the brightest cluster often is young (<15Myr) and the mass of the most massive cluster is determined by the number of clusters formed, which is strongly related to the SFR. In the figure, the colored lines are lines of different cluster mass functions (schechter with some M*. ). The gamma indicates the factor between star formation rate and cluster formation rate, i.e. they find that CFR = 0.08 SFR, which is sort of low. This SFR indicator agrees well with other indicators.\n\nUsing the fading of clusters, an old cluster that is very bright can indicate a burst in SFR some time ago, and its luminosity and age give an estimate of the peak SFR of that galaxy (or galaxy merger). Here cluster disruption effects need to be taken into account (which is difficult).\n\n## Thursday, 31 July 2008\n\n### An Imprint of Super-Structures on the Microwave Background due to the Integrated Sachs-Wolfe Effect\n\nBenjamin R. Granett, Mark C. Neyrinck, Istv\u00e1n Szapudi (IfA, Hawaii)\n\nWe measure hot and cold spots on the microwave background associated with supercluster and supervoid structures identified in the Sloan Digital Sky Survey Luminous Red Galaxy catalog. The structures give a compelling visual imprint, with a mean temperature deviation of 9.6 +\/- 2.2 microK, i.e. above 4 sigma. We interpret this as a detection of the late-time Integrated Sachs-Wolfe (ISW) effect, in which cosmic acceleration from dark energy causes gravitational potentials to decay, heating or cooling photons passing through density crests or troughs. In a flat universe, the linear ISW effect is a direct signal of dark energy.\n\nFIG. 1.\u2014 Stacked regions on the CMB corresponding to supervoid and supercluster structures identified in the SDSS LRG catalog. We averaged CMB cut-outs around 50 supervoids (left) and 50 superclusters (center), and the combined sample (right). The cut-outs are rotated, to align each structure\u2019s major axis with the vertical direction. Our statistical analysis uses the raw images, but for this figure we smooth them with a Gaussian kernel with FWHM 1.4\u000e. Hot and cold spots appear in the cluster and void stacks, respectively, with a characteristic radius of 4\u000e, corresponding to spatial scales of 100 M pc\/h inner circle (4\u000e radius) and equal-area outer ring mark the extent of the compensated filter used in our analysis. Given the uncertainty in void and cluster orientations, small-scale features should be interpreted cautiously.\n\n## Thursday, 24 July 2008\n\nFrom the paper 'Red Nuggets at z \u223c 1.5: Compact passive galaxies and the\nformation of the Kormendy Relation' by Damjanov et al (0807.1744) I chose these two plots.\n\nWe had discussions before about these tiny galaxies that Mariska and Pieter investigated. These authors do sort of the same job, but at slightly lower redshift (1.5-ish). The left plot shows the effective radius - stellar mass plane, with the dots and contours being local SDSS red galaxies. The bigger points with error bars are their (and some other) red galaxies at higher redshift, which appear to small. I show this plot, because the arrows indicate the approximate track of evolution due to three different processes: dry mergers, pure stellar mass growth without changing size and adiabatic expansion (stellar mass loss makes the systems less bound). All three processes seem incapable of transforming the galaxies towards the low - z counterparts.\n\nThe right plot shows the galaxies in the stellar mass density - effective radius plane (Kormendy relation). Here they are all on the same trend, with the high redshift galaxies smaller and denser than their local red SDSS partners. Color coding here is redshift, which appears to hint at some evolution: the higher the redshift of the galaxy, the smaller and denser it is. The main part of the evolution takes place at 1.1 < z < 1.5.\n\n## Thursday, 3 July 2008\n\n### What's wrong with this picture?\n\n(or, at least, highly suspicious--and why?):\n\nfrom \u00a0Morioka et al., arXiv:0807.0101, PASJ in press. \u00a0Black dots are H-alpha emitting galaxy candidates (via a narrowband filter selection), grey regions are masked-out bright stars. \u00a0The authors use this sample to compute the clustering and luminosity function of star-forming galaxies at z=0.24, and note that the clustering in this field is stronger than in the COSMOS field. \u00a0First one to post the right answer in comments wins a beer at the next borrel.\n\n## Wednesday, 25 June 2008\n\n### It's the same!\n\nFrom arXiv:0806.3278\n\nTitle:\nCorrelations between MIR, FIR, H$\\alpha$, and FUV Luminosities for SWIRE galaxies\n\nThe figure shows the correlation between observed H-alpha + 24 micro (y-axis, left-hand panel) and H-alpha + 8 micro (y-axis, right-hand panel) luminosities with the extinction-corrected H-alpha luminosities (x-axis) for star-forming galaxies selected from the Spitzer-SWIRE fields.\n\nFilled circles: Normal galaxies\nOpen circles: Dwarf galaxies\nLines: Best nonlinear (solid) and linear (dotted) fit\n\n## Friday, 6 June 2008\n\n### SXDF SMGs & BzKs\n\nfrom Takagi et al., http:\/\/arxiv.org\/abs\/0806.0888\n\nThe authors attempt to investigate whether submillimeter galaxies can be\nidentified by simple color cuts. The answer is: probably not, with the\nresolution of current submm instruments.\n\n### Spectroscopic Confirmation Of An Extreme Starburst At Redshift 4.547\n\nCapak et al., http:\/\/arxiv.org\/abs\/0806.0657\n\nThis is a set of images of an extreme object at z=4.5 in the COSMOS survey. \u00a0It is the most distant mm source not associated with an optically bright quasar. The rest-frame UV and Lya imaging (the first five panels on the left) show emission near the lower left of the panes, although no emission is detected in the B-band because it falls blueward of the Lyman break. At longer wavelengths, the emission shifts to the upper left; the panel on \u00a0the far right shows radio contours.\n\nThe estimated star formation rate is 1000-4000 Msun\/yr, based on several indicators. The authors argue against significant AGN activity -- which would mean this SFR could be a severe overestimate -- because there is no xray detection and because an optical spectrum shows no hint of an AGN. \u00a0But, as the authors note, an AGN could lie outside the optical slit. \u00a0In fact I think this a fairly likely explanation since the authors placed the slit on the center of the UV emission (lower left), whereas an AGN would be expected to be associated with the longer wavelengths (upper right), which is where the most of the stellar mass and radio activity is.\n\n### Evidence for a Stellar-Dominated UV Background and Against a Decline of Cosmic Star Formation Beyond z~3\n\nFrom Faucher-Giguere et al (http:\/\/arxiv.org\/abs\/0806.0372). The authors use the Lyman-alpha forest opacity to estimate the photoionizing background at 2 < z < 4.2. After subtracting the contribution from AGNs, they suggest that stellar sources are dominant (and thus may be responsible for reionization). Perhaps more remarkably, they determine a cosmic star formation rate that is flat, at odds with the well accepted Hopkins and Beacom (2006) curve.\n\n## Friday, 30 May 2008\n\n### Radio jet duty cycles in nearby galaxies\n\nfrom Shabala et al., arXiv:0805.4152\n\nThis figure shows the fractile distribution of radio source ages in four different stellar mass bins. There appears to be a strong trend whereby more massive galaxies host older radio sources, suggesting that the \"on phase\" of radio activity lasts longer for these galaxies. The on-time and the gas cooling rate show the same dependence on stellar mass, suggesting that the two are probably linked (i.e. the availability of fuel governs whether an AGN is on or off). Elsewhere in the paper the authors argue that higher-mass galaxies also exhibit more powerful and frequent radio jets. If true, this may be further evidence for a link between radio AGN and the shutdown of star formation.\n\n## Friday, 23 May 2008\n\n### Galaxy Size Problem at z=3: Simulated Galaxies Are Too Small\n\n(http:\/\/arxiv.org\/abs\/0805.3150 by M.K. Ryan Joung (Princeton), Renyue Cen (Princeton), Greg Bryan (Columbia))\n\nThe authors run zoom simulations and find the simulated galaxies are too small to match the observations after corrections (blue line, bottom panel). I suspect that their feedback isn't strong enough to disrupt the inner star formation though.\n\n## Friday, 18 April 2008\n\n### Red Galaxy Growth and the Halo Occupation Distribution\n\nMichael J. I. Brown et al astroph 0804.2293\n\nThis is from the paper \"The Halpha Galaxy Survey V. The star formation history of late type galaxies\", by Phil James et al. astro-ph\/0804.2167\n\nThey have SFRs from Halpha, stellar masses from K and R band photometry (all with the 1m Kapteyn Telescope) and gas masses from Westerbork neutral hydrogen observations for local late type field galaxies. Here they plot the star formation timescale (Mstar\/SFR) and gas depletion timescale (Mgas\/SFR) for galaxies as a function of mass and type. The dashed lines indicate the age of the universe. The fact that the star formation timescale for low mass\/late type galaxies is similar to the age of the universe and their gas depletion time is much longer, whereas it is reversed for the high mass\/earlier type galaxies is used as an argument that the star formation history of very late type galaxies is constant over the age of the universe and the stellar mass gradually builds up, an that for more bulgy galaxies the bulk of the star formation happens in short bursts of high SFR.\n\nThe possibility of having a higher SFR in the past is not mentioned...\n\n### Predicted OVI-galaxy cross-correlation\n\nFigure 2 of Ganguly, Cen, Fang, Sembach, http:\/\/arxiv.org\/abs\/0803.4199\n\nThe authors use a CDM simulation which includes IGM metal enrichment from superwinds to predict the galaxy-OVI absorber cross-correlation at low redshifts; or, as in the figure above, the fraction of galaxies with an OVI absorber within a given distance, at different galaxy luminosities, absorber strengths, and projected absorber-galaxy separations. They find that the correlation length depends strongly on galaxy luminosity (with faint, low-mass galaxies having more nearby absorbers on average) but not on absorber strength. Only ~15% of OVI absorbers come from >L* galaxies, implying that IGM enrichment may be predominantly due to many faint sources rather than a few bright ones.\n\nThey note also that these results are somewhat preliminary and their simulation resolution may cause problems for the lowest-mass galaxies, but these will be a valuable starting point for comparison to upcoming large COS surveys.\n\n## Friday, 11 April 2008\n\n### The energy output of the Universe from 0.1 micron to 1000 micron\n\nFrom http:\/\/arxiv.org\/abs\/0803.4164.\n\n### Evolution of the field galaxy pair fraction\n\nFigure 13 of Hsieh et al., http:\/\/arxiv.org\/abs\/0804.1604\n\nThis plot shows the average number of galaxy companions as a function of redshift for different pair separations. With increasing separations, the evolution of the pair fraction decreases. Assuming these pairs represent early-stage mergers, this may imply that the infall\/merging timescales are changing with redshift: at high redshift it takes longer for a galaxy to finish merging (i.e. go from 20 kpc to 0 kpc) than at low redshift, relative to the inital (r=150 to 50 kpc) infall. The authors suggest that such a change in timescale may be due to dark matter halos at lower redshift being more concentrated: since the density is lower in the outskirts of highly-concentrated halos, the dynamical friction timescale at large radii is longer, and therefore one might expect merging galaxies to spend more time at larger radii (thus increasing the large-separation pair fraction) at lower redshifts.\n\n### The MBH-Sigma relation in the last six billion years\n\nFigure 2 from Woo et al., astro-ph 0804.0235\n\nThe M_BH-sigma relation of active galaxies.\nLeft panel: local Seyferts with sigma from Greene & Ho (2006) and our own M_BH estimates consistently calibrated with our estimates for distant samples (black circles); local Seyferts with M_BH, measured via reverberation mapping (Onken et al. 2004; magenta circles)\nRight panel: new measurements at z=0.57 (red stars); Seyfert galaxies at z=0.36 from our earlier work (blue circles). The local relationship of quiescent galaxies (Tremaine et al. 2002; black points) are shown for comparison as a solid (Tremaine et al. 2002) and dashed (Ferrarese & Ford 2005) line.\n\n## Friday, 28 March 2008\n\nFrom http:\/\/arxiv.org\/abs\/0803.3944. The author postulates that a natural explanation for the observed metallicity gradient in DLAs can be explained via dense, metal poor disks and less dense metal rich outflows.\n\n### Star formation in BCGs\n\n(Figure 10 of O'Dea et al., http:\/\/arxiv.org\/abs\/0803.1772)\n\nUpper limits on the mass deposition rate (derived from X-ray emission measurements) vs. star formation rate for brightest cluster galaxies. Filled circles denote the maximum mass deposition rate (assuming no gas heating), while open circles are the rates derived from detailed cooling-flow model fits.\n\nThis paper discusses results from a Spitzer survey of 62 brightest cluster galaxies that exhibit optical line emission, specifically the ~50% of those galaxies that show excess infrared emission. While four of these appear to be dominated by AGN, they claim that the remainder show evidence for star formation (from L_IR, CO measurements, and Halpha luminosity). The above figure then appears to show a strong correlation between mass deposition from the ICM and star formation, and therefore such cooling may be the fuel source for the SF activity in these galaxies. Furthermore, the MDR exceeds the SFR, indicating that some reheating mechanism may be at work. It should be noted that all the points in this figure are formally upper limits, so in fact the cooling rate could be entirely consistent with the SFR.\n\n## Friday, 14 March 2008\n\nTitle: The contribution of star formation and merging to stellar mass buildup in galaxies\nAuthors: Niv Drory (1), Marcelo Alvarez (2) ((1) MPE, Garching, Germany, (2) KIPAC-Stanford, USA)\nComments: Accepted for publication in ApJ\nSubjects: Astrophysics (astro-ph)\nThe authors take data from the FORS Deep Field (FDF), 5500 galaxies with redshifts between 0 and 5. They obtain stellar masses and SFRs as well as photo-z's. By integrating the SFR over time they calculate, as a function of mass, the change in number density of galaxies of that mass due to star formation. They compare that to the actual change of the mass function to obtain the contribution that is from anything other than star formation, being mainly merging and accretion (assuming that tidal stripping and so on are negligable). They call this the assembly rate and that is what is shown in the figure (the y-axis normalized to have the relative change), as a function of z and mass (in both plots). See the paper for selection effects...\n\n## Monday, 10 March 2008\n\n### Are SNIa a two-component family?\n\nIn astro-ph\/0803.1130, Dahlen, Strolger & Riess report on their HST survey for high redshift SN Ia. Their results strengthen the argument that the SNIa rate drops at high redshift. The immediate interpretation of this is that SN Ia only start after some long delay. Their favourite model has a delay time of 3.7 Gyr and is shown as the solid line in the Figure. The solid points in the Figure shows the observed SN Ia rate.\n\nNow the problem is that a number of groups have recently argued, fairly convincingly, that SN Ia at lower redshift clearly fall into two categories: A group of delayed explosions and a group of \"prompt\" explosions - ala SN II. Three such models are shown as non-solid lines in the Figure and the match to the observations fails to excite :) What gives? The authors argue that dust obscured star formation might explain the differences, but it is not settled.\n\n## Friday, 7 March 2008\n\n### The evolution of submillimetre galaxies: two populations and a redshift cut-off\n\nWall, Pope, & Scott 2008, MNRAS, 383, 435\n\nThese authors find reasonably secure counterparts for 35\/38 SCUBA sub-mm sources in GOODS-N. This plot shows the relationship between redshift (combination of spectroscopic and photometric redshifts) and rest-frame 850 micron luminosity (which is also illustrated by the size of the circular plotting symbols). The black symbols are those below the median luminosity, and the blue symbols are above. \u00a0The curves show the detection limits; since the noise varies strongly over the SCUBA map, a different completeness curve is shown for the location on the map of each detected galaxy. \u00a0The fact that these curves flatten at high redshift is due to the negative K-correction.\n\nOne notes an apparent lack of high-luminosity sources at z<~1.5 and of low-luminosity sources at z>~2.5. \u00a0This is interpreted as an aspect of the generic downsizing trend of star-formation. \u00a0The authors split the sample in half by luminosity, and model the evolution of the luminosity function of the two samples independently as a function of redshift. \u00a0But the qualitative conclusions remain the same, and based on the data you'd have to be pretty brave to conclude very much more than that. \u00a0I'll post a few more thoughts in the comments, but those will probably only be relevant to those who have actually taken a look at this paper.","date":"2017-06-27 07:01:10","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 1, \"mathjax_display_tex\": 0, \"mathjax_asciimath\": 0, \"img_math\": 0, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.7306892275810242, \"perplexity\": 2723.865344907561}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2017-26\/segments\/1498128321025.86\/warc\/CC-MAIN-20170627064714-20170627084714-00577.warc.gz\"}"} | null | null |
Християнсько-соціальна народна партія (, , , CSV) — люксембурзька християнсько-демократична політична партія. Партія була створена у 1944 році. Партія має 26 місць із 60 у парламенті Люксембургу та 3 місця із 6 виділених для Люксембургу в Європарламенті (входить до фракції Європейської народної партії).
Партія очолює теперішню урядову велику коаліцію, до якої входить також Люксембурзька соціалістична робітнича партія (ЛСРП).
Історія
16 січня 1914 року створена Партія правих, що стояла біля витоків CSV. У 1944 році на базі Партії правих створена Християнсько-соціальна народна партія.
На перших виборах після Другої світової війни у 1945 році партія отримала 25 з 51 місць (до абсолютної більшості голосів не вистачило одного місця). З 1945 по 1974 роки партія очолює уряд. У 1974 році партія переходить в опозицію вперше, коли лідер Демократичної партії Гастон Торн стає прем'єр-міністром у коаліції з ЛСРП.
У 1979 році партія знову повертається в уряд після його перемоги на виборах. П'єр Вернер стає прем'єр міністром. 1984 році представник партії Жак Сантер стає прем'єр міністром. У 1995 році уряд очолює Жан-Клод Юнкер, а Жак Сантер стає президентом Європейської комісії.
З 2004 року партія очолює урядову коаліцію разом із Люксембурзькою соціалістичною робітничою партією.
Участь у виборах
Посилання
Офіційний сайт партії
Партії Європарламенту від Люксембургу
Політичні партії Люксембургу
Християнсько-демократичні партії | {
"redpajama_set_name": "RedPajamaWikipedia"
} | 7,874 |
package com.lightcrafts.ui.print;
import com.lightcrafts.ui.print.PrintLayoutModel.LengthUnit;
import static com.lightcrafts.ui.print.Locale.LOCALE;
import javax.swing.*;
import javax.swing.border.Border;
import java.awt.*;
import java.awt.event.ItemEvent;
import java.awt.event.ItemListener;
class PositionPanel extends JPanel implements PrintLayoutModelListener {
private PrintLayoutModel model;
private DimensionTextField leftText;
private UnitComboBox leftUnit;
private DimensionTextField topText;
private UnitComboBox topUnit;
private boolean readingFromModel; // prevent update loops
private boolean writingToModel;
private JPanel titlePanel; // intermediary container allows title borders
PositionPanel(PrintLayoutModel model) {
this.model = model;
model.addListener(this);
titlePanel = new JPanel();
titlePanel.setLayout(new BoxLayout(titlePanel, BoxLayout.Y_AXIS));
Border border = BorderFactory.createTitledBorder(
LOCALE.get("PositionTitle")
);
titlePanel.setBorder(border);
addLeft();
titlePanel.add(Box.createVerticalStrut(3));
addTop();
setLayout(new BorderLayout());
add(titlePanel);
}
private void addLeft() {
leftText = new DimensionTextField();
leftUnit = new UnitComboBox();
updateLeft();
leftText.setListener(
new DimensionTextField.Listener() {
public void dimensionChanged(double left) {
if (! readingFromModel) {
writingToModel = true;
LengthUnit unit = leftUnit.getSelectedUnit();
model.setImageX(left, unit);
writingToModel = false;
}
}
}
);
syncTextWithUnit(leftText, leftUnit);
Box box = createLabelledText(
LOCALE.get("LeftLabel"), leftText, leftUnit
);
titlePanel.add(box);
}
private void addTop() {
topText = new DimensionTextField();
topUnit = new UnitComboBox();
updateTop();
topText.setListener(
new DimensionTextField.Listener() {
public void dimensionChanged(double top) {
if (! readingFromModel) {
writingToModel = true;
LengthUnit unit = topUnit.getSelectedUnit();
model.setImageY(top, unit);
writingToModel = false;
}
}
}
);
syncTextWithUnit(topText, topUnit);
Box box = createLabelledText(LOCALE.get("TopLabel"), topText, topUnit);
titlePanel.add(box);
}
// Update a dimension text field when its corresonding units change:
private static void syncTextWithUnit(
final DimensionTextField text, final UnitComboBox unit
) {
unit.addItemListener(
new ItemListener() {
public void itemStateChanged(ItemEvent e) {
if (e.getStateChange() == ItemEvent.SELECTED) {
double oldDim = text.getDimension();
LengthUnit oldUnit = text.getUnit();
LengthUnit newUnit = unit.getSelectedUnit();
double newDim =
newUnit.fromPoints(oldUnit.toPoints(oldDim));
text.setUnit(newUnit);
text.setDimension(newDim);
}
}
}
);
}
private static Box createLabelledText(
String name, DimensionTextField text, UnitComboBox units
) {
Box box = Box.createHorizontalBox();
box.add(Box.createHorizontalGlue());
box.add(new JLabel(name + ':'));
box.add(Box.createHorizontalStrut(3));
box.add(text);
box.add(Box.createHorizontalStrut(3));
box.add(units);
return box;
}
private void updateTop() {
double y = model.getImageRect().getY();
LengthUnit unit = topUnit.getSelectedUnit();
y = unit.fromPoints(y);
topText.setUnit(unit);
topText.setDimension(y);
}
private void updateLeft() {
double x = model.getImageRect().getX();
LengthUnit unit = leftUnit.getSelectedUnit();
x = unit.fromPoints(x);
leftText.setUnit(unit);
leftText.setDimension(x);
}
public void layoutChanged(PrintLayoutModel source) {
if (! writingToModel) {
readingFromModel = true;
updateLeft();
updateTop();
readingFromModel = false;
}
}
public static void main(String[] args) {
JPanel panel = new JPanel(new BorderLayout());
panel.add(new PositionPanel(new PrintLayoutModel(100, 100)));
JFrame frame = new JFrame("PositionPanel Test");
frame.setContentPane(panel);
frame.setLocation(100, 100);
frame.pack();
frame.setVisible(true);
}
}
| {
"redpajama_set_name": "RedPajamaGithub"
} | 9,127 |
\subsection{Distinguishing forward and backward prediction}
We draw a distinction between two forms of prediction of~$Y$ from $X$:
\emph{forward} prediction models the mechanism by which $X$ influences $Y$;
\emph{backward} prediction forecasts $Y$ from $X$ indirectly, by exploiting correlations through the context $W$.
Because~$W$ may be redundantly encoded within $X$, we cannot simply remove~$W$ from the features to evaluate the predictive power along the forward pathway. Instead, we define forward and backward prediction based on conditional independence statements involving $Y,h(X),$ and $W$.
\begin{definition}[Forward and backward predictors]
A hypothesis $h:\Xcal \to \Ycal$ is a (pure) forward predictor of $Y$ if $h(X)$ is independent of $W$, $h(X) \bot W.$
A hypothesis $h$ is a (pure) backward predictor of $Y$ if $h(X)$ is conditionally independent of $Y$ given $W$, $h(X) \bot Y \vert W.$
\end{definition}
In the backward baselines we introduced, we determine a prediction based on a function $g:\Wcal \to \Ycal$, so that all of the predictive power comes from $W$. This ensures that after conditioning on $W$, the prediction is independent of the outcome.
\begin{fact}
Both predictors~$\gs$ and $\gh$ are pure backward predictors.
\end{fact}
Most classifiers, however, will be not be pure forward or pure backward predictors, but instead $h(X)$ will have some correlation with $Y$ that goes through $W$ and some correlation that is independent of $W$. By comparing the loss achieved by a classifier~$h$ to one of our backward baselines we can understand how close to a backward predictor the classifier is.
While viewing context $W$ as a confounder of $X$ and $Y$ provides a natural motivating story, we note that the theory and application of backward baselines in the following do not actually assume a specific causal structure between $X,Y,$ and $W$.
\subsection{Conclusions}
Our contribution has a normative, a theoretical, and an empirical component.
We argue that the distinction between predicting the future of an individual and reproducing the past is central to the debate around where and how we should use statistical methods to make consequential decisions.
The effectiveness of backward prediction, when observed, should question support for prediction as policy, and instead redirect focus toward interventions that target the background conditions.
Theoretically, we begin to develop a statistical learning theory of backward baselines.
The theory helps simplify the landscape of possible backward baselines, while clarifying how to interpret different backward baselines.
A notable outcome of our theory is that it supports the use and interpretation of a backward baseline that requires no observed outcomes.
At the outset, it was not obvious that a meaningful backward baseline without measurement of the target variable is possible.
This finding enables \emph{auditing without measured outcomes}: An investigator can probe a predictive system with access to only background variables and predictions.
On the empirical side, we show the strength and versatility of backward baselines on a variety of datasets. Utilizing multiple waves of longitudinal panel surveys, our evaluation is careful about the temporality of features and outcomes. Along the way, we contribute to a better empirical understanding of how machine learning leverages past contexts to predict future life outcomes.
In conclusion, we propose backward baselines as a simple, broadly applicable tool to strengthen evaluation and audit practices in the use of machine learning.
\subsection{Medical Expenditure Panel Survey (MEPS)}
For extensive documentation and background on this survey, see: \url{https://www.meps.ahrq.gov/mepsweb/}
\paragraph{Data sources and use conditions.}
Our dataset is constructed from the 2019 MEPS data. The MEPS 2019 Full Year Consolidated Data File (HC-216) is available online at \url{https://meps.ahrq.gov/mepsweb/data_stats/download_data_files_detail.jsp?cboPufNumber=HC-216}. The same website contains extensive documentation regarding features and data collection. The MEPS data use agreement is available online: \url{https://meps.ahrq.gov/data_stats/download_data/pufs/h216/h216doc.shtml#DataA}.
\paragraph{Features.}
Features for Round 3 of Panel 23 and Round 1 of Panel 24 have a suffix of 31 or 31X in the data. We include all of these in the dataset, as well as all demographic features:
FCSZ1231, FCRP1231, RUSIZE31, RUCLAS31, FAMSZE31, FMRS1231, FAMS1231, REGION31, REFPRS31, RESP31, PROXY31, BEGRFM31, BEGRFY31, ENDRFM31, ENDRFY31, INSCOP31, INSC1231, ELGRND31, PSTATS31, SPOUID31, SPOUIN31, ACTDTY31, RTHLTH31, MNHLTH31, CHBRON31, ASSTIL31, ASATAK31, ASTHEP31, ASACUT31, ASMRCN31, ASPREV31, ASDALY31, ASPKFL31, ASEVFL31, ASWNFL31, IADLHP31, ADLHLP31, AIDHLP31, WLKLIM31, LFTDIF31, STPDIF31, WLKDIF31, MILDIF31, STNDIF31, BENDIF31, RCHDIF31, FNGRDF31, ACTLIM31, WRKLIM31, HSELIM31, SCHLIM31, UNABLE31, SOCLIM31, COGLIM31, VACTDY31, VAPRHT31, VACOPD31, VADERM31, VAGERD31, VAHRLS31, VABACK31, VAJTPN31, VARTHR31, VAGOUT31, VANECK31, VAFIBR31, VATMD31, VAPTSD31, VALCOH31, VABIPL31, VADEPR31, VAMOOD31, VAPROS31, VARHAB31, VAMNHC31, VAGCNS31, VARXMD31, VACRGV31, VAMOBL31, VACOST31, VARECM31, VAREP31, VAWAIT31, VALOCT31, VANTWK31, VANEED31, VAOUT31, VAPAST31, VACOMP31, VAMREC31, VAGTRC31, VACARC31, VAPROB31, VACARE31, VAPACT31, VAPCPR31, VAPROV31, VAPCOT31, VAPCCO31, VAPCRC31, VAPCSN31, VAPCRF31, VAPCSO31, VAPCOU31, VAPCUN31, VASPCL31, VASPMH31, VASPOU31, VASPUN31, VACMPM31, VACMPY31, VAPROX31, EMPST31, RNDFLG31, MORJOB31, HRWGIM31, HRHOW31, DIFFWG31, NHRWG31, HOUR31, TEMPJB31, SSNLJB31, SELFCM31, CHOIC31, INDCAT31, NUMEMP31, MORE31, UNION31, NWK31, STJBMM31, STJBYY31, OCCCAT31, PAYVAC31, SICPAY31, PAYDR31, RETPLN31, BSNTY31, JOBORG31, OFREMP31, CMJHLD31, MCRPD31, MCRPB31, MCRPHO31, MCDHMO31, MCDMC31, PRVHMO31, FSAGT31, HASFSA31, PFSAMT31, MCAID31, MCARE31, GOVTA31, GOVAAT31, GOVTB31, GOVBAT31, GOVTC31, GOVCAT31, VAPROG31, VAPRAT31, IHS31, IHSAT31, PRIDK31, PRIEU31, PRING31, PRIOG31, PRINEO31, PRIEUO31, PRSTX31, PRIV31, PRIVAT31, VERFLG31, DENTIN31, DNTINS31, PMEDIN31, PMDINS31, PMEDUP31, PMEDPY31, AGE31X, MARRY31X, FTSTU31X, REFRL31X, MOPID31X, DAPID31X, HRWG31X, DISVW31X, HELD31X, OFFER31X, TRIST31X, TRIPR31X, TRIEX31X, TRILI31X, TRICH31X, MCRPD31X, TRICR31X, TRIAT31X, MCAID31X, MCARE31X, MCDAT31X, PUB31X, PUBAT31X, INS31X, INSAT31X, SEX, RACEV1X, RACEV2X, RACEAX, RACEBX, RACEWX, RACETHX, HISPANX, HISPNCAT, EDUCYR, HIDEG, OTHLGSPK, HWELLSPK, BORNUSA, WHTLGSPK, YRSINUS
\paragraph{Demographic features.}
The full list of demographic features we use is:
\begin{itemize}
\item AGE31X
\item SEX
\item RACEV1X
\item RACEV2X
\item RACEAX
\item RACEBX
\item RACEWX
\item RACETHX
\item HISPANX
\item HISPNCAT
\item EDUCYR
\item HIDEG
\item OTHLGSPK
\item HWELLSPK
\item BORNUSA
\item WHTLGSPK
\item YRSINUS
\end{itemize}
\paragraph{Target variable.}
We construct the target variable by summing up the following features:
\begin{itemize}
\item OBTOTV19 --- NUMBER OF OFFICE-BASED PROVIDER VISITS 2019
\item OPTOTV19 --- NUMBER OF OUTPATIENT DEPT PROVIDER VISITS 2019
\item ERTOT19 --- NUMBER OF EMERGENCY ROOM VISITS 2019
\item IPNGTD19 --- NUMBER OF NIGHTS IN HOSP FOR DISCHARGES, 2019
\item HHTOTD19 --- NUMBER OF HOME HEALTH PROVIDER DAYS 2019
\end{itemize}
We label all instances \emph{positive} ($1$) where the sum is strictly greater than $3$. We label all other instances \emph{negative} ($0$). This leads to 53.17\% positive instances. Hence, an all ones predictor achieves 46.83\% classification error.
\paragraph{Full set of figures.} Figure~\ref{fig:meps-zeroone-full} shows all results for the zero-one loss, Figure~\ref{fig:meps-squared-full} for the squared loss, and Figure~\ref{fig:meps-roc-full} for ROC curves.
\begin{figure}
\includegraphics[width=0.98\linewidth]{results/meps_zeroone_barplot_alltests.pdf}
\caption{Baselines on MEPS for varying features and classifiers (zero-one loss)}
\label{fig:meps-zeroone-full}
\end{figure}
\begin{figure}
\includegraphics[width=0.98\linewidth]{results/meps_squared_barplot_alltests.pdf}
\caption{Baselines on MEPS for varying features and classifiers (squared loss)}
\label{fig:meps-squared-full}
\end{figure}
\begin{figure}
\includegraphics[width=0.98\linewidth]{results/meps_rocplot.pdf}
\caption{Baselines on MEPS for varying features and classifiers (ROC curves)}
\label{fig:meps-roc-full}
\end{figure}
\subsection{Survey of Income and Program Participation (SIPP)}
Extensive documentation and background information on this survey is available from the websites of the US Census Bureau: \url{https://www.census.gov/programs-surveys/sipp.html}
\paragraph{Data availability and conditions.}
The SIPP data provided by the US Census Bureau are in the public domain. We use the first two waves of the SIPP 2014 Panel data, available here:
\begin{itemize}
\item Wave 1: \url{https://www.census.gov/programs-surveys/sipp/data/datasets/2014-panel/wave-1.html}
\item Wave 2: \url{https://www.census.gov/programs-surveys/sipp/data/datasets/2014-panel/wave-2.html}
\end{itemize}
\paragraph{Features.}
The dataset we derive from the 2014 SIPP panel data uses a set of $50$ variables constructed from one or multiple variables appearing in the SIPP raw data in Wave 1. The list below shows each feature we use (in capital letters) followed by the original SIPP feature(s) it is derived from.
\begin{itemize}
\item LIVING\_QUARTERS\_TYPE : tlivqtr
\item LIVING\_OWNERSHIP : etenure
\item SNAP\_ASSISTANCE : efs
\item WIC\_ASSISTANCE : ewic
\item MEDICARE\_ASSISTANCE : emc
\item MEDICAID\_ASSISTANCE : emd
\item HEALTHDISAB : edisabl
\item DAYS\_SICK : tdaysick
\item HOSPITAL\_NIGHTS : thospnit
\item PRESCRIPTION\_MEDS : epresdrg
\item VISIT\_DENTIST\_NUM : tvisdent
\item VISIT\_DOCTOR\_NUM : tvisdoc
\item HEALTH\_INSURANCE\_PREMIUMS : thipay
\item HEALTH\_OVER\_THE\_COUNTER\_PRODUCTS\_PAY : totcmdpay
\item HEALTH\_MEDICAL\_CARE\_PAY : tmdpay
\item HEALTH\_HEARING : ehearing
\item HEALTH\_SEEING : eseeing
\item HEALTH\_COGNITIVE : ecognit
\item HEALTH\_AMBULATORY : eambulat
\item HEALTH\_SELF\_CARE : eselfcare
\item HEALTH\_ERRANDS\_DIFFICULTY : eerrands
\item HEALTH\_CORE\_DISABILITY : rdis
\item HEALTH\_SUPPLEMENTAL\_DISABILITY : rdis\_alt
\item AGE : tage
\item GENDER : esex
\item RACE : trace
\item EDUCATION : eeduc
\item MARITAL\_STATUS : ems
\item CITIZENSHIP\_STATUS : ecitizen
\item FAMILY\_SIZE\_AVG : rfpersons
\item HOUSEHOLD\_INC : thtotinc
\item RECEIVED\_WORK\_COMP : ewc\_any
\item TANF\_ASSISTANCE : etanf
\item UNEMPLOYMENT\_COMP : eucany
\item SEVERANCE\_PAY\_PENSION : elmpnow
\item FOSTER\_CHILD\_CARE\_AMT : tfccamt
\item CHILD\_SUPPORT\_AMT : tcsamt
\item ALIMONY\_AMT : taliamt
\item INCOME\_FROM\_ASSISTANCE : tptrninc, tpscininc, tpothinc
\item INCOME : tpprpinc, tptotinc
\item SAVINGS\_INV\_AMOUNT : tirakeoval, tthr401val
\item UNEMPLOYMENT\_COMP\_AMOUNT : tuc1amt, tuc2amt, tuc3amt
\item VA\_BENEFITS\_AMOUNT : tva1amt, tva2amt, tva3amt, tva4amt, tva5amt
\item RETIREMENT\_INCOME\_AMOUNT : tret1amt, tret2amt, tret3amt, tret4amt, tret5amt, tret6amt, tret7amt, tret8amt
\item SURVIVOR\_INCOME\_AMOUNT : tsur1amt, tsur2amt, tsur3amt, tsur4amt, tsur5amt, tsur6amt, tsur7amt, tsur8amt, tsur11amt, tsur13amt
\item DISABILITY\_BENEFITS\_AMOUNT : tdis1amt, tdis2amt, tdis3amt, tdis4amt, tdis5amt, tdis6amt, tdis7amt, tdis10amt
\item FOOD\_ASSISTANCE : efood\_type1, efood\_type2, efood\_type3, efood\_oth
\item TRANSPORTATION\_ASSISTANCE : etrans\_type1, etrans\_type2, etrans\_type3, etrans\_type4, etrans\_oth
\item SOCIAL\_SEC\_BENEFITS : esssany, esscany
\end{itemize}
These variables represent features derived from columns in the original data source via our own data cleaning and processing script. In particular, we discount columns that have more than 10\% missing values.
\paragraph{Demographic features.}
The full list of six demographic features we use is:
\begin{itemize}
\item AGE
\item GENDER
\item RACE
\item EDUCATION
\item MARITAL\_STATUS
\item CITIZENSHIP\_STATUS
\end{itemize}
\paragraph{Target variable.}
The target variable is constructed based on the feature thcyincpov in Wave~2, which reflects the household income-to-poverty ratio in the 2019 calendar year, excluding Type~2 individuals. Type~2 individuals are individuals that lives in the household for some month but no longer reside there.
We threshold thcyincpov at 3 so that all instances with thcyincpov strictly greater than 3 are labeled positive ($1$) and all others are labeled negative ($0$). This leads to 51.12\% positive instances. Hence an all ones predictor has accuracy 48.88\%.
\paragraph{Full set of figures.} Figure~\ref{fig:sipp-zeroone-full} shows all results for the zero-one loss, Figure~\ref{fig:sipp-squares-full} for the squared loss, and Figure~\ref{fig:sipp-roc-full} for ROC curves.
\begin{figure}
\includegraphics[width=0.98\linewidth]{results/sipp_zeroone_barplot_alltests.pdf}
\caption{Baselines on SIPP for varying features and classifiers (zero-one loss)}
\label{fig:sipp-zeroone-full}
\end{figure}
\begin{figure}
\includegraphics[width=0.98\linewidth]{results/sipp_squared_barplot_alltests.pdf}
\caption{Baselines on SIPP for varying features and classifiers (squared loss)}
\label{fig:sipp-squares-full}
\end{figure}
\begin{figure}
\includegraphics[width=0.98\linewidth]{results/sipp_rocplot.pdf}
\caption{Baselines on SIPP for varying features and classifiers (ROC curves)}
\label{fig:sipp-roc-full}
\end{figure}
\subsection{ProPublica COMPAS Recidivism Scores}
\paragraph{Data sources and use conditions.}
We use the COMPAS score dataset collected and made available by Problica~\cite{angwin2016machine}, which is widely used througout the algorithmic fairness literature. The Propublica COMPAS score dataset is available online: \url{https://github.com/propublica/compas-analysis}
The data repository does not specify a license or data use agreement.
\paragraph{Demographic features.}
We use the following demographic features avilable in the dataset:
\begin{itemize}
\item `race',
\item `age',
\item `juv\_fel\_count', `juv\_misd\_count', `juv\_other\_count' : juvenile priors
\item `prior\_count'
\end{itemize}
\paragraph{Target variable.}
We use \emph{two-year recidivism} ('two\_year\_recid') as the target variable.
\paragraph{Predictor.}
Since we lack training data, we instead audit COMPAS scores as a black-box.
The column in the data corresponding to COMPAS scores is called `decile\_score' and provides score deciles. To obtain a predictor we fit a single-variable model to predict the target variable from the score deciles. This amounts to a recalibration of the score values to the target variable, ensuring that we obtain the best possible predictor we can from the score deciles.
\paragraph{Full set of figures.}
Figure~\ref{fig:COMPAS-full} shows all results we report on the COMPAS dataset.
\begin{figure}[ht]
\includegraphics[width=0.98\linewidth]{results/COMPAS_zeroone_barplot_alltests.pdf}
\includegraphics[width=0.98\linewidth]{results/COMPAS_squared_barplot_alltests.pdf}
\includegraphics[width=0.98\linewidth]{results/COMPAS_rocplot.pdf}
\caption{Baselines on COMPAS for varying features and metrics}
\label{fig:COMPAS-full}
\end{figure}
\clearpage
\section{Reference implementation of backward baselines}
\label{sec:code}
\lstset{basicstyle=\footnotesize\ttfamily,breaklines=true}
\begin{lstlisting}[language=Python]
from sklearn.ensemble import GradientBoostingClassifier
from sklearn.metrics import accuracy_score
from sklearn.model_selection import train_test_split
def backward_baselines(X, y, features, model):
"""Compute backward baselines.
Parameters
----------
X : numpy.ndarray
data matrix (n, d)
y : numpy.ndarray
target variable (n,)
features : list
list of column names
model : object
model supporting fit and predict
Returns
-------
dict
Scores of all backward baselines.
"""
X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.33)
scores = {}
# XYY
model.fit(X_train, y_train)
scores['XYY'] = accuracy_score(model.predict(X_test), y_test)
# WYY
baseline = GradientBoostingClassifier()
baseline.fit(X_train[features], y_train)
scores['WYY'] = accuracy_score(baseline.predict(X_test[features]), y_test)
# WY^Y
baseline.fit(X_test[features], model.predict(X_test))
scores['WY^Y'] = accuracy_score(baseline.predict(X_test[features]), y_test)
# WYY^
baseline.fit(X_test[features], y_test)
scores['WYY^'] = accuracy_score(baseline.predict(X_test[features]),
model.predict(X_test))
# WY^Y^ requires new train/test split
X_testA, X_testB, y_testA, y_testB = train_test_split(X_test[features],
model.predict(X_test), test_size=0.5)
baseline.fit(X_testA, y_testA)
scores['WY^Y^'] = accuracy_score(baseline.predict(X_testB), y_testB)
return scores
\end{lstlisting}
\subsection{Medical Expenditure Panel Survey (MEPS)}
The Medical Expenditure Panel Survey (MEPS) is a set of large-scale surveys of families and individuals, their medical providers, and employers across the United States, aimed at providing insights into health care utilization. We work with the publicly available MEPS 2019 Full Year Consolidated Data File. The dataset we consider has 28,512 instances corresponding to all persons that were part of one of the two MEPS panels overlapping with calendar year 2019. Specifically, Panel 23 has Rounds 3--5 in 2019, and Panel 24 has rounds 1--3 in 2019. Round 3 of Panel 23 and Round 1 of Panel 24 are the first of each panel in 2019. The survey distinguishes between demographic variables and variables corresponding to survey questions in of the rounds of the two panels. We create a prediction task whose goal is to predict a full-year outcome from Round 3 of Panel 23 and Round 1 of Panel 24. The target variable measures the total health care utilization across the year. We create a roughly balanced binarization of the target variable. A precise definition and further details are in the appendix.
We compute backward baselines in terms of the features \emph{age}, \emph{race}, \emph{age} and \emph{race} together, as well as all variables designated as \emph{demographic} by the survey documentation. These include additional variables relating to age, race and ethnicity, marital status, nationality, and languages spoken. Figure~\ref{fig:meps-zeroone} summarizes our findings. In particular, backward baselines trained on all demographic background variables match nearly all of the predictive performance of the classifiers trained on all features, similarly across three different prediction models. An extended set of figures is included in Appendix~\ref{app:experiments}.
\begin{figure}[t]
\includegraphics[width=0.98\linewidth]{results/meps_zeroone_barplot.pdf}
\includegraphics[width=0.98\linewidth]{results/meps_squared_barplot_logreg.pdf}
\includegraphics[width=0.98\linewidth]{results/meps_rocplot_logreg.pdf}
\caption{Backward baselines on MEPS, columns are different features, rows are different classifiers (random forest, gradient boosting, logistic regression) and metrics (zero-one loss, squared loss, ROC curves). Label $XYY$ denotes standard training and testing, label $WYY$ is the backward prediction baseline, label $WY\hat Y$ is the backward rounding baseline. Gray dashed line indicates performance of constant predictor. Error bars represent a standard deviation across $10$ random seeds.}
\label{fig:meps-zeroone}
\end{figure}
\subsection{Survey of Income and Program Participation (SIPP)}
The Survey of Income and Program Participation (SIPP) is an import longitudinal survey conduced by the U.S.~Census Bureau, aimed at capturing income dynamics as well as participation in government programs.
We consider Wave 1 and Wave 2 of the SIPP 2014 panel data. The target variable is based on the official poverty measure (OPM), a cash-income based measure of poverty. We compute this measure based on Wave 2 data. We again discretize the measure to obtain to roughly balanced classes for our binary prediction task. The goal is to predict this outcome based on features collected in Wave 1. After cleaning and preprocessing our data contains 39720 rows and 54 columns. We consider background variables \emph{education}, \emph{race}, \emph{education} and \emph{race} together, as well as all demographic variables, specifically, \emph{age}, \emph{gender}, \emph{race}, \emph{education}, \emph{marital status}, \emph{citizenship status}. In Figure~\ref{fig:sipp-main}, we restrict our attention to the logistic regression model. The other models perform similarly and the full set of results can be found in Appendix~\ref{app:experiments}.
\begin{figure}
\includegraphics[width=0.98\linewidth]{results/sipp_zeroone_barplot_logreg.pdf}
\includegraphics[width=0.98\linewidth]{results/sipp_squared_barplot_logreg.pdf}
\includegraphics[width=0.98\linewidth]{results/sipp_rocplot_logreg.pdf}
\caption{Backward baselines on SIPP.}
\label{fig:sipp-main}
\end{figure}
\subsection{ProPublica COMPAS Recidivism Scores}
A proprietary recidivism risk score, called COMPAS, was the subject of a notorious investigation into racial bias by ProPublica~\cite{angwin2016machine} in 2016. As part of the investigation ProPublica released a dataset of COMPAS scores about defendants associated with two-year recidivism outcomes.
The dataset released by ProPublica has significant and well-documented issues that make it inadequate for the development of new risk scores as well as fairness interventions~\cite{bao2021its, barenstein2019propublica}.
In experimenting with the COMPAS data set, our primary goal is to demonstrate the effectiveness of backward baselines in auditing problematic risk predictors.
The results of backward baselines echo earlier findings that the performance COMPAS scores can be achieved by simple models~\cite{rudin2020age, wang2022pursuit}.
Note that we do not have access to the training data used for producing the COMPAS scores as is common in algorithmic audit scenarios. This is, fortunately, not required for evaluating backward baselines. We only need the scores, as well as associated demographic information. Figure~\ref{fig:compas-main} evaluates backward baselines against the COMPAS scores. The results are rather striking in how well backward baselines do in comparison. In particular, a single feature (prior convictions) appears to account for all of the predictive power of the COMPAS score.
\begin{figure}
\includegraphics[width=0.98\linewidth]{results/compas_zeroone_barplot.pdf}
\includegraphics[width=0.98\linewidth]{results/compas_squared_barplot.pdf}
\includegraphics[width=0.98\linewidth]{results/compas_rocplot.pdf}
\caption{Backward baselines on COMPAS}
\label{fig:compas-main}
\end{figure}
\subsection{Our contributions}
In this work, we propose simple and effective statistical methods called \emph{backward baselines} to test if---and to which extent---a predictive model reproduces the past.
We build a theory for backward and forward prediction and show how backward baselines elucidate the extent to which a given predictor uses each prediction pathway.
We evaluate backward baselines on representative tasks that involve predicting future outcomes from individual-level covariates.
Across different tasks and models, we observe predicting the past to be a strong mechanism for forecasting the future.
\paragraph{Predicting the past.}
To introduce our discussion of backward prediction, we consider an explicit data generating process that moves through time. In Figure~\ref{fig:causal-nature}, we depict the temporal dynamics, in the form of a causal graph, with time evolving from left to right. We think of $X$ as individual-level covariates measured today, and $Y$ as an outcome of interest to be measured in the future.
In addition to the standard supervised learning variables, we also model
an additional \emph{context} variable~$W$---predating the measurement of the covariates or outcome---that may directly influence both~$X$ and~$Y$.
Concretely,~$X$ could represent a record of an individual's educational, personal, and financial history, used to predict income~$Y$ measured in~$10$ years, and $W$ could represent specific demographic features from the past, like childhood household income.
\begin{figure}[b]
\centering
\begin{subfigure}{0.5\textwidth}
\centering
\begin{tikzpicture}[scale=0.15]
\tikzstyle{every node}+=[inner sep=0pt]
\draw [black] (30.8,-27.5) circle (3);
\draw (30.8,-27.5) node {$W$};
\draw [black] (38.8,-18.8) circle (3);
\draw (38.8,-18.8) node {$X$};
\draw [black] (46.2,-27.5) circle (3);
\draw (46.2,-27.5) node {$Y$};
\draw [black] (32.83,-25.29) -- (36.77,-21.01);
\fill [black] (36.77,-21.01) -- (35.86,-21.26) -- (36.6,-21.94);
\draw [black] (40.74,-21.09) -- (44.26,-25.21);
\fill [black] (44.26,-25.21) -- (44.12,-24.28) -- (43.36,-24.93);
\draw [black] (33.8,-27.5) -- (43.2,-27.5);
\fill [black] (43.2,-27.5) -- (42.4,-27) -- (42.4,-28);
\end{tikzpicture}
\end{subfigure}
\begin{subfigure}{0.3\textwidth}
\centering
\parbox{\textwidth}{
\noindent\emph{Generating $\Dist$:}
\begin{itemize}
\item $W \sim \Dist_W$
\item $X \sim \Dist_{X\vert W}$
\item $Y \sim \Dist_{Y \vert X,W}$
\end{itemize}
}
\end{subfigure}
\caption{Example data generating process for covariates $X$, outcome $Y$, and context $W$.
Time starts from the left with context $W$ and evolves forward to the right, realizing $X$ then $Y$.}
\label{fig:causal-nature}
\end{figure}
This explicit temporal model elucidates the distinction between \emph{forward} prediction and \emph{backward} prediction. Forward predictors model how the present measurements $X$ causally effect the future outcome $Y$, effectively controlling for $W$. Backward predictors estimate the outcome by first inferring the past context $W$ from $X$, then predicting $Y$ based on $W$. In other words, backward prediction provides information about $Y$ that could equally be explained by the past context $W$.
\paragraph{Backward baselines.}
Machine learning practitioners often build models using any and every predictive pathway available, including the backward pathway. Our goal is to elucidate and disentangle the prediction pathways a given predictor uses.
To this end, we introduce backward baselines: Given a predictor, backward baselines provide a careful accounting of the predictor's use of the forward and backward predictive pathways.
The baselines are lightweight to run, only requiring input-output access to the predictive model, and are built on simple, but rigorous statistical foundations.
For instance, a key challenge in reasoning about backward prediction is that the context $W$ is typically robustly encoded within an individual's covariates $X$.
That is, even if we explicitly censor the attributes defining the context, backward prediction from $X$ may still be possible, if the context $W$ is recognizable from $X$. Backward baselines handle this statistical subtlety gracefully, providing guaranteed estimates of the forward and backward predictive power, regardless of how redundantly $W$ is encoded in $X$.
This work establishes backward baselines as an effective tool for investigating predictive models. Our perspective is \emph{not} that the backward prediction pathway is inherently problematic. Rather, we advocate that investigators use backward baselines to understand and contextualize performance numbers in prediction tasks. Adding backward baselines to the standard ``report card'' for supervised learning would add clarity about the underlying mechanism of prediction. This clarity, in turn, would help to inform debates about whether machine learning is an appropriate tool for the task at hand. If model builders cannot find a predictor that improves significantly over backward baselines, we should hesitate before turning prediction into policy.
\section{Introduction}
\label{sec:intro}
\input{intro}
\section{Backward baselines}
\label{sec:baselines}
\input{baselines}
\section{Properties of backward baselines}
\label{sec:theory}
\input{theory}
\section{Empirical evaluation of backward baselines}
\label{sec:experiments}
\input{experiments}
\section{Discussion}
\label{sec:discussion}
\input{discussion}
\section*{Acknowledgments}
We thank Rediet Abebe for insightful and formative interactions throughout the course of this work. We thank Ricardo Sandoval for providing us with code for the SIPP data and the associated prediction task. \textbf{MPK} is supported by the Miller Institute for Research in Basic Science and the Simons Collaboration on the Theory of Algorithmic Fairness. Authors listed alphabetically.
\bibliographystyle{alpha}
\subsection{Basic properties}
Here, we establish some basic properties about backward baselines.
These properties are intuitive, but also reveal subtleties in what we can(not) conclude about backward and forward prediction from backward baselines.
We start with three simple properties of backward baselines, that help us to compare the predictive power from $X$ to the predictive power from $W$.
\begin{proposition}
\label{prop:basic}
The following properties of backward baselines hold.
\emph{(a)}~~ There exists a predictor $h^*:\Xcal \to \Ycal$ that achieves loss at most the backward prediction baseline.
\begin{gather*}
\ell_\Dist(Y,h^*(X)) \le \ell_\Dist(Y,\gs(W))
\end{gather*}
\emph{(b)}~~If $h:\Xcal \to \Ycal$ is a backward predictor, then its loss is at least the backward prediction baseline.
\begin{gather*}
\ell_{\Dist}(Y,\gs(W)) \le \ell_\Dist(Y,h(X))
\end{gather*}
\emph{(c)}~~ If $h:\Xcal \to \Ycal$ is a forward predictor, then $\gh$ is comparable to a constant predictor. Formally,
\begin{align*}
\ell_\Dist(h(X),\gh(W)) \ge \argmin_{\yhat \in \Ycal}~ \E[\ell(h(X),\yhat)]\quad\text{and}\quad
\ell_\Dist(Y,\gh(W)) \ge \argmin_{\yhat \in \Ycal}~ \E[\ell(Y,\yhat)]\,.
\end{align*}
\end{proposition}
These straightforward properties provide a foundation for reasoning about backward and forward prediction.
Proposition~\ref{prop:basic}(a) establishes that the backward prediction baseline is reasonable minimum standard for predictive accuracy from $X$.
Proposition~\ref{prop:basic}(b)-(c) can be viewed as one-sided tests that let us demonstrate that a hypothesis is not a (pure) backward or forward predictor.
We emphasize the direction of these one-sided tests. If a predictor $h$ only achieves loss comparable to the backward prediction baseline $\gs$, it is tempting to conclude that $h$ must be a backward predictor.
This conclusion is not generally true.
In particular, it could be that $h$ achieves (at least some of) its predictive power in the forward direction, and by coincidence achieves the same accuracy as the best backward predictor.
In this case, we may still decide to reject $h$, on account of its mediocre accuracy, but cannot reliably reject on the basis of being a backward predictor.
\subsection{Rounding recovers optimal backward prediction}
As discussed, we can define backward baselines in terms of the optimal predictor $\gs$ of $Y$ from $W$, and also in terms of the backward-rounded predictor $\gh$ of $h(X)$ from $W$.
In generality, these two predictors realize different baselines; however, if $h(X)$ is an accurate predictor of $Y$, then intuitively, it would seem that the baselines over $\gs$ and $\gh$ might be similar.
For instance, for classification according to the zero-one loss and regression according to the squared loss, these predictors have closed forms.
\begin{align*}
\begin{array}{lcc}
\text{Zero-one}\qquad & \argmax_{\yhat \in \Ycal} \Pr[Y = \yhat \vert W = w]\quad & \argmax_{\yhat \in \Ycal} \Pr[h(X) = \yhat \vert W = w] \\
& ~ & \\
\text{Squared}\quad &\E[Y \vert W = w] & \gh(w) = \E[h(X) \vert W = w]
\end{array}
\end{align*}
We introduce the following technical conditions, which are useful for analyzing various properties of backward baselines.
\begin{definition}[Confidence]
\label{def:confident}
A classifier $h:\Xcal \to \Ycal$ is (over)confident on $Y$ over $W$ if
\begin{gather*}
\Pr[h(X) = \gs(W)] \ge \Pr[Y = \gs(W)].
\end{gather*}
\end{definition}
Intuitively, confidence says that $h(X)$ does not underestimate the probability that $Y$ takes it's most likely value within the context $W$.
Such (over)confidence of classifiers is typically observed in practice \cite{guo2017calibration}.
\begin{definition}[Weak calibration]
\label{def:calibration}
A predictor $h:\Xcal \to [0,1]$ is weakly calibrated\footnote{This notion of weak calibration was introduced recently by \cite{gopalan2022lowdegree}, who refer to it as degree-$2$ calibration.} to $Y$ over $W$ if
\begin{align*}
\E[Y \vert W] = \E[h(X) \vert W]\qquad\text{and}\qquad
\E[Yh(X) \vert W] = \E[h(X)^2 \vert W].
\end{align*}
\end{definition}
Weak calibration rules out predictors that blatantly ignore variation in $Y$ based on the context $W$ (including pure forward predictors).
Definition~\ref{def:calibration} relaxes traditional notions of calibration~\cite{dawid} and is implied by loss minimization, both in theory and our experiments. We show that under these conditions, backward rounding obtains optimal prediction of $Y$ from $W$.
\begin{proposition}[Informal]
\label{prop:gh-equals-gs}
For a confident classifier $h:\Xcal \to \set{0,1}$ or a weakly calibrated predictor~$h:\Xcal \to [0,1]$, we have $\gh = \gs$ for the zero-one loss and squared loss, respectively.
\end{proposition}
The interchangeability of $\gs$ and $\gh$ may be useful practically and conceptually.
For instance, the analysis of Proposition~\ref{prop:gh-equals-gs} reveals that the backward rounding baseline lower bounds the backward prediction baseline, $\ell_\Dist(h(X),\gh(W)) \le \ell_\Dist(Y,\gs(W))$.
\subsection{Measuring forward predictive power}
A key motivation for our study of backward baselines was the observation that, given a hypothesis $h$, determining the extent of forward prediction may be challenging.
We show that under natural conditions, the backward rounding baseline for $\gh$ reveals insight into the forward predictive power of $h$.
Conveniently, evaluating this baseline only requires black-box access to the predictive model and $(X,W)$ samples---not labels $Y$.
The lightweight nature of the baseline makes it an appealing option to audit for backward prediction, especially for proprietary predictive models.
Concretely, we show that the backward rounding baseline gives insight into the covariance between $h(X)$ and $Y$ after conditioning on $W$.
\begin{proposition}
\label{prop:cov}
Suppose a classifier $h:\Xcal \to \set{0,1}$ is confident on $Y$ over $W$.
Let $\ell_W(h,\gh)$ denote the backward rounding baseline $\Pr[h(X) \neq \gh(W) \vert W]$ conditioned on $W$. Then,
\begin{gather*}
\Cov(h(X),Y \vert W) \le \Var(h(X) \vert W) = \ell_W(h,\gh) \cdot (1-\ell_W(h,\gh)) \le \Var(Y \vert W)\,.
\end{gather*}
If a predictor $h:\Xcal \to [0,1]$ is weakly calibrated to $Y$ over $W$, then
\begin{gather*}
\E[(h(X) - \gh(W))^2] = \E[(Y - \gs(W))^2] - \E[(Y - h(X))^2] = \E_W[\Cov(Y,h(X) \vert W)]\,.
\end{gather*}
\end{proposition}
In other words, if $h(X)$ carries lots of information about $Y$, even after conditioning on $W$, then the backward rounding baseline will be large.
The arguments to establish Proposition~\ref{prop:cov} are elementary, but the conclusions are powerful.
An auditor, who is given only black-box access to a classifier or predictor $h$, can reliably determine when $h$ is a backward predictor by evaluating the backward rounding baseline without any labels $Y$ from the true distribution.
Concretely, the backward rounding baseline allows the auditor to establish an upper bound on the amount of information about $Y$ contained in $h(X)$ that isn't explained by $W$.
In the classification setting, the bound obtained by the rounding baseline is an inequality, but is tighter than the bound given by the backward prediction baseline.
In the regression setting, the rounding baseline also characterizes the difference between the backward prediction baseline and the expected loss of $h$, which would otherwise require labeled outcomes $Y$ to evaluate.
In Appendix~\ref{app:proofs}, we describe an additional backward baseline for classification, which use labels from $Y$ to gives an exact characterization of the forward predictive power of $h$.
\subsection{Backward baselines and demographic parity}
When $W$ is defined by demographic features that are considered to be sensitive attributes, forward prediction recovers the notion of \emph{demographic parity} from the literature on fair machine learning \cite{fta}.
While a natural desideratum for equal treatment under a decision rule, the shortcomings of demographic parity as a notion of fairness have been documented extensively \cite{fta,liu2018delayed}.
As such, requiring pure forward prediction may result in unintended and undesirable consequences, just as blinding predictors of a sensitive attribute can.
Exploring the analogy between backward baselines and fair prediction sheds new light on demographic parity and stereotyping.
In Appendix~\ref{app:fairness}, we formalize a duality between forward and backward prediction.
Translating the duality into the language of fairness, the optimal unconstrained prediction decomposes into the optimal prediction under demographic parity plus the optimal ``stereotyping'' prediction that makes its judgments solely based on the sensitive attribute.
| {
"redpajama_set_name": "RedPajamaArXiv"
} | 2,128 |
\section{Introduction}
The flux transport dynamo model has emerged in recent years as the most promising
theoretical model for explaining different aspects of the solar cycle. While
the flux transport dynamo model
may not yet be unanimously accepted in the solar physics community and
doubts are often raised about its validity, no other alternative model of the
solar cycle has been studied to the same depth. Following an early paper by
Wang, Sheeley \& Nash (1991) proposing the basic idea, the first two-dimensional
models of the flux transport dynamo were constructed by Choudhuri, Sch\"ussler \&
Dikpati (1995) and Durney (1995). From 1995 onwards, about a dozen papers by different
groups on the flux transport dynamo have by now received more than 100 citations
according to ADS (Choudhuri, Sch\"ussler \& Dikpati 1995; Durney 1995; Dikpati
\& Charbonneau 1999; Charbonneau \& Dikpati 2000; K\"uker, R\"udiger \& Shultz
2001; Dikpati \& Gilman 2001; Nandy \& Choudhuri 2002; Dikpati et al.\ 2004;
Chatterjee, Nandy \& Choudhuri 2004; Dikpati, de Toma \& Gilman 2006; Dikpati
\& Gilman 2006; Choudhuri, Chatterjee \& Jiang 2007). During the same period,
we are aware of only three papers dealing with alternate models of the solar dynamo
which received more than 100 citations (R\"udiger \& Brandenburg 1995; Charbonneau
\& MacGregor 1997; Beer, Tobias \& Weiss 1998). Interestingly, two of the
authors of these papers dealing with alternate models (R\"udiger, Charbonneau)
later became votaries of the flux transport dynamo and wrote important papers
on this subject (Dikpati \& Charbonneau 1999; K\"uker, R\"udiger \& Shultz 2001).
This simple consideration of the citations data makes it amply
clear that the flux transport dynamo model has received much more attention in
recent years than any alternate model of the solar cycle. If the flux
transport dynamo model proves to be incorrect, then we shall be left with no
other theoretical model that can explain various aspects of the solar cycle
in such detail. It is therefore important to critically assess the flux
transport dynamo model and to examine if the doubts and uncertainties about
this model are serious enough. This is attempted here.
\section{Basics of the flux transport dynamo}
The basic idea of solar dynamo theory is that the toroidal and the poloidal
components of the Sun's magnetic field sustain each other through a feedback loop.
It is easy to see that the poloidal magnetic field can be stretched by
differential rotation to generate the toroidal magnetic field. Since the
differential rotation of the Sun has now been mapped by helioseismology, this
is now a well-understood process.
The complementary process of generation of the poloidal field from the toroidal
field is less well established. There have been historically two schools of thought.
Parker (1955) suggested and then Steenbeck, Krause \& R\"adler (1966) elaborated
that the helical turbulence in the solar convection zone can twist the toroidal
field to give rise to the poloidal field. This process is called the $\alpha$-effect
and is possible only if the strength of the toroidal field is such that the magnetic
energy density is less than the energy density of turbulence. It is estimated
that the toroidal field cannot be stronger than $10^4$ G in order to be twisted
by turbulence. The second school of thought is due to Babcock (1961) and
Leighton (1964). Sunspot pairs forming out of the toroidal magnetic field
have tilts produced by the Coriolis force (D'Silva \& Choudhuri 1993)---tilts
increasing with latitude in accordance with Joy's law. According to the
Babcock--Leighton viewpoint, the decay of the tilted sunspot pairs gives rise
to the poloidal magnetic field.
Early solar dynamo models in 1970s and 1980s usually assumed that the poloidal
field is generated by the $\alpha$-effect. This assumption had to be questioned
when magnetic buoyancy calculations based on the thin flux tube equation (Spruit
1981; Choudhuri 1990) indicated that the toroidal field at the base of the Sun's
convection zone is as strong as $10^5$ G (Choudhuri \& Gilman 1987; Choudhuri 1989;
D'Silva \& Choudhuri 1993; Fan, Fisher \& DeLuca 1993). Weaker magnetic fields would
be affected by the Coriolis force in a way that is not consistent with observational
data. Although there are some mechanisms of suppressing the Coriolis force (Choudhuri
\& D'Silva 1990; D'Silva \& Choudhuri 1991), these are not expected to be very effective
inside the solar convection zone. Since helical turbulence in the convection zone
will not be able to twist such a strong toroidal field, the Babcock--Leighton (BL)
mechanism seems to be the best option for generating the poloidal field.
One requirement of any dynamo model is that a dynamo wave has to propagate
equatorward, in order to explain the appearance of sunspots at lower latitudes
with the progress of the solar cycle. According to what is called the Parker--Yoshimura
sign rule (Parker 1955; Yoshimura 1975), the $\alpha$-coefficient and the differential
rotation $\Omega (r, \theta)$ have to satisfy the following condition in the northern
hemisphere
$$\alpha \frac {\partial \Omega}{\partial r} < 0 \eqno(1)$$
in order to produce equatorward propagation. Now, the BL mechanism can also be
mathematically represented by a coefficient $\alpha$ appearing in the equations
exactly like the $\alpha$-effect. It is clear from the observations of sunspot
tilts that the $\alpha$ corresponding to the BL mechanism has to be positive in
the northern hemisphere. Since helioseismology finds $\partial \Omega/ \partial r$
to be positive in the lower latitudes where sunspots are seen, it appears that
condition (1) is not satisfied and a dynamo model in which the poloidal field
is generated by the BL mechanism may not reproduce solar-like behaviour.
The Parker--Yoshimura sign rule (1) was derived without considering the effects
of the meridional circulation. It is known that the meridional circulation
of the Sun advects the poloidal field poleward near the solar surface (Wang, Nash \&
Sheeley 1989; Dikpati \& Choudhuri 1995; Choudhuri \& Dikpati 1999). Although the
meridional circulation is poleward just below the Sun's surface, its nature deeper down
is still not unanimously established from observational data. Since this circulation
is driven by the turbulent stresses in the convection zone, the meridional circulation is expected on theoretical
grounds to be confined within the convection zone. The simplest assumption is that
of an equatorward return flow at the bottom of the convection zone. Choudhuri,
Sch\"ussler \& Dikpati (1995) showed that an equatorward meridional
circulation at the bottom of the convection zone can overrule the condition (1)
and can make the toroidal field produced there shift equatorward with time, reproducing
the solar behaviour.
\begin{figure}
\center
\includegraphics[width=6cm]{fig1.eps}
\caption{A cartoon explaining how the flux transport dynamo works.}
\end{figure}
Figure 1 is a cartoon representation of the flux transport dynamo. The tachocline
at the bottom of the convection zone is the region of concentrated differential rotation
where the strong toroidal field is produced. This toroidal field rises to the solar
surface due to magnetic buoyancy to produce sunspots. At the surface the BL mechanism
acts on the decaying sunspots to generate the poloidal
field. This poloidal field is carried poleward by the meridional circulation
as seen in the observational data.
Ultimately the poloidal field has to be brought to the bottom of the convection
zone, where the strong differential rotation can act on it. We shall make some
comments on the transport of the poloidal field in the next section. Apart from
modelling the solar cycle, such flux transport dynamo models are now being used
to model different aspects of stellar cycles (Jouve, Brown \& Brun 2010; Karak,
Kitchatinov \& Choudhuri 2014).
\section{Two types of dynamo and modelling irregularities}
\def\tc{\tau_{\rm conv}}
\def\tt{\tau_{\rm tach}}
\def\ta{\tau_{\rm adv}}
As mentioned in the previous section, the poloidal field generated by the BL mechanism
near the solar surface has to be transported to the bottom of the convection zone in
order for the dynamo to operate. The two obvious ways of doing this is through diffusion
and through advection by the meridional circulation. Let us look at these possibilities.
The turbulent diffusion within the body of the convection zone is expected to be much
stronger than that within the tachocline. Hence the diffusion time $\tc$ within the
convection zone has to be much shorter than the diffusion time $\tt$ within the tachocline.
Now let $\ta$ be the advection time by meridional circulation. It is necessary
for $\ta$ to be shorter than $\tt$ in order for the equatorward propagation of the
toroidal field at the bottom of the convection zone, overcoming the condition (1).
Now the conditions $\tc < \tt$ and $\ta < \tt$ can be satisfied in two possible ways:
$$\tc < \ta <\tt \eqno(2)$$
or
$$\ta < \tc <\tt. \eqno(3)$$
There have been two types of solar dynamo models corresponding to these two possibilities.
The dynamo model developed by Choudhuri and his collaborations (Nandy, Chatterjee, Jiang, Karak)
satisfy (2) and is known as the high-diffusion or diffusion-dominated model, in which the
transport of the poloidal field takes place primarily due to diffusion. On the other hand,
the dynamo model developed by Dikpati and her collaborations (Charbonneau, Gilman, de Toma)
satisfy (3) and is known as the low-diffusion or advection-dominated model, in which the
transport of the poloidal field takes place primarily due to advection by meridional circulation. The differences
between these two types of models have been systematically studied by Jiang, Chatterjee \&
Choudhuri (2007) and Yeates, Nandy \& Mackay (2008).
Both types of solar dynamo model have been able to reproduce various regular aspects of
the solar cycle. However, the high-diffusion model satisfying (2) succeeds better in
explaining the dipolar parity of the Sun (Chatterjee, Nandy \& Choudhuri 2004; Hotta \&
Yokoyama 2010) or the lack of significant hemispheric asymmetry (Chatterjee \& Choudhuri
2006; Goel \& Choudhuri 2009). After explaining the regular aspects of the solar cycle, the
thrust of research in the last few years has been to explain the irregularities of the solar
cycle. It appears that the high-diffusion model satisfying (2) gives much better agreement
with observations when modelling the irregularities of the solar cycle. This is a vast
subject. We make only a few general remarks. The readers are referred to a recent review
(Choudhuri 2014) for a more detailed discussion.
It has been known for a while that fluctuations in the poloidal field generation mechanism can
produce irregularities in the solar cycle (Choudhuri 1992). Within the framework of the
flux transport dynamo, Choudhuri, Chatterjee \& Jiang (2007) suggested how such fluctuations
arise. The BL mechanism for the poloidal field generation depends on the tilts of bipolar
sunspots. One observationally finds a scatter in the tilts around the average given by
Joy's law---presumably produced by the buffeting of rising flux tubes by convective
turbulence (Longcope \& Choudhuri 2002). This introduces a randomness in the BL mechanism,
for which we now have strong observational support (Dasi-Espuig et al.\ 2010; Kitchatinov
\& Olemskoy 2011). If the irregularities of the sunspot cycle arise in this way, then
Jiang, Chatterjee \& Choudhuri (2007) found that the high-diffusion model can explain
the observed correlation between the polar field at the sunspot minimum and the strength
of the next cycle---a correlation which the low-diffusion model cannot reproduce. It may
be noted that at the end of cycle 23 there were theoretical efforts in predicting the strength
of cycle 24 on the basis of dynamo models. On incorporating the data corresponding to the
weak polar field at the end of cycle 23, Choudhuri, Chatterjee \& Jiang (2007) found that
cycle 24 comes out as a weak cycle in the high-diffusion model---which is expected on the
basis of the correlation found in this model. However, Dikpati \& Gilman (2006) predicted
from their low-diffusion model that cycle 24 would be exceptionally strong. By now there
is enough evidence that the prediction of the high-diffusion model is much closer to the
truth, as seen in Figure~2.
\begin{figure}
\center
\includegraphics[width=8cm]{fig2.eps}
\caption{The monthly sunspot number plot for the last few years, indicating the
theoretical predictions. The upper star is the peak of cycle~24 predicted by
Dikpati and Gilman (2006), whereas the lower star is what was predicted by Choudhuri,
Chatterjee and Jiang (2007). The circle on the horizontal axis indicates the time when
these predictions were made (in 2006).}
\end{figure}
Since the strength of the meridional circulation sets the period of the dynamo (Dikpati \&
Charbonneau 1999), it is no wonder that variations in the meridional circulation also
produce irregularities in solar cycles. Karak \& Choudhuri (2011) found that such fluctuations
introduced in the high-diffusion model can explain the Waldmeier effect, which the low-diffusion
model cannot explain at all. This provides another support in favour of the high-diffusion
model. Recently the high-diffusion model has been used to model the grand minima. A grand
minimum can be caused either by the weakness of the poloidal field during the sunspot minimum
(Choudhuri \& Karak 2009; Olemskoy, Choudhuri \& Kitchatinov 2013)
or by the weakness of the meridional circulation (Karak 2010).
On considering both these effects simultaneously, Choudhuri \& Karak (2012; see also
Karak \& Choudhuri 2013) found that they
can explain the statistics of occurrence of grand minima.
It should be clear from the above discussion that the high-diffusion model is a better
description of what is happening inside the solar convection zone. Apart from the two
poloidal field transport mechanisms mentioned at the beginning of this section, a third
possible mechanism has been recognized recently: downward turbulent pumping (Karak \& Nandy 2012;
Jiang et al.\ 2013). The effect of this is similar to high diffusion. On including downward
turbulent pumping in the low-diffusion model, the model starts behaving somewhat like
the high-diffusion model.
\section{Inadequacies of the present models}
In spite of the success in modelling different regular and irregular aspects of the
solar cycle, the flux transport dynamo model at present has several inadequacies. We
now point out some of them.
Since the differential rotation within the tachocline is strongest in high latitudes,
there is a tendency of strong toroidal fields being produced in high latitudes (Dikpati
\& Charbonneau 1999; K\"uker, R\"udiger \& Schultz 2001). The intriguing question is
why sunspots appear only at the lower latitudes. One suggestion by Nandy \& Choudhuri (2002; see also Guerrero \& Mu\~noz 2004)
is that the meridional circulation penetrates slightly below the bottom of the convection
zone, ensuring that the toroidal field produced at the high latitudes is pushed into the
stable layers to avoid sunspot eruptions at high latitudes. While this hypothesis has
been questioned by some authors (Gilman \& Miesch 2004), the fact that torsional oscillations
begin at high latitudes before the beginning of the sunspot cycle lends a strong support
to this hypothesis (Charkraborty, Choudhuri \& Chatterjee 2009). Some authors (Hotta \&
Yokoyama 2010; Mu\~noz-Jaramillo et al.\ 2010) artifically restricted the sunspot eruptions
to low latitudes by confining the $\alpha$-coefficient to low latitudes without providing
any physical justification for this. We have to admit that at present there is no
concensus amongst dynamo theorists why sunspots do not appear at high latitudes.
Magnetic buoyancy and the BL mechanism, which are essential ingredients of the flux transport
dynamo, are inherently three-dimensional. They can be treated only rather crudely in
two-dimensional models. Choudhuri, Nandy \& Chatterjee (2005) found that two widely used methods
for specifying magnetic buoyancy give quite different results when all the other things are
kept the same. The best way of treating the BL mechanism in two dimensions is also debated.
Nandy \& Choudhuri (2001) concluded that using the $\alpha$-coefficient and using the double
ring procedure proposed by Durney (1995) give similar results. However, recently Mu\~noz-Jaramillo
et al.\ (2010) have claimed that the double ring procedure is the superior procedure.
Perhaps the next step is to construct kinematic models in which magnetic buoyancy and
the BL mechanism are treated in three dimensions. Yeates \& Mu\~noz-Jaramillo (2013) have
initiated such calculations. It remains to be seen whether this approach reproduces
the results of two-dimensional models.
Since there are no sunspots during a grand minimum, we expect that the BL mechanism will not
be operative at that time. If the BL mechanism is the only mechanism for generating the
poloidal field, then we do not understand how the dynamo comes out of a grand minimum.
Most probably we need something like the traditional $\alpha$-effect to pull the dynamo
out of a grand minimum (Karak \& Choudhuri 2013; Hazra, Passos \& Nandy 2014). Does this
$\alpha$-effect operate all the time along with the BL mechanism or does it become effective
only during grand minima when magnetic fields are weaker? At present, we have very little
understanding of these issues.
Finally, the usual assumption in any mean field theory like the solar dynamo theory is that
fluctuations have to be small compared to the mean fields. Since the magnetic field exists
in the form of flux tubes within the convection zone, this is certainly not true. How the
presence of flux tubes affects the mean field theory has still not been studied adequately
(Choudhuri 2003). We certainly need to take account of the flux tubes in order to explain
certain aspects of the sunspot cycle. For example, one mechanism for producing the observed helicity
of active regions is that the poloidal field gets wrapped around rising flux tubes (Choudhuri
2003; Choudhuri, Chatterjee \& Nandy 2004; Chatterjee, Choudhuri \& Petrovay 2006; Hotta \&
Yokoyama 2012). Presumably, the mean field theory somehow captures the essence of magnetic
field dynamics even though the fluctuations are larger than the mean.
\section{Recent challenges to the flux transport dynamo}
Although the inadequacies of the present dynamo models described in the previous section
makes it clear that we still do not understand many aspects of these models, these
inadequacies do not pose a threat to the validity of the flux transport model itself.
We now come to some recent developments which raise questions whether the flux transport
dynamo model is the correct model for the solar cycle.
As indicated in Figure~1, flux transport dynamo models usually assume a single cell of
meridional circulation spanning one hemisphere of the convection zone. There is enough
observational evidence for a poleward flow in the upper layers of the convection zone.
While the equatorward return flow in the lower layers is still not established by observational
data, such a flow is needed to overcome the Parker--Yoshimura sign rule (1) so that we get
solar-like behaviour (Choudhuri, Sch\"ussler \& Dikpati 1995). Of late, several groups
have claimed to find evidence of the equatorward return flow around the middle of the
convection zone rather than its bottom (Hathaway 2012; Zhao et al.\ 2013; Schad, Timmer
\& Roth 2013). It is possible that there are additional cells of meridional circulation
below this return flow, although the presently available observational data are not capable of settling
this issue. The important question facing us now is whether the flux transport dynamo
model can work if the equatorward return flow is at the middle of the convection zone
rather than at its bottom where the toroidal field is produced by differential rotation.
Let us first consider the situation that there is shallow cell of meridional circulation
with the return flow at the middle of the convection zone, with no flows underneath.
Guerrero \& de Gouveia Dal Pino (2008) showed that a solar-like behaviour (i.e.\
butterfly diagrams corresponding to equatorward propagation) can still be
obtained if there is equatorward turbulent pumping. Since the existence of equatorward
pumping is less well established than the existence of downward turbulent pumping, we address the
question whether we can obtain solar-like behaviour without such pumping. Jouve \& Brun
(2007) considered radially stacked multiple cells in which the flow at the bottom of the
convection zone was poleward and solar-like behaviour was not reproduced. Recently Hazra,
Karak \& Choudhuri (2014) found that solar-like behaviour can be obtained as long as
there is an equatorward flow at the bottom of the convection zone even if there are multiple
cells of meridional circulation with an equatorward return flow in the middle of the convection zone. Although the
flux transport dynamo model was historically developed by considering initially a single cell
of meridional circulation, it seems that the model can still work with more complicated
meridional circulation as suggested by recent observations. Only if future observations
show that there is no equatorward flow at the bottom of the convection zone, the validity
of the flux transport dynamo model will have to be questioned.
\section*{Acknowledgements}
I thank DST for partial support through a J C Bose Fellowship.
\def\apj{{\em ApJ}}
\def\aap{{\em A\&A}}
\def\sol{{\em Sol. Phys.}}
\def\mn{{\em MNRAS}}
| {
"redpajama_set_name": "RedPajamaArXiv"
} | 5,960 |
A 31-year old man, who works at the Ministry of Public Health, has been charged with a sexual offence allegedly committed on a 14-year old boy.
The man was not required to plea to the charge that was read to him by City Magistrate, Leron Daly.
Police alleged that the man engaged in sexual penetration of a child at the National Park between June 21, 2015 and October 22, 2015. The accused is attached to the Public Health Ministry as a liaison officer.
Bail was refused based on the fact that the defendant has conflicting addresses.
Magistrate Daly upheld the prosecution's objection and remanded the accused to prison until June 12, 2017.
The names of the accused and the alleged victim have been withheld because Guyana's Sexual Offences Act prohibits the publication of information that may lead to the identification of the minor. | {
"redpajama_set_name": "RedPajamaC4"
} | 2,301 |
/**
* Module dependencies.
*/
var express = require('express');
var bodyParser = require('body-parser');
var api = require('./lib/api.js');
var http = require('http');
var path = require('path');
var morgan = require('morgan');
var app = express();
// all environments
app.set('port', process.env.PORT || 3000);
app.set('views', path.join(__dirname, 'views'));
app.set('view engine', 'ejs');
app.use(morgan());
app.use(bodyParser.json());
app.use(bodyParser.urlencoded({extended: true}));
app.use(express.static(path.join(__dirname, 'public')));
if ('development' == app.get('env')) {
var errorhandler = require('errorhandler');
app.use(errorhandler());
}
app.use('/api', api);
http.createServer(app).listen(app.get('port'), function(){
console.log('Express server listening on port ' + app.get('port'));
});
| {
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} | 3,338 |
{"url":"https:\/\/socratic.org\/questions\/if-a-coin-is-dropped-from-a-height-of-80-m-how-fast-will-it-be-travelling-when-i","text":"# If a coin is dropped from a height of 80 m, how fast will it be travelling when it hits the ground? What assumptions, if any, do you need to make?\n\nSep 13, 2017\n\n${v}_{f} =$-$40 \\frac{m}{s} \\hat{j}$\n\n#### Explanation:\n\nIn case of free fall\n\n${v}_{f} = \\sqrt{2 \\cdot g \\cdot h}$\n\nso ${v}_{f} = \\sqrt{2 \\cdot 10 \\cdot 80}$\n${v}_{f} = 40 \\frac{m}{s}$.\n\nwe didn't assumed anything .\n\nThe derivation of the equation is from 3rd equation of motion.","date":"2020-09-21 03:01:04","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 5, \"mathjax_inline_tex\": 1, \"mathjax_display_tex\": 0, \"mathjax_asciimath\": 0, \"img_math\": 0, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.9777822494506836, \"perplexity\": 783.2726936204313}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2020-40\/segments\/1600400198887.3\/warc\/CC-MAIN-20200921014923-20200921044923-00593.warc.gz\"}"} | null | null |
Q: Calculate the value of a floating-point coordinate in a 2d-matrix Suppose I have a 2D matrix that has 2 rows and 2 columns with these values:
x=0, y=0 => 1
x=1, y=0 => 2
x=0, y=1 => 3
x=1, y=1 => 4
I can calculate the values for cells with integer coordinates, such as (0,0) and (1,0), etc. by a simple lookup.
However I need to do this for any floating-point coordinate.
From intuition I got to the following assumptions thus far:
(0.25, 0) I believe would be 0.75 x 1 + 0.25 x 2
(0, 0.25) I believe would be 0.75 x 1 + 0.25 x 3
(0.5, 0.5) I believe is the sum of all 4 cells divided by 4
However I could be completely wrong.. I couldn't think of the right terms to look this problem up.
My goal is to be able to calculate the value of any coordinate like (0.25, 0.25) but I think I may have forgotten some basic matrix rules from my maths classes, because the best I can come up sounds a bit complicated for what I'm trying to do.
My current idea is to calculate the distance from every cell "centre" (for which I know the value) and using the Pythagorean theorem calculate the distance of each cell, and then average the cell values based on their distance from the point.
Is there a simpler approach perhaps?
A: You have a two dimensional function $f : \mathbb{R}^2 \to \mathbb{R}$ and the values $f(0,0)$, $f(0,1)$, $f(1,0)$ and $f(1,1)$ in your initial matrix.
If you want more values, here it seems $f(x,y)$ for $(x,y) \in [0,1]^2$, you must make some assumption about $f$.
A simple assumption is that $f$ is a linear function on $[0,1]^2$.
Under this assumption you can use linear interpolation.
Interpolation along the axes gives:
$$
f(x,y) = (1-x) f(0,y) + x f(1,y) \\
f(x,y) = (1-y) f(x, 0) + y f(x, 1)
$$
we combine this into
$$
f(x,y) = (1-x)[(1-y)f(0,0) + y f(0,1)] + x [(1-y) f(1,0) + y f(1,1)]
$$
Note that if the four corner values do not lie on a common plane, this function will be some quadratic function through those four points.
You can fiddle with the example here. (Move the four sliders with the corner values in the middle view)
| {
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} | 9,471 |
<?php
declare(strict_types = 1);
namespace Domain\Handler\Image;
use Domain\{
Command\Image\SpecifyDimension,
Repository\ImageRepository
};
final class SpecifyDimensionHandler
{
private ImageRepository $repository;
public function __construct(ImageRepository $repository)
{
$this->repository = $repository;
}
public function __invoke(SpecifyDimension $wished): void
{
$this
->repository
->get($wished->identity())
->specifyDimension($wished->dimension());
}
}
| {
"redpajama_set_name": "RedPajamaGithub"
} | 9,700 |
{"url":"http:\/\/hackage.haskell.org\/package\/synthesizer-core-0.8.1\/docs\/Synthesizer-Causal-Displacement.html","text":"synthesizer-core-0.8.1: Audio signal processing coded in Haskell: Low level part\n\nSynthesizer.Causal.Displacement\n\nSynopsis\n\n# Mixing\n\nmix :: (C v, Arrow arrow) => arrow (v, v) v Source #\n\nMix two signals. Unfortunately we have to use zipWith semantic here, that is the result is as long as the shorter of both inputs.\n\nraise :: (C v, Arrow arrow) => v -> arrow v v Source #\n\nAdd a number to all of the signal values. This is useful for adjusting the center of a modulation.\n\n# Distortion\n\ndistort :: Arrow arrow => (c -> a -> a) -> arrow (c, a) a Source #\n\nIn Synthesizer.Basic.Distortion you find a collection of appropriate distortion functions.\n\n# Preprocessing of control curves\n\nmapLinear :: (C a, Arrow arrow) => a -> a -> arrow a a Source #\n\nmapExponential :: (C a, Arrow arrow) => a -> a -> arrow a a Source #","date":"2019-06-20 18:32:43","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 0, \"mathjax_display_tex\": 0, \"mathjax_asciimath\": 1, \"img_math\": 0, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.7531678080558777, \"perplexity\": 5209.619542279587}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 20, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2019-26\/segments\/1560627999263.6\/warc\/CC-MAIN-20190620165805-20190620191805-00441.warc.gz\"}"} | null | null |
Pedaliodes tairona är en fjärilsart som beskrevs av Adams och Bernard 1977. Pedaliodes tairona ingår i släktet Pedaliodes och familjen praktfjärilar. Inga underarter finns listade i Catalogue of Life.
Källor
Praktfjärilar
tairona | {
"redpajama_set_name": "RedPajamaWikipedia"
} | 3,032 |
T G Fraser
# The Makers of the Modern Middle East
with Andrew Mango and Robert McNamara
# Contents
Preface and Acknowledgements
1 The Birth of Nationalisms
2 Wartime Promises and Expectations
3 Arabs and Zionists in Paris
4 San Remo and Sèvres: the Flawed Peace
5 The Middle East Rebels and the Peace Settlement Revisited
6 From War to War
7 Conclusion: The Legacy
Notes
Further Reading
# Preface and Acknowledgements
Historians have long known that the settlements negotiated at the end of the First World War had ramifications well beyond Europe. Much of Volume VI of H W V Temperley's monumental study _A History of the Peace Conference of Paris_ , published in 1924, was devoted to the affairs of the Middle East and the attempts to set in place a peace settlement with the Ottoman Empire and its successors. As such, the contributors ranged across Turkey, Syria, Iraq, Egypt, Palestine and Persia, as well as the Zionist movement. Since then, there have been many investigations of how the region was transformed during the critical years between 1914 and 1923, some of them becoming classic studies.
This book approaches the problem of post-war reconstruction from three very different perspectives; namely, the emerging but increasingly insistent claims of Arab nationalism, Turkish nationalism and Zionism. Whilst these movements, which recast the political shape of the region in spite of the imperial ambitions of the triumphant European powers, transcend any individual, three leaders emerged, who by any reckoning became the makers of the modern Middle East. The Hashemite Prince Feisal, with British encouragement, raised the standard of Arab nationalism against centuries of Turkish rule, only to see his hopes of an Arab kingdom destroyed, albeit with compensation for him in Iraq and for his brother in Transjordan. From an obscure university position in the north of England, the Russian-born scientist Dr Chaim Weizmann enlisted the support of key British politicians for a Jewish national home in Palestine in the shape of the Balfour Declaration, and then translated that document into a British League of Nations Mandate for Palestine charged with bringing it into effect. The Turkish soldier Mustafa Kemal came to prominence in the successful defence of the Gallipoli peninsula in 1915, and then went on to lead and inspire his country's defiance of the victorious Allied powers to establish a modern, secular Turkish republic, becoming Atatürk, the 'Father of the Turks'. What their movements achieved, and failed to achieve, are part of their legacies nearly a century later.
This volume was suggested to me by Dr Barbara Schwepcke of Haus Publishing, who realised that the deliberations of the post-First World War Peace Conference relating to the Middle East could be approached from three very different perspectives. This was apparent from three volumes she had published in _The Makers of the Modern World_ series under the editorship of Professor Alan Sharp: namely, Andrew Mango, _From the Sultan to Atatürk: Turkey_ ; Robert McNamara, _The Hashemites: The Dream of Arabia_ ; and my own, _Chaim Weizmann: The Zionist Dream_. This book, thus, attempts to bring these studies together into an account of a seminal period of Middle Eastern history.
The Middle East is an area both of fascination and controversy. As an historian who has taught and researched its history at universities in Northern Ireland and the United States for over four decades, I have been lucky enough to have visited its countries many times, in the belief, taught me years ago by the late Professor L F Rushbrook Williams, that it is essential for a scholar to get the 'feel' for the societies under review. His kindly interest in my work as an apprentice historian of the Middle East and South Asia is a memory I will always cherish. I have never encountered anything other than the hospitality for which the Middle East is justly renowned, and I retain the fondest memories of the people I have met and who have educated me in its affairs. If I have become convinced of anything, it is that those brought up in the West should have a proper appreciation of, and acknowledge, just how much world civilisation has owed to the contributions of the peoples of the Middle East.
Unfortunately, it is also a part of the world which has endured more than its fair share of turmoil and tragedy, and this, too, must be acknowledged and understood. Tragic events in the Middle East have become standard fare in the headlines for decades, and it is, alas, all too tempting to develop an indifference towards them, or worse. Such a path is neither realistic nor justifiable. This book proceeds from the belief that a sympathetic, but not uncritical, understanding of Middle Eastern affairs is a sine qua non for the informed citizen. _The Makers of the Modern Middle East_ , then, analyses a critical series of events before, during, and after the Paris Peace Conference when the future shape of the Middle East as we have come to know it came into focus.
I am particularly grateful to my fellow authors Andrew Mango and Robert McNamara for their tolerance as I worked with their texts, and for their general advice. Barbara Schwepcke of Haus and Jaqueline Mitchell patiently encouraged me through the unfamiliar experience of making a coherent text from three volumes. Janet Farren deployed her customary skills in assisting with the preparation of the work for the publisher. The Series Editor of _The Makers of the Modern World_ , Alan Sharp, read and commented on the text, as, amidst all the other priorities of academic life, did Dr Leonie Murray of the University of Ulster, saving me from many errors of expression and emphasis. Finally, my wife, Grace, was, as ever, an unfailing source of critical understanding and support.
T G Fraser, MBE
Emeritus Professor of History and Honorary Professor of Conflict Research,
University of Ulster
1
# The Birth of Nationalisms
The Middle East on the eve of war
In 1900 the Middle East was barely, if we may borrow Prince Metternich's dismissal of Italy, a 'geographical expression'. In the early 21st century its affairs could not be ignored. At the end of the First World War, the term 'Middle East' was being used by the British, who had come to dominate the region as the result of military conquest, and it has since passed into common usage, which may serve as some defence against accusations of Eurocentrism. Definitions of the region have varied over time, but the limits of this book are marked by the boundaries of what was then the Ottoman Empire. The Turks emerged in the 8th century CE when the Seljuks, guided, according to national legend, by a grey wolf, conquered territories in central Asia. Their name is commemorated in the modern city of Seljuk in Anatolia. Converting to Islam, the Turks, led by the House of Osman, commonly known as the Ottomans, came into conflict with the Christian Byzantine empire, heir to ancient Rome. In 1453, the armies of Mehmed II, 'the Conqueror', took Constantinople, a pivotal event in world history.
At its height, the Ottoman Empire extended from the Turkish heartland in Anatolia across Egypt and North Africa, conquering much of the Arab territories as far as the Shatt al-Arab waterway, and in Europe pressing through the Balkans to the gates of Vienna. The Sublime State, as it was officially known, was both an Asian and a European empire, its capital uniquely spanning two continents across the narrow Straits of the Bosphorus, one of the most strategic waterways in the world. Constantinople, or Istanbul as it was known to the Turks, with its incomparable skyline etched by the mosques of Aya Sophia, Sultanahmet and Süleymaniye, the first of these also a reminder of the region's Roman and Byzantine inheritance, was one of the great cities of the world. It was then both imperial and cosmopolitan. From his accession in 1876 until his forced abdication in 1909, the empire was ruled by Abdülhamid II, who, like the Habsburgs and the Romanovs, presided over a fascinating range of peoples and religions.
The Ottoman Empire in the new century
At the heart of Abdülhamid's empire were the Turks, numbering, perhaps, some 10 million. The empire was ruled by the House of Osman, the Sultan uniting with his temporal rule the office of Caliph, or protector of the Islamic faith. By the early 20th century, the empire was the last remaining major Islamic polity in a world dominated by the imperialisms of the major Christian powers and Japan, a fact which bound the Turks to their Arab subjects, of whom there were around 7 million. This fact also attracted Muslims across the Islamic world, not least those of British India. Amongst the cities of the empire were Mecca and Medina, the holy cities of Islam, and Jerusalem, sacred to Jews, Christians and Muslims, the world's three great monotheistic faiths. Whilst the bulk of the empire's Muslims, belonged to the Sunni, or 'Orthodox', branch of Islam, in the historic lands of the Tigris and Euphrates were Najaf and Karbala, the holy cities of the Shias, whose people did not instinctively identify with Ottoman rule. Shias, the minority branch of the Islamic faith, believed that the true successors of the Prophet Muhammad were his son-in-law 'Ali and his descendants. The two cities held particular sanctity for the Shias since 'Ali was buried in Najaf and his son, Husayn, who had been killed in battle, was buried in Karbala. They found an affinity with those across the border in Persia, or Iran as it became in 1935, which was the main centre of Shia power. The Shias of the Tigris and Euphrates did not sit entirely comfortably in an empire in which the dominant Turks, as well as most Arabs, were Sunnis, and this was to pose problems in later years once independence came to the region.
Nor was it an homogeneously Muslim empire, since there were also significant Jewish and Christian minorities. Jews were to be found in the holy cities of Judaism, Jerusalem, Safed, Tiberias and Hebron, as well as in considerable numbers in Baghdad, where they had lived since the Babylonian captivity of the 6th century BCE. Jerusalem, especially its Old City, held a unique place because of its significance for Jews, Christians and Muslims. This deep religious feeling found its focus for Jews in the Western Wall, the only remaining fragment of their Temple which the Roman conquerors of Jerusalem had left intact, while for Muslims the adjacent Dome of the Rock and Al-Agsa Mosque comprised the Haram al-Sharif (the 'Noble Sanctuary'), their most sacred shrine after Mecca and Medina. For Jews the site was the Temple Mount. Also in the Old City was the Church of the Holy Sepulchre, sacred to Christians. In more recent years, as we will see, Zionist Jews from eastern Europe had also begun to settle. Around Mount Lebanon were the Maronites, a Christian denomination enjoying close links with France and Rome. The region's Byzantine heritage survived, too, since the Patriarch of Constantinople was the acknowledged head of the eastern Christian Church, as well as of the empire's thriving Greek community. İzmir, or Smyrna, on the Aegean coast, the second city of the empire in terms of population, was half-Greek, while it was estimated that there were some 150,000 Greeks residing in Constantinople. It was inevitable that they would be suspected of partiality towards their kinsmen across the border, who had won their independence in the 1820s.
The position of two other substantial non-Turkish minorities, the Kurds and Armenians, was even more problematic, not least because large numbers of them were also to be found in other countries. Outside the Ottoman Empire, the Muslim Kurds were a minority population in the north-west of neighbouring Persia, whilst the Christian Armenians were stretched across Turkey, Persia and Russia, whose officials were not above encouraging their national aspirations. Armenians were also aware of the success of the Christian Slavs in prising the Turks out of the Balkans. The Turks, in turn, used the Kurds as a counter to the Armenians. Massacres of Armenians in 1895–6 set an uneasy precedent. When we also include smaller communities such as the Alawites, Chaldaeans, Circassians and Druzes, then the rich diversity of the empire becomes clear, although, as its former Habsburg rival was discovering, this was not always an advantage in an age of burgeoning nationalisms.
Although it was emphatically a Muslim polity, believers in other monotheistic religions were accorded recognition through the _millet_ system, under which they ran their own affairs. _Millet_ status was accorded to the Latin Catholic, Greek Orthodox, Armenian Catholic, Armenian Gregorian, Syrian and United Chaldaean, Maronite, Protestant and Jewish communities. Nor did the Jews forget that it was the Turks who had given refuge to many of them after their expulsion from Andalucia in the late 15th century. The _millet_ system both acknowledged and respected the empire's rich variety.
It was, of course, in the Balkans that the most immediate threat to the empire lay. From the time when the unfortunate Grand Vizier Kara Mustafa had failed in his bid to take Vienna in 1683, the Habsburg armies, led by their great commander Prince Eugene, had steadily pushed the Turks back through the Balkans. Austrian expansion came to rest with the de facto acquisition of the Ottoman provinces of Bosnia and Herzegovina in 1878, a poisoned chalice for the dynasty if ever there was one, but by then the Turks were being further challenged in the Balkans. If the Austrians had led the charge to expel the Turks from central and south-eastern Europe, their task was taken up by the Russians, who encouraged the Serbs and Bulgarians to move for independence, just as they had earlier done with the Greeks. By the time of the Congress of Berlin in 1878, Romania, Serbia and Montenegro were also independent, and Bulgaria was soon to follow. The empire's long-standing dominance in the Balkans finally came to end in the Balkan Wars of 1912–13, which left it with a rump of territory in eastern Thrace, although crucially still in possession of Istanbul and the Bosphorus and the Dardanelles, which linked the Black Sea to the Aegean, the Mediterranean and the seas beyond.
By then, it may truly be said that it had become a Middle Eastern empire. The Ottoman Empire still held suzerainty over Egypt, with its fertile Nile valley and the historic cities of Cairo and Alexandria, but this had become a fiction. Since 1882, the country had been ruled by the British, whose interest was generated by the opening in 1869 of the Suez Canal, which provided a key route to their possessions in the east, notably the Indian Empire. Their proconsuls, men like Lords Cromer and Kitchener, paid no heed to the Sultan. Then, in 1911–12, Italy seized Tripolitania and Cyrenaica in a war notable for the first use of bombs dropped from aircraft, a dismal precedent for the century to come. Italy's colonial adventure also marked the emergence of a young Ottoman major, Mustafa Kemal. In effect, the Turks had been shut out of their historic lands in North Africa as well as in Europe.
The 'Young Turks'
If it were an empire in geographical retreat, the seeds of renewal were there, nevertheless. The Ottoman state entered the First World War on the side of the Central Powers in 1914 in a reckless gamble by a group of adventurers, led by a triumvirate consisting of two young career officers, Enver and Cemal, and one civilian, Talât. Enver, the leading spirit, was 33 years old in 1914, Cemal was 42 and Talât 40. Enver became Commander-in-Chief (formally Deputy Commander-in-Chief, since the Sultan was nominal C-in-C), Cemal Navy Minister, commander of the Southern Front and Governor of Syria (which included Lebanon and Palestine), and Talât Minister of the Interior and then Grand Vizier (Prime Minister). These leaders of the Committee of Union and Progress, or Young Turks, as they were known in the West, had risen to power and fame in Ottoman Macedonia in the first decade of the 20th century. Their character had been moulded by their experience in fighting the irregular bands of Balkan nationalists – Slav Macedonians, Bulgarians, Greeks, Serbs and, finally, Albanians. Nationalist irregulars were known in Turkish as _komitacı_ (committee-men), a designation which became a byword for ruthlessness, violence and treachery, but also reckless courage. Such men were needed to carve nationally homogeneous states out of a multinational empire – a process which involved massacres, deportations and the flight of millions of refugees. Enver, Cemal and Talât were Turkish _komitacıs_ in a literal sense, too, as leaders of the Committee of Union and Progress (CUP), whose members were known as Unionists ( _İttihatçı_ ). They were initiated in quasi-Masonic ceremonies in which oaths were sworn on guns and holy books. They conspired against the absolutist regime of Sultan Abdülhamid II, forced him to reintroduce constitutional rule in 1908, deposed him in 1909 and seized power in a coup in 1913. They believed initially that constitutional rule would reconcile all the ethnic communities of the Ottoman Empire and turn them all into loyal Ottoman citizens under the banner of freedom, fraternity and justice. It was their version of the ideals of the French Revolution, which they admired as the 'Great Revolution'. But they admired Napoleon even more and also the German and Japanese militarists whose example confirmed their belief that might was right.
Like many other young officers, Mustafa Kemal was attracted to revolutionary politics in the hope that they might transform the fortunes of the empire. When the Young Turks acted against the Sultan in 1908, he was a member of their movement, although not a prominent one. Mustafa, to give him his original name, was born some time in the winter of 1880–1 in the cosmopolitan city of Salonica, now Thessaloniki in Greece. His father, Ali Riza, worked in the timber trade and as a customs officer, providing a decent middle-class income for his young wife Zübeyde. Mustafa was only a child when his father died, but he remained close to his mother, even after her remarriage. In 1899, he entered the imperial war college, doing well there and proceeding to Staff College. That he was an able and assiduous student is amply born out by his subsequent career. No less significantly, he was also attracted to politics, leading to a brief arrest and effective banishment to a military unit in Damascus. Here, too, according to his own account he helped spread revolutionary ideas in Beirut, Jerusalem and Jaffa.
Various staff and regimental appointments followed the Young Turk revolution, but it was Italy's invasion of Tripolitania and Cyrenaica which gave him the opportunity to make his mark. Travelling in disguise through British-ruled Egypt, he was soon in action against the Italians. With a small force of Turkish regulars and thousands of Arabs, he helped pin down the Italian forces on the coast. It was to no avail, however. Faced with the ability of the Italian fleet to bombard Beirut and the Dardanelles, as well as more immediate threats in the Balkans, the empire was forced to cede its two provinces in October 1912. His return to Turkey saw him posted as military attache to Sofia the following year, which brought promotion to lieutenant-colonel. If in 1914, he was not amongst the most prominent officers in the Ottoman army, he was certainly a well-trained and serious-minded professional, who had experienced active service against a modern European enemy. He also had an acute political brain.
Despite its defeats, the Ottoman state punched well above its weight. This was partly due to the hardihood and courage of Turkish conscripts. 'The Turkish peasant will hide under his mother's skirts to avoid conscription, but once in uniform he will fight like a lion', a Russian expert on Turkey wrote during the war. But there was another reason, to which most Western observers were blind and which historians have come to notice only recently. While the rural masses were illiterate and ignorant of the modern world, there was an elite of experienced and well-trained Turkish civil servants and army officers. Although the reforms of the 19th century (known as the _Tanzimat_ , meaning 'the (re)ordering') were routinely decried in the West as inadequate and a sham, by the beginning of the 20th century Ottoman administration compared well with that of other contemporary empires – so much so that many of its former subjects came to regret its eventual dissolution. A recent study suggests that in the Arab lands placed under British and French Mandates at the end of the First World War, there was little improvement for indigenous Muslims in such basic areas as average life expectancy, education, communications and public order. Ottoman civil administration was organised on French lines, while in the army French and British advisers were largely replaced by Germans from the reign of Abdülhamid II onwards. The efficiency of Ottoman governors and commanders was often overlooked by Western critics, however, who decried their rule as backward and corrupt. Foreign observers also overlooked the fact that many of the Greeks, particularly along the Aegean coast, were immigrants from the newly independent Greek kingdom who found life under Ottoman rule more rewarding than in their own country. The Young Turks scored their only diplomatic success in 1913 when the Balkan allies fell out among themselves, allowing Enver to reclaim Edirne (Adrianople) and with it eastern Thrace up to the river Meriç (Maritza/Evros) as the last Ottoman foothold in Europe. If the empire was no longer a European power, it had not ceased to be of interest to the powers of Europe.
The Ottoman Empire and its Arab population
By the eve of war, the Ottoman Empire was predominantly a Middle Eastern empire, whose future was likely to turn on relations between the Turks and their most numerous subjects, the Arabs. At the outbreak of the First World War, the Turks had ruled the heartlands of the Arab World encompassing the modern-day states of Syria, Iraq, Jordan, Israel, Saudi Arabia and Arab North Africa for four centuries. Syria, Iraq, Jordan and Palestine were known as the Fertile Crescent due to the important rivers, notably the Tigris and Euphrates, that provided the water resources that made the areas conducive to human settlement. The Ottomans, the last of the great Islamic Turkish tribes to forge a major empire, had conquered the Arab lands in 1517, ruling them, without serious opposition, until the beginning of the 20th century. Only in the last decades of Ottoman rule did proto-nationalist challenges begin to become evident in the Arab territories.
When it emerged in the 7th century CE, Islam was initially synonymous with being Arab. However, within a century of the Arab conquests, religion rather than ethnicity or nationality became 'the Supreme bond', which partly accounts for the willingness of the Arabs to accept Muslim Turkish overlords. Another reason was the nature of Ottoman rule. While ostensibly one of the most centralised empires in the world with all power held by the Sultan, this was, as one observer noted, 'make-believe'. Outside the main urban centres, such as Damascus, Aleppo, Mosul and Baghdad, government control was weak and the Arabic-speaking societies of the Fertile Crescent were split into groupings based on family, tribal, ethnic and religious ties. While Turkish-speaking governors, in theory, held supreme power in the Arabic-speaking regions, in practice linguistic barriers and a lack of military power meant they were dependent on local tribal leaders, the urban rich and religious leaders to maintain even a modicum of influence. These leading groups were known as the _a'yan_ or 'notables'. The politics of these notables was the dominant fact of political life in the Ottoman Middle East in the 19th and early 20th century.
One area of the Arab world held particular significance, Palestine. Although the word 'Palestine' was widely understood to refer to the area, it was not even a single provincial entity under the empire, with the northern part lying under the _vilayet_ , or administrative district, of Beirut and the southern region constituting the _sanjak_ of Jerusalem, while across the river Jordan spread the _vilayet_ of Syria. The Palestinians reflected the broader Arab society of the empire in that there were identifiable Christian communities, especially in cities like Bethlehem and Nazareth, which had associations with the life of Christ, but the overwhelming majority were Sunni Muslims. Palestinian Arab society was predominantly agricultural. While there was some industry, for example the soap trade of Nablus, most urban economic activity, such as handicrafts, weaving and construction, was related in some way to the agricultural sector. The main inhibiting factor for Palestinian agriculture was, as it has remained, the availability of water for irrigation, or rather the comparative lack of it. The country's principal river, the Jordan, was unsuitable for irrigation purposes, and hence the peasant cultivators of Palestine had to be careful that their farming methods and crops were adapted to this and did not cause the erosion of what fertile soil they had. The winter crops were wheat and barley, while in the summer sesame and durra were harvested. Palestinian figs and olives were well known, and sheep and goats provided the livestock, well adapted to the hilly terrain of the country's interior.
The cultivators were the _fellahin_ , who constituted the backbone of the Palestinian population. Passionately attached to the land they farmed, their title to it was often insecure, at least by European standards. The land of Palestine was held under various systems, decided according to the Turkish land law of 1858. Much of it was designated as state, or _miri_ , land, which was then allotted to peasant cultivators, subject to continuous cultivation. Under the _Musha'a_ system, land was rotated, which at least ensured that everyone would have a share of the better land, but did not encourage soil improvement or fertilisation. A further significant element of the Palestinian population were the Bedouin, who led a nomadic way of life, chiefly in the Negev Desert in the south but also in Galilee. While village leaders were important in their locality, power and status in Palestinian society rested primarily with the urban elites, who were also extensive landowners. The leading Palestinian _a'yan_ families, the Husaynis, Nashashibis, Khalidis, Jarallas and Nusseibehs, were to provide the leadership of Arab Palestine for the period under review. The Husaynis enjoyed particular prestige since they had provided the city's mayor and for a long period the religious office of Mufti of Jerusalem had generally been held by a member of the family. In time, the Husaynis were to emerge as the driving force behind Palestinian Arab nationalism.
The emergence of Arab nationalism
For many years, it was widely accepted that Arab nationalism, in its early stages, arose from contact with the West. Unsurprisingly, the first signs of a distinctively Arab nationalism begin to emerge in the urban areas of Ottoman Syria, where European and American cultural and educational influence was beginning to grow in the late 19th century in tandem with increased Western political and economic penetration of the region. European and American missionary work was linked to the Holy Places in Palestine but also grew from a desire, especially among Protestant congregations, to convert Muslims. Direct proselytisation was illegal but there seems to have been a vague, and ultimately forlorn, hope that Arab Christians might transmit their faith to Muslims. A handful of Syrian Christians, educated in the American and French missionary schools in the Lebanon that were established in the 19th century, began to develop a quasi-secular Arab nationalism, however. This included the revival of many classical Arabic literary texts and the translating of Western texts into Arabic. In the 1860s a Syrian Christian, Ibrahim al-Yaziji, articulated an early vision of Arab nationalism. He viewed the Ottoman conquest as a disaster for the Arabs who had regressed from being a technically advanced and learned civilisation to one that remained mired in backwardness and more interested in religion than science. Throwing off the Ottoman yoke, in his view, would allow the Arabs to resume their previous trajectory of learning and advancement. However, this secular vision of Arab nationalism was anathema to the vast bulk of Muslim Arabs, who remained committed to, or at least dispassionate about, the Ottoman Empire.
George Antonius, in his 1938 book _The Arab Awakening_ , perhaps the key text of modern Arab nationalism, saw the genesis of Arab nationalism within these very small cultural movements in late 19th-century Ottoman Syria. Since the Second World War, there has been increasing scepticism regarding some of Antonius's claims regarding the origins of Arab nationalism and his account of the Arab Revolt during the First World War, however. Even a sympathetic observer notes that it is not only 'a work of historical narrative, but also of political advocacy'. Relying essentially on oral evidence, Antonius almost certainly overplayed the role of a small Lebanese grouping, the Secret Society, which distributed placards agitating against the Ottomans in the late 1870s. This agitation, it is likely, was more to do with particular local factors involving Maronite Christians than the genesis of an Arab nationalism aimed against the Turks.
Some 30 years later there were more concrete signs of a nascent Arab nationalism. The spur was the 1908 Young Turk revolution. Arab reaction was initially enthusiastic. The initial phase of liberalism delivered by the CUP saw political activity permitted in the empire, including the formation of specifically Arab parties. Yet it soon became clear that the Young Turks' flirtation with liberalism and pluralism was merely a veneer behind which lurked a Turkish nationalist agenda, which reinforced tendencies towards centralisation and Turkification already evident in the Ottoman Empire. Indeed, there is little evidence that the Young Turks drove forward these policies to any greater extent than the old regime had. However, by briefly opening up Ottoman politics, they made it harder to go back to the old authoritarian system.
After 1912, in a reaction to the end of the period of reform, parties with an agenda of Arab autonomy began to emerge in Syria. The most important of these, according to Antonius, was the Decentralisation Party. Other bodies of importance, again in Syria, were secret societies with similar manifestos including _al-Fatat_ (the Young Arab Society) and _al-Qahtanyia_. Antonius would seek later to link these groupings into the Hashemite revolt against the Ottomans from 1916, thereby creating a bond between the more urban-based nationalism of the streets of Damascus and that of the arid deserts from which the Hashemites sprung.
According to its critics, however, Antonius's vision of the origins and development of Arab nationalism was exaggerated and fallacious. The pro-independence or autonomy-minded Arabs of Syria were a tiny minority, numbering around 350 members according to a recent authoritative survey, and Hashemite ambitions were nearly all to do with their own aggrandisement rather than a high-minded commitment to Arab nationalism. Today, the dominant scholarly interpretation of the origins of Arab nationalism is C Ernest Dawn's hypothesis that the stirrings of Arab nationalism in the early part of the 20th century emerged not from Western-influenced Christian Arabs but from reform-minded Muslims in the religious elite. It also arose from the conflict among the Arab notables and the elite, particularly in the major cities such as Damascus. Those who held favour, land and office due to Ottoman patronage tended to support the _status quo_ while those excluded from this spoils system began to agitate against it. Even among the recalcitrant, there was little desire for complete independence. Most Arabs would have been content to 'remain within the frame of the Ottoman unity, as long as their proper place was recognised by the Turkish rulers'. There were also enormous differences between city and countryside. Writing nearly 90 years ago, the influential English Arabist Gertrude Bell was perhaps closer than Antonius to the true state of Arab nationalism around the early years of the 20th century when she wrote, 'There is no nation of Arabs; the Syrian merchant is separated by a wider gulf from the bedouin than he is from the Osmanli [Ottoman]...'. At the beginning of the 20th century national politics in Syria remained 'an urban game largely isolated from village needs and wishes'.
The Hashemites
When the standard of Arab independence from the Turks was raised, this came not from the urban elite, but from a somewhat unexpected source, the Hashemites, the leading family in one of the empire's most remote districts, the Hejaz. The Hejaz was a narrow strip of land that extended from just south of what is now the Jordanian port of Akaba to nearly as far as the northern border of the Yemen. It now lies within the Kingdom of Saudi Arabia, although it was then a _vilayet_ of the Ottoman Empire. Indeed it was practically the only part of the Arabian Peninsula where the writ of the Ottomans ran at all. Situated on a barren and inhospitable stretch of coastline, its importance lay in the fact that two of the holiest sites of Islam lay within it: Mecca, the holiest city, and Medina, the first city to accept the word of Prophet Muhammad. It was remote from the capital, poor and thinly populated. Indeed, it is estimated that towards the end of the 19th century, the combined population of the three main towns of the Hejaz – Mecca, Medina and Jeddah – was little more than 100,000, with perhaps another 400,000 nomadic tribesmen in the hinterland around them. The territory lacked natural resources and much of the urban population was devoted to the study and practice of religion.
Its main source of income was the influx of pilgrims from all corners of the Muslim world, who as part of their religious duty were compelled, at least once in their life, to make the annual _haj_ to the Holy Places at Mecca. The presence of the holiest cities of Islam within the Hejaz conferred considerable benefits upon the area. It was not subject to conscription or normal levels of Ottoman taxation. Indeed, it tended to be a net recipient of aid, as well as receiving subventions from relatively wealthy Muslim states such as Egypt. It has been argued that 'religion determined the social, economic, and, to a lesser degree, the political history of western Arabia [i.e., the Hejaz] in the nineteenth century'. It remained a pre-modern, highly traditional society. There were little outward signs of nationalism or other modern political ideas permeating the area during the 19th century, and nor is there much evidence that before the beginning of the 20th century the Hashemites showed any great political ambitions.
Nearly 13 centuries after the death of the Prophet, those who were descended from him were entitled to use the title 'Sherif' (usually translated as eminent, distinguished or noble). Among the most important of these Sherifian families was the House of Beni Hashem (hence 'Hashemites'), from the Prophet's Quraysh tribe. Sherif Hussein ibn Ali of the Hashemites filled the most important position in the Hejaz, as Grand Sherif and Emir of Mecca, from 1908. Hussein's branch of the Hashemites had been raised out of relative obscurity when, during the 19th century Muhammad Ali, the ruler of Egypt, who had ruled over the Hejaz, installed Hussein's grandfather as Grand Sherif and Emir of Mecca.
The power that came with this position tended to be more religious than political and the Hashemites, though Arab, were also part of the Ottoman establishment. The independence of the Grand Sherifs was circumscribed by the presence of a Turkish governor or _Vali_ in Medina and the presence of some 7,000 troops. However, communications with Istanbul before the completion of the Hejaz railway in 1908 were slow and difficult, and distance from the imperial capital generally allowed the Emir of Mecca a reasonable degree of autonomy. Yet, as one writer in the 19th century stated, the Emir of Mecca was still a 'mere creature of the Porte, removable at the pleasure of the Sultan. Besides, he has no influence whatever, political or spiritual, beyond his own assigned district'. Indeed the ultimate control of the Ottomans over the Hashemites and Hejaz was demonstrated by the practice of bringing important members of leading families of the Hejaz, such as the Hashemites, to the capital as enforced guests of the Sultan.
However, it should also be borne in mind that Ottoman rule and the Turkish garrison also afforded a degree of security for the Hejaz. The Arabian Peninsula was a dangerous place with plenty of tribes and religious rivals (the Imam of Yemen, the Wahhabis and by the early 20th century the rising power of Ibn Saud) seeking to extend their influence. Since 1800 the British had been busy securing key positions and acquiring allies amongst the various Emirs on the coastal peripheries of the peninsula.
The Caliphate
When, after his accession, Abdülhamid II emphasised that as ruler of the Ottoman Empire he held the title of Caliph, there were voices of opposition. Some were proto-Arab nationalists who demanded the restoration of an Arab Caliphate. Some prophetic traditions, of admittedly dubious origin, claimed that the Caliphate could only be held by members of the Prophet's own tribe, the Quraysh. Dissent also came from British government officials – many in the India Office and Indian Civil Service – who did not like the Ottoman Sultan having such potential influence over the near 100 million Muslims in British India. One retired British civil servant suggested the Hashemite Emir of Mecca, a member of the Quraysh, would be a more pliable Caliph of Islam 'for he lives by the side of our road to India and would be as completely in our power as the Suez Canal'. It was a prescient comment, for the idea of a relationship between the Hashemites and the British would come to the surface again at a critical point in Middle Eastern affairs, albeit in the context of Arab nationalism rather than the Caliphate.
The Rise of Sherif Hussein
Hussein ibn Ali was born in 1853 in Istanbul. Half-Circassian, half-Arab, his family connections to the Aoun clan, a branch of the Hashemites, were what made him important, as he was 37th in the line of descent from the Prophet. There were approximately 800 members of the rival Aoun and Zaid clans who could claim this sacred lineage. At various times, one branch or the other would be ascendant and would hold the title of Emir or Grand Sherif of Mecca. In the 1880s and 1890s, the Zaid branch was dominant.
At the time of the outbreak of the First World War, Hussein was over 60. Nonetheless, he was a striking looking, black-robed, turban-clad figure with an almost snow-white beard. T E Lawrence, the British army officer who would have a key role in the Arab Revolt, described him as 'outwardly so clean and gentle-mannered as to seem weak; but this appearance hid a crafty policy, deep ambition, and an un-Arabian foresight, strength of character and obstinacy'. Hussein was in many respects a charismatic figure, learned in Arabic literature and familiar with the intrigues of international diplomacy. His Ottoman upbringing had also bred some rather unattractive qualities in the Sherif. According to Lawrence, 'Hussein when young had been honest, outspoken... [but] he learned not merely to suppress his speech, but to use speech to conceal his honest purpose. The art, over-indulged, became a vice from which he could not free himself.'
His early years are shrouded in mystery. We do know that as a leading scion of the Hashemite family he was an enforced guest of the Sultan for more than 15 years from 1892 or 1893 to 1908. His confinement, if it could be even called that, was extremely benign. The Sultan, not wishing to be accused of treating a Sherifian badly, had Hussein, his wife and four sons, Ali (1879–1935), Abdullah (1880–1951), Feisal (1883–1933) and Zeid (1898–1970), established in a comfortable villa on the Bosphorus. Three of the four sons (Ali, Abdullah and Feisal) were to become kings of three of the successor states of the Ottoman Empire.
Hussein became a prominent citizen in the capital, and was, in many respects, assimilated into the Ottoman way of life. Turkish appears to have come as easily to him as Arabic. He was, though, extremely strong-willed and independent-minded, and was probably too dangerous a figure to have ever been left to return to the Hejaz by the despotic Sultan Abdülhamid II. However, events intervened. When the Young Turks assumed power in 1908, Abdülhamid's powers were truncated, and he was deposed after a year. The position of Grand Sherif of Mecca fell vacant around the same time as the revolution, thanks to the deposition of the holder Sherif Ali Abdullah ibn Muhammad and the sudden death of his successor. Hussein was a leading candidate for the position, although his succession was by no means a formality. He was helped by his political views and an ability to ingratiate himself with key players. A deeply reactionary figure in many respects, he was not an admirer of the Young Turks, and his hostility to the new government may well have attracted Abdülhamid to Hussein's candidature. There is also some evidence that the British government viewed him as a suitable candidate, thanks to Hussein's timely overtures to the British Ambassador to Constantinople, in which he claimed to have written to Arab chiefs in the Hejaz to influence them to favour British interests in the Arabian Peninsula. Abdülhamid also viewed the Caliphate and the loyalty this engendered amongst his Islamic subjects as a key element in his survival. It was in his interests therefore to have a figure opposed to the Young Turks in the important position of Grand Sherif of Mecca. Hussein, according to his son Abdullah, pledged that if the CUP made life too difficult for Abdülhamid, he could have asylum in the Hejaz.
Hussein as Sherif and the Ottomans
In 1908 Hussein was made Sherif and returned to the Hejaz. However, there is some evidence that once he had done so, Hussein raised his sights and began to contemplate that he, not the Ottoman Sultan, should be Caliph. His son Abdullah testifies in his memoirs that Hussein was loyal to the Ottomans at this time and that his main argument with Istanbul was the secularising reforms of the CUP. In his view, the Young Turks, 'were ill advised when they converted the Imperial Caliphate administration into a racial "Constitutional" government and replaced the Islamic and therefore ultimately Arab supervision of the State by a Western juridical control'. In contrast to this, right from the beginning of his reign, Hussein made clear that traditional Islamic law, the _Sharia_ , was what guided him. Hussein's priority upon arrival in the Hejaz was to consolidate his power base and increase his influence at the expense of the Turkish _Vali_. Indeed, by 1911 the British were reporting that Hussein had completely outmanoeuvered the various _Vali_ sent there and the government of Mecca was essentially in his hands. A British dispatch from 1914 reported that on his arrival in 1908, Hussein had 'created a good impression, and it was hoped that he would not prove extortionate and would restore security in the country about Mecca'. After initial clamping down on brigandage, Hussein appears to have tolerated it. The British consul in Mecca reported that the murderers of three Indian pilgrims had links to the Grand Sherif.
However, Hussein needed to be circumspect in his challenges to the various _Vali_ and Ottoman authorities, for going too far could lead to his deposition. Indeed his earliest achievement was to bring the increasingly fractious Bedouin tribes adjacent to the Hejaz under control. The Ottomans, who after 1910 had much greater military priorities in the Balkans and in Libya, encouraged Hussein to extend his power into eastern Arabia and to assert Ottoman control against the two independent tribal leaders Ibn Saud and the Idrisi of Asir. According to the British consul in Jeddah, Hussein viewed these campaigns as a means by which he could consolidate his own power and autonomy. But the tentacles of Ottoman and Turkish control over the Hejaz were beginning to grow, not wither. Telegraph wires linked the capital to the Hejaz from the end of the 19th century and by 1908, communications were revolutionised by the completion of the Hejaz railway that linked Damascus to the city of Medina and the other Holy Places. The railway was greeted with considerable hostility by the Bedouin tribes of the Hejaz, who viewed the 'Iron Donkey' as a serious threat to their main sources of income: the guiding, transportation and occasional robbing of pilgrims. Significantly, the Young Turks appear to have viewed the railway and its eventual extension to Mecca as the cornerstone of the consolidation of more direct Ottoman rule in western Arabia. Indeed Medina, the town at the end of the railway line, began to come under much greater Ottoman influence in the years up to 1914.
Hussein, upon his installation as Sherif, encouraged attacks on the trains and he assiduously resisted entreaties from the Young Turks to extend the line down to his power base at Mecca. It is clear, however, that Hussein's autonomy in the years leading up to the outbreak of the First World War was becoming increasingly circumscribed. His son Abdullah complained about the tyranny of the Turks to the French Ambassador in 1912 and around this time the first tentative contacts between Abdullah and the British may have taken place. The key event in the deterioration of the Hashemite position was the installation of Vehib Bey as the _Vali_ in April 1914. Made of much more formidable stuff than his predecessors, he soon began clipping Hussein's wings. Vehib was determined that the dual control over the Hejaz would end and more direct Ottoman rule be established. Hashemite supporters in the administration were summarily dismissed and replaced by Ottoman placemen. Abdullah's contacts with the British, seeking their support for autonomy for the Hejaz, in February and April 1914, appear to have been directly motivated by the growing pressure being placed on his father by Vehib. It is clear that Ibn Saud, Hussein's great rival for supremacy in Arabia, who was also subject to Ottoman sovereignty, had far more autonomy in the isolated Nejd territories of central Arabia.
Hussein's clashes with the Ottomans were very much related to his own desires for self-aggrandisement and protection from the increasing encroachments on his powers by Ottoman officials. His Arab nationalist credentials were 'questionable'. Indeed, there is little evidence of any significant Arab nationalist pressures in the Hejaz. Within the socio-economic makeup of the region there were none of the key groupings (journalists, army officers and intellectuals) that were present at the creation of other nationalisms. To speak of 'nationalism' in the Hejaz, therefore, is a misnomer. The Arab Revolt, there at least, sprang almost entirely from a clash over power between the Hashemites, who considered themselves an elite whose privileges and autonomy were being threatened, and the Ottomans, who wanted to forge a modern centralised state. If the Ottomans had shown more skill in handling Hussein, the Sherif would have been most unlikely to lead a revolt against the Ottomans. The revolution in international politics brought about by the First World War, especially the willingness of all powers to support persons or groupings with grievances within their enemies' territories for subversive purposes, would provide Hussein with the means to take advantage of a unique opportunity to expand his power.
The Zionist movement
It was into this complex and evolving world of the Ottoman Empire and Arab politics that from the early 1880s the movement of Jews from eastern Europe began. Its immediate cause was the persecution and discrimination felt by the world's largest Jewish community, that of the Russian Empire's Pale of Settlement. At the time of Chaim Weizmann's birth in 1874, the Tsarist empire, which had acquired much of Poland in the late 18th century, held the largest Jewish population in the world. From 1772 onwards, the Jews were compelled to live in the western parts of the empire in an area designated the Jewish Pale. While many of them lived in cities like Vilnius, Odessa and Warsaw, or in large towns like Pinsk, many others grouped together in small towns known in Yiddish, the lingua franca of Eastern Europe's Jews, as _shtetls_. Weizmann's birthplace, Motol, was just such a _shtetl_.
The movement Hibbat Zion ('Love of Zion'), which pioneered the migration of Jews to Palestine, was founded in 1882. It was essentially a response to renewed persecution of the Jews in the Tsarist empire, and, despairing of assimilation, its members looked instead to Palestine. In November 1884, their first conference was held at Katowice, just across the border in Prussian Silesia. Anti-Semitism had been on the increase in the empire, stoked by its political and economic problems and the growth of Slavophile sentiments, but what gave it new impetus was the assassination in St Petersburg in March 1881 of Alexander II the 'Tsar Liberator', so called on account of his emancipation of the serfs, albeit in a manner which did not much benefit them. Of the six revolutionaries convicted of the murder, one was a young Jewish woman, Khasia Helfman. This event served to unleash a series of pogroms, as anti-Jewish riots were known, which began soon after the coronation of Alexander III and swept across areas as far apart as Warsaw and Odessa. Then, on 3 May 1882, the 'May Laws' were enacted which placed the Jews of the empire under even more severe restrictions than they had so far endured. Increasingly marginalised within the empire, hundreds of thousands of Jews emigrated, some across the border to the more tolerant Habsburg lands, others further afield to Britain and, especially, to the United States. Between 1882 and the outbreak of war in 1914, some 2.6 million Russian Jews emigrated to America, most of them to New York.
In 1882, a small group of Hibbat Zion members made their way to Palestine, where their first settlements were Rishon le-Zion, Rosh Pinnah and Petah Tikvah, followed by others such as Rehovoth, Hadera and Metulla. The settlements were not an immediate success, for the simple reasons that they were inadequately funded and that the settlers were inexperienced farmers. It was an inauspicious beginning for modern Jewish settlement in Palestine, which might have fallen at the first hurdle had it not been for the intervention of Baron Edmond de Rothschild, philanthropist and scion of the great French banking and winemaking dynasty. As the little settlements started to founder, Rothschild was persuaded to help, providing considerable financial backing, albeit at the cost of close supervision by his agents. With their assistance, a wine industry was created, followed by citrus production, which succeeded in stimulating an economic base for the settlement. These were the precursors of political Zionism.
Zionism had no single point of origin. The Jews were too widely dispersed, and their situations too different, for that. Although ideas of political action began to surface amongst Jewish intellectuals in the 19th century, the term itself appears to have been used first by the Austrian Nathan Birnbaum in April 1890 in his journal _Selbstemanzipation_. 'Zion' referred, of course, to Jerusalem. Although he created the term 'Zionism', Birnbaum was to part company from it later. Neverthless, his ideas anticipated those of another Viennese who is regarded as the real father of modern Zionism, Theodore Herzl, or in Hebrew, Benyamin Ze-ev Herzl.
Theodore Herzl
Herzl's origins were in the German-speaking Jewish middle class of the Habsburg Empire, a world away from the _shtetls_ to the east. He was born on 2 May 1860 in the city of Pest, which in 1872 united with its twin across the Danube to become Budapest, the capital of the Hungarian part of the empire. In 1878, he became a law student at the University of Vienna, then one of the most culturally vibrant cities in Europe, albeit one in which anti-Semitism was beginning to stir. Although he gained employment as a state lawyer, his real ambitions lay in literature, and while he struggled to have his plays accepted he found his niche, that of a writer of feuilletons for the press. These were short, finely crafted pieces much prized by educated Viennese, and in 1888 he was engaged to write them for the _Wiener Neue Freie Presse_ , the capital's leading newspaper.
Two things conspired to change Herzl's essentially assimilationist position. The first was the growing success in Viennese municipal politics of the Christian Social Party led by Dr Karl Lueger. Lueger, who was prepared to espouse anti-Semitism to advance his party's fortunes, was elected Lord Mayor of Vienna in 1895, and although Emperor Franz Josef refused three times to confirm him in the position, such was his popularity in the city that he assumed the office in 1897, holding it until his death in 1910. Adolf Hitler was later to extol his virtues in _Mein Kampf_. If confirmation were needed of the rising tide of anti-Semitism in Europe, then Herzl received it as Paris correspondent for his newspaper at the time of the Dreyfus affair in 1894–5. Captain Alfred Dreyfus, an assimilated Jew, was convicted, wrongly as it was later shown, of selling military secrets to Germany. On 5 January 1895, Herzl witnessed the formal degradation of Dreyfus in the courtyard of the École Militaire in Paris. What particularly appalled Herzl about this miserable spectacle was the crowd outside chanting 'Death to the Jews'. The success of Lueger's party in March that year further exposed the degree of anti-Semitism in two of Europe's most sophisticated cities, Paris and Vienna, and set the scene for the book Herzl was to publish the following year.
His book, or rather pamphlet, was published in Vienna and Leipzig on 14 February 1896. It had the somewhat ponderous title of _Der Judenstaat: Versuch einer modernen Lösung der Judenfrage_ , normally rendered in English as _The Jewish State: An Attempt at a Modern Solution of the Jewish Question_ , though a more accurate translation would be _The Jews' State_. Based on his recent dismal experiences in Vienna and Paris, his premise was essentially the pessimistic one that the pursuit of assimilationism was a false trail. The fact that Jews had given their loyalty to and had tried to enrich their countries through their contributions to the economy, art and science was in vain. The history of anti-Semitism, he went on to argue, had made the Jews into a people who could make a state. He foresaw the need for an organisation to work towards this, proposing a Society of Jews which would prepare the way and a Jewish Company which would carry the project forward. There were two possible locations for such a state. The first was Argentina, which he argued had plenty of good land and a small population. The other was their historic homeland of Palestine. If that were to be granted by the Ottoman Sultan, it could become an outpost of Western civilisation. Such was the essence of his book, which went on to describe the future state in romantic, not to say visionary, terms. The idea of a Jewish state, and an organisation to bring it into being, had entered the public domain.
For many, perhaps most, assimilationist Jews of western and central Europe, Herzl's book opened up issues about anti-Semitism that they had hoped were becoming a thing of the past. The 19th century had seen Jews advance into prominent positions in various European countries. Some of them were converts to Christianity, for example, the German composer Felix Mendelssohn and the British statesman Benjamin Disraeli, both favourites of Queen Victoria. Others held to their Jewish faith, asserting that they were a religious community like the Catholics, Anglicans or Lutherans. It was from the assimilationist Jews that some of the most determined opposition to Zionism came. In the winter of 1896/7, Herzl nevertheless worked single-mindedly to put his ideas into effect. His efforts culminated in the First Zionist Congress at Basle in Switzerland in August 1897. A seemingly modest affair of 197 delegates, it was historic, and the programme it approved was brief and to the point. The purpose of Zionism was to secure a home for the Jews in Palestine. In order to achieve this, Jews were to be encouraged to settle there, an organisation was to be created, Jewish national sentiment was to be fostered, and government consent secured. The achievement of the Zionist programme might have seemed a distant dream, but the essential first step had been taken. While Herzl was well aware that Zionism had to negotiate with the Ottoman rulers in Istanbul, whose writ ran in Palestine, notably absent from his analysis, then and later, were the Arabs of Palestine.
The men and women of the Second _Aliya_ , or 'Immigration', which began in 1904, were impelled by the failed Russian revolution of 1904–5 and the renewed spate of pogroms which broke out in its wake. What marked them out from their immediate predecessors were their socialist convictions allied to a belief that the Jews needed to work for themselves as part of their national development. An historic initiative of the Second _Aliya_ was the adoption and fostering of the Hebrew language. Most arrivals at that time would have spoken Yiddish, and would almost certainly also have known Russian or possibly Polish. German, of course, was the language of choice for the cultivated Central European Jewish middle class. Hebrew was the sacred language of the scriptures and worship in the synagogue, revered as such. But revival of language was an integral part of the story of national reawakening in Europe, and Zionism proved to be no different. The driving force behind this development was Eliezer Ben Yehuda, originally Perlman, who settled in Palestine in 1882, and who preached, and practised, the exclusive use of Hebrew. Ben Yehuda clearly recognised the need to bring this ancient language into the modern age if it were to have any future, and this was embodied in the ten-volume Hebrew dictionary, _Thesaurus Totius Hebraitatis_ , he published from 1910. His lead was enthusiastically taken up by the new immigrants, although regarded with suspicion and disfavour by many orthodox Jews for whom Hebrew was a sacred language not to be used for mundane matters.
Foundations were also being laid in other ways. In 1908, Dr Arthur Ruppin set up the Palestine Office in Jaffa, the purpose of which was to bring some impetus and organisation to land purchase. The following year, in the apparently unpromising sand dunes to the north of the ancient Arab port of Jaffa, a start was made on a new suburb which in time was to grow into a thriving Jewish metropolis. This was called Tel Aviv, 'the hill of the spring'. By 1914 it had attracted around 2,000 inhabitants. The driving force behind it came from the Russian Jewish immigrant Meir Dizengoff, who became chairman of the Town Council in 1910, and whose name was to become synonymous with the city's development for almost three decades. Although it was to suffer a serious setback during the war, under Dizengoff's direction Tel Aviv was to expand dramatically in the 1920s and 1930s, in time overshadowing Jaffa. Elsewhere, in the years preceding the First World War, Jews were settling in Haifa and new suburbs were springing up in Jerusalem. In short, however modestly, Zionism was establishing the basis for subsequent urbanisation. It was all very different to established Turkish and Arab societies.
Chaim Weizmann: origins of a Zionist leader
The man who was to assume such a pivotal part in the future of the Middle East, Dr Chaim Weizmann, was far from the centre of these events, even although he had been involved in Zionist affairs almost from the start. The small community of Motol shaped the first 11 years of Weizmann's life. Apart from its two synagogues, it had little of what later generations would term amenities. But by the standards of the Pale at that time, Weizmann's family enjoyed a decent, if modest, lower middle-class way of life. Ozer Weizmann, Chaim's father, was engaged in the timber trade, the mainstay of the local economy, employing men to cut logs which were then tied into rafts and floated down the rivers Pina, Bug and Vistula to Danzig, as modern Gdansk was then called, on the Baltic. Rachel Leah, Ozer's wife, had 15 children, of whom 12 survived into maturity. Chaim was her third.
If the Weizmann household was comfortable by the standards of the time, it was only won at the price of hard work on the part of Ozer and Rachel Leah, and in the knowledge that for the Jews life in the Pale could always be precarious. From the age of four until he was 11, Chaim Weizmann attended _cheder_ , the little schools which provided instruction in Hebrew and the Jewish law and scripture. While he seemingly had no high opinion or kindly memory of some of his teachers, they embedded in him a profound sense of his own Jewish identity, reinforcing the atmosphere he absorbed at home. Although he was to outgrow his origins, the values of Russian Jewry were to be the essential element in his later devotion to Zionism, setting him apart from, and often at odds with, some of the most prominent Jewish figures in Western Europe and the United States. This sense of where he was grounded comes across vividly in his first surviving letter, written in 1885 to Shlomo Sokolovsky, his tutor in the Russian language, which he needed to acquire in order to advance his education. Weizmann was concerned to reassure him that he would not abandon Judaism, and expressed his ardent support for the new Hibbat Zion movement. Interestingly, in view of the central role it was to assume in his life, he mentioned England, a country which he could only have imagined, as the one European state that would look favourably on the Jews.
It was, then, armed with a growing knowledge of Russian to add to his Yiddish and Hebrew, that Weizmann left Motol to begin his secondary education at the Real-Gymnasium in Pinsk, some 25 miles (40 kilometres) away. Two things stand out from his time there, each of which was to mould his subsequent career. Few things can be as inspirational in a young life as a schoolmaster or schoolmistress with talents beyond the ordinary and so it proved with Weizmann, since his interest in science, and chemistry in particular, was captured and fostered by a teacher called Kornienko.
Of even greater significance for the future were Weizmann's contacts with Pinsk's large and varied Jewish community, since Jews formed the majority of the town's population, with a wider social and educational mix than any he had so far encountered. The town's professional and business classes were strongly assimilationist, but amongst Jews of Weizmann's social background the new Hibbat Zion movement had taken hold. Its local leader was Rabbi David Friedman, who had been a leading figure at the Katowice conference. As Kornienko had done with chemistry, Friedman clearly fired the adolescent Weizmann, who worshipped in the synagogue attached to his house, and in the evenings plodded the streets of Pinsk raising money for the cause. Such was his introduction to the nascent Zionist movement with which his name was to become indelibly linked. Although he was later to become somewhat dismissive of Pinsk, this was with the experience of a great city like Berlin behind him. Unprepossessing and drearily provincial Pinsk might have been, but it shaped him just the same.
Weizmann: scientist and Zionist
At the age of 19, Weizmann decided to pursue his higher education in Germany. His opportunity came when he was offered a part-time position as teacher of Hebrew and Russian at a leading Jewish boarding school at Pfungstadt. This was evidently a miserable time for him. He was homesick, poorly fed and repelled by the prevailing assimilationism of the German Jews he encountered. After two terms, he returned home in poor health. Though Pfungstadt had been an acute disappointment, an upturn in his father's business affairs now enabled him to enrol at the prestigious Charlottenburg Polytechnikum in Berlin in 1893. Apart from a break back in Pinsk in 1895–6, Weizmann studied there until 1897 when he followed his mentor, Professor Bystrzycki, to the University of Fribourg in Switzerland, from which he graduated with his doctorate _magna cum laude_ in 1899. He now had the credentials needed to follow an academic career in chemistry, which he began as a _Privat Dozent_ , which carried no formal salary but was the vital first step, at the University of Geneva.
To his later chagrin, Weizmann was not present at the historic Basle Congress, but that did not mean that during his time in Berlin he was not fully caught up in the beginnings of Zionism nor watching these events with keen interest. There is a symmetry between his progress in Pinsk and that in Berlin. In the former, he had been inspired by Kornienko and Friedman, whereas in Berlin if Bystrzycki fostered his scientific development, his evolution as a Zionist was in no small measure the result of his association with the writer and philosopher Asher Zvi Ginsberg, who had adopted the name Ahad Ha'am, 'One of the People'. Weizmann wrote in his autobiography that he was to Zionist students like himself what Mazzini had been to Young Italy. While Weizmann was to develop a marked talent for quarrelling with his fellow Zionists, Ahad Ha'am, who died in Tel Aviv in 1927, was not one of them. However, unlike Herzl, actually having visited Palestine in 1891, Ahad Ha'am knew that the Arabs would not readily surrender to the Zionists, and sounded a warning to that effect.
Weizmann's view of _Der Judenstaat_ was that it contained nothing that was original, and that it ignored the work of others, like Birnbaum. There was certainly truth in this, but he also conceded that what gave the book its force was the personality of its author. Herzl's unique gift to Zionism was the fact that he moved from writing the book, which could have become no more than a historical curiosity, to organising and inspiring the First Zionist Congress. Weizmann should have attended this as a delegate from Pinsk, but that year his father's business fortunes declined, and he decided to travel to Moscow in an attempt, unsuccessful as it turned out, to sell a dyestuff formula he had developed. Moscow, of course, was technically barred to him as lying outside the Pale, and the difficulties he encountered made him late for the Congress.
He was able to make up for this absence at the Second Zionist Congress at Basle in 1898, and from then on was a regular attender and participant. During this time he made the acquaintance of the leading Russian Zionist, Menahem Mendel Ussishkin, an early member of the Hibbat Zion movement in Odessa. Over the years this gifted, if sometimes turbulent, man was to become a key collaborator of Weizmann, joining him in the presentation to the Paris Peace Conference, although the two parted company over the issue of partition in the late 1930s, shortly before Ussishkin's death in 1941.
Weizmann began to make his mark at the Fifth Zionist Congress in 1901 on a subject which was to capture his imagination, education, and in particular the concept of a Jewish university. In December 1901, a youth conference, largely inspired by Weizmann, led to the establishment of a group within Zionism known as the Democratic Faction. At the Fifth Zionist Congress which took place immediately afterwards, his Democratic Faction introduced a motion asking for a preparatory study for a Jewish university. Despite something of a spat with Herzl, the idea was taken forward. That there was no permanent rift between the two men was demonstrated the following year when Herzl asked Weizmann to draw up a plan for a Jewish university. Although the idea proved premature, Weizmann continued to nurse it, and it led to an important meeting. After visiting his family in Pinsk for Passover in 1903, he made his way to Warsaw to meet Nahum Sokolow, who chaired a local committee on behalf of the proposed university. It was the beginning of a remarkable partnership. Born in Russian Poland in 1861, Sokolow was an author of distinction in both Hebrew and Polish. Moving to London in 1914, he was to become an indispensable aide to Weizmann in the critical negotiations of the First World War, joining him in presenting the Zionist case in Paris in 1919, as well as writing a classic history of the Zionist movement.
Even more important during this period was Weizmann's growing attachment to an attractive young Russian medical student, Vera Chatzmann, whom he met at the Jewish Club in Geneva in November 1900. Although he was eight years her senior, Weizmann and Vera shared a love of music, and they began to meet for tea in the Café Landolt in Geneva. But Weizmann was still making his way in the academic world and increasingly involved in the world of Zionism, while Vera had her medical degree to complete.
The 'Uganda Offer'
Herzl was driven by the concept of the _Judennot_ , the need of the Jews to find relief, and confirmation that the dawn of a new century had not altered this need came with a new outbreak of pogroms in the Tsarist empire, normally associated with the activities of the monarchist societies commonly known as the Black Hundreds. Weizmann soon found himself caught up in this, Zionism's first major crisis. In the week of Passover and Easter 1903, crowds rampaged through the city of Kishinev, now Chisinau in Moldova, killing some 50 Jews, injuring over 1,000 and destroying 1,500 houses. The Kishinev pogrom, which was but the first in a series, confirmed Herzl in his pessimistic forecast of the Jews' future. At this point, on 20 May 1903, his colleague Leopold Greenberg, editor of the _Jewish Chronicle_ , had a fateful meeting with Joseph Chamberlain, the British Colonial Secretary. Chamberlain told him that Kishinev had convinced him that Herzl was right to argue that the Jews needed to get out of Eastern Europe, but questioned where they could go. The Zionists had been talking of possibilities in El Arish in the Sinai Desert and of Cyprus, but Chamberlain dismissed these, suggesting instead land in East Africa, where he believed that a million people could be settled. In subsequent communications with Chamberlain, this offer was confirmed as fertile land in what would later become Kenya, though it has always been known as the 'Uganda Offer'.
Herzl was well aware that East Africa was not Palestine, but was all too conscious of what was happening in the Russian empire, which he had just visited, and that the world's greatest empire was holding out the possibility of a rescue plan. It was on that basis that he presented the offer to the Sixth Zionist Congress in Basle in August 1903. The Congress voted on the somewhat tortured resolution that it appoint an advisory committee to assist a smaller committee which was to go to East Africa to investigate the possibility, but everyone knew that what was really at stake was the principle. The vote went in Herzl's favour by 295 to 178, but with 132 abstentions. What mattered was the nature and scale of the opposition, with which Weizmann was fully engaged. What was interesting about the opposition was that it was rooted in the large Russian delegation, including those from Kishinev, the very people whose fate Herzl sought to ease.
Weizmann, still a delegate from Pinsk, denounced the Uganda scheme at a meeting of the Russian delegation, concluding with the peroration that the British would make them a better offer. It was a sulphurous affair, in which Weizmann's father and brother supported Herzl, and it was to get still worse. Ussishkin, who had been absent in Palestine at the time of the Congress, launched a bitter attack on the Uganda project when he returned to Russia. Then the Russian leaders, the _Neinsager_ or 'Nay-sayers' as they were known, met at Kharkov to pass a resolution denouncing Herzl for violating the original Basle Programme of 1897, which had committed the movement to Palestine. With his movement in disarray, Herzl laboured throughout the winter of 1903/4 to effect some kind of reconciliation, but for some time he had been suffering from heart problems and on 3 July 1904 he died, aged only 44. The 'Uganda Offer' did not long survive him, being rejected at the Seventh Zionist Congress in 1905. Leadership of the movement passed to David Wolfssohn, a German Jew of Lithuanian birth, whom Weizmann caustically dismissed as possessing neither personality nor vision. That Zionism was now led from Berlin was to become a matter of some consequence a decade later, although that could not have been foreseen at the time.
Weizmann, Manchester and British politics
In 1904 Weizmann moved to the University of Manchester in the north of England. The circumstances are not altogether clear, but he saw no future in Geneva, and he had a good doctorate, backed up by a number of patents and research papers. Despite his opposition to it, the 'Uganda Offer' had shown that British politicians were responsive to Zionism, and he had a letter of introduction to Professor William Henry Perkin of the University of Manchester, whose chemistry department he knew had a good reputation. Perkin was willing to rent him a laboratory, and with this somewhat unpromising beginning Weizmann set about learning English and gaining a foothold in the university. It says something for his determination that by January 1905 he was ready to give his first chemistry lecture in English, and in July he was appointed assistant in the chemistry department. When Vera completed her medical degree in Switzerland the following year, the way was open for them to marry. With Weizmann often absent on Zionist business, and money sometimes scarce, it was a hard enough start to the marriage, but it survived, and Vera subsequently went on to her own distinguished medical career. Their first son, Benjamin, was born in 1907, followed by Michael in 1916.
Manchester was a far cry from the hurly-burly of continental Zionist politics, but neither was it a backwater. A highly political city, the Conservative Member of Parliament for its Eastern Division since 1885 had been Arthur James Balfour. A lifelong bachelor, communicant in both the Presbyterian Church of Scotland and the Anglican Church of England, he had an interest in philosophy beyond what was normally expected of politicians, publishing respected books on the subject. His languid manner concealed a man of steel. From 1887 to 1891, he had held the demanding post of Chief Secretary for Ireland, and his handling of that country's affairs at a particularly turbulent time had earned him the title 'Bloody Balfour' and forced him to carry a pistol for several years. Becoming Prime Minister in 1902, he presided over an administration which tore itself apart on the issue of tariff reform. At the end of 1905, he resigned in favour of the Liberals, provoking a general election. It was, of course, his Colonial Secretary who had raised the prospect of the 'Uganda Offer', and Balfour was sufficiently interested in the matter to find out why the Zionists had turned against it. The essential link was his Conservative Party chairman in Manchester, Charles Dreyfus, who was also chairman of the Manchester Zionist Society. It was Dreyfus, a keen supporter of the Uganda scheme as it happened, who recommended to Balfour that he should meet Weizmann as one of its leading opponents. It was to prove the most fateful encounter of Weizmann's life.
Their meeting took place on 9 January 1906 in the Queen's Hotel in Manchester's Piccadilly, in the midst of the general election which resulted in Balfour losing his seat. Balfour was clearly concerned to find out why the 'Uganda Offer', which he had supported, had aroused such opposition, especially since he felt that it offered a practical way forward. Weizmann responded by emphasising the spiritual side of Zionism, which he maintained could only be fulfilled by Palestine, and asked if he were to offer Paris instead of London would Balfour accept it. To Balfour's reply that they already had London, Weizmann countered that the Jews had had Jerusalem when London was still a marsh. It is difficult to gauge the real impact of this meeting, particularly since Balfour made no effort to maintain the contact, but his niece and biographer Blanche Dugdale recorded how he often referred to the conversation and the impression Weizmann had made on him. For his part, Balfour wrote in his introduction to Sokolow's _History of Zionism_ that their conversation had converted him to the view that if a home were to be found for the Jews it would have to be in Palestine. Weizmann, too, was convinced of the importance of this.
Balfour was a sophisticated political veteran, but Weizmann was also in contact with the young Winston Churchill, who, having defected from the Conservatives, was contesting North-west Manchester in the Liberal interest. The two men met on two occasions in the course of the election. As Colonial Secretary in 1921–2 Churchill was to become a major influence on the affairs of Palestine, while his later career belongs to history. In short, far from being an isolated outpost, Manchester was offering Weizmann openings in British politics which he could scarcely have imagined when he moved there, and which were to prove of incalculable value in the years ahead.
Manchester also provided him with his Zionist base. His opposition to Herzl and the 'Uganda Offer' had made him _persona non grata_ with Leopold Greenberg of the _Jewish Chronicle_ , and he was not invited to address Zionist meetings in the capital. Instead, he used Manchester as a base to tour the scattered Jewish communities in the cities of the north of England, as well as in Glasgow and Edinburgh. These poor Jewish groups responded to him in a way in which the British Jewish elite did not. In 1909, many of the most prominent Anglo-Jewish figures, including Leopold de Rothschild, Claude Montefiore, Sir Philip Magnus, Robert Waley Cohen and Osmond d'Avigdor Goldsmid, denounced what they saw as opinions which alienated them from other Englishmen. They were supported in this by the Chief Rabbi, who issued a statement to the effect that the Jews were a religious community and not a nation. This was a portent of the opposition Weizmann was to face in 1917.
In 1907, Weizmann undertook his first visit to Palestine, a climactic moment in his life. It was his introduction to the land which had long been the focus of his dreams. If his autobiography is to be believed, the experience was not altogether positive. He particularly disliked Jerusalem, whose Jewish life he castigated as lacking in dignity and existing on charity. His attitude did not greatly change over time, it seems, although he did note the potential of Mount Scopus for erecting a building which could reflect the city's Jewish legacy. What, of course, he was encountering in the city was the community of pious, often elderly, and generally poor Jews who were supported through the _Hallukah_ , charitable collections taken in the synagogues of Europe. Although this system had existed for generations, Weizmann, the modern man of science, could not believe that its dependants had anything to offer a future Jewish homeland. Neither was he greatly impressed by many of the more recent Jewish colonies, since they, too, he felt, were dependent on charity, albeit of a different kind. Nor did he like the fact that they were employing Arab labourers. However, he did note with approval a number of settlements where recently arrived Russian Jews, who had come into the country from 1904, were offering better hope for the future through the enterprise they were showing, not least through their ability to compete with Arab labour.
Although he never forgot his origins in the Pale, and regularly sent money home to help his younger siblings with their education, Weizmann was becoming increasingly settled in England, and his ties with Pinsk were becoming more tenuous, especially with the death of his father in 1911. His scientific reputation was also growing. By 1913, he could claim an enviable list of patents and scientific papers. When Perkin moved to the chair of chemistry at Oxford in 1913, Weizmann felt that the quality of his research and commitment to teaching made him an obvious candidate to succeed him, but the Manchester chair went to a rival candidate, while Weizmann had to console himself with the new title of Reader in Biochemistry. While professorships at British universities were less common than they have since become, and there was certainly no shame to his failure to get the chair, equally there is no doubt that Weizmann regarded what had happened as a major setback. An alternative did present itself in the form of an invitation to head a department in the Zionist Organisation in Berlin, but while in his disappointment he was tempted to accept, Vera absolutely refused to go. Weizmann swallowed his pride and remained in Manchester, with what fateful consequences for Zionism we now know.
That he would soon rise to the summit of the movement was far from obvious. Wolfssohn still directed affairs from Berlin, while others, Ussishkin, Sokolow and Ha'am amongst them, were established figures, as were the distinguished authors Israel Zangwill and Max Nordau, whose writings had put them at the forefront of intellectual life, while the American Louis D Brandeis was about to come to the fore in that vibrant Jewish community. Although we know a great deal about the Zionist movement before 1914, much more than is known about the state of Arab aspirations, the fact remains that its prospects were problematic. The Turks were in no mood to surrender anything of their position in Palestine to the Jews, any more than they were to the Arabs, who were a considerable majority of the population.
Ottoman diplomacy and the European crisis: Germany and Britain
Historically, the European powers which had been most concerned in the affairs of the Ottoman Empire had been Austria, Britain and Russia, although the French and Italians had also managed to rob it of North African possessions. Unlike them, Germany had not attempted to plunder the empire, but in the late 19th century Berlin took an increasing interest in its affairs. This was powerfully symbolised by Kaiser Wilhelm II's state visits in 1889 and 1898. On the latter occasion he visited Damascus and Jerusalem, where a breach had to be made in the city's historic wall at Jaffa Gate to allow his somewhat theatrical entry on a charger. It was Germans who constructed the Hejaz railway and, more significantly, from 1899 the ambitious railway which was projected to run from Istanbul through Anatolia to Baghdad and Basra. Under the auspices of the Baghdad Railway Company, construction began in 1903, but such was the difficult nature of the terrain that it was never to be completed. German and Austrian banks also financed the Oriental Railway linking the capital with Central Europe and German finance was behind the city's electricity and telegraph services.
This economic penetration of the empire was not unique to Germany, however. Anxious to bring their armed forces more into line with those of their European rivals, the Turks looked for help to the two obvious candidates, the British to overhaul their navy, the Germans to reform the army. A British naval mission led by Admiral Arthur Limpus arrived in 1912. The money to transform the navy was raised through enthusiastic public subscription, patriotic women even selling their hair, with the result that in 1911 work began on Tyneside on the dreadnought battleship the _Reshadieh_ , while in 1914 another dreadnought then being built in Britain for the Brazilian navy was purchased as the _Sultan Osman I_. With these two powerful vessels due for completion in the summer of 1914, the Turkish navy would have become a force to be reckoned with, especially in the Black Sea where the Russians had no warships able to match them, and against the Greeks in the Aegean.
German influence in the army went back to 1883 when Colmar von der Goltz had headed a military mission, beginning his years of exemplary service to the empire, which were only brought to end with his death from typhus while commanding in Mesopotamia in 1916. A new German mission came in 1913 under Liman von Sanders. Yet, while Germany's economic and military influence in the empire was marked, this did not mean that the Sublime State would automatically enter any future conflict on its side. Anglo-French influence remained well entrenched in the economy. Armstrong Vickers owned the docks on the Golden Horn, while British interests predominated in such diverse economic areas as the Euphrates and Tigris Steam Navigation Company, Istanbul's telephone system and the Ottoman Bank, as well as in the navy. The French, too, had a significant economic presence. On 28 June 1914, however, when Archduke Frank Ferdinand, heir to the Austro-Hungarian Empire, and his wife Sophie were assassinated in the former Ottoman city of Sarajevo, events were set in train which four years later saw the Middle East transformed in ways which few could have envisaged.
2
# Wartime Promises and Expectations
What the future of the Middle East might have been if the world had not gone to war in 1914 no one can now tell, but what is indisputable is that the First World War had a dramatic impact on the region, leaving a legacy that remains to this day. Once war began, it soon became clear that this was a struggle on an epic scale, forcing the powers to speculate on what a peace settlement might look like. It was not inevitable that the Ottoman Empire would enter the war on the side of the Central Powers, but in November 1914 the rulers of Turkey joined their fate to that of Berlin and Vienna. Despite the fact that Turkish military forces were less technologically advanced than those of the other powers, Germany and Austria-Hungary had gained a major asset.
The Turks threatened Britain at two key points in the Middle East. The first was the Suez Canal through which Britain was drawing troops and supplies from India, Australia and New Zealand. The other was the Persian Gulf, the source of oil for the five fast battleships of the _Queen Elizabeth_ class, the cutting edge of the Royal Navy. Turkish troops were ominously close to the recently developed British oil facilities at Abadan, across the Persian border. Just as dangerous to the Entente powers was Turkey's appeal in the Islamic world, through the office of Caliph, since France recruited widely in her North African territories, while the Indian Army, the British Empire's sole professional reserve, drew heavily on the Muslim community in the north-west of the subcontinent. Moreover, the fertile plains of the Punjab were dangerously close to the turbulent Muslim tribal regions of the frontier bordering on Afghanistan, where Britain's writ was precariously held by eight regular British battalions and their Indian compatriots of the Punjab Frontier Force. From their stations at Quetta and Mardan, guarding the mountain passes and the crossings of the Indus, these men were the sentinels of British India, but many were Muslims. Finally, Turkey had a long frontier with Russia, whose armies were hard pressed enough at the hands of the Germans and Austrians. The Ottoman Empire held the strategic Straits of the Bosphorus and the Dardanelles, control of which blocked the British and French from using that route to the Black Sea ports to assist their Russian ally. There was never any doubt that war with Turkey would have to take second place to the main fronts in Europe, but neither could it be ignored in Petrograd, Paris, and especially London. Far too much was at stake for that.
Turkey's entry into the war
In the febrile diplomatic climate following the Sarajevo assassinations, the Turks explored where their best options might lie. Cemal made overtures to the French, who were not interested. Russia, it seems, was the main Turkish preoccupation, understandably so. On 22 July, the day before the fateful Austro-Hungarian ultimatum to Serbia, Enver opened negotiations with Germany. Turkey's strategic and military importance had been well understood in influential German circles. In his celebrated book _Germany and the Next War_ , published in 1912 but running through many editions, General Friedrich von Bernhardi noted the strategic threat posed by Turkey to the British position in Egypt as well as the possibility that pan-Islamism might shake Britain's hold on India. On 2 August, with Austria-Hungary and Serbia already at war and the day after Germany's critical declaration of hostilities against Russia and general mobilisation of its army, Germany and Turkey concluded a secret alliance treaty. Bizarrely, in view of all that had passed between Vienna and Berlin, it pledged the two countries to neutrality in the Austro-Serb conflict. In the event of active military intervention by Russia, thus giving Germany a _casus foederis_ with regard to Austria-Hungary, this _casus foederis_ would also apply to Turkey. With Germany's declaration of war on Russia this had already been overtaken by events. Germany also pledged itself to placing its military mission at Turkey's disposal, while the Turks agreed that the mission should have an effective influence on their army. Finally, Germany promised to defend Turkish territory. What is plain is that fear of Russia was the key to the operation of the alliance. Whether the agreement firmly bound Turkey to enter the war on Germany's side is less clear, since two months were to elapse before hostilities began against the Russians. The ambiguities and apparent inconsistencies in the treaty almost certainly reflect the fact that it was being drafted as the hectic diplomatic events in Europe unfolded. Even so, it is instructive of the way Turkish thinking had gone, as well as the direction a future military relationship would take.
Unaware of the treaty, but conscious of the strength of German influence, the British played for time. One reason for this was the view of Lord Kitchener, now Secretary of State for War, but with a wealth of Indian and Egyptian knowledge behind him, that Britain had to avoid war with Turkey until the troops of the Indian Army, then being rushed to the European front, had passed through the Suez Canal. It is too easily forgotten that the only professional reserves at the British Empire's disposal on the outbreak of the First World War were the men of the 3rd Lahore and 7th Meerut Divisions and the Secundrabad Cavalry Brigade of the Indian Army, which arrived safely in France from the end of September. What the British war effort would have been without them, Sikhs, Dogras, Baluchis, Jats, Punjabi Muslims, Garwhalis, Pathans and Nepali Gurkhas, trained for the mountain warfare of the North-West Frontier of India but now deployed on the very different and unfamilar plains of France and Flanders, is hard to imagine. Critically for the British war effort, they did come through the Suez Canal without hindrance.
It is a paradox that what helped persuade Turkey's rulers towards war against the Entente powers was not so much the army's link with Germany but a series of events affecting the navy, where British influence under Admiral Limpus was strong. This chain of events began on 28 July 1914 with the decision of the First Lord of the Admiralty, Winston Churchill, to acquire the two battleships under completion, and on 3 August the British embassy was told to inform the Turks that the _Sultan Osman I_ , which was about to embark on sea trials, was being requisitioned. In doing this, Churchill was undoubtedly motivated by the considerable additional strength these two powerful ships would bring the Royal Navy's battle line, but his action provoked predictable fury in Turkey. Compensation was, however, at hand from an unexpected quarter. On the outbreak of war, Germany had a small squadron in the Mediterranean, the modern battlecruiser _Goeben_ accompanied by the light cruiser _Breslau_ , commanded by Admiral Wilhelm Souchon. After a brief action in the western Mediterranean, the squadron was ordered to head for Istanbul, instead of the Austrian naval base at Pola in the Adriatic, as the British commanders seem to have assumed. Evading the Royal Navy's hapless pursuit, on 10 August the two ships entered the Dardanelles and the following day were purchased by the Turkish government, in response, so the British were informed, to their detention of the _Sultan Osman I_. While not equal to the gunpower of the two ships seized by the British, they were modern vessels well able to dominate the Black Sea, and their presence in Istanbul under the Turkish flag immeasurably strengthened the German link.
On 29 October, Admiral Souchon forced the issue. Now commanding the Turkish ships _Sultan Selim_ and _Midilli_ , as his command had been renamed, he bombarded the Russian Black Sea ports of Odessa, Sevastopol and Novorossisk. War with Russia, France and Britain followed immediately. On 14 November, the Sultan issued a call for jihad, or holy war, against the three enemy powers, but, contrary to the hopes and expectations of men like Bernhardi, throughout most of the Islamic world this fell with a dull thud. In India, the influential Nizam of Hyderabad issued a _firman_ rallying Muslims to the Allied cause, and, even more significantly, the call drew no support from Sherif Hussein, the Guardian of Islam's Holy Places.
Weizmann and Britain's war aims
The fate of Turkey now became an Allied war aim. This was evident almost from the start. On 9 November 1914, the British Prime Minister Herbert Asquith made a speech in London's Guildhall in which he raised the future of the Ottoman Empire. In an early move, Egypt was proclaimed a British protectorate, erasing the fiction of Ottoman suzerainty. The possible fate of Palestine also excited the interest of the distinguished Liberal Herbert Samuel (1870–1963), Member of Parliament for Cleveland. A first-class graduate of Oxford University, Samuel had already made his mark in British history by becoming the first Jew to sit in the Cabinet, if we discount the Anglican Benjamin Disraeli. A representative of the assimilated Jewish elite that Weizmann instinctively distrusted, Samuel, by his own admission, had taken no real part in Zionism until the war with Turkey gave him cause to think about it. On the same day that Asquith delivered his Guildhall speech, Samuel visited his Cabinet colleague the Foreign Secretary Sir Edward Grey, arguing that in the event of a Turkish defeat they should think about the possibility of a Jewish state in Palestine.
Meanwhile, Weizmann, who had made a difficult journey back from an attempted family holiday in Switzerland, was also alive to the new possibilities, and here again the Manchester connection proved to be invaluable to him. A useful conduit proved to be a bright young journalist on the _Manchester Guardian_ and Zionist colleague in the city, Harry Sacher. Shortly after his return to Manchester, Weizmann met over dinner C P Scott, editor of the newspaper for over four decades and a man with ready access to the highest reaches of the Liberal Party. Evidently intrigued by his new acquaintance, Scott invited Weizmann to his house to discuss Jewish affairs. After Weizmann had confided in him his hatred of the Russian Empire, which was candid of him given that the two countries were fighting on the same side, and spoken of the Jewish hopes for Palestine, Scott pointed out that there was now a Jew in the Cabinet, adding that he would like to put him in touch with the Chancellor of the Exchequer, David Lloyd George.
Seizing the opportunity, Weizmann followed up the meeting with a letter to Scott on 12 November, in which he argued that if Britain could encourage Jewish emigration to Palestine as a British dependency, then the Jews could develop it and help safeguard the Suez Canal. This was precisely the line of argument which he was to refine over the next few years, and which would form the basis of the case he eventually placed before the Peace Conference. Equally, there is no doubt that Weizmann instantly grasped the implications of Asquith's Guildhall speech, since on the same day of his letter to Scott he also wrote to Ahad Ha'am in quite excited terms, saying that the speech should prompt them into action, and that in the event of victory Britain would be in control of Palestine.
Scott proved to be as good as his word. At a breakfast meeting with Lloyd George on 27 November, he raised the future of Palestine. Lloyd George seemed interested in the idea of some kind of partly Jewish state, and revealed that Samuel had already discussed this with him. He responded positively to Scott's idea of a meeting with Weizmann, suggesting that this should also include Samuel. This could not take place for a couple of months, but Scott had opened up a crucial contact, since Lloyd George was destined to be in a position to shape the course of events. While that lay in the future, Lloyd George was already one of the leading, not to say most contentious, figures in British political life. Born in Manchester in 1863 of Welsh origin, he had been Chancellor since 1908, had played a significant part in the search for an Irish settlement between 1912 and 1914, and was to go on to hold the key offices of Minister of Munitions in 1915–16 and Minister of War in 1916. Then, in December that year, he replaced Asquith to lead Britain to victory in the war, and came to play a central role in the subsequent Peace Conference.
Weizmann had his first meeting with Samuel on 10 December 1914. Samuel revealed that he had been quietly watching Zionism for some time, and that with Turkey in the war, the realisation of its aims was possible. He wanted Weizmann to keep in contact. The promised meeting with Lloyd George took place over breakfast on 15 January 1915. The account Weizmann gave in his autobiography, which places the meeting in early December 1914, says that Samuel, Scott and the Labour MP Josiah Wedgwood were also present. In general, Lloyd George seemed well disposed to what he heard from Weizmann, advising him that he could expect opposition from the assimilation-supporting Jewish community, and especially from the rising Liberal politician Edwin Montagu, who was, as it happened, Samuel's cousin. Weizmann also recollected that Samuel revealed the fact that he was preparing a memorandum which he was going to give to the Prime Minister.
Although Samuel never actually joined the Zionist Organisation, he pressed ahead with his memorandum, which he first circulated to colleagues in January 1915, followed by a revised version in March. What he argued was that, lying as it did so close to the vital artery of the Suez Canal, Palestine should not be allowed to fall under the control of a major European power such as France or Germany. Instead, he suggested that it should become a British protectorate. On the question of Zionism, he admitted that the time was not ripe for the creation of a Jewish state in Palestine, but that under a British protectorate regulated Jewish immigration could lead in time to a Jewish majority which could be granted some form of self-government. It does not seem that Samuel's document excited any great degree of interest amongst his colleagues. Asquith, in particular, was totally dismissive, but, just the same, the idea of a future British administration in Palestine which could encourage Jewish aspirations had entered into political discourse at the highest level. Its time had not yet come, but it would, and Samuel made sure that Weizmann and Scott were aware of feelings in the Cabinet.
What he learned from Samuel of the Cabinet's response prompted Weizmann to gather his thoughts together in a long letter to Scott on 23 March. He now believed that the mood in Cabinet was sympathetic to the realisation of Zionist aspirations in Palestine, and to their presentation at a peace conference, but that there was a reluctance to make the country a British responsibility. What he was referring to was a section of Liberal opinion which was opposed to a policy of annexation. On the other hand, there was the belief that Palestine should not come under another major power. That led him to the conclusion that Palestine should be a temporary British protectorate, to the mutual advantage of Britain and the Jews. Such an arrangement, he argued, would help guard the Egyptian border, earn Britain the thanks of Jews around the world, and enable the Jews to act as a bridge between East and West.
It is clear that both Weizmann and Samuel were working in the same direction. That this was the case was confirmed by Scott on 15 April when he related to Weizmann a dinner conversation with Samuel and Lloyd George in the course of which they had raised the question of Zionism. Samuel had spoken warmly about it, and Scott observed to Weizmann that Lloyd George was more important than Asquith, correctly as events were to demonstrate.
The Ottoman Empire at war
These events in London took little account of the unfolding war in the Middle East, where the Turks were proving to be redoudtable fighters, despite some initial setbacks. In the winter of 1914/15, Enver led an Ottoman army to destruction in the snows of the mountains of eastern Anatolia on the Caucasian front, which stretched far from the nearest Ottoman railhead, but lay conveniently close to the Russian broad gauge rail network. In the south, Cemal pushed to the Suez Canal, which some of his units managed to cross, but the Egyptians failed to rise against their British overlords who drove the Turks back into Palestine. Unsuccessful in their attacks, the Turkish army then scored two notable victories in defensive battles. It beat back the British-Anzac and French attempt to break through the Gallipoli peninsula to Istanbul in 1915, and checked a British advance from Basra to Baghdad the following year, surrounding a British force and forcing it to surrender at Kut al-Amara. It was the high point of the Ottoman war effort, which had an effect on Allied perceptions. The British army came to respect 'Johnny Turk' as a good fighter, but Allied governments and diplomats vowed revenge: the Turks' successful defence of Gallipoli and their dogged resistance in Mesopotamia and Palestine had prolonged the war and vastly increased its cost in casualties and resources. Allied statesmen, whose miscalculations had been exposed, became determined to eliminate once and for all the danger which, they believed, the Turks posed to their empires. This difference in perceptions between soldiers and civilians was to play an important part in post-war developments, which showed that the soldiers had the more realistic view of Turkey's strength.
The bloody battles in Gallipoli, in which each side lost a quarter of a million men dead and wounded, laid the foundations of the career of the young and amibitious Colonel Mustafa Kemal. Staff Colonel Mustafa Kemal was now 34 years old. He had with some difficulty secured the command of a Turkish division held in reserve on the peninsula when the British and Anzacs landed on 25 April 1915. When the First World War broke out, he was known as an independent-minded Unionist and a critic of Enver and of the subservience of the Ottoman army to the Germans. Nevertheless his initiative and personal courage, which helped contain the first Allied landings, impressed Field Marshal Liman von Sanders, the German commander of the Ottoman troops at Gallipoli, and when the British made a second landing on the peninsula at Souvla Bay, Kemal was appointed commander of the forces that held the line against them. Later legend has it that Kemal's rising star was noticed immediately by friend and foe alike. In fact, the British did not distinguish him from other Ottoman commanders, and Enver denied him publicity in Turkey. But he won appreciation where it mattered – among other Turkish commanders. Mustafa Kemal resisted German interference in Turkish military dispositions and left Gallipoli in a huff before the Allied withdrawal in December 1915. Promoted Brigadier – the highest rank he was to achieve during the war – he was given command of an army corps which was being laboriously transferred to the Eastern Front in order to halt the Russian advance. He arrived in an area devastated by the fighting and by the deportation of the Armenians who had dominated it economically.
The Armenian question
Armenian nationalist revolutionaries had originally joined the Young Turks in the ranks of the opposition to Abdülhamid II, but after the reintroduction of the Constitution in 1908 their ways parted. While the Young Turks' ideal was equality in a centralised state, the demands of Armenian, as of other Christian nationalists, ranged from the recognition of special rights through autonomy to outright independence for their community. Unlike Ottoman Greeks and Bulgarians, Ottoman Armenians had no existing national state which they could join. But when the Russians conquered the Caucasus, and particularly after the Russian gains at the expense of the Ottomans in 1878, the number of Armenian subjects of the Tsar increased, as Armenians long resident in the Caucasus were joined by immigrants from Turkey, who found greater scope for their energies under Christian Russian rule.
According to Armenian sources, in 1912 there were some 1.3 million Armenians in 'Russian Armenia' (the Caucasian provinces) against 1 million in 'Turkish Armenia'. True, there were tensions between the Armenians and their Tsarist rulers, who favoured their own version of Eastern Orthodox Christianity over the Armenian (Monophysite) Gregorian Church, and who fitfully pursued a policy of Russifying their subjects. Even so, as Christians, the Armenians had more in common with the Russians than with Muslim Turks, and although by the end of the 19th century they did well in both the Ottoman and the Tsarist empires, the latter was more advanced and opportunities in it accordingly more promising. The decision of the Young Turks to throw in their lot with the Germans against the Russians was a tragedy for the Armenians who found themselves divided between the two combatants. The majority kept their heads down. But for nationalist Armenian revolutionaries who had used terrorism first against their own kinsmen to gain control over them, then against the Ottoman state and occasionally against Tsarist officials they disliked, the Ottomans' calamity was the Armenians' opportunity.
Disaster threatened to overwhelm the Ottoman state in 1915 when the Western Allies landed in Gallipoli and the Russians advanced deep into eastern Turkey. Armenian revolutionaries had been preparing for that day. They had infiltrated fighters and stockpiled arms in eastern Turkey; they had formed volunteer units to help the Russian army. As the Russians advanced, Armenian nationalist revolutionaries organised uprisings and acts of sabotage behind the Ottoman lines. This compromised the Armenian community as a whole. In April 1915, the Young Turk leadership – and Talât in particular – became convinced that the removal of all Armenians from the war zone and from the vicinity of the railways leading to it was a military necessity. It would also remove once and for all the threat of losing yet another portion of the Turkish homeland to local Christians who, as experience showed, would, if successful, get rid of their Muslim neighbours by fair means or foul. For centuries Muslims and Christian Armenians had lived in reasonable amity side by side to their mutual benefit. Now fear and hatred gripped both communities, many of whose members became convinced that they were faced with a stark choice: kill or be killed.
Large-scale deportations have not been rare in history. The Ottomans had transferred their unruly kinsmen, the Turcoman tribesmen, from Asia to their new conquests in the Balkans; they had also moved Christian Armenians and others to repopulate Istanbul after the conquest. They had received Jews and Arabs deported from Spain after the reconquista, and then from the 18th century onwards, hundreds of thousands of Muslims forced out of the Balkans, southern Russia and the Caucasus.
In the 19th century, more than a million Circassians were expelled by the Russians from the Caucasus. Hundreds of thousands of them perished before they could start a new life in the Ottoman Empire. Many of the survivors were resettled in eastern Anatolia, which Armenian nationalists were claiming for themselves. The Circassians were a martial people: some of the refugees preyed on settled Ottoman subjects, others found employment in the Ottoman army and gendarmerie. In 1915, as the Russians threatened them again in their new homes, discipline could not restrain the Circassian gendarmes. In some instances, instead of protecting Armenians during the deportation, they killed them. In any case, the best-trained gendarmes had been sent to the front and their duties in the Ottoman countryside had been taken over by raw recruits, including released convicts. In some cases gendarmes escorting columns of deported Armenians sold them to Kurdish tribesmen who robbed, and then killed, the Armenians and raped their women. Undisciplined gendarmes, Kurdish tribesmen and bandits of all sorts, whose numbers had been swollen by deserters, took a heavy toll of the deportees. Others died of malnutrition and disease, which affected even larger numbers of Muslims, for as Armenian civilians were driven south to Syria, at least as many Muslim civilians – Kurds and Turks alike – were fleeing west from the advancing Russians and their Armenian auxiliaries.
In absolute numbers more Muslims than Armenians perished in Anatolia, but while Armenian deaths from all causes accounted for more than a third of their community, the Muslims lost one-fifth, and remained in possession of the land. Moreover, the sufferings of the Armenians were well documented. There were American missionaries and consuls in the area, as the United States was not at war with the Ottoman Empire; German officers and civilians also witnessed atrocities. The sufferings of the Muslim population passed largely unnoticed by Western observers. Even so, the fate of the Armenians was a gift to Allied propagandists, and could be used to counter Austro-German accusations of Russian atrocities against the Jews, who had similarly been deported from the war zone in their hundreds of thousands.
Britain and the Hashemites
The failure of the Gallipoli campaign, and the overriding demands of the Western Front, meant that the British had to look for potential allies against the Turks, and fortunately for them links already existed. In February 1914, Sherif Hussein's second son Abdullah, who was a member of the Ottoman parliament, had paid a visit to the British High Commissioner in Egypt, Field Marshal Lord Kitchener. The visit was, to all intents and purposes, a courtesy call. However, Abdullah took the opportunity to tell Kitchener that there was a growing crisis in the Hejaz between the Sherif and the new Turkish _Vali_. He requested British support in the event of an attempt to depose his father. Specifically he asked that they use their influence with Istanbul and block Turkish troops from being transported through the Suez Canal.
This support, which was unlikely to have been granted, was not needed. It was soon reported that the differences between Hussein and the Turks had been settled amicably. However, the British continued to hear of persistent rumours of dissatisfaction in the Ottoman Arab world. At a subsequent meeting in April 1914 with the Oriental Secretary to the British Residency in Cairo, Ronald Storrs, at the Khedive's palace in Cairo, Abdullah reported that negotiations in Istanbul had not gone well and his father had requested that he ask the British government to enter into a quasi-protectorate with the Emir of Mecca that would forestall any Turkish aggression. There was no prospect of this in April 1914. Britain's relations with the Ottoman Empire, while not having the warmth of hitherto, remained fundamentally correct. The following day, after consulting Kitchener, Storrs told Abdullah he could not expect any British support, although Elie Kedourie suggests that the rejection was not as categorical as it seemed. However, Storrs, Kitchener, the Governor-General of the Sudan Reginald Wingate, and the intelligence department in the British-run Egyptian War Office all appear to have recognised that the situation in Arabia in 1914 afforded opportunities for the British government to exploit should the Ottomans go to war against the Entente.
In September 1914, Kitchener ordered Storrs to reactivate contacts with Abdullah, as it became increasingly evident that Turkey was likely to enter the war on the side of the Central Powers. He was to ascertain the attitude of Sherif Hussein should hostilities break out between the Entente and Turkey. Abdullah, in a guarded reply, confirmed that the Hashemite position was essentially favourable to the British, though it appeared that there would be no outright rebellion against the Ottomans unless they struck first to circumscribe the independence of Hussein. The British replied that they would protect Hussein against aggression, but also raised the tantalising possibility that a favourable outcome of the war might include the replacement of the Ottoman Sultan as Caliph by an Arab figure. Storrs, who was ordered to transmit the reply, may have greatly exceeded his instructions from London, promising much more wide-ranging support to Hussein and the Arab cause than he was authorised to give. Hussein, on 8 December 1914, replied that he could not break with the Ottomans at present but would do so should a suitable moment arrive. He also stated that 'there no longer exists a Caliphate... for their [the Ottomans'] rule projects... deeds that are all contrary to religion. The Caliphate means this, that the rule of the book of God should be enforced, and this they do not do.'
Storrs seems to have taken further local initiatives without referring to London, which committed Britain almost completely to the general cause of Arab nationalism and an Arab Caliphate. Most notably, in December 1914 he issued a sweeping proclamation from the government of Great Britain to the natives of Arabia and the Arab provinces, pledging support for Arab independence and declaring that the Caliphate was the right of a member of the Prophet Muhammad's tribe, the Quraysh, i.e. someone like Sherif Hussein. This was followed in April 1915 by a pledge to support Arab independence, declaring British opposition to annexations by any of the Great Powers in the Holy Places or the Arabian Peninsula. These British assurances appear to have done enough to keep Hussein in play.
The evolution of British policy towards the Arabs
By the spring of 1915, the British were beginning to think seriously about the ultimate fate of the Ottoman Empire. Kitchener, in a remarkably prescient paper in March, proposed that 'it is to our interests to see an Arab Kingdom established in Arabia under the auspices of England, bounded in the north by the Valley of the Tigris and Euphrates and containing within it the chief Mahomedan Holy Places, Mecca, Medina and Kerbala'. Kitchener believed that in the aftermath of victory, Russia's position in the Middle East would be immeasurably strengthened and that Britain needed to think of acquiring territory or influence from the Mediterranean to the Persian Gulf to protect the route to India. Indeed, he gave serious consideration to the construction of a railway from Alexandretta on the Mediterranean coast to Basra at the head of the Gulf on which British forces could be rapidly deployed to reinforce the India garrison. There was a general disagreement in the Cabinet as to what Britain should seek. Asquith, while sharing Sir Edward Grey's disquiet about a territorial carve-up, concluded that if a scramble for Ottoman possessions took place, Britain would be neglecting its duty if it did not seek something for itself.
In April 1915, the government appointed a committee chaired by Sir Maurice de Bunsen to examine what Britain's likely interests would be in the event of a Turkish defeat, particularly since France and Russia would also be eyeing up the possibilities. While its work had no practical effect, its deliberations do indicate the direction of British thinking on the region, even at this stage of the war. One possibility was of an empire reformed along federal lines, which would give national self-expression to Turks, Arabs and Armenians. The British liked federal schemes, as they had shown in Australia, and were to try them in other parts of their empire, mostly without success. But in the event of a break-up of the Ottoman Empire, de Bunsen's committee recommended that Britain should acquire Mesopotamia from Basra at the head of the Persian Gulf to Mosul, her oil interests in that part of the Middle East being paramount. This area would be connected to the port of Haifa. The French would have their interests recognised in the districts around Damascus and Beirut, while the Straits would go to Russia, fulfilling a long-standing ambition for access to the Aegean and Mediterranean. Palestine would require special agreement amongst the three Christian allies, Protestants, Catholics and Orthodox each having interests there. Muslim and Jewish interests were of less importance, it seems.
Meanwhile, in January 1915, Sir Henry McMahon had become High Commissioner in Egypt in succession to Kitchener. He began taking tentative soundings on how to encourage the Arabs to split with the Ottomans. In the east and centre of the Arabian Peninsula the British were enjoying considerable success in acquiring support from the smaller Arab tribal rulers: the Emir of Kuwait, Ibn Saud, then ruler of Nejd, and the Idrisi of Asir had all been brought firmly into the British orbit by mid-1915. At the same time, Hussein was coming under growing pressure from the Turks openly to support the Caliph's call for jihad. Indeed, he was showing considerable support for it in theory, though in practice this amounted to little more than the staging of a few demonstrations. Instead, Hussein emphasised to the Turks the vulnerability of the coast of the Hejaz to British attacks from Egypt and the Sudan. In secret, though, Hussein was plotting bolder moves – an alliance with the British. The motivation for this is unclear. It is claimed that Hussein's main ambition was to become Caliph, yet there is little evidence of his Arabism at this point. Rather, a key factor in motivating his disillusion with the Ottomans appears to have been his uncovering in January 1915 of a plot to unseat him by the CUP. Only the outbreak of war had prevented its implementation.
In March 1915, Hussein, still inclined to seek compromise with the Turks, sent his son Feisal with the incriminating documents about the attempted plot to the Grand Vizier in Istanbul. This may have been an elaborate subterfuge to allow Feisal to make contact in Damascus with the Arab nationalist groups _al-Fatat_ and _al-Ahd_. However, Feisal's initial impressions of these were that they were insufficiently strong to revolt against the Ottomans without the support of outside powers. Feisal proceeded to Istanbul, where he stayed for a month attempting to reach agreement with the Turkish government over the issue of the plot against his father. The leading figures in the government, the Sultan, the Grand Vizier, Talât and Enver all disavowed any knowledge of the plot and promised to transfer the Turkish governor. However, the Turks also made clear that they would not go any further to strengthen Hussein's position until he fully endorsed and declared jihad against the British. Feisal promised loyalty to the Sultan and agreed to provide forces to help the upcoming Turkish attack on Suez. However, this was a tissue of lies. In reality, he was deeply dissatisfied with the Turks and confirmed his view that the present situation could not continue.
On his way back to the Hejaz in May 1915, Feisal stopped off again in Damascus to consult with the nationalists. They had been grievously weakened by a Turkish crackdown since the last meeting. Many of the Arab-manned Ottoman divisions in the Fertile Crescent had been broken up and their troops sent to the fronts at Gallipoli and the Caucasus. There was little or no prospect of a successful rebellion centred on dissident army officers in Syria. The nationalists urged the Hashemites to seek an agreement with the British on the basis of terms they had agreed and drawn up in the document referred to by Antonius as the 'Damascus Protocol' and to go into open revolt against the Sultan. The document set out the terms under which the Arabs would form an alliance with Britain and take up arms against the Turks. It was a wide-ranging demand for independence of all the Arabic-speaking territories of the Ottoman Empire. Feisal was sceptical that it would be acceptable to the British. He also had little hope that a revolt would succeed. In spite of his doubts, however, this document formed the essence of Hussein's first letter in July 1915 to McMahon.
Feisal continued to hedge his bets at every stage: again promising support from the Hejaz to Cemal, who had been Turkish commander in Syria since December 1914, and who frequently and forcefully beseeched Hussein to declare jihad. Feisal, while an advocate of revolt at some stage, was cautious about the timing. When he, his father and his brother Abdullah met for a council of war in June 1915, Feisal stated that he was anxious to see Turkey significantly weakened before the Arabs took the field. Abdullah, however, was anxious to proceed with all possible haste. He seems to have been motivated by a fear that, unless the Arabs moved quickly, they would lose any rights at the Peace Conference:
The war could have only one consequence for the Arabs: they would remain in the noose of [tyrannical] government whether the Turks and Germans or the French and British won; it was necessary to proclaim the Arab movement and [thus] escape through war the necessary consequence of submission to alien rule.
Abdullah was the Hashemite most committed to rebellion. This had come to the notice of the Ottoman authorities who, he claimed, tried to buy him off with offers of high office (the position of _Vali_ in Yemen). He later confided in T E Lawrence that even without the war there would have been an uprising, started by Hussein and his confederates taking pilgrims hostage during the _haj_. This action was intended to draw in the Great Powers, including Britain and France, to force a compromise, which would gain Hussein immunity from Turkish pressure in the future. This rather fanciful plan was mooted to take place in 1915, but the war had forced its postponement.
Hussein backed Abdullah's reasoning that now was the time to make a claim for a seat at the post-war peace conference. It was decided to offer the British an alliance in return for their acceptance of the demands in the Damascus Protocol. An unsigned letter from Hussein was sent to Sir Henry McMahon with a letter from Abdullah to Ronald Storrs dated 14 July 1915 enclosed.
Some historians are sceptical of Hussein's sudden espousal of Arab nationalism. Mary Wilson, for instance, sees it as essentially self-serving. Hussein's main motivation was his dislike of the secularising and centralising impulses of the CUP. Indeed, suspicion of the secular CUP leadership in Istanbul was a key motivating factor for many in the Hejaz. Hussein believed the Ottomans had forfeited their right to the Caliphate and he was the most suitable leader to assume the position. However, to have emphasised Islamic zealotry as the primary motivation for rising against the Ottomans might have led the British, who had the empire with the greatest Islamic population, to have had second thoughts about backing Hussein. It was much safer to wrap the Hashemite cause in the banner of Arab nationalism, which at this time presented no threat to British interests. Efraim Karsh goes further; the Arab Revolt:
was Hussein's personal bid for an empire. The Sherif was no champion of national liberation seeking to unshackle the 'Arab Nation' from the chains of Ottoman captivity: he was an imperialist aspirant anxious to exploit a unique window of opportunity for substituting his own empire for that of the Ottomans.
Historical opinion is united in agreement that Hussein's motivations had little to do with Arab nationalism. However, there is dispute about what Hussein's ambitions actually were. Were they to build a personal empire or to win the Caliphate? The evidence remains unclear.
The McMahon-Hussein Correspondence
By July 1915, the British position in the Middle East had deteriorated substantially. The Anglo-French attack on Gallipoli, aimed at dealing a knock-out blow to Turkey, had clearly failed and the Expeditionary Force would withdraw by the end of the year. Hussein was now in a position to secure a premium from the British for leading a revolt against the Turks. Reflecting this, Hussein's opening gambit, his letter of 14 July 1915, was certainly a bold one. (This is the first in the sequence of letters that came to be known as the McMahon-Hussein correspondence.) He demanded that he be recognised as king of an Arab state encompassing the whole of the Arabian Peninsula (apart from Aden) as far north as Mersina and bounded by the Mediterranean, the Red Sea, the Persian Gulf and Persia. This would include all of modern-day Syria, a slice of southern Turkey, Israel-Palestine, Jordan, Iraq, Saudi Arabia, the Gulf States and most of Yemen. He also wanted Britain to approve the proclamation of an Arab Caliphate. Unsurprisingly, British officials in Cairo thought Hussein's requests unrealistic. Ronald Storrs, the Oriental Secretary, later wrote: 'It was at the time and still is my opinion that the Sherif opened his mouth and the British Government their purse a good deal too wide... We could not conceal from ourselves (and with difficulty from him) that his pretensions bordered upon the tragi-comic.'
Nonetheless, the blow to British confidence caused by the setback at Gallipoli is surely evidenced by the decision not to reject out of hand what were in many respects the outrageous demands of a minor Arab potentate. Instead, via the High Commissioner to Egypt Sir Henry McMahon, the British government decided to engage in a lengthy sequence of correspondence (some ten letters) with Hussein. The McMahon-Hussein exchange culminated in a military alliance between Britain and the Hashemites that was to be maintained for more than 40 years. However, the exchanges were less clear-cut and more ambiguous regarding the political agreements that were made. In essence, the questions left unresolved revolved around the degree of Arab independence and the territorial extent of this Arab state. Why was this the case? Elie Kedourie argues that the British replies were 'at once deliberately vague and unwittingly obscure'. McMahon believed his task was to tempt 'the Arab people onto the right path, detach them from the enemy and bring them on to our side'. He perhaps crafted the correspondence more carefully than he is sometimes given credit. It was in British interests that Hussein might think that more was on the table than was really being offered, while at the same time, the vagueness of the correspondence meant that the British promises would contain so much ambiguity that no objective reader would be able to decipher what exactly had been promised. The words chosen allowed a certain degree of deniability.
McMahon's first response was sent on 30 August 1915. It was an understandably evasive reply supporting the liberation of the Arabs from Turkish rule and an Arab Caliphate. However, McMahon felt it was premature to discuss boundary details in the heat of war, while Turkey remained in occupation, and when there were increasing signs that Hashemite influence in Syria was very weak and the Syrian Arabs were tending to align themselves with the Ottomans. Hussein replied on 9 September demanding a precise delineation of the boundaries of the putative Arab state. He wrote, ominously, that a failure to deal with the matter might be taken 'to infer an estrangement or something of the sort'.
It is possible the correspondence might have ended at this point in disagreement or that the British would have taken a stronger line with Hussein. However, new developments had occurred: primarily a secret mission to Cairo by Muhammad Sherif al-Faruqi, an Arab staff officer in the Ottoman army and apparently a leading figure in the Arab nationalist group al-Ahd. In an interview with Brigadier-General Gilbert Clayton, Chief of Military Intelligence in Cairo, in the autumn of 1915, he revealed that Syrian Arab nationalist societies would take up arms on the side of the British. In return for this they wanted explicit British support for an independent Arab state. If they did not get such an assurance, they would provide full support for Turkey and Germany in the war. It is now generally accepted that al-Faruqi exaggerated the strength of Arab nationalism and his contacts with the Turks and Germans. There is no evidence that the Turks had any interest in appeasing Arab nationalism and the Germans would not lightly have undertaken negotiations behind the back of their ally. Nonetheless, the interview and the reports that were drawn from it appear to have led British officials and soldiers in Cairo to conclude that a deal acceptable to Sherif Hussein must be put on the table as soon as possible. Lord Kitchener in London was strongly supportive of keeping the Arabs on side. 'You must do your best to prevent any alienation of the Arabs' traditional loyalty to England', he stated unambiguously. He may well have believed that an Arab rebellion in Syria led by dissident army units might still save the Gallipoli campaign, which was teetering on the edge of collapse.
McMahon was given considerable leeway in drafting a reply by Sir Edward Grey, who was reasonably well disposed to a strategy of wooing the Arabs. Grey, nonetheless, feared that promising too much to the Arabs might cause friction with the French, who would probably perceive Hussein to be a British proxy. McMahon, without fully consulting all the relevant Whitehall departments, especially India Office colleagues who were aghast when they learnt of what had been offered, dispatched his letter to Hussein on 24 October 1915. This key British pledge became so critical to the future course of relations with the Arabs, and especially to the debate over Palestine, that the key passage must be quoted:
The two districts of Mersina and Alexandretta and portions of Syria lying to the west of the districts of Damascus, Homs, Hama and Aleppo cannot be said to be purely Arab and should be excluded from the limits demanded. With the above modifications, and without prejudice to our existing treaties with Arab chiefs, we accept these limits... Subject to the modifications, Great Britain is prepared to recognise and support the independence of the Arabs in all regions within the limits demanded by the Sherif of Mecca.
What did McMahon mean, and what were the implications of what he said? Support for the independence of the Arabs seems plain enough, and was taken at face value. When, therefore, the post-war system of Mandates was put in place it was seen by the Arabs as reneging on an obligation, and treated as such. As for Palestine, on 12 March 1922, McMahon wrote to the Colonial Office, pleading that it had been his intention to exclude Palestine from his pledges to Hussein. He argued, somewhat limply, that the reason why he stopped with Damascus was that he could not think of anywhere further south that he could use for purposes of definition. A year later, Clayton, who had helped draft McMahon's letters, assured Samuel, by then High Commissioner to Palestine, that there had been no intention of including Palestine. On 23 July 1937, McMahon confirmed publicly in a letter to _The Times_ that he had not intended to include Palestine in the area which was to be the independent Arab kingdom. While these letters must be treated with some respect, it must be remembered that McMahon and Clayton were writing at a time when the future of Palestine had become a matter of acute concern, which it had not been in 1915.
It has been argued that if 'district' is taken as synonymous with _vilayet_ , (Ottoman province) then Palestine was excluded, since it lay to the west of the _vilayet_ of Syria. But this hardly stands up against the fact that there were no _vilayets_ of Homs or Hama, while there was a _vilayet_ of Aleppo, which included Alexandretta. If McMahon could not think of anywhere south of Damascus, places such as Dara'a, a rail junction with a line leading to Haifa, Amman and Aqaba, could have been identified. Crucially, of course, neither Palestine nor Jerusalem was mentioned. It is hard to escape the conclusion that by identifying districts to the west of the four cities of Damascus, Homs, Hama and Aleppo, McMahon was looking to the future of the Christian, and possibly Druze, communities of what was to become Lebanon, where Britain's ally France had long-standing interests. Whether or not Palestine was part of the area pledged to Hussein has been, and doubtless will continue to be, endlessly debated, but the essential point was that the Arabs believed it to be part of their inheritance from the British.
The Sykes-Picot Agreement and the Arab Revolt
It was in the knowledge of these negotiations, but unknown to Hussein, that Britain entered into an agreement with France in 1916, essentially dividing the Middle East between them. The Sykes-Picot Agreement, called after its authors, Sir Mark Sykes and François Georges Picot, reflected many of the ideas of the de Bunsen committee. France was to have the stretch of the Mediterranean coast north of the port of Acre, while Britain's area was to be oil-rich Mesopotamia together with an enclave around Haifa. Other Arab areas were to become British or French protectorates. What this implied for the pledge of Arab independence hardly needs stating, but what was also significant was the emergence of an entity called 'Palestine', the boundaries of which were close to what later became the British Mandate, although without the Negev Desert in the south. Palestine was to be international, since Britain was conscious of Catholic and Orthodox concerns over the Christian Holy Places, but also wished to keep the French at a distance from the Suez Canal. Cutting as it did across any sense of a united independent Arab kingdom, the Sykes-Picot Agreement was to be excoriated by the Arabs once its terms were revealed in the aftermath of the Bolshevik revolution in Russia.
Just five months later, on 5 June 1916, Hussein raised the standard of revolt, but it turned out to be rather a damp squib. Both he and Britain's Arab Bureau had greatly exaggerated the likely extent of the revolt. For example, in his letter to McMahon of 16 February 1916, Hussein implied that 100,000 Arab soldiers in the Ottoman army would defect to his revolt. The Arab Bureau strongly backed this supposition as well. However, it never happened. The vast majority of Arab troops remained scrupulously loyal to the Ottoman Empire. It would appear that the Arab Bedouin forces, virtually all irregulars, that Hussein was able to field never exceeded 15,000 men. Moreover, the geographical extent of the Arab Revolt was limited as well. No rising took place in Syria or Palestine due to Cemal's pre-emptive action in crushing potential dissidents among the Arabs in the army. Indeed, to keep the rebellion going, Britain had to lavish large amounts of money and arms on the Arabs. Direct British military involvement was limited mainly to the provision of advisers and occasional naval and air support.
The limited nature of Hussein's revolt was a disappointment to the British though they were glad to see a revolt had at least occurred. After an initial success with the capture of Mecca, the Arab forces made little progress. Utterly lacking in any tactical ability and fearful of exposing themselves to Ottoman artillery, their only other initial success was the capture of the Red Sea port of Jeddah and that was only because the British provided naval and air support. Taif did not fall until September 1916, while Turkish forces held Medina until early in 1919, months after the conclusion of hostilities. By mid-July 1916, the revolt was running out of steam. Hussein found it difficult to maintain a disciplined force in the field and desertion was rife. Feisal, the most militarily astute and the bravest of Hussein's sons, confided to Colonel Cyril Wilson in August 1916 that the Turks would prevail if they took the offensive. Soon afterwards Feisal requested British landings on the coast of the Hejaz to aid the revolt. Hussein, apparently undisturbed by his growing military problems, proclaimed himself King of the Arabs in October 1916. However, the British had become deeply concerned and at the end of 1916 it was decided to step up aid to Hussein. His subsidy was increased from £125,000 to £200,000 a month. Large quantities of rifles were also supplied – far in excess of Hussein's requirements. The subsidy was vital for the Revolt since gold, rather than appeals to patriotism, was the key to recruiting Bedouin tribesmen. However, haggling over the price often hindered the timely execution of military operations as did the general lack of discipline of the Bedouins. Battles would be broken off due to fallings-out between apparently allied tribesmen and on one memorable occasion even to stop for coffee. T E Lawrence, who became the Arabs' key military adviser from the end of 1916, was often critical of the tendency of Bedouin forces to go home with plunder before achieving their objective. The strategic direction of the Revolt was increasingly removed from Hussein's hands, with Colonel C E Wilson, commanding the British military mission to the Hejaz, and Clayton taking increasingly influential roles, Clayton coordinating much of British support for the Arab Revolt through the Arab Bureau.
The Arab Bureau
In 1916, William Reginald ('Blinker') Hall, Director of the Intelligence Division, recruited David Hogarth, an eminent British archaeologist of the Near and Middle East, to join a group of British officers and officials who would co-ordinate British dealings with the Arabs – this was the Arab Bureau, which would have an influential role in forthcoming events. Hogarth subsequently recruited one of his protégés, T E Lawrence, and an Arabist, Gertrude Bell. Cairo became the base of the Arab Bureau from March 1916. Clayton headed up the bureau and Ronald Storrs had a role as well. The Arab Bureau provided information, reports and policy briefings on Syria, Arabia and Palestine for the British government. Its most notable publication was the _Arab Bulletin_ , a confidential briefing book, which was circulated to senior British officials from spring 1916.
The Bureau is usually characterised as extremely francophobic. Clayton, Hogarth, Lawrence, Bell and the new British High Commissioner to Egypt, Reginald Wingate, certainly exhibited antipathy towards French aims in the Middle East. They viewed the Hashemites as a potential means of reducing or eliminating French influence in Syria. Some historians have tended also to view the Arab Bureau as a group of innocents and enthusiasts entirely taken in by the Arab cause and the Hashemites. They, it is claimed, were determined to see their protégés and their cause achieve at least some of their post-war goals at the expense of the French. Some historians reason that the cause of this was its members' guilt over the contradictions between the Sykes-Picot Agreement and the Hussein-McMahon correspondence. What the Arab Bureau was most interested in, however, was the expansion of British imperial interests in the Arab world. Its members saw a loose confederation nominally under Hussein but informally controlled by Britain as the best means of achieving this. They also saw this as a means of reducing, if not eliminating, French influence in the Arab World. T E Lawrence, in an oft-quoted passage written after the war, suggested the possibility of formal constitutional links between Britain and the successor Arab state of the Ottoman Empire: 'My own ambition is that the Arabs should be our first brown dominion, and not our last brown colony.'
Feisal and Lawrence
T E Lawrence, a young subaltern, the illegitimate son of an Anglo-Irish landowner, was perhaps the most important figure in the Arab Bureau, and certainly became the most celebrated. Both man of action and intellectual, his role in it was due primarily to a knowledge of the Middle East gained during his extensive travels there before the First World War. He had developed an enthusiasm for traditional Arab culture as well as a hostility towards modernisers, be they Young Turks or French missionaries and educators. Unsurprisingly, the anti-French views of the Arab Bureau influenced him as well. After a mission in early 1916 to Mesopotamia, where he witnessed the incompetent British campaign, he was ordered to Jeddah with Storrs in October 1916, with a brief to appraise the Arab Revolt. He would spend the next two years in Arabia playing a leading role in it.
Lawrence certainly had a major impact on the Revolt, which was struggling desperately by the time he arrived. It was clear by October 1916 that the Turks held the military initiative. There was no prospect of the Arabs being able to take Medina. Furthermore, there was no sign that Hussein was attracting support outside the narrow confines of the Bedouin tribes, and what support was forthcoming was entirely due to bribes funded by British subsidy.
Lawrence quickly concluded that the Revolt needed to focus around the most dynamic of Hussein's sons, Feisal: 'I felt at first glance that this was the man I had come to Arabia to seek – the leader who would bring the Arab Revolt to full glory', he wrote later. Lawrence recognised that Feisal was not without faults – he viewed him as excessively tribal in his allegiances. The alternatives, his three brothers, were far worse: Ali suffered from ill health, Zeid was too young and callow, and Abdullah, the most obvious choice, was considered by Lawrence to be too much of a politician and not enough of a statesman. In any case, Lawrence considered him militarily incompetent. He was able to persuade the head of the Arab Bureau, Clayton, of the merits of this despite some reluctance on his part. Feisal was not a universally popular choice for leadership among the Arab Bureau. Abdullah had been the most enthusiastic about launching the Revolt and, moreover, had initiated the contacts with the British. Feisal, on the other hand, had been the most reluctant to rebel. However, as the Revolt had developed, his attitude towards the Ottomans had hardened and while he remained open to the possibility of rapprochement (see below), he considered it increasingly unlikely that any acceptable deal could be reached.
Clayton became increasingly dependent on Lawrence for information on the Arab Revolt and operations in the northern Hejaz and Lawrence went from being a minor figure to a major influence due to his ability to control the information that was reaching Cairo. From November 1916, he became liaison officer to the Arab Revolt. This gave him a central role in deciding on Feisal's strategy. His control and supervision of the British subsidy and arms deliveries gave him real power. However, his brilliance was in his ability to forge a working partnership with Feisal and other Arabs by adapting himself successfully to the sensitivities of Arab culture. His tact and diplomacy helped smooth over some of the serious problems that faced the Anglo-Hashemite alliance.
There seems to be little doubt that Lawrence's arrival proved to be a major spur to the Arab Revolt. His key tactical decision was to utilise the Arabs' great advantage: their mobility thanks to their skills with camels and horses. Their great disadvantage was their vulnerability to casualties, which could not be afforded as Arab morale was extremely fragile. It was better, Lawrence recognised, to use the open spaces of the desert to avoid a war of contact but instead fight one of detachment. Attacks would only be pressed home when the Arabs had the tactical advantage. Lawrence, therefore, aligned Arab tactics and strategy with their military resources and capabilities as well the geography of the Hejaz. In his view, attacks should be generally confined to soft targets such as railway lines, infrastructure and supply convoys rather than frontal assaults on Turkish infantry, which tended to end in disaster. He saw little point in pressing home attacks on major Turkish concentrations such as at Medina. The inability of the Arabs to stand up to artillery bombardment precluded this. It was much better to leave the 25,000-strong garrison bottled up, where it remained impotent for the course of the war. Instead, little pinprick attacks, similar to the raids that were a frequent occurrence in the early 20th century Arabian Peninsula during peacetime, would keep the Arabs in the field and build up their confidence. He also allowed the Arabs to keep plunder from their attacks. It was simply pointless to enforce Western military discipline on nomadic Bedouins when they could simply up and leave if they were not happy with their conditions. In key engagements, including the capture of Akaba in July 1917, Lawrence demonstrated considerable tactical flair and the ability to exploit a military situation.
Feisal was now transformed from being one of a number of brothers to _primus inter pares_. He would eclipse his elder brother Abdullah and ultimately even his father. He became the driving Arab force behind the Revolt. Having spent much of his childhood in Istanbul, he and his brothers were not natural Bedouin. Indeed many Arabs would have considered them _effendi_ , a term describing Arabs of noble rank who had received a modern secular education and had adopted Western clothing and concepts. As soon as they returned to Mecca, however, their father had insisted that they act like Bedouin. They were sent out into the wilderness without comforts to get back to their roots. However, their upbringing isolated them from their fellow Bedouin. As Lawrence noted, the four sons of Hussein 'were natives of no country, lovers of no private plot of ground. They had no real confidants or ministers; and no one of them seemed open to another, or to the father, of whom they stood in awe.'
Lawrence and Feisal's relationship was the key to the successes that the Arab Revolt enjoyed. Feisal always gave the orders, while Lawrence merely advised. It was simply unrealistic for Lawrence to give orders to Feisal – he had to persuade him and then let Feisal direct his men. Both Feisal and his father were at times extremely difficult to deal with. Nonetheless, Lawrence and Feisal forged a useful partnership. Part of the reason for the closeness was that Lawrence was willing to confide some of the most secret aspects of British policy to Feisal. In February 1917, he explained to him that the McMahon correspondence had been superseded by the Sykes-Picot Agreement and France was going to have a major role in the post-war settlement in the region. Moving north and spreading the Revolt into Syria was the only way of forestalling French claims there. Lawrence's revelations appear to have been motivated by proposals of the small French military mission in the Hejaz to stage an attack on the port of Akaba. He persuaded Feisal that this was meant to bottle the Arabs up in the Hejaz and leave the French a free hand in Syria. Feisal now knew that it was vitally important for him to move north and take Damascus and the main Syrian cities.
The first sign that the tactics Lawrence advocated would work was seen in the attack on the coastal town of Wejh, which was far to the north of Jeddah and Mecca and would provide a base from which operations against the Hejaz railway could be carried out. It also pointed to the extension of operations out of the Hejaz and into Syria itself. Supported by British naval forces, the town fell to Feisal's men on 23 January 1917. From here, the Arabs were able to conduct their hit-and-run operations against the Hejaz railway. The Ottomans, forced to divert ever more resources into keeping the railway open, stood on the defensive for the rest of the campaign. They were, as Lawrence had desired, bottled up in Medina.
Lawrence disappeared from view for much of the spring and early summer of 1917. He went far into Syria in an attempt to ascertain for himself the extent of support from tribal groupings for the Arab Revolt. This appears linked to his desire to drive Feisal northwards. Upon his return to the Hejaz in June 1917, he directed an operation against Akaba. The capture of the port convinced the British commander in the Middle East, General Sir Edmund Allenby, of Lawrence's talent and the usefulness of the Arab Revolt. He saw Lawrence's guerrilla attacks as a means of tying down large numbers of Ottoman troops at relatively little cost to the British. For the next year, from their base at Akaba, Lawrence and Feisal led operations against Turkish forces in the towns of Maan and Amman and on the Damascus–Medina railway line, though he was never able completely to sever that link and the Ottoman garrison at Medina remained intact until well after the armistice. When Allenby and the British forces began their advance into Syria in the summer and autumn of 1918, the Arab irregular army provided a useful distraction on the flanks of the advance, though its impact tended to be exaggerated by Lawrence and the Arab leadership.
The Zionists and the British government
By 1916, then, certain key issues in the Middle East had become intertwined. At their heart was the ultimate fate of the Ottoman Empire, where Britain had entered into ill-defined commitments to their new Hashemite allies, while harbouring ambitions of its own and having to take into account the sensitivities of the French and the Russians. All of this held potential for trouble in the future, but there was, of course, the added dimension of Zionist hopes over Palestine, which had been heightened as the result of Turkey's entry into the war. In Palestine itself, the Jews were naturally fearful for their position, given the fact that most of the recent settlers were from Russia, with which Turkey was now at war. The governorship of Syria and Palestine was in the hands of Cemal, who distrusted equally the political ambitions of Armenians, Jews and Arab nationalists, so much so that he went down in Arab memory as 'Cemal the Butcher', and was assassinated in 1922 by an Armenian. The Jews of Palestine were spared some of the worst of his attentions by the American Ambassador to Constantinople, Henry Morgenthau, and the fact that the Germans did not wish to alienate Jewish opinion. Even so, Cemal cracked down hard on Zionist activity. By the end of 1915, over 11,000 Jews had fled or been deported, mostly to Egypt. While some Jews were accepted for service in the Ottoman army, in 1917 Cemal ordered the evacuation of the new settlement of Tel Aviv. As the economy started to collapse, hunger hit the Arab and Jewish population alike.
The response of young Jews who had been expelled to Egypt had been to rally to the British cause, forming the Zion Mule Corps, a transport company, which served with distinction at Gallipoli in 1915. Its commanding officer was an adventurous Irish Protestant, Lieutenant-Colonel John Henry Patterson DSO, who in 1916 published his account in _With the Zionists in Gallipoli_. So convinced was Patterson of the potential of the men he had led, that on his return to London he campaigned for the recruitment of Jewish battalions, three of which subsequently fought under his command in Palestine. Patterson, who has a reasonable claim to be regarded as one of the founders of the future Israel Defence Forces, retained an interest in Zionism for the rest of his life. The Jewish driving forces behind the Mule Corps were Joseph Trumpeldor, a one-armed veteran of the Russo-Japanese War who had become the first Jewish officer in the Tsarist army, and Vladimir, or Ze'ev, Jabotinsky. An Odessa-born journalist, Jabotinsky had begun to make his mark as an orator at the pre-war Zionist Congresses, and had already clashed with Weizmann over the proposed Hebrew University. In the 1920s he was to quarrel fundamentally with Weizmann, seceding from the Zionist Organisation in 1925 to form the right-wing Revisionist Zionists. He is generally acknowledged to be the founder and intellectual dynamo behind the Zionist right, which eventually came into its inheritance in 1977 with the election victory of Menachem Begin, and which has been a powerful force in Israeli politics ever since.
Jabotinsky, and the tradition he later inspired, are important for any understanding of the evolution of Zionism, but another young man who found himself in Egypt at that time was to find his fortunes intertwined with those of Weizmann. This was David Ben-Gurion, originally David Gryn, from Plonsk in the Polish part of the Russian empire, who had emigrated to Palestine in 1906. Their passionate commitment to Zionism apart, he and Weizmann could not have been less alike. Whereas Weizmann was tall, urbane and familiar with the educational systems of Russia, Germany, Switzerland and Great Britain, Ben-Gurion was short and feisty, his higher education confined to a brief spell studying law in Istanbul, which had been cut short by the outbreak of war. Perhaps the clue to Ben-Gurion's attitude to the older man was his observation in old age that compared with draining the swamps of Galilee the lobbying of the well-dressed Zionists in Western Europe was futile.
Notwithstanding these events, which were to change the political map of the Middle East, the main British front was in France and Flanders, where the war had taken on almost unimaginable dimensions with the small British Expeditionary Force, the famous 'Old Contemptibles' of 1914, transformed into the first mass army in British history. But that brought problems, not least in the area of munitions where supply failed to match the needs of the army. This was particularly true of the artillery, and by the spring of 1915 what became known as 'The Great Shell Scandal' rocked British politics, playing no small part in the formation of a new coalition government in May. As a result, a new Ministry of Munitions was created, under the direction of David Lloyd George, charged with ensuring that the Army received the supplies it needed.
A particularly pressing need was for a plentiful supply of acetone, an essential ingredient in cordite, the propellant for shells and bullets, and a substance on which, as it happened, Weizmann had worked in the course of his researches into fermentation. His findings attracted the attention of the research scientists at the large Nobel munitions works at Ardeer near Irvine in Ayrshire, but a major explosion at the factory in 1915 proved to be a setback. Weizmann had, however, already been approached by the Admiralty through Sir Frederick Nathan, who had particular responsibility for cordite, and this approach was confirmed, it seems, at a meeting with the First Lord, Winston Churchill. While the records relating to the key meetings are somewhat elliptical, Weizmann apparently met Lloyd George again through Scott's good offices in June 1915, and from then on he had the green light to work on the mass production of acetone from maize. Working for the government meant that he had to take leave of absence from the University of Manchester and move to London. There is no question but that his work contributed significantly to the British war effort. Moreover, it gave him a new-found financial security, and it was to be the road which took him from provincial obscurity in a northern town to the hub of British politics.
It was no less a person than Lloyd George who gave currency to the link between Weizmann's work on acetone and the subsequent Balfour Declaration on Zionism. According to his account, he asked Weizmann what honour he would like to be recommended for in recognition of his work. Weizmann's reply was that he wanted nothing for himself, but something could be done for his people who had aspirations of returning to their ancient homeland. Lloyd George's claim that this was the origin of the Balfour Declaration need not be taken at face value, since the dynamics were much more complex than that, but he returned to it in November 1944 when writing a foreword to a volume honouring Weizmann on his 70th birthday. The rather more prosaic truth was that by 1916 Weizmann had rendered a significant service to the British state and was now a respected figure in the eyes of those at the heart of government. This assumed even greater significance after December 1916 when Lloyd George succeeded Asquith, whose interest in Zionism had never been great, as Prime Minister with none other than Balfour as his Foreign Secretary. But since Samuel had followed Asquith into political exile, an influential ally had also been lost.
Lloyd George's coalition brought into the War Cabinet Alfred, Lord Milner, one of the country's most fertile imperial thinkers, and a key figure in the Boer War and subsequent reconstruction of South Africa. Sensitive to political change, Milner's mission in life was to advance ways of preserving the British Empire through the principles of imperial unity and federation. In 1910, he had been instrumental in inspiring a new group known as 'The Round Table', which began to publish an influential journal of the same name. Amongst its members, Leo Amery, Conservative Member of Parliament for South Birmingham from 1911 and Assistant Secretary to the War Cabinet, and Lord Robert Cecil, Minister of Blockade from 1916 to 1918 and son of the late Conservative Prime Minister the Marquess of Salisbury, were to join Milner in providing crucial support for what became the Balfour Declaration, while another, Reginald Coupland, was to become a key influence on Weizmann's thinking in later years and would help to decide the future fate of Palestine. In 1917, Milner's influence in the War Cabinet was at its height, with his acolytes well placed. In addition to Milner, Amery and Cecil, Weizmann was to find two other invaluable allies at the heart of the bureaucracy which was now driving the war effort. The first was a man of diverse talents and connections, the Right Honourable William Ormsby-Gore, Conservative MP for Denbigh, heir to the 3rd Baron Harlech, and husband of the daughter of the Marquess of Salisbury. More pertinently, his knowledge of the Middle East had recently been gained as an intelligence officer in the Arab Bureau in Cairo, and in 1917 he held the influential positions of Parliamentary Private Secretary to Milner and an Assistant Secretary to the War Cabinet. Ormsby-Gore was to prove a staunch ally of Weizmann's over many years. The other was Sir Mark Sykes, also a member of the Cabinet secretariat. Sykes was a wealthy Catholic landowner, 6th Baronet and Conservative MP for Hull, who had become an expert on Turkish affairs, and a champion of its subject nationalities, the Arabs, Armenians and Jews. He was, of course, the British part of the Sykes-Picot Agreement, with which his name will always be associated, and by 1917 he had a particular brief with regard to Palestine. Weizmann was to describe him as one of Zionism's greatest finds. Tragically, Sykes was to die of influenza in Paris in February 1919 when part of the British delegation to the Peace Conference, aged only 39.
The evolution of the Balfour Declaration
Before examining the negotiations leading to the Balfour Declaration, it is as well to consider the situation in which Britain and its allies found themselves during 1917. At sea, the Battle of Jutland in 1916 had not delivered the kind of Nelsonian victory tradition demanded, while in the course of 1917 Germany's strategy of unrestricted submarine warfare threatened to choke off Britain's essential supplies. On land, the great Somme offensive launched with such high hopes in July 1916 had finally spluttered to a halt, while the French army had only held Verdun at appalling cost. The disastrous French offensive of 1917, which provoked a mutiny in its army, and the British campaign at Passchendaele were to be no more successful. The overthrow of the Tsar in March 1917, and the subsequent turn of events in Russia which resulted in the Bolshevik seizure of power in November, threatened to free veteran German and Austro-Hungarian divisions for service elsewhere. On the Italian front, October saw the Italian army almost shattered by the Austrians and Germans at Caporetto. The one positive development was the entry of the United States into the war on 6 April, but this tested the loyalty of large ethnic groups in the country, such as the Irish, with their memories of the Famine and the recent Easter Rising, or the Jews, who had no reason to support a Russian alliance. In short, the British needed support from wherever it could be found. Weizmann was clear that British motives behind the Balfour Declaration combined idealism with the pressures of war, especially with regard to what was happening in the Jewish communities of Russia and the United States.
In January 1917, Sykes was anxious to make contact with the leaders of British Zionism, but needed to know who they were and what they wanted. His intermediary seems to have been an anglicised Armenian, James Malcolm, who sounded out Weizmann's old adversary from the time of the Uganda controversy, Leopold Greenberg of the _Jewish Chronicle_. Somewhat surprisingly, Greenberg pointed to Weizmann and Nahum Sokolow, who had come to London the previous year and was now active in Zionist affairs. On 28 January, Malcolm introduced Weizmann and Greenberg to Sykes. What Sykes wanted was a statement of the Zionist position, which is exactly what Weizmann, Sokolow and others had been working on for some time. The memorandum which he was given was called an 'Outline of Programme for the Jewish Resettlement of Palestine in Accordance with the Aspirations of the Zionist Movement'. It dealt with the future of Palestine under a suzerain government, which was not named but could be inferred. It called for the present and future Jewish population of Palestine to be recognised as the Jewish nation with full civic, national and political rights. Jewish immigrants would be encouraged and helped to purchase land. The suzerain government was to establish a Jewish company to foster Jewish settlement. The document also introduced a new term, coined by Sokolow, to the effect that Palestine was to be recognised as the Jewish National Home. Here were the bare bones of what Weizmann was to present to the Peace Conference two years later.
Events took a decisive step forward at a meeting held on 7 February 1917 at the home of Dr Moses Gaster, a long-standing English Zionist. Insisting that he was there in a private capacity, which probably fooled no one, Sykes met a group of leading Zionists, including Weizmann, Sokolow, Samuel, Lord Rothschild, James de Rothschild, Joseph Cowen, Herbert Bentwich and Harry Sacher. They were concerned to put to Sykes that what they wanted was a British protectorate which would operate under the terms of the memorandum he had received. What they did not want was for the country to be put under some form of internationalisation, which was really code for an Anglo-French condominium. Sykes assured them he was sympathetic to the idea of a Jewish Palestine and that he did not anticipate a problem with the Russians, but was wary of French intentions in the area, even though he did not consider that they had any claims. The Italians would simply follow the French, he said. He was not, of course, in a position to reveal his own recent agreement with the French over the future disposition of the Turkish lands.
It was agreed that Sokolow should argue the Zionist case with the French. Sykes openly put it to the Zionists that they would be challenged by the growing strength of Arab nationalism, and advised that if they obtained Jewish support in other matters then he felt that the Arabs could be managed. This was to form an important element in Weizmann's subsequent negotiations with Feisal. From a letter to Jabotinsky sent the following day, it is clear that Weizmann was well aware of the meeting's significance, although his enthusiasm for Sykes was tempered somewhat by the feeling that the Arabs, and not the Zionists, were his priority. Four days after this historic meeting, Weizmann was elected president of the English Zionist Federation, enabling him to negotiate with the government on these crucial issues from a recognised position.
From this tentative beginning, momentum built in the spring of 1917. What seems to have exercised the British most at this stage was the likely attitude of the French to any move over Palestine. Weizmann was warned of this by Balfour at a meeting on 22 March. It seems that Balfour took some convincing of Palestine's value to the British. His suggestion was that if they could not get an agreement with France, then the Zionists should aim for an Anglo-American condominium, an idea which did not greatly tempt Weizmann. This theme was also taken up by Lloyd George when he breakfasted with Weizmann and Scott on 3 April. The real significance of these meetings was that Weizmann and Zionism were being taken seriously at the highest level, important because large British forces were poised to advance into Palestine, but they also put into context the somewhat prolonged mission Sokolow undertook in Paris and Rome in April, May and June. It was far from a waste of time, however, since on 4 June Jules Cambon of the French Foreign Ministry wrote to him expressing sympathy with his cause. This was an invaluable document to have. Sokolow's lengthy absence, of course, meant that in London the spotlight fell on Weizmann.
It was at this point that Weizmann at last got wind of the Sykes-Picot Agreement through the good offices of Scott. The proposal that France should acquire part of northern Palestine, and that the rest should be internationalised ran directly counter to Zionist hopes for a British protectorate. It was clearly vital to explore this, and make it clear where the Zionists stood. Weizmann did this on 25 April at a meeting with Lord Robert Cecil, who was running the Foreign Office during Balfour's absence in the United States. There were three options for Palestine, he explained; namely, a British protectorate, an Anglo-French condominium and internationalisation. What the Jews wanted was the first of these. They trusted Britain to allow Jewish development, and grant self-government at the appropriate time. Joint rule with the French would simply lead to confusion and intrigue. Moreover, he pointed out that French colonial policy was one of assimilation to French, and Catholic, values. Internationalisation would pose a strategic threat to Egypt. Weizmann then turned to the Sykes-Picot Agreement, which he outlined with remarkable accuracy. This, he said, would combine the faults of internationalisation and a condominium, as well as partitioning Palestine. Cecil appears to have been convinced, and he advised Weizmann to mobilise world Jewish opinion in support of a British protectorate.
Clearly, the key to such a strategy lay with the large American Jewish community, whose leader Justice Louis D Brandeis had the ear of President Woodrow Wilson. Born in Kentucky in 1856, in 1916 Brandeis had become the first Jew to be appointed to the Supreme Court. In 1914, he had accepted the presidency of the Provisional Executive Council for General Zionist Affairs, and as such was the acknowledged leader of American Zionism. Two days before his meeting with Cecil, Weizmann had contacted Brandeis, emphasising that from the Zionist perspective it was imperative that Palestine should become a British protectorate. Amongst other things, what was concerning him were anti-annexationist views coming from the American administration. It was vital that Brandeis should meet Balfour to impress this upon him. Brandeis met Balfour on several occasions during his American visit, and the two men seem to have agreed on the need for a future British administration in Palestine.
It was Brandeis in June 1917 who warned Weizmann that an American mission was coming to the Middle East, and that he should contact it. From Sykes and Ormsby-Gore he learned that this was an initiative of Henry Morgenthau, former Ambassador to Constantinople, in an attempt to negotiate a separate peace with Turkey. The idea of some kind of deal which would leave the empire intact was as unwelcome to the British as it was to Weizmann, and it was Balfour who suggested that he intercept Morgenthau's party at Gibraltar and persuade him to drop the idea. In a somewhat cloak-and-dagger operation, Weizmann travelled to Gibraltar, accompanied by an armed intelligence officer, but he need not have worried, since Morgenthau soon saw the futility of the idea. In any case, the United States and Turkey were not at war. The real significance is the extent to which Weizmann was now trusted by the government, and the success of his mission certainly did his credibility no harm.
While events were clearly moving Weizmann's way, his activities had rung alarm bells amongst his old adversaries in the Anglo-Jewish elite, expressed through the Conjoint Foreign Committee, which brought together the Board of Deputies of British Jews and the Anglo-Jewish Association. On 24 May 1917, they published a statement in _The Times_ under the title of 'Palestine and Zionism – Views of Anglo-Jewry'. While they supported the concept of making Palestine a spiritual centre for the Jews, they were strongly opposed to Zionism's political programme, arguing that for Palestine to be regarded as a Jewish homeland would undermine what the Jews had achieved in their native countries. Their action brought to a head the latent tensions within British Jewry over the question of Zionism, with Weizmann and the Jewish peer Lord Rothschild writing letters of rebuttal to _The Times_. Weizmann's letter, which was published on 28 May, asserted in no uncertain terms that the Jews were a nationality, and added that Zionism was not seeking an exclusive position in Palestine. The result of this controversy was that on 17 June the Board of Deputies voted, albeit by a narrow majority, to reject the 'Statement', and the Conjoint Foreign Committee was dissolved. This was far from the end of the campaign against a pro-Zionist policy, since a determined enemy was lying in wait in the one of the great offices of state. This was Edwin Montagu, Secretary of State for India, of whose hostility to Zionism Lloyd George had warned three years before.
The Balfour Declaration
On 13 June, Weizmann wrote to Sir Ronald Graham of the Foreign Office pressing for a British declaration of support for the Zionist position on Palestine, which he claimed, with some exaggeration, they had been negotiating for the past three years. Weizmann was at pains to point out the recent expressions of support for Zionism in influential German and Austrian newspapers. By coincidence, Balfour had just received a minute recommending that the government issue an assurance of British sympathy for Zionism. He was, therefore, in a receptive mood when Weizmann, Graham and Lord Rothschild came to see him on 19 June. Balfour agreed that the time had come to issue a declaration of support, and asked them to submit a draft which he could put to the War Cabinet. He also assured them that he was opposed to an Anglo-French condominium, and that he favoured joint Anglo-American control, but felt that this would not find favour with Lloyd George or the Americans. In reporting this to his colleagues, Weizmann suggested that the draft should talk in terms of a Jewish National Home in Palestine, precisely the formula the War Cabinet ultimately agreed. The drafting was done by a committee chaired by Sokolow while Weizmann was in Gibraltar.
Various versions were discussed, including one by Herbert Sidebotham, a non-Jewish journalist on the _Manchester Guardian_ , who was strongly pro-Zionist. His rather turgid version was not accepted, but is, nevertheless, well worth noting for his use of the striking phrase that the national character of the Jewish state should be as Jewish as the dominant national character of England was English. Weizmann was to utter a somewhat terser version of this when responding to a question at the Peace Conference, and its implications were to echo for years, not always to his advantage. In discussing this episode in his book _Great Britain and Palestine_ , which he published in 1937, Sidebotham refrained from mentioning that he was most probably the _fons et origo_ of the phrase. Harry Sacher was also influential in the working of a draft declaration. On 18 July 1917, the agreed draft was given to Balfour by Lord Rothschild. It was admirably brief, and would have committed the British government to reconstituting Palestine as the National Home of the Jewish People, and to discussing with the Zionist Organisation how this would be done. If the Zionists had reason to hope for early action, then they had not reckoned on the Byzantine ways of the British decision-making process, nor on the opposition the draft provoked.
As the Zionist draft circulated, a number of suggested amendments were put forward, the most significant being one from Milner which proposed that the declaration should commit Britain to securing a home for the Jews in Palestine. The matter came before the War Cabinet on 3 September, in the absence of Lloyd George and Balfour. While Cecil and Milner and the South African General Jan Smuts were supporters of the idea, a powerful opponent had also been asked to attend. This was Edwin Montagu, who had recently been appointed Secretary of State for India, entrusted with carrying forward the reform scheme which was to emerge under his name and that of the Viceroy, Lord Chelmsford. Since India's wholehearted participation was vital at this stage of the war, his views mattered. The Indian Army formed a large part of the imperial forces in both Palestine and Mesopotamia, and it recruited heavily amongst Indian Muslims. Montagu felt passionately that the idea of a Jewish National Home undermined his status as a Jewish Englishman, and he expressed this in no uncertain terms in a memorandum which he entitled 'The Anti-Semitism of the Present Government'. The War Cabinet had before it Lord Rothschild's letter, a suggested reply by Balfour, Milner's alternative version, and Montagu's philippic against the whole idea. Montagu spoke to his memorandum, emphasising his central belief that the proposal would undermine the position of Jews everywhere. Others argued that the idea of a Jewish state in Palestine would not affect the position enjoyed by Jews in countries like Britain, but would strengthen it in countries where they did not have equal rights. Cecil argued against any postponement of the matter, pointing to the enthusiasm of the Zionist Organisation, especially in the United States, and the value of having them on the Allied side. Even so, it was felt prudent to consult the other Allies, especially the Americans.
With the proposed declaration seemingly hanging in the balance, Weizmann deployed all his diplomatic skills to help secure it. The first attempt to put Lord Rothschild's draft before President Woodrow Wilson through his aide Colonel Edward M House produced a rather tepid reply on 10 September, to the effect that a declaration of sympathy could be made but without any commitment. Wilson's problem was that his country was not at war with Turkey. When Weizmann learned of the tone of House's message, he immediately contacted Brandeis, emphasising the urgent need to secure Wilson's endorsement. Brandeis met House on 23 September, and the following day he telegraphed to the effect that the President was entirely sympathetic to the proposed declaration.
Frustrated and somewhat perplexed by the influence Montagu was having, Weizmann was also actively lobbying on the domestic front. On 19 September, he met Balfour, who promised to use his influence with the Prime Minister, and then, a week later, he was able to snatch a few moments with Lloyd George, who issued peremptory instructions that the matter be tabled at the next Cabinet meeting. With the matter now due to come back before the War Cabinet, on 3 October he and Rothschild wrote to Balfour expressing their alarm that the proposed declaration was being opposed by a prominent Jew whom they did not actually name, but who was, of course, clearly identifiable. What they sought to drive home was that the declaration had been submitted on behalf of an organisation which represented the will of a people who had the right to be regarded as a nation.
The day after receiving Weizmann's letter, the War Cabinet resumed its consideration of the matter. Balfour opened the discussion by warning his colleagues that the Germans were trying to woo the Zionists. Conceding that Zionism was opposed by some wealthy British Jews, he believed it had the support of American and Russian Jews. He saw no contradiction between a national focus in Palestine and the assimilation of Jews into other countries. His justification for a declaration was that the Jews passionately wanted to regain their ancient homeland. Finally, he read the letter of support Cambon had given Sokolow, and referred to Wilson's favourable attitude, although others noted the difference in tone between the telegrams sent by House and Brandeis. Montagu responded by asserting that he was a Jewish Englishman and that the Jews were a religious community, asking how he could negotiate with the Indians if it was announced that the British government believed that his National Home was in the Turkish empire. Most native-born Jews, he claimed, were hostile to Zionism; its supporters, on the other hand, were foreign-born Jews like Weizmann, a native of Russia.
Strong opposition was also voiced by George Curzon, Earl of Kedleston, former Viceroy of India and now Leader of the House of Lords. Widely travelled in the Middle East, Curzon knew Palestine and did not think much of its potential as a future home for the Jews. More importantly, he asked how it was proposed to get rid of what he called the country's Muslim majority. The government should have nothing to do with the proposed declaration, he concluded. Knowing where the arguments were likely to go, Milner had tried to square the circle in advance of the meeting. Just before the start of the War Cabinet meeting, he asked Amery to draft a formula which might satisfy both the Jewish and pro-Arab critics. Amery's hastily-composed text added to Milner's earlier draft that nothing should be done to prejudice the rights of the existing non-Jewish population of Palestine or those enjoyed by Jews in other countries. It was agreed to put this to Wilson as well as to the Zionists and their opponents.
Faced with this fresh delay, Weizmann once again moved to secure the backing he needed. On 9 October, he cabled Brandeis with the new version of the proposed declaration, stressing the need to secure Wilson's endorsement as well as that of the American Zionists. In fact, House had already received it from Balfour, and the American embassy in London had also sent it direct to Wilson. On 16 October, House informed the British of Wilson's approval, with the proviso that it not be made public, and on the following day Brandeis was able to confirm this to Weizmann. The American Zionists made two suggested amendments to the proposed text. These were concerned with the phrasing concerning the rights and political status of Jews in other countries and a preference for the term 'Jewish people' rather than 'Jewish race'. It seems that these issues were already being addressed by the British Zionists. Meanwhile, Weizmann was also mobilising Zionist opinion at home, with some 300 synagogues and societies registering their support for a declaration.
When the War Cabinet met for what proved to be its final discussion of the topic on 31 October, Balfour met his critics head-on. He emphasised the propaganda they could conduct in Russia and the United States, since the majority of Jews in these countries were behind Zionism. Once again, he was dismissive of the assimilationist fear of double allegiance. Montagu was not there to counter this, since he had left for India. As to Curzon's point about the unsuitability of Palestine, he claimed that if the country were properly developed it could sustain a much larger population, an argument which Weizmann was to use in the years to come. As to what was meant by the term 'National Home', his argument is interesting in view of later developments, since he said it did not necessarily mean the early establishment of a Jewish state, but would be some kind of British, American or other protectorate which could become a focus of Jewish national life. Curzon, the only one who had actually seen the country at first hand, remained pessimistic, but was grudgingly prepared to acknowledge the political value of what was being proposed. The way was now open for the Cabinet to authorise the Declaration, which was issued in a letter from Balfour to Lord Rothschild on 2 November:
His Majesty's Government view with favour the establishment in Palestine of a national home for the Jewish people, and will use its best endeavours to facilitate the achievement of this object, it being clearly understood that nothing shall be done which may prejudice the civil and religious rights of existing non-Jewish communities in Palestine, or the rights and political status enjoyed by Jews in any other country.
Weizmann later recalled that at the conclusion of the Cabinet meeting, Sykes brought the Declaration out to him with the exclamation that it was a boy. If it was not quite all that Weizmann had hoped for, its birth was more down to him than anyone else, and he knew that history was in the making, referring to it in a letter to Rothschild as the Magna Carta of the Jews. That evening, his wife later recorded, the Weizmanns and some friends formed a circle at his home and danced a Hassidic dance in celebration. A month later, there was a large demonstration in London of Jewish gratitude for the Declaration, which was addressed by Cecil, Samuel, Sykes and Ormsby-Gore, as well as Weizmann. If the British government had hoped to influence the course of events in Russia, the Declaration might have succeeded, since Russian Jews were, indeed, stirred by it, but by then the second revolution had robbed it of any real potential. The Declaration was followed, on 14 February 1918, by a letter from Stéphen Pichon of the Foreign Ministry to Sokolow, assuring him that the French were in agreement with the British over what he rather tepidly termed a 'Jewish establishment' in Palestine, a phrase which allowed later interpretation.
The collapse of the Ottoman Empire
From the Zionist perspective the Balfour Declaration could not have come at a better time, since the Turkish positions in Palestine and Syria were about to fall to the British. The Turkish army still had fighting spirit in 1917, fending off two attacks on Gaza by Sir Archibald Murray's Egyptian Expeditionary Force. But in June 1917 the lacklustre Murray was replaced by Sir Edmund Allenby under whose leadership the strength of the imperial forces, Australian, British, Indian and New Zealand, together with their Arab and Palestinian Jewish allies, began to tell. Taking Gaza and Beersheba, on 11 December 1917 Allenby entered Jerusalem through the same gate the Kaiser had used, but in his case pointedly on foot. From then on, Britain's was the decisive voice in the fate of Palestine. By this time, the Turkish war effort was faltering on all fronts.
Soon after the first Russian Revolution in February 1917, the Tsarist army had disintegrated. On the Caucasian front, territory seized by the Russians, who had made some attempts to prevent inter-communal killings, was taken over by Armenian militias. The militias avenged themselves on local Muslims for the fate of their kinsmen deported two years previously. Then, after the Bolshevik Revolution in November 1917, the Soviet government had sued for peace and been forced to accept the loss of the western portion of the Tsarist empire (from Finland through Poland to the Ukraine), and, subject to a referendum, territory the Russians had gained from the Ottomans in 1878.
The collapse of Russia, a full year before the collapse of Germany in November 1918, tempted Enver into another adventure. Ottoman troops had earlier been dispatched to Galicia (now divided between Poland and Ukraine) to reinforce the Austro-Hungarians against the Russians. Just as the front held by the Ottomans against the British in Palestine and Mesopotamia was about to crumble, Enver withdrew more troops from it and ordered them to move into the Caucasus beyond the 1878 Russian frontier. He overrode the objections of the Germans who had their own plans for a puppet government in Georgia and for control of the oilfields in Baku (held precariously by a British force after the Russian collapse). As he pursued his dream of a Turkic empire stretching all the way to central Asia and eyed territories about which he was woefully ill-informed, Enver weakened the defence of the Turkish core of the empire – Anatolia and eastern Thrace.
The elderly, weak-willed Sultan Mehmed V (Mehmed Reşad) died in July 1918. He was succeeded by his younger brother, the 57-year-old Vahdettin, who took the title of Mehmed VI. Mustafa Kemal had made a favourable impression on him earlier that year when he accompanied him on a tour of the Western Front. They were both critical of the Unionist leadership and their conduct of the war. Vahdettin thought he could use Kemal, while Kemal banked on the favour of his new sovereign for his own designs. While Vahdettin was vacillating, suspicious, ill-informed, woolly-minded and fearful for the safety of his throne, Kemal was clear-headed and realistic. This allowed him to turn the relationship to his advantage. It was also Kemal who had the clearer grasp of the Ottomans' military weakness, which he witnessed in August 1918 when he accepted a command on the Syrian front, this time under his old commander Liman von Sanders. A year earlier, when he had refused to serve another German commander, Field Marshal Erich von Falkenhayn, Kemal had urged on the Ottoman high command in Istanbul the urgent need to withdraw troops from Galicia, renounce Enver's Caucasian adventure, and concentrate all available forces for the defence of Anatolia. By the time Kemal returned to Syria, a month after Vahdettin's accession to the throne, the position of the Ottoman forces had become desperate. Jerusalem had been lost to General Allenby's British imperial forces the previous December, and a weakened Ottoman army was trying to hold a line in northern Palestine, with headquarters in Nazareth. The British broke through in September, a month after Kemal's arrival on the front. Thereafter his main concern was to escape capture and to save as many of his troops as he could for the defence of Anatolia.
By the autumn of 1918, out of the total of 2.85 million men conscripted in the Ottoman Empire during the war, only 560,000 still bore arms, and of these only a quarter were available for combat. Some of the best troops – eight well-equipped divisions at full strength – had been dispatched to the Caucasus and northern Persia, where they could not affect the course of the war. Half a million deserters roamed the interior of Anatolia. As the military situation worsened, talk of a separate peace began to be heard in Istanbul. President Woodrow Wilson's peace proposals seemed to offer a way out. In a speech to Congress in January 1918 Wilson had formulated the principles which, he believed, should inspire the peacemaking. He set them out in the Fourteen Points, of which the Twelfth declared:
The Turkish portion of the present Ottoman Empire should be assured a secure sovereignty, but the other nationalities which are now under Turkish rule should be assured an undoubted security of life and an absolutely unmolested opportunity of autonomous development, and the Dardanelles should be permanently opened as a free passage to the ships and commerce of all nations under international guarantees.
This was not a bad bargaining offer to the embattled Ottomans. Moreover, the rhetoric of President Wilson and of the Young Turks coincided in one important respect: disregarding the fact that they were fighting to save an empire, the Young Turks had posed as the champions of the peoples of the East against the imperialists. Wilson seemed to echo them. Although by then the United States was fighting on the side of the British and French empires, Wilson proclaimed loftily: 'In regard to these essential rectifications of wrong and assertions of right, we feel ourselves to be intimate partners of all the governments and peoples associated together against the imperialists.' No wonder that as they tried to avert the impending catastrophe, many Ottoman patriots saw a lifeline in Wilson's principles. Moreover, Wilson's Twelfth Point echoed the statement made three days earlier by Lloyd George. The Allies, he said, were not fighting 'to deprive Turkey of its capital, or of the rich and renowned lands of Asia Minor and Thrace, which are predominantly Turkish by race'.
In a first response in February 1918, the Ottoman foreign minister agreed that the diverse nationalities in the empire should be granted their own institutions. In spite of reverses in the field and weakening morale, the Ottomans still wielded considerable bargaining power at the time. But the Unionist leadership was unable to make up its mind on how to end the disastrous war into which they had led the country. Enver still believed in a German victory and kept Talât Pasha's Cabinet in the dark about the worsening situation on the front. Even the defeat of the last German offensive on the Western Front in July 1918 did not shake the government out of its indecision. The opportunity to make peace on favourable terms was lost.
On 15 September, the Bulgarian army crumbled before the assault of the Allied forces in Macedonia. Four days later Allenby scattered the Turkish troops holding the front in northern Palestine. Talât Pasha had earlier gone to Berlin to discuss a united response of the Central Powers to Wilson's peace terms. Unable to agree among themselves, the Central Powers sued for peace separately. The first to collapse was Bulgaria. Passing through the Bulgarian capital, Sofia, on his way back home, Talât Pasha witnessed the disintegration of the army which had guarded the western approaches to Istanbul. The game was up. Talât acknowledged this with characteristic bluntness, saying 'We have eaten shit!' Four years later, Sir Horace Rumbold, British High Commissioner in the Ottoman capital, was to use the same image, in a slightly more polite form. 'If the Greeks crack,' he wrote, 'we may expect to eat dirt to an unlimited extent and this is not a form of diet that has ever agreed with me, though Pellé [the French High Commissioner] and Garroni [his Italian counterpart] may flourish on it.' But no one, and least of all Lloyd George, expected such a reversal of fortune when the Allies emerged triumphant from the First World War.
Talât's Cabinet finally resigned on 13 October. On the same day Enver sent a last message to all Ottoman forces urging them to prevent the loss of any more Turkish territory before the conclusion of an armistice. The CUP was finally out of office. But it still held the majority of seats in parliament, which could once again exercise its powers under the Constitution. The CUP also controlled the security forces in the capital and dominated the provinces through its local organisations. In opposition, in power and then again in opposition, the CUP represented modernity. Nationalism was the dominant ideology in the world, and Wilson's advocacy of the self-determination of nations confirmed its legitimacy. In the crumbling Ottoman state, it was the CUP which championed Muslim nationalism as it melded into Turkish nationalism. There were few men of experience in politics, the administration or the army who had not collaborated with the Unionists in the ranks of the opposition to Sultan Abdülhamid. Later, most of them had served Unionist governments or been members of the CUP. In the circumstances, it was the critics of the leadership within the party, and particularly of its decision to side with Germany in the war, who took over from the defeated Unionist triumvirate.
Peace negotiations
Talât was succeeded by a distinguished soldier, Ahmed İzzet Pasha, an outspoken opponent of the war policy of the triumvirate, who had nevertheless served with distinction as overall commander of the Caucasian front before the Russian Revolution. Ahmed İzzet was a bluff German-trained officer of Albanian origin, born in Macedonia. His long-standing association with the Germans showed in his moustache in the style of Kaiser Wilhelm II. More importantly, he was attached to the Ottoman dynasty with all the strength of the Albanian ideal of besa – the tradition of total loyal commitment to a patron. When an Albanian state emerged in 1913 from the Ottoman defeat in the Balkan wars, he had been offered the position of head of state as Prince of Albania. Ahmed İzzet refused, saying that it would be a step down for a servant of the Ottoman Sultan. It was, as the Turkish saying had it, 'to dismount a horse in order to ride a donkey'.
Ahmed İzzet's Cabinet included three prominent Unionist critics of the triumvirate: Cavid, who as Finance Minister had extracted every penny he could from Enver's German allies, Fethi (who later took the surname Okyar), an early political patron of Mustafa Kemal, and a naval officer, Rauf (later Orbay), who had risen to fame during the Balkan Wars as captain of the Ottoman cruiser _Hamidiye_ , evading capture as it raided the coasts of the Balkan allies. While German influence was strong in the army, the Ottoman navy, which had had British advisers before the war, was traditionally pro-British, and Rauf felt, as it proved, an exaggerated confidence in British good intentions.
Mustafa Kemal, who was busy reorganising the remnants of Ottoman forces on the Syrian front, had sensed that a change of government was necessary to end the hostilities. Presuming on his friendship with the new Sultan Vahdettin, he advised him to appoint Ahmed İzzet Pasha Grand Vizier, and asked for himself the post of War Minister. The telegram was delayed, and Ahmed İzzet was appointed without the benefit of Mustafa Kemal's advice. As a professional soldier, the new Grand Vizier preferred to keep the post of War Minister for himself.
The first job of the new Ottoman government was to establish contact with the Allies. The abject condition of the country showed through the high-flown Ottoman chancery rhetoric of the decree appointing Ahmed İzzet to the post of Grand Vizier:
Whereas it is our most particular wish that the effects produced by the present war, which has been waged with extreme violence for more than four years, on the general affairs of our dominions and their good order and discipline should be rectified, and that concord and general amity should be established among all classes of our people, it is our expectation that you apply your well-known zeal and devote the greatest care to the choice of powerful and efficient measures to obtain the means to bring to a successful conclusion the political initiatives we have undertaken in order to achieve these aims and, at the same time, to secure the supremacy of religious and civil law, the stability of safe and orderly government, to make perfect the condition of ease and well-being of our people, supplying them with the necessities of life without further delay and facilitating the satisfaction of general needs.
In other words, the country is prey to anarchy and lawlessness, people are at each other's throats, they are at their wits' end with hunger and privation. Please do something about it quickly, and make sure that the Allies respond to our political overtures.
At the beginning of October, the Sultan had sent a personal representative to Bern who arranged that the agent of an Armenian Ottoman dignitary Boghos Nubar Pasha should communicate his peace terms to the British minister in Switzerland, Sir Horace Rumbold. Vahdettin proposed that the Arab provinces should become autonomous under his suzerainty, that the Greek islands off Turkey's Aegean coast should be returned to the Ottoman state along with Bulgarian gains in the Balkan Wars, and that the British should help him destroy the CUP and should maintain him on the throne. In exchange he offered an alliance with Britain and reforms under British control. In other words, if the British made good the territorial losses the Ottoman Empire had suffered under the rule of the Young Turks, he was prepared to place himself under British protection. What Vahdettin did not realise was that while he was ready to trade the independence of his state for its nominal territorial integrity and his survival as Sultan, his subjects had other ideas. So too did the British, who were already in possession of the Ottomans' Arab provinces. Nubar Pasha, on whose good offices the Sultan relied, was soon afterwards to demand from the Allies a large slice of Ottoman territory for an independent Armenian state.
A few days later, the British received a similar offer from an independent-minded Unionist, Rahmi, who had run İzmir and the surrounding country as his personal fiefdom during the war, had protected the large community of Allied subjects who lived and traded there and had prevented the deportation of Armenians from the area. Rahmi had one additional request – that Britain should replace Germany as Turkey's paymaster by guaranteeing the Ottoman currency. Where the Sultan had used an Armenian, Rahmi had used a Greek as an intermediary. Neither realised that the days of the multi-ethnic Ottoman state were numbered, and that the employment of local Christians to represent the Ottoman state could no longer placate eiither the Allies or the local Christian communities. Both these attempts to initiate peace talks failed.
Ahmed İzzet had better luck. This time the intermediary was the British General Sir Charles Townshend, who had surrendered to the Turks after a six-month siege at Kut al-Amara in Mesopotamia in the spring of 1916. While 70 per cent of the 3,000 British rank-and-file who surrendered at Kut had died in captivity – many during death marches through the desert, others due to appalling conditions in POW camps – Townshend had been held in a comfortable villa on the island resort of Büyükada (Prinkipo), the largest of the Princes' Islands in the Sea of Marmara near Istanbul. He had even been invited to tea by Enver. When he heard that Ahmed İzzet was forming a new Cabinet, Townshend offered to transmit the Ottoman peace proposals to Admiral Sir Somerset Calthorpe, commander of the British Mediterranean Fleet, who had his headquarters on the Greek island of Lemnos in the Aegean.
On 16 October, the Ottoman Cabinet decided to seek a separate peace, after hearing a report on the military situation. 'We have six or seven thousand men left on each front [Syria, Mesopotamia and Thrace],' the Ottoman General Staff told Ahmet İzzet's Cabinet. 'It's so bad you could invade the country with a handful of bandits.' The delay in facing military facts had bred an exaggerated pessimism which was to weaken the hand of Ottoman negotiators. The following day, Ahmed İzzet received Townshend and accepted his offer to go to Lemnos. But, first of all, the composition of the Ottoman delegation and its instructions had to be decided. This did not prove easy. The Sultan, fearful and suspicious as ever, complicated matters.
On 23 October, Admiral Calthorpe informed the Ottoman government that he had been authorised to sign an armistice on behalf of the Allies. On hearing this, Ahmed İzzet sought the Sultan's approval for a delegation led by the Ottoman army commander in İzmir, the port from which the Ottoman emissaries would set off for Lemnos. The Sultan disagreed and asked that the chief of the delegation should be his brother-in-law, Damad Ferid Pasha. ( _Damad_ means son-in-law, and the title was conferred on Ferid when he became the second husband of Mediha, the daughter of Sultan Vahdettin's father, Abdülmecid I.) 'The man is mad,' objected Ahmet İzzet. He was not the first to say so.
Ferid's highest job in the Ottoman civil service had been that of First Secretary at the Ottoman embassy in London. When in 1888 Mediha had asked the reigning Sultan Abdülhamid II (Vahdettin's elder brother) to send Ferid back to London, this time as ambassador, he had replied, 'Sister, the London embassy is not a school, it's an important embassy and the appointment should go to somebody who has experience and understanding of international politics.' Later, when the CUP came to power, Ferid extolled it to the skies. But as he failed to win promotion, he had joined the opposition Liberty and Concord Party (known in the West as the Liberal Union). Here, too, he had been unlucky. When the CUP was briefly out of power at the beginning of the Balkan Wars, the Sultan had proposed that Ferid should head the delegation to the peace talks in London. Ferid had refused, saying that he could not sign away any part of Ottoman territory, as this would violate the Constitution. 'The man is mad', said the elderly Grand Vizier Kâmil Pasha, who had known that territorial losses were inevitable. Ferid had thereafter twiddled his thumbs in his wife's mansion on the Bosphorus. Where in Britain politics often revolved round the country houses of the aristocracy, in the late Ottoman Empire political decisions were taken and plots hatched in yalıs, wooden seaside mansions of princes and pashas on the shores of the Bosphorus. In later years many of these yalıs were burned down. A few survive in the hands of business tycoons. Damad Ferid's (or rather his wife's) _yalı_ now houses a restaurant patronised by university professors.
At the Sultan's insistence, Ahmed İzzet called on Damad Ferid and heard out his views on the armistice:
As soon as I see the Admiral [Calthorpe], I shall propose an armistice treaty based on the territorial integrity of the [Ottoman] state. If the Admiral won't accept this, I will ask for a cruiser immediately and go straight to London. On arrival, I will have an audience with the King and say 'I was an old friend of your father's. I expect you to accept my wishes.' Having thus ensured that our proposals are accepted, I'll rescue the state from the catastrophe into which the Unionists have plunged it.
However, he could not leave immediately as he had to pack his clothes. When he was ready, he would leave on the Sultan's yacht, taking with him the secretary of the Greek Patriarch. A year later, the Patriarch was to sever all relations with the Ottoman state and demand that the Ottoman capital should come under Greek rule.
The above nonsense confirmed Ahmed İzzet's original estimate of Damad Ferid's capacity. Loyal to the Sultan as he was, Ahmed İzzet insisted that the Cabinet should be free to choose its own chief negotiator. Sultan Vahdettin gave way with bad grace, but insisted that the instructions to the Ottoman delegates should specify that 'the rights of the Sultanate, the Caliphate and of the Ottoman dynasty should be protected', and that the autonomy to be given to some provinces should be administrative and not political. Ahmed İzzet objected that these were matters to be settled in the peace treaty and not in an armistice agreement. Once again the Sultan gave way, but asked that the armistice should at least ensure the safe return of an Ottoman prince who was cut off in Libya.
Having warded off – for a short period of time, as it proved – the Sultan's interference, Ahmed İzzet's Cabinet chose Rauf, the patriotic naval officer, as chief negotiator. He was told that he could agree to the opening of the Straits and to the reduction in size of the Ottoman army to peacetime strength. However, no Greek warships should be allowed through the Straits, which would be defended by the Ottoman army. British control officers would be allowed until the conclusion of peace, but no Allied forces should land anywhere in the territories that the Ottomans still controlled, and there should be no interference in the Ottoman administration. Any conditions incompatible with the honour of the Ottoman state should be rejected. German and Austro-Hungarian troops and officials should be given at least two months to leave the country, but civilians from these countries should be allowed to stay on, if they wished, lest Germany and Austria-Hungary decide to retaliate by expelling from their territories Ottoman students, whose number was estimated at 15–20,000.
The insistence on decent treatment of the Ottomans' German and Austrian allies shows that, in spite of wartime friction between the Turks and their German advisers, there was little animosity against them. On the military level, the alliance had worked well. True, the importance of German commanders in the Ottoman war effort was often exaggerated in Britain and France. Their most important help had been in communications, staff work and, of course, supplies. The Germans had worked hard to maintain and extend Ottoman railways; the Austro-Hungarians had provided a motor transport unit on the Caucasian front. In Turkish popular tradition, the Germans stood for precision in everything.
'How do you make a good pilaff?' a German officer asks a Turkish army cook in a well known joke. 'You need enough rice, enough fat, enough water, and cook the rice long enough' the cook replies. But the German wants precise information. 'What do you mean by enough?' he asks. 'It's obvious, Sir,' says the cook, 'enough to make a good pilaff.'
The Germans had their own stories of the happy-go-lucky attitude of Ottoman officers. One day, a German officer was horrified to see that his Ottoman companions were using a map of Gallipoli while fighting the British in Palestine. 'It's the wrong map,' he cried. 'What do you mean by wrong map?' replied the Ottoman. 'It served us well enough all through the campaign in Galicia.' Later these good-natured stories gave way to angrier reminiscences, and today many Turks will tell you that in the First World War, the Germans evacuated their wounded by rail, but left the Turks to die in the desert. This is true, but there were many more Turks than Germans, and the Germans fought in a foreign country while the Turks were, at least theoretically, at home among the Arabs.
The Germans left the Ottoman Empire in good time, but the other conditions on which the Ottoman armistice negotiators were to insist were sacrificed. Rauf and his fellow delegates were acutely aware of the weakness of the Ottoman state and of its urgent need for peace. They did not realise that, late as it was to conclude a separate peace under favourable conditions, there was still room for bargaining. Germany had not yet surrendered and the Allies wanted above all to send their navies through the Turkish Straits in order to cut off German troops in south-eastern Europe and the Caucasus. What is more, they had conflicting ambitions in the Near East. The instructions communicated to Admiral Calthorpe after difficult consultations in London and Paris defined a first bargaining position, but the admiral was told that he could make concessions, provided the Straits were opened, its fortifications placed under Allied control, the Germans expelled and the Ottoman army demobilised. This Ahmed İzzet's government was, in any case, prepared to concede. But it did not have to agree to peace at any price. There was no domestic pressure for unconditional surrender. In spite of widespread hardships, there were no military mutinies or civil disturbances in the areas under Ottoman control. The Istanbul government did not fear the disaffection of the Sultan's Muslim subjects. What terrified it was the prospect of a rising by local Christians, above all by the numerous Greeks in the capital.
In Turkish eyes, Greece was a Johnny-come-lately in the ranks of the Allies. Greece was still neutral when Allied troops under French command landed in Salonica in October 1916. It was under the protection of the Allies that the Greek Prime Minister Eleftherios Venizelos had formed a provisional government in the city and declared war on Bulgaria and the Central Powers. Greek troops thereafter fought under French command against the Bulgarians and Germans on the Macedonian front, and the Allies made use of Greek territory to prosecute the war with the Ottoman state. But there had been no fighting between Greek and Ottoman troops. Greece was not consulted when Admiral Calthorpe sat down to negotiate an armistice with the Ottoman delegation. However, the Ottoman government was well aware that Greek nationalists, who had found a champion in Venizelos, coveted Constantinople (Istanbul) as well as Smyrna (İzmir) and the surrounding area. The Turks felt that they had been defeated by the British and not by the Greeks, and resented the idea that the latter should figure among the victorious Allies, particularly in the streets of the imperial capital.
Negotiations between Admiral Calthorpe and Rauf opened on 27 October on board HMS _Agamemnon_ , which was anchored in Moudros Bay (Mondros in Turkish), a natural deep-water harbour on the island of Lemnos. The delegations met in the captain's large day cabin, comfortably furnished with Persian rugs, which opened on to a pleasant stern walk. Both sides behaved with impeccable good manners. Calthorpe made some concessions to the Turks. But these concerned conditions on which he had not been instructed to insist. Only one concession was to prove important. Where the Turks had originally been asked to withdraw all their troops from former Tsarist territory in the Caucasus (and north-west Persia, whose neutrality had been violated by both sides during the war), the final text stipulated that 'the remainder [of the Ottoman troops] [is] to be evacuated if requested by the Allies after they have studied the situation'. The Ottoman troops sent by Enver to the Caucasus and Persia had not affected the course of the war. But these fresh divisions, well-armed with weapons from Tsarist arsenals or handed over by the Germans, were to become the nucleus of the Turkish national army when the War of Independence started a year later. A condition in the armistice calling for consultations with the Turkish government to determine the strength and disposition of Ottoman troops which were to maintain internal order after the demobilisation of the bulk of the Ottoman army, allowed Turkish nationalists to keep this military nucleus in order to avert the final catastrophe – the occupation and partition of the whole of Turkey.
The way had been opened for this by the insertion into the text of the armistice of Article 7 which read: 'The Allies have the right to occupy any strategic points in the event of a situation arising which threatens Allied security.' The condition that a threat should arise to justify occupation was included as a concession to the Turks. But it was of no practical effect, since it was the Allies who would decide whether they were threatened. Article 7 meant that the Allies could occupy any part or the whole of Turkey if they were so minded. Rauf had stood out against this clause, but he finally gave way when Calthorpe threatened to break off negotiations. The armistice agreement was signed late in the evening of 30 October.
Immediately after the signing, Calthorpe gave a letter to Rauf promising that only British and French troops would be used to occupy the Straits and that a small number of Turkish soldiers would be allowed to remain when the forts were occupied. This promise was kept. Calthorpe said also that he had passed on the Turkish requests that no Greek warships should sail to Istanbul or İzmir, and that Istanbul should not be occupied unless the Turkish government failed to maintain order there. The request was indeed passed on – but as the Turks were to discover before long, the Allies turned a deaf ear to it.
Calthorpe described the final ceremony in a letter to his wife:
I had champagne on ice in readiness as I knew that all was going to be well and there was hand-shaking, toasting and polite speeches. Raouf Bey made me a very graceful little speech thanking me for my hospitality and consideration to him as a technical enemy, and he delighted me, and I am sure you, by saying that our twins [whose photograph decorated the cabin] had also taken an important part in this historic event. He said that their cheery smiling faces had been a source of inspiration and encouragement to him in his most difficult and anxious hours. He had often come in and looked at them and they had told him what to do for the cause of humanity. Wasn't that nice
Rauf returned to Istanbul on 1 November, convinced that he had won the confidence of the British and had secured the best possible terms. 'Our country's rights and the future of the Sultanate have been wholly saved as a result of the armistice we have concluded,' he told journalists, adding:
First, I discovered that the British are not aiming at the destruction of the Turkish nation. Second, I saw that our country, contrary to what was expected, will not be occupied. I assure you that not a single enemy soldier will disembark in Istanbul... Yes, the armistice we have concluded is beyond our hopes.
The Grand Vizier, Ahmed İzzet, was pleased with what Rauf had achieved. Rauf's main concern now was to avoid inter-communal clashes, which would give the Allies grounds for occupying Ottoman territory. He insisted, therefore, that irresponsible statements, likely to increase tension between Muslims and non-Muslims, and in particular between Turks and Greeks, should be avoided. One such statement was attributed to Damad Ferid Pasha, who was reported to have said that Ahmed İzzet's government was plotting to massacre Greeks in Istanbul. Damad Ferid was clearly peeved at his exclusion from the armistice negotiations, but his behaviour was symptomatic of the antagonisms which were breaking out within the Ottoman ruling class. The CUP had made many enemies during its six years in power. There were dissensions within its ranks as well as between it and the ramshackle opposition represented by the Liberal Union, which, disastrously for the fate of the monarchy, Sultan Vahdettin supported.
Immediately on his return, Rauf went to the palace to report on the results of his mission. But Vahdettin pleaded tiredness and said that he would receive him a few days later. When the Sultan finally granted an audience, Rauf took the opportunity to complain about Damad Ferid's behaviour. 'I love Ferid Pasha as a good husband to my sister,' Vahdettin replied deceptively, 'but I do not share his views. I am particularly opposed to his political opinions. That's why we disagree strongly.' Then he blurted out: 'There is a nation out there, which is like a flock of sheep. It needs a shepherd to look after it. I am that shepherd.'
Events were to show that no one was less qualified to be a shepherd, and that the Sultan shared the illusion of Damad Ferid and the publicists of the Liberal Union that the Allies would allow the Ottoman state to survive and keep its territory if only it made friends with the non-Muslim communities and made room for foreign business, schools and missionaries. This illusion was fed by a nostalgia for the times of Abdülhamid II, when foreigners and local Christians, including the bulk of the Armenians, prospered. A return to the golden age of Abdülhamid, coupled with the abandonment of the late monarch's pan-Islamism which had threatened Britain and France, was the bait that Vahdettin and the Liberal Union offered the Allies. But the Allies were not tempted.
Departure of the Young Turks
Before this became clear, the Istanbul press, which had been freed from censorship in June 1918, directed its anger at the CUP, including critics of the triumvirate who were now members of the Cabinet. The attacks redoubled when the CUP leadership – Enver, Cemal, Talât and a handful of close associates, including the former police chief in the capital – slipped out of Istanbul in the night of 1/2 November on board a German U-boat. The following day they arrived in German-occupied Crimea. None of them was to see Turkey again.
In Istanbul, Ahmed İzzet's Cabinet was accused by the opposition of collusion in the flight or, at least, incompetence in failing to prevent it. This gave the Sultan the opportunity to press for the exclusion from the government of former members of the CUP. Rather than comply with what he saw as an abuse of the sovereign's prerogative, Ahmed İzzet submitted his resignation on 11 November 1918 after less than a month in office.
He was succeeded by an even older man, Ahmed Tevfik Pasha, who had been the last Grand Vizier of Sultan Abdülhamid. As he saw monarchies tumble first in Russia, then in Austria-Hungary and Germany, Vahdettin feared betrayal by his own ministers. In the case of Ahmed Tevfik, he thought that he could count, at least, on family loyalty, as the new Grand Vizier's son was courting and was soon to marry Vahdettin's daughter. Thus with a fearful and suspicious Sultan on the throne, yesterday's men – Enver, Cemal and Talât – were replaced by the men of the day before yesterday. It was in their company that Sultan Vahdettin would preside over the demise of the Ottoman Empire. But if the historic polity of the Ottoman Empire had been defeated, the nature of what would replace it at the hands of the victorious British remained to be seen. For the moment, however, Britain seemed to be the arbiter of the Middle East.
3
# Arabs and Zionists in Paris
The formal ending of hostilities between the British and Ottoman empires on 31 October 1918 did not bring peace to the Middle East for very long. To the observer, Britain's power seemed paramount, its fleet anchored in the Bosphorus dominating the Turkish capital with its guns, and its victorious forces throughout the region, occupying such historic cities as Jerusalem, Baghdad, Karbala and Damascus. Of Britain's former rivals, Austria-Hungary had dissolved, Russia was in the grip of revolution and civil war, while Germany was defeated. Britain's allies, France, Italy and Greece, while all harbouring ambitions of their own at the expense of the defeated Ottoman Empire, had not played much of a part in its defeat, certainly not compared with the million-strong army Britain had mustered from across its empire. A new area of British imperial endeavour seemed to be opening up. The most powerful man in the Middle East was now Sir Edmund Allenby, judged one of the war's most successful British commanders, in a not exactly overcrowded field. In 1919, he was awarded his Field Marshal's baton, became Viscount Allenby of Megiddo and Felixstowe, and was appointed High Commissioner in Egypt and the Sudan, the former having been declared a British protectorate on the outbreak of war. Behind the impressive façade of British power lay other realities, however.
In international affairs, Britain's clear priority was the peace settlement with Germany, not the future of the Middle East. The British were also preoccupied with the situation in Russia, not least since the disruption caused by the war had brought industrial unrest at home, with fears for the spread of revolutionary ideas. Glasgow was a particular concern. Disturbances in India were to culminate in the Jallianwala Bagh tragedy at Amritsar on 13 April 1919. The murder of two unarmed members of the Royal Irish Constabulary in County Tipperary in January 1919 signalled the start of Ireland's war for independence. In Egypt, too, Allenby was soon confronted by disturbances demanding freedom from British rule. His problems were made no easier by the fact that his troops were understandably anxious to go home after long years of service and separation. More important than all of these disturbing developments was the sober fact that Britain would now have to implement the web of agreements and promises entered into in the course of the war. High expectations had been raised amongst Arabs and Jews, who had thoughts of their own as to how these might be realised as the war was ending. Even in defeat, some Turks were also beginning to glimpse a way forward from the ruins of the Ottoman Empire, Mustafa Kemal not the least of them. It was soon all too apparent that the Middle East was far from being an open book on which the British, or the French, Italians or Greeks for that matter, could write their imperial decrees. Things had moved on from 1914, as the victors were soon to learn.
The Zionist Commission
Even before the war's end, the Zionists had been keen to explore on the ground the possibilities opened up by the Balfour Declaration. Their chance to do so came in December 1917 when the British government suggested that a Zionist Commission should go to Palestine. Weizmann was the obvious choice as chairman. The commission's purpose was to establish a link between the Jews and the British military authorities, but it was also to co-ordinate relief for the Jewish population, help with the rebuilding of Jewish institutions, much needed as a result of the war, and to make political connections with the Arabs. Its terms of reference were later expanded to include Weizmann's favourite project of a Jewish university. Although it was intended that the commission's membership should include Jews from the principal Allied countries, the situation in Russia precluded this, and the Americans declined to take part since they were not at war with Turkey. The Italian member was Angelo Levi-Bianchini, a naval officer, and the French appointed the distinguished scholar Sylvain Levi, Professor of Sanskrit at the elite College de France, who, however, was not a Zionist. Weizmann's other colleagues were the veteran English Zionist Joseph Cowen, Dr David Eder, a former student of Sigmund Freud, and Leon Simon, a distinguished civil servant, while his old friend Ormsby-Gore acted as his liaison officer. This was also the opportunity for Weizmann to explore relations with the Palestinian Arabs, an ambition he had been harbouring for at least a year.
Weizmann left for the Middle East in early March 1918, having first been received in audience by King George V, a mark of how far he had come since 1914. Given wartime conditions, it was a far from easy journey, and it was the end of the month before he arrived in Cairo _en route_ to Palestine. His first contact with the High Commissioner in Egypt, Sir Reginald Wingate, and Clayton, now Chief Political Officer to Allenby's army, seemed positive enough, though the question of Arab attitudes to possible Zionist intentions was raised. Weizmann finally arrived at Tel Aviv on 4 April, and was immediately welcomed by Allenby at his nearby headquarters. While Allenby impressed him, Weizmann quickly concluded that the military authorities had no real grasp of the Balfour Declaration, and that they were very conscious of the position of the Arabs. With his army planning its next advance, it was obvious that Allenby would not want a restive Palestine at his back, and Weizmann was alive to that. Disquieting signs were there, as he soon found out. On 11 April, Storrs, now Military Governor of Jerusalem, attended a function in the city at which speakers asserted Palestine's Arab identity. Storrs later recalled the Arab reaction to the Balfour Declaration, which was that they had been relegated to the position of 'non-Jewish communities' and that there was in it no reference to their political rights.
Weizmann became quickly aware of the political temper of the Palestinian Arabs, informing Ormsby-Gore on 16 April that they were not disposed to accept what the Zionists were saying. Two days later, he wrote home, giving Vera his thoughts on what he had seen. Jerusalem had impressed him no better than it had on first acquaintance. Once again, he lamented its lack of Jewish institutions and the nature of its Jewish inhabitants. The Jewish colonies elsewhere, on the other hand, excited his keen admiration, despite the effects of over three years of war. What was obviously giving him real cause for concern was the partiality of the British military for the Arabs. He confided in Brandeis that the Arabs believed it was the British government's intention to set up a Jewish government and expel them, and that, as a result, they were highly suspicious of the commission. With his pessimistic view of Palestinian Arab attitudes now uppermost in his mind, Weizmann responded positively to a suggestion from Clayton that he should meet Feisal, Britain's principal Arab ally.
The journey to the camp of Feisal's Arab army was something of an adventure, in the course of which Ormsby-Gore came down with dysentery. Weizmann was able to approach close to the Turkish lines, watch Feisal's army at work, and witness T E Lawrence's preparations for his raids on the Hejaz railway. The meeting with Feisal went well. Weizmann explained the nature of the Zionist Commission, said that it wished to allay the fears of the Arabs, and hoped for Feisal's support. Feisal's answers seemed to indicate that he looked favourably on what he had heard, and Weizmann made his way back to Palestine convinced that he had enlisted the sympathy of the real leader of Arab nationalism. He wrote to Vera that Feisal held no high opinion of the Arabs of Palestine. There is no doubt that Weizmann came away from this meeting with the belief that here, at last, was the Arab leader with whom he could work. Subsequent events were to prove him both right and wrong. The fact that he had engaged so positively with Feisal led to the conclusion of the Feisal-Weizmann Agreement of January 1919, which strengthened his hand at the Peace Conference. But events were to show that the leadership of the Arab national movement, and particularly of the Palestinian Arabs, did not lie with Feisal, and that Weizmann was building too many hopes on their relationship. In a letter to Balfour on 17 July, he enthusiastically set out the prospects should Feisal enter Damascus, dismissing the Arabs of Palestine as of merely local significance. Before leaving Palestine, Weizmann was to see the realisation of a project which he had embraced and encouraged for many years. On 24 July, in a ceremony attended by Allenby, Weizmann spoke at the laying of the foundation stone of the future Hebrew University on Mount Scopus.
The Hashemites, the Balfour Declaration and the post-war settlement
Dismissing as he did any potential for reaching an accommodation with the Arabs of Palestine, Weizmann set great store by his meeting with Feisal. There is little evidence, however, that Feisal or the Hashemites endorsed or even envisaged any kind of a Jewish state in Palestine. The public announcement of the Balfour Declaration had brought no response from Sherif Hussein. While many Syrian notables loudly complained about the Declaration, Hussein remained conspicuously silent. Indeed, he ordered his sons to calm the apprehensions of their followers about British intentions. When David Hogarth, the head of the Arab Bureau, called on the king on 4 January 1918, Kedourie reports that Hussein 'enthusiastically assented' to Zionist settlement in Palestine and was '[unconcerned] over the Balfour Declaration and Zionist aims'. This seems curious: Hussein had continued to argue that Palestine was part of the area to be made independent. Moreover, Hogarth's mission to Hussein appears to have deliberately downplayed the Declaration and emphasised that the commitments that the British had made to Zionism had to be 'compatible with the freedom of the existing [Arab] population both economic and political...'. It can be argued that Hussein by no means endorsed the creation of a Jewish state or even an autonomous homeland for the Jews. However, Hussein appears to have been blind to the consequences of the Balfour Declaration.
Hussein also appears to have been ignorant, or pretended to be so, of the likely post-war settlement, which would see a considerable role for France in the administration of Syria. Mark Sykes, accompanied by Picot, had visited Hussein in April 1917 and given some details of their Agreement. It is a matter of dispute as to how much information was given to him. If Hussein had been in any doubt as to what it contained, the _Manchester Guardian_ had published it in full on 26 and 28 November 1917 following its leaking by the new Bolshevik government in Russia, and this had been circulated by Cemal, the Turkish Governor of Syria. Despite all this evidence, Hussein remained in denial. Wingate wrote that it is 'evident that King Hussein has in no degree abated his original pretensions concerning Syria and apparently still nourishes illusion that through the good offices of His Majesty's Government he may be installed, at any rate nominally, as overlord of [a] greater part of the country'. Wingate tellingly argued against disabusing Hussein of this notion as he might abdicate.
Hussein appears to have believed that once the war ended in the Middle East, traditional Anglo-French rivalry would reassert itself and the British would take the side of the Arabs. Lawrence had convinced Feisal:
that his escape was to help the British so much that after the peace they would not be able, for shame, to shoot him down in its fulfillment: while if the Arabs did as I intended, there would no one-sided talk of shooting. I begged him to trust not in our promises, like his father, but in his own strong performance.
In other words, it was vital for Feisal to make significant military progress to ensure the Arab case was heard at the war's conclusion. As it was, Cemal had attempted to break the Anglo-Hashemite alliance by using the Sykes-Picot Agreement as evidence of British perfidy. Feisal had received communications from Cemal, and Lawrence had agreed that he should respond. Lawrence was aware that Britain was in secret negotiations with conservative elements in the Turkish leadership and did not see why Feisal should not do likewise. Also Lawrence appears to have allowed the correspondence because it was better that it happened with his knowledge than in secret.
Feisal continued to be open about corresponding with Cemal, and in the summer of 1918 Cemal's proposals grew more serious. He had been willing to concede independence to Arabia and autonomy to Syria in return for the Arabs changing sides. Lawrence had been particularly alarmed by correspondence in June 1918, which outlined Feisal's conditions for a rapprochement with the Turks, which included handing over Amman as well as the Hejaz to Hussein. Lawrence, aware of all this, sent a warning telegram to Hussein, who ordered the ending of the correspondence.
The Occupation
The British government gave Allenby instructions to treat, so far as military exigencies permitted, the territories captured by the Arabs as Allied 'territory enjoying the status of an independent state (or confederation of States) of friendly Arabs... and not as enemy provinces in temporary military occupation...'. When Allenby met with Feisal in Damascus in October 1918, it was explained that while Feisal was to have the administration of Syria, it was to be a French protectorate. Also the coastal areas from Palestine to the Gulf of Alexandretta were to be under direct French rule. Feisal objected strongly. He did not want to be protected or advised by the French. Lawrence had been told that Sykes-Picot was dead in the water; now it appeared to be alive and well.
Meanwhile, the French had begun to arrive in the Levant. However, French numbers were puny in comparison with the British – only a few thousand soldiers against nearly a million British and imperial troops. It was Britannia's writ that ran through the Middle East. Lloyd George was aware of this. He informed the War Cabinet in October 1918 that the Sykes-Picot Agreement was outdated in the new circumstances of an overwhelming British contribution to the conquest of the Middle East. France's influence in the Middle East was based solely on British sufferance. The British conquest of the Levant and the Balfour Declaration had more or less ensured that French aspirations in Palestine were not going to be met. Indeed by the summer of 1918, the French Foreign Office and at least some colonial opinion was of the view that Palestine was lost and the French would have to seek compensation elsewhere. There was also, for annexationists in both France and Britain, the ominous new diplomatic language of President Wilson. This talk of self-determination and open diplomacy made the implementation of secret deals in the Middle East immensely more complex.
As a result, Feisal was initially in a strong position in Syria. On 30 September 1918, the Allies had created a series of zones in occupied Turkish territory. These were: Occupied Enemy Territory Administration South, made up of Palestine, which the British controlled; Occupied Enemy Territory West, encompassing the coastal littoral of Syria and Lebanon, which French forces were to administer; and Occupied Enemy Territory East, made up of the interior of Syria, which Feisal's Arabs were allowed to control jointly with British forces. In overarching, virtually dictatorial, control of all three sectors was General Allenby. In practice, as he controlled the military forces, the French or Feisal could do little of significance without his agreement. Allenby, though, was extremely concerned about the potential for trouble from the competing ambitions of the Arabs and the French. He confided in a letter to the new Chief of the Imperial General Staff, General Sir Henry Wilson, that he believed that only if the French exercised considerable tact would there be any prospect of placating Arab opinion. He foresaw that politics in the occupied territories, especially in Palestine and Syria, would be difficult because of the competing claims of the Jews, Arabs, the European powers and other minorities. Attached to this letter was a memorandum from Hogarth of the Arab Bureau. While Hogarth claimed to be happy to leave Syria to the French, he warned that Arab opinion believed that this was incompatible with political independence and that Britain would be accused of having tricked the Arabs into betraying Islam (i.e. the Caliph, the Sultan of Turkey). Britain would also be open to charges of hypocrisy in its repeated declaration of self-determination for small nations.
The first crisis soon arose. Arab forces dashed from Damascus to Beirut and the other coastal towns as Turkish resistance collapsed in early October. An Arab government was proclaimed in these regions. The French, who had been allocated Lebanon as recently as 30 September 1918, were furious. This, in their mind, was a breach of the wartime agreements. It fuelled suspicions of Feisal and the British. Allenby was forced to accelerate the advance of his troops towards Beirut, as it became increasingly clear that there might be a Franco-Arab clash. He attempted to get Feisal to withdraw. Feisal warned that he might be forced to abdicate if he did not get assurances that the withdrawal would be only temporary and did not imply any abdication of Arab or Hashemite rights in Lebanon. He was reassured that the divvying up of the occupation areas was a temporary solution until the Peace Conference had made its decision. This allowed Feisal to give way to the French and let them take over Beirut and the other coastal towns.
Feisal's problems were not simply confined to the Great Powers. The Syria and Lebanon that he occupied had suffered from widespread famine in the previous two years of war. Eyewitnesses spoke of emaciated, hungry children in Beirut 'dying in the gutters'. Influential Damascenes remained suspicious and resentful of the imposition of Feisal upon them by force of arms. The large Christian minorities in both Lebanon and Syria viewed the Hashemites with distaste. An American report on Syria concluded that the country was deeply divided between those who were desirous of immediate annexation by France and those, mainly Muslim, who believed Arabs could rapidly evolve politically and did not require French tutelage. This last group could be driven into the arms of the Turks if the French were not careful. Feisal and his followers attempted to win hearts and minds in the countryside by restarting Ottoman welfare schemes. They also invested some of their British subsidy in buying off Syrian notables. In spite of this, Feisal's authority in Syria was limited.
The British did not ease Feisal's problems by asking him to remain in a military role rather than becoming involved in local politics, and making a Syrian political leader, Ali Riza Pasha, governor of all the occupied territories. Independent-spirited and with no loyalty to Britain, France or Feisal, Riza Pasha began to encroach on French-occupied areas in Lebanon. Feisal, knowing this was popular with the Syrian population, could not object. However, it significantly impacted on his own ability to get on with the French. The British realised their mistake and removed Riza Pasha at the end of October and transferred his powers to Feisal. However, the Emir remained 'largely a figurehead, which nationalist organisations manipulated for their own purposes'. Indeed, they tended to limit his room for compromise. Feisal was also overburdened with responsibility. He not only had to try to keep control in Syria, he was also to represent the Arabs at the Peace Conference. He would spend a considerable amount of 1919 in Europe. His protégés in Syria, seemingly with little awareness of the political realities, undermined him by seeking political advances far too quickly.
The British and the French continued to appease Arab opinion in the last couple of months of 1918. Perhaps motivated by the continuing fall-out from the revelation of the Sykes-Picot Agreement, the disquiet in the Arab world about the Balfour Declaration and the need to impress the Americans that they were committed to the new diplomacy of self-determination, two declarations were issued to the Arabs in 1918. The first was the Declaration to the Seven. The Seven were a small committee of Syrian nationalists with whom the British had been in contact. Issued by Mark Sykes with official British government approval in mid-1918, the Declaration reiterated the recognition of Arab independence in the Arabian Peninsula. Sykes felt he could go no further without French agreement. After discussions between London and Paris, a new Anglo-French Declaration was issued on 9 November 1918. It explicitly committed the British and French to 'the complete and definite emancipation of the peoples so long oppressed by the Turks and the establishment of national governments and administrations deriving their authority from the initiative and free choice of the indigenous populations'. It carefully avoided the use of words like independence. As one commentator has put it, the declaration did not contradict the Sykes-Picot Agreement, 'it only concealed its most crucial details'. Indeed, the Declaration was for British ministers not a conversion to the principle of national self-determination but a hard-headed decision to use this new Wilsonian language of diplomacy for traditional balance-of-power ends. In this case it would be used to weaken the French case for territory in the Middle East. The Arab cause, therefore, appeared to be in a very strong position on the eve of Feisal's departure for the Peace Conference. When these promises turned out to be unfulfilled, the Arabs felt an understandable sense of bewilderment and betrayal.
Feisal leaves for Europe
Feisal realised that he was unlikely to gain the loyalty of the Christians of Syria and Lebanon if he associated the Hashemites and the Arab cause too closely with Islam. Therefore, on 11 November 1918, the day of the Armistice in Europe, he spoke to a large crowd in Aleppo, denouncing the rule of the Ottomans. He made it clear that he realised that the loyalty of the Revolt he led depended on it not being motivated by personal or familial aggrandisement and that he was not a tool of the Western Powers. Pointing to the Anglo-French Declaration, he noted that independence would come if the Arabs organised orderly and stable government. The most important emphasis of the speech was his declaration that he was an Arab before anything else. He decried religious sectarianism and declared all religions equal before the law. In the ten days that followed, Feisal toured Syria and Lebanon. He generally received a warm welcome, but in Beirut, with its large Christian population, it was mainly Muslims who welcomed him with enthusiasm, suggesting problems ahead.
On 21 November 1918, Feisal left for Europe on a British warship. The British government, on the advice of Lawrence, had been convinced that it was in Britain's interests to invite him to the Peace Conference. Feisal would make the Arab case for self-determination and the cause would have a chance of attracting American support. King Hussein had agreed that Feisal would act as his plenipotentiary at the Peace Conference. Feisal was accompanied by a small delegation of Arabs, including Nuri al-Said, an Arab nationalist officer in the Ottoman army who had joined the Arab Revolt in 1916, and had become Feisal's chief-of-staff. Lawrence also acted as Feisal's chief adviser.
The French were unhappy with Britain's decision to invite Feisal to the Peace Conference. They knew that Feisal coveted all of Syria and were therefore anxious to exclude him. They also knew that Feisal might prove to be an attractive figure to the Americans and their campaign for national self-determination. After their attempt to prevent Feisal coming failed, they tried appeasement. On his arrival in Marseilles, he was decorated with the Croix de La Legion d'Honneur prior to going on a tour of the recent battlefields of the Western Front. He was treated as a distinguished guest but not as a plenipotentiary with the right to speak on behalf of the Arab nation.
An Anglo-French gentlemen's agreement
Excluding France from Syria was precisely what many in the British government wanted; none more so than the Lord President of the Council, Lord Curzon. (Curzon ran the Foreign Office for most of 1919 as Arthur Balfour was busy with the peace treaties; he became Foreign Secretary in October 1919.) He reflected the widespread view within British government circles that France should not be allowed to straddle British lines of communication to India and the British Empire in the Far East. With German ambitions destroyed, the essential bond between the British and the French was no longer present. Instead Anglo-French relations might revert back to the days of the Fashoda Crisis, when a colonial dispute in the Sudan in 1898 had brought the two powers to the brink of war. Other advocates of using the Arabs to keep the French out of the Middle East included the Arab Bureau in Cairo and Foreign Office officials such as Arnold Toynbee. They were given plenty of opportunities to put their case.
T E Lawrence, on his return from the Middle East, addressed the British Cabinet's Eastern Committee. He put forward a bold proposal for the administration of the post-war Middle East: that Feisal should administer Syria, while Mesopotamia should be split into two areas under Zeid and Abdullah. The War Office and the Foreign Office were supportive of Lawrence's grand design. However, the India Office, long sick of what they considered the indulgence of the Hashemites by their departmental colleagues, was bitterly opposed. A truncated version of this plan would eventually emerge in 1922. By then Syria would be lost both to the Hashemites and to the wider cause of Arab nationalism.
In the meantime, Lloyd George had become increasingly obsessed with the Middle East. He had begun to view it as a blank canvas on which a new order could be drawn. Greek claims in Asia Minor could be endorsed, as could Jewish demands for a homeland in Palestine. Armenians and Kurds could carve out nation states. Arab states could be established under the tutelage of the British. Egypt would be made a kingdom under British supervision. Local client states could be cheaply brought under an umbrella of British power. In such a scenario only small forces would be required to maintain British power and influence in the region. What role the French would play in all of this was unclear.
The British would have liked to exclude the French from Middle Eastern arrangements completely. However, this proved impossible. France's involvement in the East had been circumscribed by the need to focus virtually all of its military efforts on the Western Front. Why should French sacrifices against the Germans at the Marne, Verdun and in Champagne be counted as less worthy of reward than the relatively easy victories won by the British in the Middle East? The British, especially Lloyd George, were aware of this claim, though as Britain had borne the brunt of the hardest fighting on the Western Front from mid-1917 this in itself carried little weight. However, the future peace of the world was more likely to be determined by cordial relations between Britain and France than by keeping the Arab cause happy. Lloyd George was to spend the first ten months of 1919 torn between his desire to rearrange the Middle East entirely on British terms and the requirement to keep France as an ally. At times, which goal was the priority was not entirely clear.
On 1 December 1918, Lloyd George and the veteran French Premier Clemenceau met in London where they made a 'gentlemen's agreement' that was to cement France's rights in the Levant and Syria. In return, Lloyd George secured enhanced gains for Britain. He was determined that Britain's share of the Middle Eastern spoils secured at such great cost in lives and money would be increased. There were more than a million British Empire troops in the Middle East at the end of 1918. Allenby's advance into Syria had been one of the few glorious British victories of the war. Lloyd George made clear to Clemenceau that he wanted control of Palestine and the area around Mosul. Mosul was wanted because of its large deposits of oil and the securing of future oil supplies had become an important aim of British policy, though by no means overarching. Clemenceau was amenable. While acknowledging the problems he might have with his colonial lobby, the French leader replied phlegmatically to Lloyd George's demands. 'You shall have it', he declared. In truth, Clemenceau did not care much for the French Empire. His main, perhaps sole, interest was in maintaining British support for French demands against the Germans. His submission to Lloyd George's demands was partially in exchange for the Prime Minister's apparently clear backing for Clemenceau's request for a unified French administration for Syria. There were also promises of a share in the spoils of any Middle Eastern oil. There was no formal paper outlining this gentlemen's agreement. Clemenceau had made his concessions. He now wanted to be assured that France's Middle Eastern ambitions would not be wholly thwarted. Lloyd George and the British government, however, were to continue to play the Feisal card, alienating the French and perhaps encouraging their Arab protégé to be more obstinate in his dealings with the French than was wise.
On 4 December, the Eastern Committee met, with Lawrence attending again. Curzon fulminated against the Sykes-Picot Agreement, which he now believed had been completely superseded by the new facts on the ground. He saw the Agreement as storing up trouble in the future with Arab opinion. However, the Foreign Secretary Arthur Balfour, aware no doubt of Lloyd George's secret understanding with Clemenceau, declared that Britain could not revisit and amend Sykes-Picot. He took the view that the Agreement could only be scrapped if the Americans pressed for it. As Lawrence's biographer notes, the conclusions of this meeting were that the British Cabinet 'was not prepared to offer Feisal anything more than sympathy'.
Undoubtedly, the British government viewed President Wilson's doctrine of national self-determination as a potentially useful tool to keep the French out of Syria. It suited British policy for the time being at least that Feisal get American help rather than British. Their policy was 'to back Feisal and the Arabs as far as we can, up to the point of not alienating the French'. Curzon was also aware that channelling the Hashemites towards Syria rather than Mesopotamia or Palestine had the potential to aid, if not save, British ambitions in the Middle East. At the same time, the French attitude on Syria was hardening. They made clear that they wanted no British discussions with Feisal regarding Syria. Syria, as far as they were concerned, was now a French responsibility and not really a matter for the Peace Conference. When Balfour met Feisal on 12 December, the latter warned him that the Arabs would go to war against the French over Syria even if the chances of success against a Great Power were negligible. Balfour assured him that his suspicions regarding French plans for Syria had little basis in fact.
Weizmann and the Zionist preparations for the Peace Conference
Weizmann's return from Palestine on 5 October allowed him no respite, rather the contrary since the war was clearly entering its final phase at bewildering speed, especially in the Middle East. With the future of Palestine now likely to be at Britain's disposal, he formed a small group chaired by Herbert Samuel, consisting of Sir Alfred Mond, a member of Lloyd George's government, Sokolow and himself, charged with producing a scheme whereby the Jewish position in the country could go forward under British trusteeship. Ormsby-Gore was also associated with its work. Weizmann also embarked upon a flurry of meetings with leading politicians, including Balfour, Cecil, Sykes, Ormsby-Gore, Samuel and the influential General Smuts, as well as key figures in British intelligence and Lawrence and Hogarth. The focus of his discussions with Cecil, Lawrence and Hogarth seems to have been the need to maintain close relations with Feisal, which clearly needed a sensitive touch. The level of access he enjoyed at this pivotal time was, once again, of incalculable value to the Zionist movement.
Also anxious to keep his American colleagues in close step with what he was doing, Weizmann explained the position at some length to Brandeis on 29 October 1918. What clearly concerned him was that in view of the rapid turn of events in the war, Zionism was hardly a priority for the Allied leaders. Even so, the situation in the Middle East had its own momentum. Weizmann naturally viewed the establishment of Feisal's position as a positive development, explaining to Brandeis how the Hashemite leader had been prepared to acknowledge Palestine as a Jewish sphere of influence in return for technical and economic assistance to the Arab states. What he portrayed as a division of the Middle East between the Hashemites and the Zionists, he feared was being undermined by the details, which were now emerging, of the Sykes-Picot Agreement, resented as it was by the Arabs. But he was also concerned by reports of growing Arab hostility to the Jews in Palestine, and by the extent of pogroms in the disintegrating empires of central and eastern Europe. In a letter to his friend David Eder in Tel Aviv, he confided his fear that if they did not secure Palestine these communities might be exterminated. His concern that the American Zionists should put their full weight behind any representation to a peace conference was repeated in a message to Brandeis sent on Armistice Day. On that historic day he had lunch with Lloyd George, arranged, it seems, by his old friend C P Scott.
Meanwhile, what was of the essence was an agreed statement of what the Zionists wanted to come out of any Peace Conference, and given the disparate nature of the movement, stretched as it was across several jurisdictions, this was not as straightforward as it might have seemed. In the circumstances, it was vital to put down a marker about what the Zionists felt should happen during this crucial interim period. After meetings with Balfour and Cecil, on 1 November 1918 Weizmann submitted to the latter a ten-point document setting this out. Acknowledging that control would be in the hands of the British, the document requested that the work of the Zionist Commission be allowed to continue and that it be made the advisory body to the military administration on matters relating to the Jewish inhabitants. In addition, the military was to assist the Zionist Commission in organising the Jewish population and encouraging Jewish participation in administration. In a matter close to Weizmann's heart, the commission was also to be permitted to carry out preparatory work for the Hebrew University on Mount Scopus. Crucially, a land commission was to be created, including Zionist Commission members, with a view to reviewing land tenure and ownership, including an examination of land registers and a possible modification of existing land law.
Significant as this statement was, it could be nothing more than a holding document until Samuel's committee had completed its work on a definitive statement of Zionist aims which would be placed in the hands of the Peace Conference. A draft was ready by the end of November, and Weizmann, understandably anxious to sound out British reactions to what they would be proposing, sent copies to Clayton in Palestine and, crucially, to Balfour. At a meeting with Balfour on 4 December, Weizmann proposed that the Peace Conference should declare Palestine to be a Jewish country under a trustee. He then revealed that they would be asking for Britain to be that trustee, and confirmed that they would want to see a Jewish population of some 4 to 5 million being built up over the next 25 years. The interview was positive, with Balfour indicating his broad agreement with what was going to be proposed, and assuring Weizmann that it did not deviate from his November 1917 Declaration.
However reassuring this might be, Weizmann still needed to secure other flanks, not least with Feisal who was also expected to press his claims before the Peace Conference. The two leaders met in London on 11 December 1918, with Lawrence acting as interpreter. Feisal began by denouncing the Sykes-Picot Agreement, a sentiment with which Weizmann concurred. He then asked for an outline of the Zionist programme. Weizmann's reply was remarkably candid, saying that they expected the Peace Conference and Feisal to acknowledge the rights of the Jews to Palestine. They would request that the country be put under British trusteeship, with a government in which the Jews would share. He also confirmed that they would request a reform of the land laws in order to permit the colonisation of 4 to 5 million Jews, while safeguarding the rights of the Arab peasantry, and reassured Feisal that there was no intention to interfere with the Muslim Holy Places. For his part, Feisal responded that he would seek to reassure the Peace Conference that the Zionist and Arab movements were in harmony, and that he would support the Jewish position. The essence of this conversation was embodied in a document drawn up between the two leaders and signed on 3 January 1919. In what was to become known as the Feisal-Weizmann Agreement, the two agreed to promote the close cooperation of the Arab State and Palestine, the boundaries of which would be defined after the Peace Conference. The Constitution and administration of Palestine would allow for the implementation of the Balfour Declaration. Large-scale Jewish immigration into Palestine was to be encouraged, while the rights of the Arab farmers would be protected. Provision was to be made for the free exercise of religion, and the Muslim Holy Places were to be under Muslim control. A commission of experts sent to Palestine by the Zionist Organisation was also to report on how the Arab State might be developed. Finally, the parties pledged to work together on all these matters before the Peace Conference. Feisal did, however, enter an important caveat, of which there are two rather different versions. In the rather opaque translation made by Lawrence, Feisal recorded that if changes were made to the establishment of the Arabs then he could not be answerable for any failure to carry out the agreement. In the version published in 1938 by George Antonius, Feisal was more specific, making the agreement absolutely dependent upon the implementation of Arab independence. In fact, the meaning is clear enough, and the subsequent collapse of Feisal's hopes in Syria rendered the agreement meaningless; but it is interesting that Feisal made it, just the same.
In anticipation of the forthcoming Peace Conference, Weizmann went to Paris at the beginning of January 1919 as part of the Zionist Mission which had been invited to present the movement's case, staying at the Hotel Plaza on the Avenue Montaigne. An early sign that things might go his way came at a meeting with the President's aide, Colonel House. Weizmann left with the clear impression that the Americans were sympathetic to the Zionist position, not least since House assured him that he had recently been briefed on the issues by Balfour. In a letter to his wife, he confided in her that the Americans favoured a Jewish Palestine under British auspices, the essence of the position he was preparing to put to the Conference. House also promised to arrange a meeting with President Wilson, which took place on 14 January. The fact that Weizmann had this level of access was in itself significant, and must have done his credibility no harm in his uneasy relations with the American Zionists. His chief concern was ensuring that the statement of policy which was to be presented to the Conference was as realistic as possible, especially given the rather different perspectives of the various Zionist groups and his contacts in British government circles. Reconciling these views was by no means straightforward, as it turned out.
For some time Weizmann had been uneasy about the attitude of the British military administration in Palestine, which he felt was too inclined to take the Arab side. It was, therefore, important to seek the views of General Sir Arthur Money, Chief Administrator in Palestine, who was then in London. Money's reaction was that the Arabs would react against the proposals in the draft document, not least where they would affect distribution of the land. In reply, Weizmann argued that unless the Jews secured a home they would be faced with a catastrophe. He also asserted the historic right of the Jews to Palestine, which, he said, was not invalidated by the fact that their expulsion had happened 2,000 years before. On the land question, he claimed that what they wanted was to break up the large estates in favour of small farmers, by implication Jewish, though this was not stated. Nevetheless, by 3 February 1919, the final text of this key document had been agreed. Much would turn on it, and its content was to underpin, in no small measure, the nature of the subsequent British Mandate for Palestine.
The 'Statement of the Zionist Organisation regarding Palestine' was signed by Lord Rothschild, by Weizmann and Sokolow on behalf of the Zionist Organisation and of the Jewish population of Palestine, by Israel Rosoff for the Russian Zionist Organisation, and by Julian Mack, Stephen Wise, Harry Friedenwald, Jacob de Haas, Mary Fels, Louis Robison and Bernard Flexner for the Zionist Organization of America. There was a noticeable absence of any French Jewish signatory. In its preamble the document asked that the Conference recognise the Jews' historic title to Palestine and their right to have their National Home there. The newly formed League of Nations was to have sovereignty over Palestine, governed by Great Britain as its Mandatory.
The choice of Britain rested on what the document claimed was the special relationship it had with Zionism, as evidenced by the 'Uganda Offer' and the Balfour Declaration. Moreover, the Jews liked the way in which Britain had approached colonial government. The British were to create the necessary conditions for the creation of the National Home, but, in an interesting move beyond the terms of the Balfour Declaration, the document also looked forward to the eventual creation of an autonomous commonwealth. In order to do that, Britain was to promote Jewish immigration and settlement while safeguarding the rights of the non-Jewish population, work together with a Jewish council, and give that council priority where public works and natural resources were concerned. On the critical question of land, the Mandatory was to appoint a commission, with Jewish representation, which would have the power of compulsory purchase, as well as making available state land and what it described as inadequately cultivated land, though the position of the existing population was to be protected. There was to be no discrimination on racial or religious grounds. The boundary of Palestine was to lie east of the river Jordan close to the line of the Hejaz railway, and include the river headwaters on Mount Hermon in the north.
The document was at pains to justify the nature of the Jews' claims to Palestine, notably that it was their historic home from which they had been violently expelled, but to which they had always hoped to return. In addition, Palestine would provide a refuge for Jews living under harsh conditions in Eastern Europe, even though it was conceded that the country was unable to take in more than a minority of them. Finally, the document pointed to what it claimed was the desolate condition of the land, which could only be developed through Jewish enterprise, as evidenced by the success of the existing settlements. These Jewish claims to Palestine had been recognised in the Balfour Declaration, and then supported by the French, Italian, American, Japanese, Greek, Serbian, Chinese and Siamese governments.
'Much the most dignified presence at the peace conference'
The Conference opened in Paris on 18 January 1919 under Clemenceau's presidency. While a wide variety of countries was present in Paris, the Council of Ten represented the principal victors; namely, the heads of government and foreign ministers of the United States, United Kingdom, France and Italy, as well as two Japanese members. Although Palestine was far from the top of its agenda, it was to the advantage of Weizmann and the Zionists that the British representatives on the Council were Lloyd George and Balfour. The Conference's dominant personalities were Clemenceau, Lloyd George and Wilson.
A British proposal that the Arab territories captured from Turkey should be subject to what was euphemistically called advice and assistance from the Mandatory Power until they were able to stand on their own two feet was agreed by the Council of Ten. The native populations would receive the right to choose which power would hold the Mandate over them. The Mandatory system would also be subject to League of Nations supervision. Stéphen Pichon, the French Minister of Foreign Affairs, proposed in February that France wanted its sphere of influence and area of direct control as proposed under the Sykes-Picot Agreement to be amalgamated into a single Mandate. He argued that France's long-standing economic, political and cultural links with the region made it the most suitable Mandatory power. France also expressed a willingness to work with Feisal provided he was willing to accept a large degree of French control over his government. The French had clearly decided that the Mandate system was not significantly different from French colonial practice in Morocco.
Feisal presented his case on 6 February 1919. By then he had already made a favourable impression on many of the assembled delegates. The American Secretary of State Robert Lansing, writing a couple of years later, was lavish in his praise. To another observer, he was 'much the most dignified presence at the peace conference'. Lloyd George was of the view that Feisal's 'intellectual countenance and shining eyes would have made an impression in any assembly'. The American journalist and Wilson's confidential translator Stephen Bonsal declared that Emir Feisal, Nuri Pasha and Lawrence 'were certainly the most resplendent figures that had ever entered the Quai d'Orsay'. Feisal had come not as a 'supplicant but to demand the rights of his people and the observance of solemn agreements which, as the emergency was over, some were inclined to forget'.
Feisal was well aware that his case had to be strong to attract the sympathy of the United States in particular. He had to prove that Allied plans for the Middle East drawn up during the war were injurious to the right of national self-determination. He also had to prove that the Hashemites were the true leaders of the Arab cause. On this last point he was adamant:
My father has a privileged place among Arabs as the head of their greatest family and as Sherif of Mecca. He is convinced of the ultimate triumph of the ideal of unity, if no attempt is made now to thwart it or to hinder it by dividing the area as spoils of war among the Great Powers.
Feisal had prepared his case in a memorandum of 29 January, pointing out how the region had been the home of ancient civilisations and held potential for the future. His basic demand was straightforward – independence for all of the Arabs from the line Alexandretta–Persia southwards, which, he argued, had been promised by the Allies during the war. The basis for this demand was that the area constituted a unit suitable for national self-determination. All the inhabitants spoke Arabic and came from the one Semitic stock; there were few nations so homogenous. Furthermore, the Arabs had fought with the Allies, fulfilling their part of the bargain. Now it was time for the Allies to do likewise. Feisal's presentation did contain some exaggerations, however. There were never the 100,000 warriors that he claimed were fielded by the Arabs. While Lloyd George picked some holes in the military contribution of the Arabs, comparing it unfavourably to Britain's commitment of more than a million troops, he remained broadly positive about their case. Pichon's attempt to assert that France had played a major role in the Middle East campaign backfired as Feisal, in the nicest possible way, accurately outlined the insignificant numbers of French troops that had fought in the region.
The Reverend Howard S Bliss, President of the Syrian Protestant College in Beirut, addressed the Council of Ten a week after Feisal. Bliss was Syrian-born, but of American ancestry. He urged that a commission be sent at once to Syria in order to allow Syrians 'to express in a perfectly untrammelled way their political wishes and aspirations, viz: as to what form of Government they desire and as to what power, if any, should be their Mandatory Protecting Power'. Clemenceau was hostile. The French had organised the attendance of a Lebanese Christian delegation, which decried any attempt to impose a primitive Bedouin emir as leader of the advanced races of Syria. Chekri Ganem, the chairman of the pro-French Central Syrian Committee, was brought forward to argue that Syria desperately needed French tutelage. Ganem argued for the separation of Syria from Arabia, as it was a different country and that to 'annex Syria to Arabia would be to do violence to the very soil from which the race and its history have sprung'. The delegation warned of the dangers of allowing the fanatically religious Hejaz to gain control of Syria because its popularity was based on Syrian Muslims, seeing this as 'the first foundations of a great Moslem (not Arabian) Empire, with the Hedjaz [sic] dynasty at the head'. Presumably for the benefit of the British, it was pointed out that certain Muslims were seeking 'a further extension of the Empire of Islam, towards Africa and towards India'. Ganem had a point; the various Christian sects concentrated in Lebanon were wary of Hashemite rule. Indeed the monolithic Arab nation which Feisal referred to was much more diverse than he claimed. Feisal had made considerable attempts to woo Lebanese Christians since he had taken Damascus, offering eminent Christians high-ranking ministerial and diplomatic posts. But these efforts to bring the Lebanese, and for that matter Syrian, Christians on side did not work. No more than a small group of Christians actively supported the Hashemite cause.
However, the French were not simply satisfied with the protection of this minority – they wanted all of Syria. However, Wilson was informed, during the course of this presentation, that Ganem's credentials as an objective observer were somewhat undermined by the fact that he had been resident in France for more than three decades. Wilson reacted by pacing the room. He was far more impressed by the Arab case and Feisal in particular. Bonsal heard him say at the end of February 1919: 'Listening to the Emir I think to hear the voice of liberty, a strange, and, I fear, a stray voice coming from Asia.'
Arguments continued to rage between the British, the French and the Americans. Britain's Colonial Secretary, Lord Milner, handled much of the negotiations with the French. Milner attempted to get the French to negotiate with Feisal. He pointed out the impossibility in the context of a Peace Conference committed to the ideal of self-determination for the French to be imposed on the Arabs of Syria as a Mandatory Power. Clemenceau, who was quite detached from the French colonial lobby, was amenable to agreeing some sort of deal with Feisal. Milner explained to Lloyd George on 8 March 1919 that the British position should be to put pressure on both sides to come to some kind of equitable solution. In a letter to Lloyd George, Milner came up with a proposal to resolve the impasse between France and Feisal: France would be given a Mandate over Syria. However, this was to be 'the mildest form of Mandate' and the native population would exercise most of the powers, while France would have control over foreign policy and development. Milner, however, was not confident that the French would accept anything short of the 'virtual ownership of Syria'.
The Zionists before the Council of Ten
The Zionist delegation was scheduled to present its case before the Council of Ten on 28 February 1919, but on the 26th Weizmann and Sokolow were informed that their meeting was being brought forward to the following day. The practical effect of this was that Jacob de Haas, who was to represent the American Zionists but who was still in London, was unable arrive in time. Much worse from Weizmann's perspective was the unwelcome news that the French Foreign Ministry was inviting two representatives of the French Jewish community. The first of these, André Spire, was a distinguished civil servant of noted Zionist sympathies. But his colleague, Sylvain Levi, was much more problematic. Not only did Levi come from a strongly assimilationist background hostile to Zionism, but he and Weizmann had crossed swords the previous year on the Zionist Commission. Members of the British and American delegations professed ignorance over Levi's invitation, but an attempt by Weizmann to lobby against him was unsuccessful. According to Weizmann's account, however, Levi was annoyed at not being trusted, and promised to say nothing against Zionism.
The Zionist Mission which presented itself before the Council of Ten in the Quai d'Orsay on the afternoon of 27 February 1919 consisted of Weizmann, Sokolow, Ussishkin, Spire and Levi. Present to hear them were the Foreign Ministers Stéphen Pichon of France, Baron Sonnino of Italy and Baron Makino of Japan, as well as the American Robert Lansing. The British Empire was represented by Balfour and Milner, who, of course, had the arguments at their fingertips, while Ormsby-Gore was also present for this particular session. The Zionists could be assured of a sympathetic hearing and reception from the British members, while Pichon, too, was familiar with the issue, having signed the French government's declaration of 14 February 1918, and personally assured Sokolow of its support for the British government's position. In his autobiography, Weizmann recollected that Clemenceau was present for the early part of the hearing, and it seems that he did stay for a short time.
The Zionist case was opened, with his customary gravitas, by Sokolow, who requested that he submit to the Council the 'Statement of the Zionist Organisation regarding Palestine', adding that the delegation had come to assert the historic rights of the Jews to Palestine, where they had created their civilisation prior to the Dispersion. Conceding the comfortable position of the Jewish communities of France, Britain, Italy and the United States, a key point in view of the nature of his audience, he nevertheless argued that they represented only a minority of a much greater world Jewish population whose needs could only be met through the establishment of a home. Sokolow then rehearsed the principal recommendations of the 'Statement' he had distributed; namely, that the Jews' historic title to Palestine be recognised together with the right to have a National Home there; that the League of Nations be granted sovereignty over Palestine with Britain as the Mandatory Power; and that Palestine be governed in such a way as to secure the Jewish National Home with the possibility of this leading to an autonomous commonwealth which would have due regard to the rights of the country's non-Jewish population and the status of Jews in other countries. Weizmann's recollection was that his colleague made a real impression on his listeners.
It was now Weizmann's turn. While he was experienced in dealing with senior British politicians and public servants, this was his debut before such an international gathering, and his main concern was to convince them of the practicalities of the Zionist endeavour. He brought with him his recent experience as president of the 1918 Zionist Commission in Palestine. Beginning by highlighting the pre-war sufferings of the 6 to 7 million Russian Jews, he argued that these had continued under the new regime. This would result in an increase in Jewish emigration, but he predicted that the capacity of Western Europe and the United States to absorb immigrants would bring them under increasing scrutiny; in view of what was to happen to American immigration legislation in the early 1920s, which introduced strict ethnic quotas, he was accurate enough. He then turned to the crucial question of Palestine. Acknowledging that there were between 600,000 and 700,000 existing inhabitants, he argued that this represented a population density of 10 to 15 per square kilometre, which he compared with 160 per square kilometre in Lebanon. As a result, he argued that some 4 to 5 million could be settled without detriment to the rights of the existing population. Such was the essence of his case. In order to promote this settlement, the proposed Mandatory Power would promote Jewish immigration and settlement, while safeguarding the rights of the existing population; work to develop the National Home in cooperation with a council representing the Jews of Palestine and elsewhere; and give that council priority in the development of Palestine's natural resources. Weizmann concluded by referring to the 1 million Jews who, he claimed, were waiting to come to Palestine, emphasising that the support of the Great Powers would be needed for this to be done.
Ussishkin, who spoke as President of the South Russian Jewish National Assembly representing some 3 million Jews, was brief, and contented himself with supporting what Sokolow and Weizmann had said. He was followed by Spire, who, while saying that he spoke on behalf of the French Zionists, conceded that they were a minority of French Jews. So far, all four had been remarkably succinct. Not so Levi, who addressed the Council for some 20 minutes, managing to undermine much of what the others had said. From the start he made it clear that he was not a Zionist, and that while a Jew by origin he was French. Even so, the first part of what he had to say did not seem greatly at odds with what had gone before. He, too, stressed the suffering of the Jews of Central and Eastern Europe, insisting that they dreamt of Palestine as the one place where their sense of nationality could be developed. He then proceeded to demonstrate that the Zionist movement had already created a foundation for further development through the fostering of the Jewish settlements which Rothschild had encouraged, as well as the opening of schools. Zionism's task, he argued, was to direct Jewish migration from Eastern Europe to Palestine.
At that point the tone of his submission changed abruptly. He said that he would now address the practical difficulties with the frankness of an historian. In the first place he pointed to the size of Palestine compared with the millions of Eastern European Jews who might go there. The country's present population was 600,000 to 700,000 Arabs, and he did not feel that an equal number of Jews could be accommodated at the standard of living they had experienced in Europe. He then turned to the nature of the prospective Jewish settlement, drawn as it would be from countries where they had been persecuted. They would, he warned, bring dangerous passions to Palestine, which, in a curious turn of phrase, he said would become a concentration camp for Jews. A further problem would be the merging of Jews from such a diverse group of countries into a single nationality, something with which the Peace Conference would be familiar. The Zionist solution to this dilemma was to be the formation of an International Jewish Council with responsibilities for Palestine, but as a Frenchman of Jewish origin he feared the dual citizenship that this might imply. Turning to the principles of the French Revolution, he then argued that as the Jews had campaigned for equal rights in the countries they inhabited, it would be shocking if they claimed an exceptional position in Palestine. The most he would concede, it appeared, was the creation of a Jewish committee to organise immigration and look after economic and social affairs in Palestine but with no political function. Notwithstanding the fact that his lengthy discourse had gone far to undo much of what had gone before, he ended by reminding the Council of the Jews' contribution to civilisation and the further contributions they might make by the shores of the Mediterranean.
There is no doubt that the nature of Levi's submission threw the rest of the delegation into confusion, but after a hasty consultation they decided against entering into a public debate with him before the Council. They were rescued from their dilemma by Lansing, who asked Weizmann whether the term 'Jewish National Home' meant an autonomous Jewish government. He replied that they did not want the latter but rather an administration, which, under a Mandatory, would be able to build up Jewish institutions. Over time, a sense of nationality would grow so that, in his striking phrase, Palestine would become as Jewish as America was American or England was English.
Made impromptu in reply to Lansing's question, this concept was to enter the political lexicon over the next few years, not always to Weizmann's advantage. Weizmann then seized the opportunity to refute Levi. Since the International Jewish Council would have no political function, the matter of dual allegiance to which the Frenchman had alluded would not arise. Conceding Levi's point that Palestine as it then existed could not absorb large numbers, he made the obvious riposte that it was their purpose to transform the country in the manner of California or the French colony of Tunisia. In the latter, he instanced that there were 8 million olive trees compared with 45,000 in 1882. To achieve this kind of change would be difficult, he admitted, but not as bad as the problems of the Jews of Eastern Europe. Finally, in a clear stroke against the assimilationist position Levi had represented so vigorously, he claimed that he spoke for 96 per cent of the Jews of the world. The delegation then left. Balfour's secretary came out to pass on his congratulations. Weizmann pointedly refused Levi's proffered hand, and accused him of betrayal. The two men never spoke again. An exultant Weizmann confided in his wife that it had been the most triumphant moment of his life.
The day after his appearance before the Council of Ten, Weizmann sought to reinforce his message in an interview with the British journalist Walter Duranty, which appeared in the _New York Times_ on 3 March. He repeated what he had said about the Jews' right to reconstitute their National Home in Palestine under British trusteeship, but he also used the interview to refine his reply to Lansing with regard to the future shape of a Jewish polity in the country. There would not, he emphasised, be the immediate creation of a Jewish state or commonwealth; rather, he conceded that for some time to come the Jews would be a minority in Palestine and they would not be imposing their will on the majority.
Generally, reaction to what had happened was positive. The French press was overwhelmingly supportive, and Clemenceau's principal adviser André Tardieu issued a statement to the effect that France would not oppose a British trusteeship for Palestine nor a Jewish state, a term which the Zionist delegation had not used. A meeting between Weizmann and his colleagues and Lansing on 29 February clearly went well. The only immediately discordant note came in a newspaper interview with Feisal, which Weizmann and his colleagues sought to counter. The result was a letter sent by Feisal on 3 March 1919 to the American Zionist Felix Frankfurter. He recalled his earlier contacts with Weizmann, assuring Frankfurter of his deepest sympathy with Zionism, whose proposals he described as modest. He did allude to difficulties which were arising in Palestine, but dismissed these as matters of detail rather than of principle. The Jews would be welcome, he claimed. Two days later, Weizmann gave a very full account of his meeting with the Peace Conference at a Zionist meeting in London. His speech included his spat with Levi and his response to Lansing's intervention to the effect that Palestine would become as Jewish as as America was American or England was English. He also read verbatim Feisal's letter to Frankfurter. Overall, his speech was one of reassurance, even euphoric in tone, and he concluded by declaring that in principle the Jewish National Home was a _fait accompli_.
Establishment of a Commission of Inquiry into Syria
The decisive meeting was held on 20 March 1919 when Wilson, Pichon, Lloyd George, Allenby and Clemenceau attempted to thrash out the issue of Syria. The French were adamant that Sykes-Picot still stood and that they should receive both Lebanon and Syria. Feisal could be accommodated under this arrangement. Lloyd George took the view that this was based on a misreading of the Agreement. Only Lebanon was to be subject to direct French control and France was bound first to accept that there would be an independent Arab state in the area in the interior of Syria. Lloyd George would not accept direct French control of Syria. Syria, he said, had been promised to the Arabs and British forces had won the war in the Middle East with their help. Allenby warned that the Arabs would revolt if the French attempted to seize Syria, which could destabilise the British position in Palestine, Mesopotamia and Egypt. At this point Wilson intervened. He declared that the Sykes-Picot Agreement was a dead letter since one party to it, the Russian empire, no longer existed. He now followed up the suggestion of Bliss and called for an inter-Allied commission to be dispatched to Syria to consult the population. Clemenceau was forced to accept the proposal. The danger of alienating the Americans was too great. He also had to pay lip service to the principle of self-determination. He did, however, insist on the expansion of the commission to look at the wishes of the peoples of Mesopotamia and Iraq, presumably to irritate the British.
However, Clemenceau remained aggrieved towards the British and the following day bitter rows continued over the Syrian question. At one stage, the French leader challenged Lloyd George to a duel. It never took place but Lloyd George, who had two trump cards, the huge British military presence in the Middle East and France's desperate need for a security guarantee from Britain and the United States, was able to win the war of words. Terms of reference for an inter-Allied Commission of Inquiry were prepared on 25 March. These emphasised the need to discover the sentiments of the Syrians and recommend what territorial divisions would promote peace and development in Syria, Palestine and Mesopotamia. On 29 March, Feisal confided in House that the commission was the best thing that he had heard of in his life. He asked if it were possible for the United States to take over as the Mandatory Power in Syria. House was doubtful that America would accept the Mandate.
Feisal's breach with the French
The British were not altogether happy with the Commission of Inquiry, since it might find that the British presence in Mesopotamia and Palestine was unwanted. Indeed, the British High Commissioner in Mesopotamia, Sir Arnold Wilson, was hostile to both Arab nationalism and the Hashemites. He had already carried out a survey, of admittedly dubious authenticity, which had found British direct rule was the preferred option and little support in Mesopotamia for a Hashemite as king. Lloyd George sought to have Mesopotamia excluded from the Commission of Inquiry on this ground on 27 March.
It would appear that pressure was now put on Feisal and the French to come to an agreement that would eliminate the need for an inquiry. The British proposed the Milner formula of 'a mild form of Mandate'. In spite of their concern that Feisal was little more than a British proxy, by this point the French had run out of options. But Feisal now made a disastrous tactical error. Through Lawrence and presumably under considerable British pressure, Feisal told the French that he was willing to accept a French Mandate. He would accept French aid and advisers and cede control over foreign policy, but he wanted Lebanon to be included in a Greater Syria. His motivation for this was that he suspected that the Lebanese Christians would inform the forthcoming commission that they wished to be protected by France. Feisal feared that he would be left with a land-locked kingdom.
The French now began to see a use for Feisal. Having him on their side would improve Anglo-French relations and, most importantly, Feisal had conceded that France had a role in all of Syria, not just the coastal region. The French calculated that once they had got their way into Syria, it would be very difficult to remove them. Once French troops were in place, Feisal could either be a puppet or could be expelled at a time of French choosing. France put forward its counter-proposals. While France would accept Greater Syria under Feisal's nominal rule, it was to be federation of tribes and the various religious groups and be subject to the advice of French advisers and soldiers. The French guessed that they would be able to manipulate tribal and sectarian divisions in Syria. They could pursue a policy of divide and conquer.
Clemenceau and Feisal met on 13 April 1919. The former conceded that France would agree to the independence of Syria subject to French troops being admitted to Damascus. Feisal refused. He believed it was a ruse to allow in a French military presence that would be very hard to dislodge. Feisal decided to return to Syria the next day. He had come to the conclusion that he would have to rely on the forthcoming inter-Allied commission to protect the independence of Syria. Feisal had been put under pressure from the British to compromise, but he would not trust the French. He rightly believed that they would betray him once they had established a military presence in Damascus.
The French still believed that Feisal was a British puppet. They remained of the view, not entirely without justification, that their erstwhile allies were reneging on the December 1918 Anglo-French Declaration under the spurious excuse of supporting self-determination for the Arabs. They noted that the British did not seem overly keen on allowing it in the Middle Eastern areas that they themselves controlled. Moreover, the French also considered Feisal to be a dangerous nationalist intent on carving out a large Arabian empire for himself. Clemenceau complained to Colonel House that Lawrence had apparently influenced Feisal's decision to reject the agreement and that a massacre of Christians was being planned by Arab nationalists in Syria. American delegates had caught sight of a French memorandum on Syria which revealed that the French expected the commission to back French goals and the Middle East to be divided on the basis of the Sykes-Picot understanding. An American official commented: 'The Near East is the great loot of the war. The fight on the question of division and mandates must be fought out here in Paris – and the sooner the better.' It would, however, take another year before the Peace Conference would make its final decisions on the settlement of the Middle East.
The emerging politics of Palestine
Notwithstanding the tone of Feisal's assurances to Frankfurter, there were distinct signs that the Arabs of Palestine were becoming increasingly uneasy about Zionist intentions. At a meeting on 1 April and in a subsequent letter, Balfour seemingly warned Weizmann that the activities of the Zionists in Palestine were creating tensions with the Arab population. In reply, Weizmann conceded both that he was worried by what was happening, which he believed was being directed from Damascus, and by what some Zionists had been saying about the nature of the National Home. He tried to reassure Balfour of Feisal's continuing support, and that the movement was committed to the terms of the 1917 Declaration, which promised to safeguard the rights of the non-Jewish population. He argued that the unrest in the country would continue until the Mandate was decided. But he was also worried by the attitude of the British military administrators in Palestine, who, he implied, did not share the pro-Zionist sympathies of Balfour and Allenby, and asked that new men be put in place. That British concerns over the situation in Palestine were not confined to Balfour was confirmed on 12 April at meetings with Lloyd George and with the influential diplomat Sir Eric Drummond. The Prime Minister's suggestion was that Weizmann should go to Palestine. In the discussion with Drummond, Weizmann asserted that Palestine was a Jewish rather than an Arab country, and must have been reassured when told that Balfour shared this view, but he was warned that they had to be careful.
In the weeks and months that followed, the affairs of Palestine inevitably receded, since the terms of the German settlement were uppermost in the minds of the Allied leaders. It was inevitably a frustrating time for Weizmann, since it was still uncertain whether a Mandate for Palestine would be awarded to Britain, or, indeed, if it would accept it. French ambitions in the region were still active, and Feisal was apparently working hard to consolidate his position in Damascus, where he returned in April. Events on the ground had their own momentum, far removed from the rarefied atmosphere of Paris. It was soon clear that cracks were appearing in Feisal's apparent entente with Weizmann. On 16 May, Lieutenant-Colonel Cornwallis, Deputy Chief Political Officer at Damascus, reported that Feisal was beginning to realise that the question of relations between the Palestinians and the Zionists was not as simple as he had thought. Cornwallis also forwarded a translation of Feisal's speech to Syrian notables in Damascus on 9 May, in which he had rallied support for Arab independence, expressions of solidarity coming from, amongst others, a delegate from Palestine.
Weizmann's suspicions about the sympathies of the British military in Palestine were also far from groundless. On 5 May, Clayton forwarded a report from Arthur Money in which he stressed the degree of opposition to the Zionist programme which had been presented to the Peace Conference, concluding that as a result the population would prefer an American or French Mandate to that of Britain. Endorsing Money's appreciation, Clayton added that 'fear and distrust of Zionist aims grows daily and no amount of persuasion or propaganda will dispel it'. On seeing this, Balfour suggested to Curzon that Samuel be consulted on how the hostility to Zionism could be allayed by the administration.
Where this new-found activism was coming from was explained in a report entitled 'The Arab Movement and Zionism', which was compiled by Major J N Camp, Assistant Political Officer in Jerusalem, on 12 August and forwarded to Curzon. Camp listed six Arab societies in Palestine, some of whose members he dismissed as 'ruffians and cut-throats', but others he knew were men of substance. With hindsight, what he had to say about al-Nadi al-'Arabi (The Arab Club), which he identified as being dominated by the Husayni family and strongly opposed to Zionism, is particularly interesting. Haj Amin al-Husayni, who was soon to come to prominence, was identified as among the leaders, though not, in Camp's view, as violent as some others. His overall conclusion was that 'practically all Moslems and Christians of any importance in Palestine are anti-Zionists, and bitterly so', and that 'Dr Weizmann's agreement with Emir Feisal is not worth the paper it is written on or the energy wasted in the conversation to make it'. So far his analysis might be held to sustain Weizmann's growing suspicion that the British military in Palestine was pro-Arab, but Camp's conclusions were rather more nuanced than that. He recommended that trouble might be averted by peaceful Jewish penetration, 'without the blaring of trumpets and without any special privileges such as Dr Weizmann and other official Zionists desire'. Britain could adopt a Mandate for Palestine, but not a Zionist Palestine. Immigrants could come in on a yearly basis as long as the land could sustain them, a policy Britain was to adopt before too long. If this occurred, the Arabs could not object if the Jews gained supremacy in 20 or 30 years, he felt.
Feisal's concerns
Before he returned to Syria in April 1919, Feisal wrote to Clemenceau. Robert de Caix, a senior French official known for his strong pro-colonial views, rejected Feisal's initial letter, which outlined the demands of the Syrian people and the basis on which he was willing to reach agreement with France. The French, according to British accounts, had become increasingly exercised by what they considered British perfidy against them in Syria. Curzon regretfully reported 'the passionate intensity' with which France meant to stick to 'her Syrian pretensions'. Feisal, too, was understandably concerned about the situation. He cabled Allenby in late May about rumours that the international commission was being cancelled and that a large French army was on the way to Syria. He warned that he could not be held responsible for what would happen in such an eventuality, but that much blood would be spilt. Allenby, as a result, warned his superiors in London that unless he could reassure Feisal that the commission would proceed, it was certain that he would raise the Arabs against the French and the British. This would endanger the whole position in Syria and Palestine and Allenby would be unable to handle the situation with the troops at his disposal. These concerns were echoed in a cable from Clayton in Cairo to Curzon, in which he warned that 'violent local disturbances may combine into a general Anti-Christian and Anti-Foreign Movement'. In British-occupied Mesopotamia the view was somewhat different. The commission was now considered a dangerous initiative and its arrival could 'undermine de facto position of European powers in the Middle East, where are [sic] military is not so strong that it can afford [to] neglect popular sentiment'.
Feisal placed far too much faith in the power of the Commission of Inquiry to give him control of all of Syria. He also completely overestimated the risks that the British and the Americans were prepared to take to protect him from the French, though he sometimes appeared to lurch into despair about his fate and that of Syria. One of his recurring motifs was that he could not understand 'why England should be so afraid of doing anything to offend the country [France], which should logically be prepared to make almost any sacrifice to avoid alienating England'. The result, as one British observer noted, was a lurking suspicion in the Emir's mind 'that the Arabs were being sold'.
Allenby visited Damascus to meet Feisal on 12 May. His arrival was greeted by organised groups of schoolchildren and patriots demonstrating for independence in an attempt to persuade him of the mass popular appeal of Syrian nationalism. Feisal addressed a gathering of notables of Syria. They endorsed a programme of independence, and voted to grant him full powers. He referred to a plan to have a pan-Syrian conference that would declare independence without reference to the Peace Conference. Allenby persuaded him not to do so. According to the British political liaison officer, the 'politicians have only two convictions: firstly they want independence, and secondly that they do not want France. Anti-French feeling is surprisingly strong amongst the people who count, and it is very doubtful whether Feisal would be permitted to bring about a rapprochement even if he wanted to.'
The King-Crane Commission
The Commission of Inquiry nearly did not get off the ground. Increasingly concerned about who garrisoned Syria, Clemenceau demanded that French troops take over from the British in advance of the commission. Lloyd George refused on the grounds that it would lead to widespread trouble in Syria. However, to stave off a complete collapse in Anglo-French relations and also possibly to forestall the commission from investigating British rule in Mesopotamia, he agreed that Britain would withdraw from the commission if France stayed out. Wilson, who had first proposed the idea had, according to one source, 'clean forgotten' about it. After an appeal from Feisal, however, he ordered the American appointees, Dr Henry C King, President of Oberlin College in Ohio, and Charles R Crane, a Chicago businessman, and their staff to proceed with the mission.
The French appear to have viewed the commission as worthless even before it reported. Picot confided to Clayton in Cairo that it was a cover 'to keep him [Feisal] in the dark while the partition of Syria is being arranged'. He later told Feisal that the commission had no standing with the Peace Conference and was a private initiative of President Wilson. Feisal refused to accept this interpretation. King and Crane were predisposed to support the French claim for a Mandate, informing Wilson that the need for harmony between Britain and France was more important 'than the will of the people of Syria'.
The commission spent April and May gathering information regarding the region before finally arriving in Jaffa in Palestine in mid-June 1919 and proceeded to travel through Palestine and Syria over the next six weeks. They left for Istanbul on 21 July. The British were informed that they intended to make their stay as short as was possible 'consistent with adequate investigation of the problems before them'. Feisal and his Syrian allies made great efforts to sell the Arab cause to the commission. Since the establishment of the Arab government in Syria at the end of the war, nationalist elites made up of urban notables and a middle stratum of intellectuals, army officers and professionals had been used to administer Feisal's Syria. They designed their greeting of the King-Crane Commission to present 'an image of a sophisticated nation eager and prepared for independence'. However, it is argued that they failed to win the allegiance of the masses. A Syrian Congress was hastily put together. The intention was that this would demonstrate the absolute rejection of French rule by the Arabs of Syria. It was a somewhat imperfect and unrepresentative body. Delegates from French-controlled areas were unable to attend and minorities, be they Shias or Christians, were under-represented.
Nonetheless, King, Crane and their delegation fanned out across the countryside of Syria and Palestine taking soundings from people. They visited more than 30 towns and received thousands of petitions and delegations from villages. There was no ambiguity in the evidence that was presented to the commission: it was all anti-French. Contrary voices, such as the Maronite Christians from Lebanon, were excluded mainly by intimidation. The commission was firmly of the view that there was practically no appetite for a French Mandate in Syria. It also believed that within Syria, 'there is raw material here for a much more promising state than we [the USA] had in the Philippines'. They stated baldly: 'In our judgment proclamation of [a] French Mandate for all Syria would precipitate warfare between Arabs and French, and force Great Britain to dangerous alternative.' Furthermore, 'England would be obliged to choose between Arabs and French with Egypt and India in background'. The only support for a French Mandate came from 'strong parties of Lebanese who demand complete separation of Lebanon with French collaboration'. The commission was in no doubt that Feisal was the key figure:
Emir Feisal despite limitation of education has become unique outstanding figure capable of rendering greatest service for world peace. He is heart of Moslem world, with enormous prestige and popularity, confirmed believer in Anglo-Saxon race; real[ly] great lover of Christians [Christianity]. Could do more than any other to reconcile Christians [Christianity] and Islam and longs to do so.
It is argued that Feisal's manipulation of the commission to exclude contrary views was a tactical blunder. Furthermore, by placing too much faith in the commission to the exclusion of accommodation with France, Feisal, according to one hostile critic, 'effectively signed away his imperial dream'. His faith in the power of the commission to influence the Peace Conference had been encouraged by the British.
The committee reported to the Peace Conference on 28 August 1919. Its recommendations were a serious problem for the policies of the Great Powers. In the most explicit terms imaginable, it made clear that only a small fraction of opinion in Syria favoured a French Mandate. It proposed that America instead take the Mandate, and if it were unwilling that Britain do so. Since it was quickly pigeonholed, the report might have merited a brief footnote, if that, but for what it revealed about the political temper of Syria and Palestine. Comparing the Balfour Declaration with what they had heard from the Zionist Commission in Palestine, the two commissioners reported that a National Home was not the same as a Jewish state, nor could the latter be brought about except by trespassing on the rights of the existing non-Jewish communities. The Zionist representatives, they said, were looking forward to the dispossession of the non-Jewish inhabitants through purchase. Referring to Wilson's speech of 4 July 1918, in which he had emphasised the need for the acceptance of any settlement by the people concerned, they reported that nine-tenths of the population were opposed to Zionism. British officers they had consulted had said that the Zionist programme could only be carried out by force of arms. They also dismissed the Zionist claim to Palestine on the grounds that the Jews had lived there 2,000 years before. While it has been suggested that the two men were the victims of propaganda, their report broadly confirms what was being heard from other sources.
The evolution of the British Mandate for Palestine
While such investigations were ongoing, the task before Weizmann and his colleagues was clearly to ensure that the British moved swiftly to confirm their commitment to a Palestinian Mandate and implementation of the Balfour Declaration. On 31 May, Curzon followed Balfour's advice and communicated to Samuel the gist of Clayton's pessimistic analysis of the situation in the country, and asked him how he thought the administration in Palestine could counter the opposition to Zionism. Samuel, Weizmann and Sokolow conferred, and on 6 June Weizmann submitted their reply in Samuel's name. It accused the administration in Palestine of not conducting its policies in accordance with the Balfour Declaration, and that, as a result, the Arabs had been encouraged in the belief that they could force the British to abandon it through agitation. The answer, it was argued, was to convince them that the matter was 'a _chose jugée_ and that continued agitation could only be to the detriment of the country and would certainly be without result'. Hence, the government should send definite instructions to the local administration that Britain would accept the Mandate for Palestine and that its terms would include the substance of the Balfour Declaration.
Balfour, previously preoccupied with the principal peace treaty terms, seems to have taken the point that something now needed to be done, especially since the Conference was winding down, and Wilson and Lloyd George would be leaving Paris shortly. On 26 June, two days before the signing of the Treaty of Versailles, Balfour addressed a memorandum to the Prime Minister, outlining his views on the shape of a Turkish settlement. This document stated that all the Arab territories should be separated from the empire and put under Mandates. France should get the Mandate for Syria, Britain that for Mesopotamia, and Palestine should be awarded either to the United States or Britain. Curzon endorsed this, with the proviso that he did not think Congress would permit any American Mandates.
With his business before the Conference concluded, Weizmann left for London. There he kept up the pressure on Whitehall, meeting Graham at the Foreign Office on 2 July. Denouncing the current administration in Palestine in no uncertain terms for its pro-Arab bias, he accused Allenby of taking no interest in the country and Clayton of being weak, while particularly castigating Storrs, the Governor of Jerusalem. In his minute on Graham's report, Curzon sourly observed that the Zionists were reaping the harvest they had sowed.
Weizmann was also conferring with Cecil with a view to pushing ahead with the Mandate. On 24 July, a somewhat mystified Philip Noel Baker, Secretary to the Commission on Mandates, wrote to the Foreign Office that Cecil and Weizmann had agreed that a draft Mandate should be drawn up and published. Balfour was non-committal, minuting that any draft Mandate should be referred to him. Even so, Weizmann's campaign seems to have succeeded, since on 4 August Curzon telegraphed Colonel John French, Acting Chief Political Officer, instructions for the guidance of the administration:
His Majesty's Government's policy contemplates concession to Great Britain of Mandate for Palestine. Terms of Mandate will embody substance of declaration of November 2, 1917. Arabs will not be despoiled of their land nor required to leave the country. There is no question of majority being subjected to the rule of minority, nor does Zionist programme contemplate this.
Echoing the memorandum which Samuel and Weizmann had submitted, the Arabs were to be told that the establishment of a Jewish National Home was a _chose jugée_ and continued agitation would be useless and detrimental.
On 11 August, Balfour felt compelled to pen a major analysis on the affairs of Syria, Palestine and Mesopotamia. Palestine was not really its main focus, since what was clearly exercising him were the continuing Anglo-French differences over Syria. Even so, what he had to say about Palestine reveals a great deal about his true feelings towards Zionism and the Arabs. Conceding that there was no intention of even going through the motions of consulting the wishes of the inhabitants, he wrote: 'The four Great Powers are committed to Zionism. And Zionism, be it right or wrong, good or bad, is rooted in age-long traditions, in present needs, in future hopes, of far profounder import than the desires and prejudices of the 700,000 Arabs who now inhabit that ancient land.' The Powers, he concluded, had made 'no declaration of policy which, at least in the letter, they have not always intended to violate'.
That autumn, the Weizmanns travelled to Palestine. It was Vera Weizmann's first visit, but she found it a sore disappointment. In particular, the trained doctor in her was appalled by what the pioneering Jewish women were doing. Their physical labour, she felt, was undermining both their health and their prospects for future motherhood. In building up the National Home, they were sacrificing their homes and diet. Before leaving for England, she sent them some flowers to thank them for their hospitality.
The Turks and European imperial ambitions
While the victorious powers had wrestled with the nature of the peace settlement with Germany and the future shape of much of Europe, they had also seen something of the emerging shape of the Middle East as a result of the representations made by Feisal and Weizmann. Otherwise, the affairs of Turkey had barely featured in the discussions in Paris, but that did not mean that events were not unfolding on the ground. Italian troops had landed in Antalya, on Turkey's Mediterranean coast in January 1919, and had begun to fan out north and west. The Turkish population did not resist them. The occupied areas had faced starvation and the lifting of the Allied blockade and the arrival of supplies brought welcome relief. But there was a more important reason for Turkish acquiescence. Many Turks, including leading nationalists, felt that occupation by 'civilised' European powers would be temporary. Mustafa Kemal was not alone in claiming to have foreseen that the Western Allies would pack up and go. Another Turkish nationalist commander, General Kâzım Karabekir, wrote in his memoirs that he had always argued that the Turks would have to fight not the Western Allies, but only the Greeks and the Armenians who wished to oust them from their homeland. The thought of their former subjects lording it over them, at best, and, more likely, killing and driving them out, as Muslims had been killed and driven out from the Balkans, was bound to galvanise Turkish resistance. 'Are you willing to be ruled by your Greek grocer?' Turkish nationalists asked as they tried to rally Turkish villagers to their cause. The threat became concrete in May 1919.
Faced with reports that Italian warships were steaming towards İzmir and that the Italians were about to occupy the city they had been promised as a reward for their part in the war, Lloyd George persuaded Wilson and Clemenceau to authorise the Greeks to land there first. The decision by the Supreme Allied Council at the Paris Peace Conference was taken on 6 May in the absence of the Italian delegation. Venizelos, who had been assiduously cultivating the Allies in Paris, was informed immediately. The previous February he had set out Greek territorial claims which included western Anatolia – the shores of the Sea of Marmara and of the Aegean with a sizable hinterland – and the whole of Thrace up to the outskirts of Istanbul. When the authorisation to land Greek troops in İzmir was communicated to him, he was ready for it.
Greek soldiers landed in the flourishing cosmopolitan port of İzmir on 15 May 1919. Cheered to the echo by local Greeks, they were blessed by Chrysostom, the Greek Orthodox archbishop, who was of course an Ottoman subject. As a first column of Greek soldiers marched towards Government House, known as the Konak, a shot rang out. Greek troops responded by firing wildly as they attacked the barracks of the small Turkish garrison, which had no option but to surrender. Captured Turkish soldiers were kicked and bayoneted. Then a mob of the local Greek underclass looted the main Turkish neighbourhood, maltreating its inhabitants. Worse was to follow as Greek troops advanced inland. The town of Aydın (after which the province of İzmir was named) was destroyed, as a weak contingent of Greek soldiers was driven out by a local Turkish resistance band, which ransacked the Greek quarter, and then the Greeks returned in force and set fire to the Turkish quarter.
The Allies, who had tried to justify the Greek occupation on the grounds that it would ensure the security of the local population, were shocked into appointing a Commission of Inquiry under the American High Commissioner in Istanbul, Admiral Bristol. Its findings were highly unfavourable to the Greeks, whom it held responsible for the incidents which had followed the landings. More importantly, it noted that the occupation had 'assumed all the forms of an annexation', and recommended that the Greek troops should be replaced by Allied troops under the authority of the Supreme Allied Commander in Asia Minor. When the report of the commission was considered by the Supreme Allied Council in Paris on 9 November 1919, Clemenceau questioned the desirability of a Greek presence in Asia Minor. His doubts were ignored. But they presaged a division in the ranks of the Allies.
Venizelos tried to hasten a peace settlement with Turkey before he was left alone to face growing Turkish resistance. But the Allies had other priorities. As a temporary measure, at the suggestion of General George Milne, the commander of British forces in Turkey, a line was drawn beyond which Greek troops were not to advance. The Milne Line, as it came to be known, also served to prevent friction between Greek forces and Italian troops which had landed south of İzmir and held the small port, known at the time in the West by its Italian name of Scala Nova, and much better known to millions of tourists today as the flourishing resort of Kuşadasi, near the ruins of ancient Ephesus. An open clash between Greeks and Italians was indeed avoided, but the latter, having lost the prize of İzmir, retaliated by being the first of the Principal Allies to offer discreet help to Turkish nationalists. They were allowed to use the facilities of Scala Nova to enter and leave the country, and to obtain military equipment, as the Italians looked the other way. Count Carlo Sforza, who had served as an Italian diplomat in Istanbul and became Foreign Minister in 1920 (refusing two years later to serve the Fascists after Mussolini's march on Rome), was critical of Lloyd George's policy of supporting (and, at times, egging on) the Greeks in their expansionist ambitions. During the five months he spent in Istanbul between December 1918 and May 1919, Mustafa Kemal was promised Italian protection should the British try to arrest him. The intermediary was Mme Corinne Lütfi, the Italian widow of an Ottoman naval officer, who was young Mustafa Kemal's intimate friend and mentor in Western manners. In Turkey, as in other parts of the Middle East, the ambitions of the victorious powers were being challenged by the growth of local political aspirations.
4
# San Remo and Sèvres: the Flawed Peace
Although the Allied leaders in Paris were understandably preoccupied with the settlement in Europe, affairs in the Middle East were developing their own momentum, since the Turks, in particular, were not long in taking matters into their own hands. By May 1919, the first stirrings of a new nationalism were already emerging across Anatolia, which, under the clear-sighted leadership of Mustafa Kemal, was to see an end to the Ottomans, the Caliphate and the Young Turks, confound the predatory ambitions of Armenians and Greeks, and within the space of a few years usher in a nation-state which bore scant resemblance to what had gone before. It was one of the most remarkable transformations of the period, not least since the Turkey which ultimately emerged proved more durable than some of the states which were being patched together in central and eastern Europe. Significantly, the focus of that nationalism was the Turkish heartland of Anatolia rather than cosmopolitan Istanbul. As this was developing far from the rarified negotiating chambers in Paris, the European powers were intent on pursuing their own agendas for the region. While they did so, Arab nationalists, their hopes for an independent kingdom still focused on Feisal, and the Zionists, pursuing their National Home in Palestine, nurtured and pursued their own aspirations.
The Turkish resistence
Traffic swirls past the statue of Hasan Tahsin in Konak (Government House) Square on the impressive newly rebuilt waterfront of İzmir. Hasan Tahsin was the pseudonym of the journalist who shot dead the standard-bearer of the first Greek detachment of occupation troops in İzmir on 15 May 1919 (and was himself killed soon afterwards). The statue, which shows Hasan Tahsin raising the Turkish flag (rather than shooting at the Greek flag) is known as the monument to The First Shot in the Turkish War of Independence. Few passers-by know that Hasan Tahsin was a member of the CUP Special Organisation, set up to conduct unconventional warfare. Hasan Tahsin's first shot had been less successful: in Bucharest in October 1914, he shot but failed to kill Noel Buxton and his brother Charles, two prominent British liberals associated with the Balkan Committee in London, who had championed Slav Macedonians against the Turks in the opening years of the 20th century and then tried in vain to enlist Bulgaria in the ranks of the Allies.
However, the first organised resistance to the Greek occupation took place not in İzmir city on 15 May 1919, but a fortnight later, on 29 May, in the seaside town of Ayvalık, further north along the eastern shore of the Aegean. Ayvalık was at the time inhabited largely by Greeks (and was then, as now, famous for its olive oil presses, rather than for the quince trees which gave the town its name). On that day, Lieutenant-Colonel Ali (Çetinkaya) ordered his regiment, quartered in the town, to open fire on the Greek troops which were moving in to occupy the area. The Greek landing was not thwarted, and Çetinkaya's regiment retreated to the interior. It had little choice in the matter. As a result of demobilisation and desertions, the regiment numbered only 150 men armed with two machine-guns. The whole area in and around İzmir, which the Greeks occupied, had been held by 4,400 Turkish soldiers commanded by 143 officers.
Hasan Tahsin, a civilian, and Ali Çetinkaya, a soldier, had in common that they were both active members of the CUP. Çetinkaya survived the war and had a colourful career. Elected a member of the Turkish National Assembly, in 1925 he shot dead a fellow MP, Halid Pasha (known as 'Mad Halid'), a general who had distinguished himself against the Armenians on the eastern front, and later become an outspoken critic of Mustafa Kemal. The following year Çetinkaya presided over the notorious Independence Tribunal (the revolutionary court), which sentenced to death the prominent Young Turk politician Cavid Bey, Ottoman Finance Minister during the First World War, who was unjustly accused of being an organiser of a plot to kill Mustafa Kemal. Today Çetinkaya is commemorated less controversially by the university which bears his name in his native town of Afyonkarahisar in western Anatolia, the first town to be regained by the Turkish army which drove out the Greeks in 1922.
The political trials and executions in 1926, which sealed the break between Mustafa Kemal and the CUP, have overshadowed the important part played by the CUP in organising early Turkish nationalist resistance after the armistice of Mudros, signed by the Ottoman Empire at the end of the First World War. As recent research shows, the CUP leadership had laid plans for resistance in Anatolia in anticipation of defeat in the First World War. But although most of Turkey's nationalist leaders after the war had been active members of the CUP, they had another, and more important, common bond. Most of them were professional soldiers who, as front line commanders, had personal experience of the deficiencies of Enver's leadership during the war and were well aware of the downside of the alliance with Germany. The CUP had been the standard-bearer of Turkish nationalism which had arisen as a response to the claims of other national communities in the Ottoman Empire. When the defeated CUP leaders fled the country discredited in November 1918, the standard passed to other hands – the hands of their erstwhile companions and rivals.
The nationalist officers who organised Turkish resistance to the partition of their country had hoped that the armistice would be a prelude to peace with honour. Nevertheless, they had taken the precaution, wherever possible, of moving troops and weapons to the interior of Anatolia out of reach of the Allied armies. When hostilities ended, their main concern was to retain command of those troops that were still under arms and to frustrate Allied efforts to disarm them. By and large they retained control of the War Ministry in Istanbul until Damad Ferid, the trusted man of the Sultan and of the Allies, became Grand Vizier in March 1919.
After the Young Turkish revolution of 1908 and particularly after the disastrous defeat of Ottoman armies in the Balkan Wars, the CUP had carried out a thorough purge of the senior command. They also put an end to the inflation of senior ranks to which Sultan Abdülhamid had had recourse to win the army's loyalty. Commanders who survived the CUP purge had their ranks reduced, and promotion during the First World War had to be won on merit and was, in any case, slow. Mustafa Kemal was a colonel when he commanded a key sector in Gallipoli, and a brigadier when he was put in charge of whole armies on the eastern and southern fronts. İsmet (İnönü), who was his chief-of-staff on the eastern front in 1916, was still a colonel when he was appointed under-secretary at the War Office a week before the armistice. It was this policy which Damad Ferid tried to reverse when he assumed office. Unsuccessful elderly generals purged by the CUP before the outbreak of the war were reinstated. A glaring example was the appointment as Military Governor of İzmir, just prior to the Greek occupation of the city, of the Ottoman commander who had surrendered Salonica to the Greeks in 1912.
The fate of İzmir strengthened the resolve of Turkish nationalist officers to retain control of the War Ministry and through it of appointments in the interior. By the time the Allies realised the key role of the War Ministry in Istanbul and moved to occupy it, Turkish military resistance had taken shape out of their reach. Three young generals, Mustafa Kemal (Atatürk), Kâzım Karabekir and Ali Fuad (Cebesoy) had hoodwinked the Sultan and his Grand Vizier and secured command of forces which became the nucleus of a new Turkish national army. The first to leave Istanbul was Ali Fuad, a close friend and companion of Mustafa Kemal from their days as cadets in the Istanbul War College. He took up command of the army corps in central Anatolia which had its headquarters in Ankara, the eastern railhead of a branch line of the incomplete Istanbul–Baghdad railway. Ali Fuad was followed by Kâzım Karabekir who was appointed commander of the army corps in the eastern Anatolian fortress town of Erzurum. This was the largest concentration of Turkish troops after demobilisation. But it numbered only some 18,000 men.
The gathering forces in Anatolia
Mustafa Kemal left Istanbul on 16 May, the day after the Greek landing in İzmir. He was armed with wide-ranging powers as inspector of all the Ottoman troops in eastern Turkey with additional jurisdiction covering most of unoccupied Anatolia where he could issue orders both to military commanders and to the civil administration. A few days later, Rauf (Orbay), who had resigned his commission in the navy, left Istanbul for the eastern shores of the Sea of Marmara. Himself of Caucasian origin, Rauf rallied to the Turkish resistance the warlike Circassians who had been settled on the eastern approaches to the capital in the second half of the 19th century when they were expelled by the Russians from their ancestral lands in the western Caucasus. The commander of the Turkish division stationed in the area was also a Circassian, and was ready to resist foreign occupation.
After his return from the Syrian front in November 1918, Mustafa Kemal had made use of all his political contacts to secure the post of War Minister in the governments which were formed in quick succession after the armistice. In several audiences he tried to reinforce the favourable opinion which the Sultan had formed of him during their trip to Germany in the last year of the war. But although he was known as a critic of the CUP leadership, he had been a member of the CUP, and the perennial losers of the Liberal Union, who came to power when Damad Ferid became Grand Vizier, did not trust him fully. Moreover, Mustafa Kemal was notoriously ambitious and, therefore, a threat to those who had finally achieved office. But suspicious as they were, the Sultan and Damad Ferid needed a commander who had influence with the remnants of the Ottoman army. The superannuated generals they rescued from obscurity were clearly incapable of ensuring the loyalty to the throne of serving officers.
The Allies had threatened to occupy areas where public order was disturbed. There had been some bandit activity in the hinterland of İzmir, although the disturbance this caused was minor in comparison with what would follow the Greek occupation. Greeks lived also in considerable numbers along the shores of the Black Sea, with prosperous Greek communities in most coastal towns, while the interior was dominated by Muslims. Many of these Pontic Greeks (named after the Euxine Pontus, the name by which the Black Sea was known in classical antiquity) had emigrated to Russia, particularly after the Russian conquest of the Caucasus, and were now in flight from the Bolsheviks. Returning to the Ottoman shores of the Black Sea, they swelled the number of local Greeks who, with their clergy in the lead, were now clamouring for a Christian Pontus state which would recreate the kingdom of the Comnenes, the last Byzantine dominion to be captured by the Ottoman Turks. Venizelos, with his eyes fixed on Aegean Turkey and ultimately on Constantinople (Istanbul), thought it more practicable to have a Greek-Armenian state around Trabzon (Trebizond), on the assumption that local Armenians deported from the area would return. In either case, local Turks felt threatened. Known as Lazes, although the Laz, properly speaking, lived only in the eastern portion of the Ottoman Black Sea coast, where they preserved their ancestral tongue, akin to Georgian, they were late converts to Islam, and, after the fashion of late converts, passionate in defence of their faith. Living in a narrow strip squeezed between the mountains and the sea, they found an outlet for their energy as seamen, but also as bandits moving in and out of their mountain hideouts.
In April 1919, the Sultan's government sent out 'Commissions of Admonition' led by Ottoman princes to persuade its subjects of different faiths to live peacefully together. It was a vain attempt, as the leaders of Christian communities, Greeks and such Armenians as survived or had returned, were determined to break away from the Ottoman state and refused to have anything to do with the imperial princes. Nor were the Muslims impressed. The princes sent out on safari looked down on the natives. On his arrival in Trabzon, Prince Cemalettin found the boys of the local high school too noisy and complained to the headmaster. 'Your school,' he wrote, 'is as noisy as a synagogue full of Jews chanting their prayers. Is this row a premonition of a rebellion in the country? Or is it that you are not in control of the school? We would like to know.'
The prince, and his master the Sultan, were soon to find out. But in the meantime, the Sultan and his Grand Vizier understood that it was not enough to send out princes to admonish rebellious subjects. Only the army could re-establish order and, the palace hoped, thus deprive the Allies of an excuse to intervene. Receiving Mustafa Kemal on the eve of his departure for eastern Anatolia, the Sultan said to him: 'Pasha, you have already rendered many services to the state. They are now part of history. Forget about them, for the service you are about to render will be more important still. You can save the state.' Apologists for the Sultan claim that this suggests he sent out Mustafa Kemal for the express (and secret) purpose of organising resistance to the partition plans of the Allies. The claim is disproved by the Sultan's own proclamation in exile when he accused Mustafa Kemal of breaking his oath of allegiance and of becoming an unbearable source of trouble for the nation.
It was not an accusation that weighed heavily on Mustafa Kemal's conscience. But many of his fellow commanders found it difficult to break with centuries of Ottoman imperial tradition. The Muslim inhabitants of Anatolia were even less ready to abandon their sovereign. Some, like the Circassians, were pulled both ways. They had experienced foreign oppression in the Caucasus and were determined not to be subjected to it in their new home. But they were passionate in their loyalty to the Sultan-Caliph. There was no Turkish popular revolt against the monarchy as there had been in Russia, Germany and Austria-Hungary. Most Muslims did not blame the Sultan, who had been largely powerless since the rise to power of the Young Turks, but rather the CUP leadership which had involved the country in a catastrophic war. The division between the largely illiterate, conservative Muslim masses and a ruling class schooled in Western culture, which had developed gradually since the introduction of the first reforms in the 19th century, had deepened as a result of the miscalculations of the Young Turks. In the eyes of the mass of Muslims, the Unionists, as the Young Turks were known in the country, were impious bunglers. The fact that resistance to foreign occupation was led by Unionists, however critical these may have been of the CUP leadership, had to be downplayed. Moreover, the Muslim population had been decimated by the war. The survivors were hungry and largely destitute. It was widely believed that the Young Turk leaders, or at least their friends, had enriched themselves while the country suffered.
The accusations were false as far as the CUP leaders were concerned. Outside their ranks as well there were probably fewer war profiteers in Turkey than in other belligerent countries. One reason was that Muslim Turks were new to trade, which had been the preserve of foreigners and of native Christians and Jews. In industry, Turks provided only 15 per cent of the capital and of the workforce. The CUP had tried to redress the balance through their 'national', or more accurately nationalist, economic policy. But this was in its early stages. The political power of the Young Turks had not yet translated into wealth. Such little wealth as there was in the countryside was in the hands of individual landowners or, particularly in the Kurdish areas, of tribal leaders, some of whom doubled up as sheikhs – leaders of Muslim fraternities. Sixty-five per cent of the total agricultural area belonged to feudal lords and large landowners, but their holdings yielded little revenue because of lack of investment and an acute shortage of manpower.
Popular resistance to the country's partition was ideological only in the sense that Muslim religious sentiment was important in animating it. However, the main stimulus was fear of dispossession at the hands of Christian minorities, which had been richer than their Muslim neighbours. During and immediately before the war, some 113,000 Turkish families, most of them refugees from the Balkans, had been settled on the Aegean coast, mainly around İzmir, in the property of deported Greeks. When Greek troops occupied the area in 1919, the original owners returned and some 80,000 Turkish settlers fled to the interior. This was exactly what Venizelos wanted. In a memorandum to Lloyd George, the Greek Prime Minister had suggested that intermigration should be encouraged between Greeks who lived outside the area in western Turkey which he claimed and Turks within it. His aim was not the continued co-existence of Greeks and Turks in a mixed society but the creation of new nationally homogeneous states.
In eastern Anatolia most of the 860,000 Armenians who lived in the area before the war had been deported. The Muslims who took over their property, and who were themselves destitute as a result of the war, resisted restitution. In the parts of southern Anatolia bordering on Syria, which the French had occupied at the end of 1918, some of the 150,000 or so Armenians who had been deported began to return and reclaim their property. It was in these areas that popular resistance to Allied occupation arose spontaneously.
Even before nationalist commanders took charge, Muslims began to form societies which campaigned against the extension of foreign rule. The first was the National Defence Society in eastern Thrace founded in December 1918. Paradoxically, there were more Greeks in Turkish eastern Thrace than in western Thrace, an area with a Muslim majority which had passed from the Ottomans to the Bulgarians and then to the Greeks. The chief city of eastern Thrace was Edirne (Adrianople), the second capital of the Ottoman Sultans, who had built some of their most splendid monuments there. All Turks were bound to resist its loss. In the Aegean area, when the first Greek advance stopped at the Milne Line, Turkish resistance took shape outside it and found expression in a congress of anti-annexation societies. In the east, similar societies were formed in Trabzon (Trebizond) and in Erzurum, areas coveted by local Greeks and Armenians. They joined forces in the Society for the Defence of Rights of the Eastern Provinces, a title which came to be adopted by civilian nationalist organisations throughout the country.
The title derived from the 'rights of nations' which President Wilson had proclaimed in a speech to the US Congress. But it also had a deeper, revolutionary resonance, echoing the third article of the _Declaration of the Rights of Man_ , voted by the French National Assembly in 1789. This proclaimed that 'the principle of all sovereignty resides essentially in the nation'. The slogan of national rights pointed to the leading role of the Young Turks in these civil self-defence organisations. They were joined by local clerics, usually muftis, who in Ottoman times, as now, were civil servants, and by local Muslim notables, usually landowners. The societies were the civilian base on which nationalist commanders relied to mobilise resistance to the foreigner and provide a semblance of legitimate authority to their efforts to enlist men and requisition supplies.
Even with local support, nationalist commanders needed time to assemble the remnants of the Ottoman army and lay hands on sufficient weapons to take the field. While they were preparing for a renewal of the armed struggle, armed resistance came from a traditional quarter. Throughout most of its history, and particularly when central authority was weak, Anatolia was prey to bandits. After the First World War, bands which had formed around renowned local outlaws were joined by tens of thousands of army deserters seeking refuge in the mountains and in the vast areas of abandoned countryside in the peninsula.
In western Turkey, the outlaws were known as _zeybek_ , and their leaders as _efe_. They wore characteristic clothes – bandoliers slung over colourful jerkins and baggy trousers – and they had developed their own forms of folk dance, which passed also to their Christian neighbours and survive in the popular _zeybekiko_ music in Greece. Revered today as folk heroes to whom monuments are erected, the _zeybeks_ and their _efe_ leaders protected and preyed upon the settled population in equal measure. Local Christians and the foreign troops (Greeks in the west, French south of the Taurus mountains) with which Ottoman Christians made common cause, knew them simply as _çete_ (usually spelled [ _t_ ] _cheté_ in contemporary documents) or bands. Turkish nationalist commanders renamed them 'national (meaning popular) forces' ( _kuva-yı milliye_ ). They tried to control them, stiffening them with regular army officers whenever they could.
Local Turkish administrators, threatened with the loss of their jobs, and landowners, who feared the loss of their land, helped the militias. Landlords were, in any case, used to employing outlaws or raising their own militias in order to hold their own against rivals, bandits and tax-collectors. The numbers of militia bands varied, as between raids many of their members returned to their villages where they were indistinguishable from other peasants. The best-known militia or outlaw leader was Demirci (Blacksmith) Mehmet Efe in the hilly country round the valley of the Menderes (Great Meander). There were some 1,800 armed men under his command divided into a dozen or so detachments. Local Christians also had their militias, the best-known among which was the Greek _Mavri Mira_ (Black Destiny) band, operating in the area of İzmit (Nicomedia) on the eastern approaches to Istanbul. But as the Greeks had a regular army in the field, the role of their militias was more limited.
The building-blocks of Turkish resistance were thus in place when the war ended. But they could only be assembled when the danger of dispossession at the hands of local Christians and their foreign protectors overcame the weariness of the Turkish population whose first care was to keep body and soul together. This danger became acute first in the east and south as the Armenians began to move in and then in the west when Greek troops landed in İzmir on 15 May 1919. Elsewhere, in central Anatolia round the city of Konya (known as the centre of the Whirling Dervishes and of intense Muslim piety), in the countryside round Ankara, and also in some Kurdish mountain areas, which were not directly threatened, people feared that the nationalists might compromise their precarious survival, which they thought might be secured more effectively if they chose obedience to the Sultan and his Grand Vizier. The nationalists therefore had to mobilise support where they could, persuading reluctant peasants in some places, and suppressing resistance to their plans in others. Nationalist commanders told the Kurds that if they made common cause with the British they would fall prey to the Armenians rather than achieve self-rule. Where persuasion failed, nationalist leaders had recourse to the violence of punitive expeditions and of revolutionary courts. Resistance which lacks the cover of a recognised government has to fight on several fronts and needs both to elicit support and to inspire fear. But before all else, it needs leadership and organisation. This is what Mustafa Kemal provided.
The rise of Mustafa Kemal
On 19 May 1919 Mustafa Kemal arrived in Samsun, a port lying at the centre of Turkey's Black Sea coast. Informed of his arrival, Kâzım Karabekir invited him to proceed eastwards to his headquarters in Erzurum where the Defence of Rights societies of the Eastern Provinces were about to meet. Instead, Mustafa Kemal travelled inland south to Amasya, a picturesque town situated in a narrow river valley, where a Turkish regiment was quartered. At the height of Ottoman power, Amasya was where imperial princes were sent as governors to learn the art of statecraft. Mustafa Kemal chose it because he could act as host there to a meeting of nationalist leaders. He was joined by Ali Fuad from Ankara and Rauf who had travelled from the shores of the Sea of Marmara. Military commanders were contacted throughout the country and their agreement was obtained to a statement declaring that the Ottoman government in Istanbul was incapable of defending the national interest, and summoning delegates from every Turkish province to make their way to a congress in Sivas in order to take the country's destiny into their own hands. In the meantime nationalist commanders and civil governors were not to surrender their posts to the Istanbul government's appointees. It was a first step to the formation of an alternative government in Anatolia, and, although none of the commanders dissented, some had reservations.
Mustafa Kemal had arrived in Anatolia as the Sultan's representative. It did not take long for British control officers in Anatolia to realise that instead of overseeing the disarming of Turkish troops and preventing attacks on local Greeks, Mustafa Kemal had set about organising Turkish national resistance to the Allies. At the insistence of the British High Commissioner, the Sultan's government recalled Mustafa Kemal to Istanbul. But he was now outside their control. From Amasya he travelled east to Erzurum where he arrived still wearing his uniform as an Ottoman brigadier with the cordon of honorary ADC to the Sultan. As the Sultan moved to sack him, Mustafa Kemal resigned his commission. Although he was not himself prepared to break free from Istanbul right away, Kâzım Karabekir stood by Mustafa Kemal and eased the way to his election, first, to the chair of the Erzurum Congress of the Eastern Provinces' Defence of Rights societies, and then to the presidency of its permanent executive (called the Representative Committee), which became the nucleus of an alternative government in Anatolia. The Erzurum Congress adopted the first text of what became known as the National Pact which proclaimed the sovereign independence and indivisibility of Ottoman lands within the armistice lines of November 1918.
Leaving Karabekir in Erzurum, Mustafa Kemal made his way to Sivas where enough provincial delegates had assembled to justify the claim that they represented the whole country. After a desultory discussion of the possibility of accepting an American Mandate, which the US Congress was in any case unwilling to take on, the Sivas Congress re-affirmed the National Pact, and demanded that the nation should be consulted before the conclusion of a peace treaty, and that the Ottoman government should be represented at the Peace Conference by delegates enjoying the people's trust.
While the nationalist congress was in progress, a British officer, Captain Edward Noel of the Indian Army, made his way from Istanbul to the town of Malatya in south-eastern Turkey where he tried to mobilise the Kurds against Turkish nationalists. Kurdish tribal leaders who aspired to independence had formed in Istanbul a Society for the Advancement of Kurdistan, which sought British support for its ambitions. Captain Noel took up their cause, but his efforts, far from undermining Turkish nationalist resistance, provided Mustafa Kemal with a propaganda weapon. The Kurds were incapable of united action, and when Mustafa Kemal ordered a detachment of Turkish troops to march on Malatya, Captain Noel and his Kurdish contacts fled to Syria. Mustafa Kemal then made maximum use of the episode to discredit Damad Ferid's government. The charge that the Grand Vizier had sought to incite wild Kurdish tribesmen to march on patriotic Turkish Muslims assembled in Sivas caused indignation in the ranks of the Ottoman ruling class. More than a century earlier, the revolutionary fervour of colonists in British North America had been similarly stiffened by the accusation that King George's generals had incited the 'Redskins' against their kith and kin.
The Ottomans and the Allies
Damad Ferid had resigned in the aftermath of the Greek occupation of İzmir. The Sultan immediately asked him to form a new Cabinet into which respected elder statesmen – the former Grand Viziers Ahmet İzzet and Tevfik – were co-opted. The imperial decree re-appointing the Grand Vizier declared in ringing tones:
At this crucial moment, when all members of the nation led by their Caliph and Sultan, the head of the six-and-a half-centuries-old dynasty, sprung from the nation's bosom, who is himself ready for any sacrifice, are united in the single aspiration to safeguard the nation in its entirety, we demand that you should devote all your energy to this sacred national cause.
The Sultan was indeed ready for any sacrifice except that of his throne.
Originally the Allies had not intended to invite Ottoman representatives to the Peace Conference before they had agreed the terms of the settlement among themselves. But the French did not want Damad Ferid to look exclusively to the British for protection. They promised that he would be heard in Paris and arranged transport for him and his delegation on board a French warship. On 17 June, a month after the landing of Greek troops in İzmir, Damad Ferid presented a memorandum to the Allies in which he blamed the CUP leadership for Turkey's entry into the war, and likened the Unionists to the Bolsheviks. 'Now,' he said, 'just as the Allies are trying to liberate the Slav people, so too they should extend their help to the Turkish people in kindness and humanity.' He then outlined his proposals, which he filled out in a second memorandum on 23 June. Even as a first bargaining position, Damad Ferid's proposals were pitched high. Not only did he ask for the territorial integrity of the Ottoman Empire to be respected, but he claimed also the Greek islands close to the Turkish coast and western Thrace which had been lost in the Balkan Wars. The Arabs could have self-rule under princes appointed by the Sultan who would also remain patron of the Muslim shrines in Arabia.
The Allies rubbed their eyes in astonishment and delivered a stinging riposte. The Turks, they said, had proved themselves incapable of ruling other races. Wherever they went, they caused destruction and the loss of prosperity and cultural vitality, which recovered only after their departure. The Allies respected Islam, but the Turks would do better in 'appropriate conditions' – in other words, cut down to size. The reply was as absurd in its insulting generalisations and national stereotypes as Damad Ferid had been in his expectations. The Allies then told Damad Ferid that they had other pressing business to attend to, and that his continued presence in Paris would serve no useful purpose. He would be informed in due course when the Allies had decided among themselves the terms of the Turkish peace settlement. Damad Ferid returned to Istanbul empty-handed and discredited, just as Mustafa Kemal was rallying the forces of Turkish nationalism and Muslim resistance in Anatolia.
As the Allies were still busy with the European peace settlement, and with Greek occupation troops corralled behind the Milne Line, the Sultan gave way to Turkish nationalist pressure. Damad Ferid resigned on 2 October 1919, barely three weeks after the conclusion of the nationalist congress in Sivas, and was replaced by Ali Rıza Pasha, a 60-year-old field marshal who had been the unsuccessful commander of the Ottoman Western Army in the Balkan War. In line with the demands of the nationalists, the Sultan decreed that parliamentary elections should be held before a peace settlement was negotiated. The new Grand Vizier made an effort to reaffirm Ottoman sovereignty in the capital, demanding that local Greeks who were Ottoman subjects should not fly the Greek flag. He tried to heal the breach with Mustafa Kemal and dispatched his Navy Minister, Salih Hulusi (another superannuated general) to negotiate with him. Nothing came of the attempt. Local Greeks refused to have anything to do with the elections, held in December 1919, which were won handsomely by Turkish nationalists.
The deterioration of Feisal's position
In late 1919 Feisal's position was weakening. The call by the King-Crane Commission on 28 August for an American Mandate over Syria had simply not been in the realm of practical politics. By the end of the summer of 1919, it was becoming increasingly clear that Wilson, thanks to his alienation of his political opponents, would have great difficulty in getting the Treaty of Versailles passed by Congress, controlled since the November 1918 election by the opposition Republican Party. Wilson had precious little political capital left. In July 1919 he returned to Washington and in September he began a national campaign for the Treaty of Versailles and the League of Nations. On 26 September 1919, in the midst of an extraordinarily demanding whistle-stop tour promoting the League and the Treaty, he suffered a paralyzing stroke. His political influence essentially ended. Ironically, the next day the King-Crane Commission report arrived in the White House. It is unlikely that Wilson ever saw it. The Wilsonian internationalist tide was ebbing. In November 1919 and March 1920, the Senate rejected the Treaty of Versailles. It also declined to take a Mandate over Armenia. Syria, and the idea of an American Mandate over it, was not even discussed by the US Congress. Indeed, General Tasker Bliss, a US delegate to the Peace Conference, had by November 1919 come to the conclusion that American arbitration of Turkish and Middle East problems was 'futile'. The report of the King-Crane Commission was never looked at by the Peace Conference and remained unpublished until 1922.
The strongest British card for defending Feisal – an emphasis on Wilsonian national self-determination – was now essentially a dead letter. Unsurprisingly, the autumn and winter of 1919 saw the British retreat in the face of French demands over Syria. This was in many ways motivated by the demands of the Chief of the Imperial General Staff, Sir Henry Wilson, and the Secretary of State for War, Winston Churchill, for realism by Lloyd George in military affairs. To put it simply, Britain could not afford to maintain its occupation of Syria. Balfour as early as 19 August, and in advance of the King-Crane recommendations, bemoaned the impact of the Syrian question on Anglo-French relations despite Britain's already well-publicised renunciation of any interest in taking a Mandate in Syria. The French press continued to denounce what they considered British attempts to deny France's rights in Syria throughout the summer.
Feisal was also disturbed when Britain made clear to him that it was going to take the Mandate over Palestine and implement the Balfour Declaration. Feisal argued that this was a return to the 'Unjust Agreement of 1916' i.e. the Sykes-Picot Agreement. Arguing that the majority of Arabs had asked for a single Mandate over Mesopotamia and Syria, he warned that if 'there is any possibility of [the] Peace Conference making a decision which is contrary to this desire and which involves a division of country, [he] cannot remain in his present position which would render him liable to the accusation that he consented to the ruin of his country'.
The British, on the basis of hard-headed political calculation, had decided to cut their losses and withdraw their support for Feisal. Since the beginning of the year, one of the more pressing problems for the British government had been the expense of the vast military forces that it had deployed both in Europe and the Middle East. Syria was, quite simply, a far lower priority than Egypt, India, Mesopotamia and Ireland. Secondly, the British had every intention of enforcing their own Mandate in Mesopotamia. How then, as Balfour noted on 9 September, could Feisal expect a larger measure of independence from the French? He further remarked, 'Neither of us want much less than supreme economic and political control to be exercised no doubt (at least in our case) in friendly and unostentatious co-operation with the Arab – but nevertheless, in the last resort, to be exercised.' Lloyd George consulted with Allenby and the Conservative Party's most influential Cabinet Minister, Andrew Bonar Law, in a series of meetings in Deauville from 9 to 11 September 1919. A decision was taken to evacuate British forces from the Syrian coast westwards to the Sykes-Picot line. The British subsidy to Feisal would be cut in half and France should take this up. This would all be done by 1 November 1919. Feisal was also instructed to come to France immediately. This was communicated to Clemenceau at a meeting on 15 September. Feisal received the news in person from Lloyd George at 10 Downing Street four days later. Feisal warned that the consequences would be bloodshed.
Feisal was now desperate for some way of avoiding a French occupation. He proposed three alternatives to the British: namely, that Allenby remain in control of the evacuated areas; an international commission to consider temporary arrangement until the Peace Conference had decided; or that the Peace Conference make an immediate decision on the fate of Syria. He also contemplated sending a mission to the United States. In spite of the fact that Arab opinion according to most British reports and the King-Crane Commission had turned very strongly against any significant Jewish settlement in Palestine, Feisal met again with Weizmann, who proposed that in exchange for Feisal's backing of the Zionist project, the Zionist movement could provide advisers and money to the Arab government. Feisal was inclined to accept the agreement provided the Zionists joined with the Arabs against the French, but Weizmann was reluctant to break with the French, arguing that they could be squeezed out of the coastal parts of Syria later.
It was inevitable that Feisal, under considerable British pressure, would once more turn to the French. Lloyd George asked Clemenceau to avoid treating 'Feisal and the Arab problem with a high hand. If this were indeed the policy of the French Government, the British Government are afraid that it would inevitably lead to serious and long continued disturbances throughout the Arab territories which might easily spread to the whole Mohammedan world.' Clemenceau took note of Lloyd George's views and began to moderate French aims. The objective remained to protect French imperial designs but now, crucially, an attempt would be made to satisfy Feisal and the British. Notably, Clemenceau prevented the French commander in Syria, General Henri Gouraud, from occupying the Bekaa Valley. However, when Feisal and Clemenceau met in October and November there was no meeting of minds between them on the issue of sovereignty over Syria. Clemenceau was determined that French troops would occupy Syria and French administrators would have virtual carte blanche to run the country as they pleased. Feisal rejected this proposal.
However, Clemenceau and the French decided to make significant concessions, and new proposals were presented to Feisal on 16 December. Now, in return for the French having the sole monopoly over provision of military and civilian advisers, who would be responsible to the Syrian government, and Feisal's acknowledgment of France as the Mandatory Power, Syria would have an independent parliament with the right to levy taxes and make laws and Feisal would be recognised as head of the new Syrian state. Additionally, France agreed not to station troops in the Arab part of Syria without the consent of the government. Feisal agreed these terms on 6 January 1920. However, Feisal had to secure popular support within Syria for the French Mandate before Lebanon would be handed over. The agreement was kept secret. A French official who communicated the terms to the British claimed the French 'were rather nervous as to whether Feisal would be able to maintain his position on his return to Syria and for this reason the agreement was to be kept secret at present and Feisal was to return with an ostensibly clear hand'.
Undoubtedly, Feisal was extremely unhappy with the agreement. He almost certainly realised that it would be difficult to sell to the radical nationalists, whose influence in Syria was steadily increasing. Conversely, Gouraud saw the new agreement as a defeat for France. He foresaw that the agreement would be interpreted by the Arabs as providing for their complete independence without any French influence.
The situation in Syria
Feisal's political influence in Syria was never all that strong. There were nationalist undercurrents there over which he had little control. His second trip to Europe at the end of 1919 reduced even this limited influence. Gertrude Bell, a member of the Arab Bureau, identified some of these problems when she visited Syria in October 1919. In her view things were falling apart as the Arab government had refused help or advice from the French while at the same time the British could not help for fear of damaging relations with the French. Therefore, she noted 'they go their own way and their way is not good'. The main centres of power were three nationalist groups: the mainly Palestinian Arab Club (al-Nadi al-'Arabi), the Syrian-led _al-Fatat_ , which controlled the Arab Independence Party (Hizb al-Istiqlal _al-'Arabi_ ), and _al-Ahd_ , which was made up of Iraqi members of the Ottoman army who had defected to the Arab Revolt. These organisations sometimes worked together for the Arab cause. Often though, they displayed more loyalty to their regional or tribal interest. In such a factional atmosphere there was also a tendency for these groupings to attempt to outbid each other with displays of nationalist fervour, which limited Feisal's room for compromise with the French.
The men left in control by Feisal and who dominated his brother Zeid were mainly from _al-Ahd_ , whose key figure was Yasin Pasha al-Hashimi. In Bell's view they were 'violent Nationalists and are out for an independent Syria and Mesopotamia without any foreign control'. Her summary of the state of opinion in Damascus was that Feisal had lost ground. In a dispatch written at the end of her visit she noted the sense of growing despair about the future in the Syrian capital:
Damascenes are exceedingly anxious at the prospect which lies before them. At the end of the year the subsidy to the Sherif will cease and the financial position of the Arab Government will be extremely precarious but even if it can contrive to keep itself in existence and succeed in preventing open disorder it is anticipated that the French in the coast provinces will foster disturbances, either by the continuance of propaganda within the Arab State, or by provocative acts towards Moslems in the area under their administration, and that on the first breach of the peace their troops will cross the frontier on the plea of restoring order.
When Feisal returned with his deal, he found that it commanded little popular support among nationalists. Another problem was the resignation of Clemenceau as French Prime Minister soon after the agreement was put into practice. The French elections at the end of 1919 had produced a conservative majority that had little interest in appeasing Arab opinion. The new French Prime Minister, Alexandre Millerand, was of the view that France had already conceded too much to Feisal. There was also the problem that Syrian nationalists and independent bandits were stepping up attacks on French forces, which angered the French government. Gouraud had no confidence in Feisal and believed that he was in the hands of the most radical nationalist elements in Syria. The British were positive about the agreement but saw little prospect that Feisal would be able to implement it. As Lloyd George noted at an Allied conference in February 1920, Feisal was not in 'a consenting frame of mind'.
Events bore out this gloomy assessment. Feisal was caught between the demands of the French and the Syrian nationalists. He desperately sought more concessions from Millerand. Specifically, he sought increased independence in foreign policy and a reduction in the size of the Lebanese state, but Millerand rebuffed the approach. On the contrary, the French Premier wanted the accords of 6 January to be amended to grant France even greater influence and control in Syria. His preference was for the division of Syria along ethnic and tribal lines, leaving it with a powerless centre. Feisal was now left with an ever-decreasing set of options. He either had to go completely over to the French and sanction the use of their troops to crush Syrian nationalists or he had to abandon all dealings with them and go over to active opposition. British reports noted the enormous pressure he was under from the extremist party. His father Hussein, perhaps out of envy of Feisal's successes, warned he would repudiate any agreement with France that did not safeguard Arab independence.
Yasin Pasha al-Hashimi, who exercised considerable influence over Feisal, had strongly opposed any pact with the French and led street demonstrations in January 1920 against the Feisal-Clemenceau agreement. Feisal's appeals for moderation fell on deaf ears. The nationalist cause meanwhile had given every nationalist but also every bandit licence to carry out attacks, especially in the coastal area. Christians and other minorities in Damascus lived in fear of being massacred. On 6 March 1920, Feisal was obliged to reconvene the Syrian National Congress that had been formed for the visit of the King-Crane Commission. It remained absolutely uncompromising in its nationalist views. It declared Feisal's accord with the French null and void and declared independence with Feisal as head of state. Palestine was proclaimed part of the new kingdom. Some time later Abdullah, Feisal's elder brother was proclaimed King of Mesopotamia. Feisal, as he had warned the British, had to go along with the nationalist tide or be overthrown.
Appeals were made to other governments for recognition. The French saw the declarations by the Syrian nationalists as conclusive evidence that Feisal had endorsed the views of the extremists. In Lebanon, Christian groupings, no doubt with the encouragement of the French, proclaimed their independence from this new Syrian state. The British also suggested that Feisal's support in Damascus among Christians and the Druze was quite weak. Millerand was determined that the declarations of the Syrian National Congress would not stand. The British were now very much in step with the French; Curzon, Foreign Secretary since the autumn of 1919, told them that the declarations were 'an unwarranted and intolerable exercise of authority' by the Syrian National Congress. However, Curzon also took the opportunity to berate the French for imperiling the British and French positions in the Middle East by 'forcing themselves into areas where the French were not welcomed by the inhabitants'. The British were especially concerned by the Syrian National Congress's claims in Palestine and Mesopotamia. Lloyd George, though, seemed to be favourable to this and Allenby argued that Britain and France should recognise Feisal as sovereign over a confederation of Syria, Palestine and Mesopotamia while tying them administratively to Britain and France. Curzon, though, felt the plan was unclear and that consultations in Mesopotamia in 1919 had suggested that there was little appetite for a Sherifian ruler.
Feisal appears not to have been concerned enough by the warnings issued by the British and French. Instead, the French were brusquely informed that they must recognise Syrian independence and withdraw their forces from Lebanon before he would return to Europe. Superficially, Feisal's position remained strong. The French appeared to have insufficient troops on the ground to drive the nationalists out. The British remained reticent about an assault on Feisal and the French also had the problem of Cilicia to the north of Syria, which Mustafa Kemal and his nationalist Turkish forces were beginning to menace. In early 1920, a French force was routed. Until these problems were resolved, there was no prospect of moving against Feisal.
However, in reality, Feisal's position was much weaker than it seemed. According to his own testimony, he was more or less forced into acceding to the independence declaration or face losing his crown. Indeed, he hoped the declaration would sate popular opinion in Syria and provide a breathing space in which he could negotiate a deal with the British and French. There were many in Syrian nationalist circles who would like to have made common cause with the Kemalists. Furthermore, the military and economic position was desperate. There were food riots in Hama just four days after the declaration of independence. Food shortages, rising prices and currency problems became increasingly acute. Politically, Feisal's position was weak. His ability to compromise with the French, which he almost certainly favoured, was constrained by extreme nationalists who brooked no compromise.
The San Remo Conference
The Treaty of Versailles came into force on 10 January 1920, even though on 19 November 1919, the American Senate had failed to ratify it. While the Treaty set the complex terms of the peace settlement with Germany, important issues remained to be resolved, not least in the Middle East. In the light of the forthcoming conference at San Remo in Italy, which would at last move forward the peace settlement with Turkey, Weizmann sought to reinforce his message with Robert Vansittart of the British Foreign Office. He was concerned to drive home that Palestine's position as the Jewish National Home should be embodied in the peace treaty with Turkey. What was perturbing him, it seems, was the possible nature of the Mandate system. The Mandates for the other areas of the former Turkish empire were to be administered in the interests of their inhabitants, while the overriding purpose of that for Palestine, as far as the Zionists were concerned, was to be the creation of the Jewish National Home, the rights of the inhabitants being safeguarded. He need not have worried, as it happened, but before the Conference took place he was to have an experience which gave him even more reason to be concerned about the future.
What Weizmann encountered at first hand was the growing strength of Arab opposition to the Jewish presence in Palestine, which he had been aware of for some time. In March 1920, he made a return visit to the country in the company of his elder son. The timing was bad, since the anger of the Arab population had been rising on a number of counts. There was growing frustration that promises they believed had been made over Arab independence were not being honoured. There was fear that the Balfour Declaration would lead to Arab subordination to the Jews as a consequence of massive Jewish immigration. Finally, there were hopes of an Arab state embracing both Syria and Palestine, ruled by Feisal from Damascus. During his temporary stopover in Egypt, Weizmann became aware of growing unrest in parts of Palestine, which had resulted in the death of, amongst others, Joseph Trumpeldor, who had been organising Jewish defence groups. On 25 March, Weizmann summed up his impressions of the current situation in Palestine in a deeply pessimistic letter to the Zionist Executive in London. In this he castigated the military authorities for what he believed was their open hostility to the Jews and partiality towards the Arabs. The prevailing view amongst the officers, he reported, was that the Balfour Declaration had been a mistake. Such British attitudes were encouraging the Arabs, and, he confided, he had lost faith in Feisal.
What then happened was tragic, but also a grim portent of what was to come in the affairs of Palestine. The proclamation of Feisal as King of Syria on 8 March 1920 by a Syrian Congress in which Palestinians were represented stirred demonstrations of support in various parts of Palestine, leading the British to ban further such events. Nevertheless, such a demonstration did take place in Jerusalem on 4 April on the occasion of the Muslim festival of Nabi Musa, which coincided with the Christian Easter and Jewish Passover. Amongst the organisers were the Mayor of Jerusalem, Musa Kasim al-Husayni, the newspaper editor Arif al-Arif and the young man who was soon to become the bête noire of both the Jews and the British, Haj Amin al-Husayni. Both Husaynis belonged to Jerusalem's most prominent Arab family. Once again, support for Feisal was the focus of the demonstration. In the violence which then followed, 5 Jews were killed and over 200 wounded, while 4 Arabs were killed and 21 wounded. Weizmann, who had gone to Haifa to celebrate Passover with his mother, who had settled in Palestine after the Russian Revolution, returned with his son to Jerusalem to find the city under military occupation. Although he had been out of the city when the violence had broken out, there is no doubt that what had happened deeply shocked Weizmann, for whom these events were all too reminiscent of the Russian pogroms, only this time under the British. Apart from what it revealed about Arab hostility, the outbreak also exposed the limitations of British power, which was far from reassuring to the Jews. Weizmann was fiercely critical of the actions of the British forces in disarming Jews. It was also alarming to the Jews that while Arif al-Arif and Amin al-Husayni were given ten-year sentences _in absentia_ , Vladimir Jabotinsky, who had sought to mobilise young Jews, was sentenced to 15 years. However, what deeply worried Weizmann was the possible impact of these events on the deliberations and decisions of the forthcoming San Remo conference, which would settle the nature of the Middle Eastern Mandates as well as prepare the way for an overall Turkish settlement.
Both Feisal and Weizmann, and the movements they led, were to be profoundly affected by the Conference's decisions. Interestingly, though, Feisal refused to attend, sending instead his chief-of-staff, Nuri al-Said, who was unable to influence the deliberations. Weizmann fared much better even although he arrived in San Remo disheartened, apprehensive, and by his own account somewhat grimy. Since the Conference lasted from 18 to 26 April, and the future of Palestine was one of the last items under discussion, he did not have much to do. It was, perhaps, a measure of the toll that recent events had taken that in the course of his train journey to San Remo, he confided in Vera his distrust of the British. He was clearly seeing clear water between the British he knew in London and those he was encountering in Palestine. Once there, however, several things occurred which relieved his anxieties. Balfour was able to reassure him that he and Curzon were agreed that the recent events in Jerusalem would not affect British policy, which had been Weizmann's main concern. He also learned that Lloyd George and Balfour were agreed that Samuel should be the first British High Commissioner to Palestine.
The future of Palestine came before the Supreme Council on 24 April 1920, chaired by the Italian Premier Francesco Nitti. Lloyd George, Curzon and Robert Vansittart were present for Britain, Prime Minister Alexandre Millerand and Philippe Berthelot of the Ministry of Foreign Affairs represented France, and Matsui Keishiro spoke for Japan. They were joined by the American Ambassador to Italy, Robert Underwood Johnson. Curzon opened by referring to the Balfour Declaration, which he grandly, if somewhat inaccurately, claimed had promised Palestine as the National Home of the Jews of the world, and which he said had been accepted by the major powers. What he wanted was that the Declaration as it stood should be incorporated into the treaty, claiming that he had resisted attempts by the Zionists to have its terms expanded. Curzon had clearly got wind of the fact that the French still had reservations. A lengthy debate with Berthelot confirmed this to be the case.
Berthelot countered by questioning several of Curzon's assertions. There had not, he stated, been any official acceptance of the Balfour Declaration by the Allied governments. While the French did not wish to thwart Britain's desire to give the Jews a National Home in Palestine, he queried what this meant. If it were to be different from other states, then it would create difficulties in the Muslim and Christian world. He was clearly thinking of France's large stake in Muslim North Africa, as well as its plans for Syria. The Christian dimension would emerge in the course of the ensuing debate. It would be best, he said, to refer the matter to the League of Nations. Curzon then treated Berthelot to a brief history lesson. He was not quite accurate in saying that Balfour had issued the Declaration on behalf of the Zionists, he said, but then went on to claim that it had been accepted by Pichon, then head of the French Foreign Office, by President Wilson, and by the governments of Greece, China, Serbia and Siam (now Thailand). The two men then wrangled for some time over exactly what Pichon had, or had not, agreed to.
Millerand adopted a rather softer line, while Nitti tried to bring the two sides to an understanding. Berthelot eagerly pounced on a statement by Matsui that his government had never accepted the Declaration as confirmation of his point that it was not official Allied policy. It then emerged that what was really troubling the French, and to an extent Nitti, was the position of the Catholic community in Palestine. The Vatican had made public its view that the French, and not the British, should be the protector of Catholic interests in the country. Lloyd George was adamant that there could not be two Mandatory powers in Palestine. The French were also keen to assert the political, as opposed to the civil and religious, rights of the non-Jewish communities of Palestine, which had been expressed in the Balfour Declaration, but Millerand conceded that he would be satisfied if this were placed on record.
The following day, the Conference returned to the question of Mandates, especially the question of boundaries. There was no repetition of the prolonged wrangling of the previous day. The border of Palestine was linked to where that of the Mosul region would be, which had been a point of contention between Britain and France. The main issue between them was where the northern border of Palestine was to lie. The Zionist hope was that it would be along the Litani River, which would include the headwaters of the river Jordan. While acknowledging their case, Lloyd George was prepared to concede that this area had never formed part of Palestine, and that, as a result, the border should be focused on the town of Dan. On hearing this concession, Berthelot asked whether the Conference could now decide that the Mandates for Mesopotamia, or Iraq as it was to be known after 1921, and Palestine should be given to Britain, and Syria to France. Nitti agreed. The formal agreement regarding Palestine was that the country's administration be entrusted to a Mandatory to be chosen by the Principal Allied Powers. The chosen Mandatory Power was Britain. The Mandatory was charged with putting into effect the Declaration of November 1917, and it was confirmed that this instruction had been adopted by the other Allies.
As the Conference ended, Lloyd George emerged to inform Weizmann of the decision to award the Palestine Mandate to Britain, with the incorporation of the Balfour Declaration as an essential proviso. He was also told that Samuel would be appointed High Commissioner, and that there would be changes in the Palestine administration. In Weizmann's view the outcome was of equal significance to the Balfour Declaration, and in his letter to Vera telling her of what had been agreed he heralded it as the dawn of a new Palestine. With a British Mandate based upon the Balfour Declaration now in his pocket, Weizmann's stature within the Zionist movement was unique and unassailable, or so it seemed.
For their part, the French viewed the Conference as a means of clearing away the obstacles to intervention against Feisal, and indeed the problem with Britain was largely dealt with at San Remo. Curzon had tried to fight a rearguard action on Feisal's behalf. His suggestion that if Feisal came to the Peace Conference, agreed to accept a proper Mandate and came to a final agreement with the French and British regarding the status of Syria and Palestine, the Allies should recognise him as King of Syria, was, however, unacceptable to Millerand. He was not willing to concede that France would have a weak Mandate in Syria, while Britain would have much greater freedom of action in Palestine and Mesopotamia. Britain was resigned to France dealing with Syria as it pleased.
The San Remo Conference had set a template for the post-Ottoman Middle East, with results that were to resonate for decades to come. France had Mandates for Syria and Lebanon, while Britain had Iraq and Palestine in its charge. Weizmann and the Zionists now had what they had hoped and worked for, namely, a British Mandate for Palestine charged with implementing the Balfour Declaration. For Feisal and Arab nationalism the outcome could not have been more different, as events were soon to show.
The end of Feisal's kingdom
After San Remo, Millerand moved to prepare the ground for an assault on Syria. General Gouraud was ordered to encourage the development of local autonomy in the country. He had advocated such a strategy earlier in the year. Gouraud also sent Robert de Caix to parley with Mustafa Kemal. A ceasefire was secured at the end of May, giving Gouraud a free hand to concentrate his forces against Feisal and the Syrians. The French plan was simple. Feisal was to be presented with an ultimatum to end all attacks on the French by Arab groups. Should this not be immediately complied with, French forces would occupy Damascus and Aleppo, disarm the Syrian forces and depose him. It would appear Millerand relished the opportunity to finish with Feisal once and for all. Substantial reinforcements were sent to Lebanon to prepare for a military solution. Gouraud was equally enthusiastic to end the 'phoney war'. French agents also sought allies among the Syrians. There were a number of groups in Syria that were anxious to see the back of Feisal's regime, the Druze and Christian populations being the most notable collaborators with the French.
On 18 May, Curzon appeared to abandon any pretense of support for Syria. While still asking that the French show moderation in their treatment of Feisal, for fear that they would drive him into the hands of the Turkish nationalists, it was recognised that France was the best judge of the 'military measures' needed to meet the local situation and that it had the right to use such measures. The following day, the French government resolved to crush Feisal and the Syrian nationalists by force. Appropriate orders were issued to General Gouraud on 22 May. He was promised considerable reinforcements that would arrive in time for a military strike in July. All other French aims in the Middle East became subordinated to gaining control of Syria. Gouraud was instructed to renounce or put on hold French rights in Cilicia in order to secure his flank from attack by the Turks, and a truce with Kemal was concluded on 1 June. By the end of June, the French had assembled sufficient forces in the Levant for a strike at Damascus.
Feisal was by now aware of French forces massing on the frontier of Syria and that France was seeking allies among Syrian notables and tribal leaders. He again sought to compromise and began to rein in the activities of the guerrillas. Similarly, the Damascus press and political parties were brought under tighter supervision. This repression was put in place to prevent any incident that would provide an excuse for the French to march on Damascus. Feisal also sent Nuri al-Said to parley with Gouraud.
Gouraud, with his forces in place and anxious to force the issue, wanted Feisal isolated in Damascus. He feared that Feisal might prevent an attack by either making a deal with Paris or securing another British intervention. Either occurrence might cheat him of the final reckoning that he now desired. Gouraud sent Nuri back to Damascus on 11 July with new and unpalatable demands including French occupation of the Rayaq–Aleppo railway, acceptance of the Mandate and the end of military conscription. Feisal rejected the demands. In response to Arab reinforcement of the border with the French zone, Gouraud moved forces into Rayaq. On 14 July, he sent a written ultimatum to Feisal demanding he accept the 11 July terms and outlining how Feisal and the Syrian nationalists had failed to comply with previous agreements. Feisal had five days to respond or face invasion and French military occupation. He made last desperate appeals to Britain to intervene. The British urged caution on the French but as Lord Hardinge, the Permanent Under-Secretary at the Foreign Office, noted, it was impossible for Britain to intervene as a result of the San Remo agreements. In his view, if the French treatment of Feisal led to trouble in the future it would be better that the responsibility should lie solely with them and that the British were not implicated.
War fever now spread through the unoccupied part of Syria. Despite some desertions, the bulk of the military officers around Feisal remained steadfast and determined to fight. However, the army was an army in name only. It was desperately short of heavy weapons, and while rifles were plentiful, ammunition was in very short supply. Feisal's attempts at negotiations with Gouraud yielded a few concessions but the French commander still made demands for the punishment of extremists, which included high-ranking officials in the army. Feisal agreed to virtually the entire French ultimatum. He began to make preparations for a military crackdown against extremists who would almost certainly oppose his capitulation. Feisal suppressed the Syrian Congress when it opposed his acceptance of the French terms, leading to an outbreak of street fighting in Damascus, which troops loyal to Feisal crushed with great force.
Gouraud, however, appears to have been playing Feisal along. On 20 July he declared that Feisal had not complied sufficiently with French demands despite desperate efforts to do so. French forces moved against Syria just after midnight of that day. Feisal, after a final and fruitless attempt to negotiate, decided to stand and fight. Arab forces attempted to block the French advance at Maysalun near Damascus. The French had more troops as well as tanks, aircraft and superior artillery. The result was the inevitable rout of the Arab forces.
Feisal returned to Damascus. Gouraud and the French now had no use for him and he was told to leave. On 1 August, Feisal and his entourage left for Europe via Haifa. Syria was now completely in French hands. Gouraud immediately implemented a divide-and-rule strategy by creating autonomous areas in Syria that would emphasise tribal, religious and ethnic divisions so as to facilitate French rule. The dream of an Arab kingdom in Syria was now gone forever. Feisal appeared to be just another nationalist that the Western Powers no longer had any use for – destined to be forgotten.
Weizmann at high tide: the Palestine Mandate
Despite Weizmann's undoubted success at San Remo, the International Zionist Conference, the first truly representative Zionist congress since 1913, which was held in London in early July 1920, proved to be far from harmonious. Weizmann's address opened with what can only be described as a paean of praise for the British leaders, Balfour and Lloyd George, of course, but also Curzon for the way in which he had defended the Zionist position at San Remo. He reminded his audience that the conditions for creating the National Home had been established, and that a sympathiser, Samuel, had been given responsibility for Palestine. If they were to make Palestine as Jewish a country as quickly as possible, then the work had to be set in hand over the next few years. Not to do so would raise a question mark against the Zionist enterprise. His hope was to settle some 30,000 to 50,000 Jews in the first year. Such a level of immigration would require land purchases which did not infringe the rights of the Arabs. A major objective, he argued, was to secure the goodwill of the Palestinian Arabs; failure to do so would poison their efforts. Echoing his earlier contacts with Feisal, he argued that Jewish expertise could assist with the development of the Arab world. In his peroration he returned to the theme that the conditions for the re-creation of the Jewish nation had been secured. It was now up to the Jews themselves to achieve it.
Despite his fine oratory and recent triumph, the conference was a far from happy experience for Weizmann, who found himself criticised by, amongst others, Ben-Gurion, who now made his debut in the world of international Zionism. Ben-Gurion's power base was starkly different to that of Weizmann; namely, the Achdut ha-Avodah, the Socialist-Zionist Association of Workers of Palestine, which had been formed in the spring of 1919. His attack on Weizmann was both bitter and personal, accusing him of creating a barrier between the administration and the Jews of Palestine. Moreover, his concessions had led to hostility on the part of the government that had helped incite Arab violence. Finally, he claimed that the Jews had been better served under the Turks than under the British, a curious notion given the Balfour Declaration. Weizmann had little difficulty in rebutting this intemperate assault on his leadership, but it did not bode well for his relationship with the Jews of Palestine, who were, after all, pivotal to the movement's success. Ben-Gurion had made his mark, and his influence was to grow significantly with the years. It was an inauspicious start to a relationship between the two men which would ultimately end on a bitter note.
More serious at the time was Weizmann's rift with Brandeis and the leadership of the large American contingent which had come to London. With his base in the Olympian atmosphere of the Supreme Court in Washington, Brandeis had always been a somewhat improbable Zionist leader, and his punctilious legal mind was repelled by what he saw of the somewhat scatty preparations for the London conference. At root, however, was a clash between how the two men saw the future of Zionism. Brandeis and his followers believed that by securing the Balfour Declaration and the British Mandate, Zionism had achieved its political purpose and objectives, and hence should now turn its hand to the economic development of Palestine. For Weizmann, the political struggle was only just beginning. Brandeis's proposal that the Zionist Organisation should focus on economic activity was clearly defeated on the floor of the conference. But Brandeis believed, seemingly with justice, that Weizmann had lobbied against his ideas for a reorganisation of the Zionist leadership, and the two leaders also quarrelled over the size of the American contribution to the budget. The breach between these two gifted men was never to be repaired. The conference concluded with Brandeis's appointment as Honorary President of the World Zionist Organisation, with Weizmann as its President. At last, Weizmann had a position of strength from which he could operate, but it had been purchased at a price, both in Palestine and the United States.
When Sir Herbert Samuel, as he had become, assumed office as High Commissioner and Commander-in-Chief in Palestine on 30 June 1920 it seemed to herald the fulfilment of Zionist dreams. Not only was his one of the main voices which had led to the Balfour Declaration, but after nearly two millennia a Jew stood at the head of Palestine's affairs. But it was not as simple as that. The achievement of the Zionist dream, at least as it had evolved under Weizmann, rested on two external conditions: sustained British commitment to the idea of a National Home and Arab, especially Palestinian Arab, acquiescence in it. Samuel's arrival in Palestine was not reassuring on either count. His journey from Jaffa to Jerusalem had to be changed to take account of rumours of plots on his life, and he had to be given an escort of armoured cars for his journey from the Jerusalem railway station to the government house on the Mount of Olives, where the outgoing Chief Administrator, Major-General Sir Louis Bols, persuaded him to sign a receipt for Palestine. It was hardly a triumphal entry, although he did receive a 17-gun salute.
Britain and the new Turkish nationalism
Mustafa Kemal had in the meantime left Sivas for Ankara, which had direct railway communications with Istanbul. He stood for election, but refused to go to Istanbul when elected to the new parliament. However, most of his companions, who were also successful in the elections, travelled there, in spite of Mustafa Kemal's insistence that the new parliament should meet in unoccupied Anatolia, just as the German parliament had met not in Berlin, but in Weimar. Left alone in Anatolia, Mustafa Kemal's control over his sympathisers in the new parliament became tenuous. Although some disagreements surfaced, parliament reaffirmed the National Pact, stiffening it with the demand that popular referendums should also be held in western Thrace and in the three provinces which the Ottomans had regained from Tsarist Russia, to determine whether local people wanted to be part of an independent Ottoman state. On 17 February 1920, parliament voted to communicate the National Pact to all Allied parliaments.
The nationalist stand of the Ottoman parliament under the complacent eyes of the Ali Rıza government was too much for the British occupation authorities, which were not mollified when Ali Rıza resigned and was replaced by Salih Hulusi Pasha, the go-between chosen to bring Mustafa Kemal back into the Ottoman fold. On 16 March 1920, with the reluctant assent of the other Allies, British troops occupied the Ottoman War Ministry and the barracks of Ottoman troops in the capital. There was some firing and a few Turkish soldiers were killed. A Turkish telegraph clerk, a refugee from Macedonia called Hamdi, achieved national fame by keeping open the line to Ankara and informing Mustafa Kemal's headquarters of the progress of the British occupation. He then made his way to Ankara and, many years later, when it was decreed that all Turks should have surnames, he chose the surname 'Sixteenth March'.
British troops moved to arrest the leading nationalists in the newly elected parliament, which immediately adjourned without fixing a date for a new session. Rauf, who had returned to Istanbul as a Member of Parliament, was among the exiles sent to Malta. The forcible entry into a freely elected Ottoman parliament of the troops of a country which prided itself on being the mother of parliaments provided Turkish nationalists with useful propaganda ammunition. There were to be no further sessions of the Ottoman parliament. The Sultan dissolved it, and his government could not organise new elections as its authority did not extend much beyond the capital. Salih Hulusi resigned and was replaced yet again by Damad Ferid, a man utterly incapable of rallying the country round him.
In the confusion caused by the British occupation and the change of government, those Turkish nationalists who had not been rounded up made their way to Ankara. They included not only Members of Parliament, but also military commanders, notably General Fevzi Çakmak, the most senior Ottoman officer to side with Mustafa Kemal, and Colonel İsmet (İnönü), Mustafa Kemal's faithful, but careful, lieutenant, who always looked before he leapt. Fevzi had earlier tried to turn Kâzım Karabekir against Mustafa Kemal, but this was not held against him. Mustafa Kemal shared the esteem in which Fevzi was held in the Turkish officer corps and made him chief-of-staff of the new Turkish national army.
The Allied occupation of Istanbul sealed Mustafa Kemal's leadership of the Turkish nationalist movement and allowed him to take the next step. This was to summon a national assembly in Ankara as a prelude to the formation of a fully fledged alternative government. The assembly called itself the Grand National Assembly and its executive became known as the Government of the Grand National Assembly. The adjective 'Turkish' was to be added later: at first the fiction was maintained that it was the Ottoman nation which was represented.
Kemal in power: the Grand National Assembly
Mustafa Kemal saw to it that his parliament and government appealed to all and sundry, Muslims and Turks. The Assembly was made up of those deputies of the last Ottoman parliament who had managed to make their way to Istanbul and of new members elected ad hoc, or, more accurately co-opted by nationalists in Societies for the Defence of Rights or by provincial notables. Some of the members of the new assembly were deemed to represent occupied areas where no elections could be held. All the members were united in their determination to resist foreign rule. But they were not of one mind when it came to tactics, and were ready to criticise the nationalist leadership when things went wrong, and to limit as far as possible the power of Mustafa Kemal, who was suspected of nurturing dictatorial ambitions.
The Assembly held its first meeting on 23 April 1920 under the slogan 'sovereignty belongs unconditionally to the nation'. This revolutionary sentiment was reflected also in the powers which the Assembly arrogated to itself, combining the functions of the legislature, executive and judiciary. Elected President of the Assembly, Mustafa Kemal was also head of government, which took the title of Committee of Executive Commissioners. The commissioners were elected singly by the Assembly, which could also dismiss them. The inspiration came from the French National Convention after the 1789 Revolution, but also from the Bolshevik Committee of Executive Commissars (known by the Russian abbreviation _ispolkom_ ). From the start, Mustafa Kemal (and to a lesser extent Kâzım Karabekir in Erzurum) tried to secure the support of the Bolsheviks, while keeping them out of the country. Ideologies were fluid, misconceptions flourished, and contradictory views were held, genuinely or for tactical reasons.
The opening of the revolutionary Assembly was marked with an Islamic ritual, excessive even by late Ottoman standards. It took place on a Friday when all male adult Muslims are meant to pray as a congregation. After prayers in the main Ankara mosque (which was also a shrine to a local holy man), members of the Assembly walked in procession preceded by a cleric holding a relic – one of the many supposed hairs from the beard of the Prophet Muhammad, venerated in the country. Imams throughout unoccupied Anatolia were ordered to recite not only the whole of the Koran, but also a lengthy compendium of the sayings attributed to the Prophet. Sheep were sacrificed in Ankara and the provinces to invoke divine blessing.
After these preliminaries, the Assembly met in the building which had served as the premises of the club of the Young Turks. It was built in what became known in Turkey as the 'national style', although Western colonial architecture, from French North Africa to the British Federated Malay States, was a more obvious source of inspiration. Refurbished and enlarged, the building was later used by the Turkish parliament for many years, then by the Republican People's Party, which Mustafa Kemal founded; it is now preserved as a museum.
The first act of the revolutionary Assembly was to send a message of loyalty to the Sultan, who was deemed to have become the captive of the Allies and to be surrounded by evil ministers who kept him ignorant of his subjects' concerns. But while the fiction was maintained, Mustafa Kemal made sure that even those members of the Ottoman dynasty who were sympathetic to the nationalist cause were kept out of Anatolia. In April 1921, Prince Ömer Faruk, son of the heir apparent Abdülmecid, eluded Allied controls and travelled secretly to the small port of İnebolu on the Black Sea which the nationalists controlled and which served as the point of entry to unoccupied Anatolia. At Mustafa Kemal's instructions, he was sent back to Istanbul and told that the time to make use of his services would come later.
Mustafa Kemal was a master tactician who used fictions when they served his purpose. He sought support wherever he could find it. In order to obtain help both from the Bolsheviks and from foreign Muslims, he went along with the argument that the Muslim world and Bolshevism had a common enemy in imperialism, and that they were, at least to some extent, compatible. Misconceptions reinforced useful fiction. Addressing a Bolshevik envoy, Mustafa Kemal declared: 'Turkey is engaged in a determined and vital endeavour, because it is battling in the cause of all oppressed nations, of the whole Orient.'
There was at the time of the Russian Civil War a ragged armed band, led by the anti-Semitic peasant bandit Makhno, which styled itself the Green Army. As green is the colour of Islam, some supporters of Turkish national resistance believed that the Green Army had been formed by Muslim Communists, and they set up a similar organisation in unoccupied Anatolia. Also called the Green Army, it attracted the Circassians who resisted control even by their fellow Muslims. But in addition to undisciplined rebel fighters, there was also a small group of Marxists in Turkey, usually rebellious children of the ruling class who had been impressed by the Spartacist movement in Germany and had pinned their hopes on the worldwide revolution preached by the Bolsheviks.
The Treaty of Sèvres
While Mustafa Kemal was consolidating his power in Ankara, the Allies continued to dither. But a peace settlement with Turkey could not be put off for ever. The Treaty of Versailles with Germany was followed by treaties with Austria, Bulgaria and Hungary. All left a legacy of bitterness which erupted in the Second World War, when the nationalist leaders of defeated nations made common cause with Nazi Germany. The Turkish settlement was more difficult, but when it finally came it proved more durable. The rise of modern Turkey provides a perfect illustration of the law of unintended consequences – in this case the beneficial consequences of Lloyd George's ill-advised policy. But an immense price in human suffering had to be paid before the benefits finally emerged.
The government which Damad Ferid formed on 5 May 1919 after the British had raided the Ottoman parliament did all it could to strangle at birth the nationalist movement in Anatolia. A week into its tenure of power, it procured from the Sheikh al-Islam, the head of the official clerical establishment in Istanbul, a fatwa declaring that the nationalist forces were rebels against the faith and that it was the duty of all Muslims to kill them. The nationalists responded by obtaining a counter-fatwa from the muftis of Anatolia, with the mufti of Ankara in the lead, saying that, on the contrary, it was the duty of all good Muslims to resist foreign occupation and free the Sultan-Caliph from foreign captivity. (Throughout Ottoman history fatwas were issued with the ease of vending machines: you put in a coin and got your fatwa.) The National Assembly in Ankara passed a law declaring that those who resisted its authority would be guilty of high treason. In Istanbul a court martial passed death sentences on Mustafa Kemal and his companions.
The war of words was reflected by clashes on the ground, as rebellions broke out in nationalist-held territory. Damad Ferid's government formed a 'disciplinary force', known also as the Army of the Caliphate, to suppress the nationalists. The pay it offered attracted a ragbag of none-too-enthusiastic volunteers, whom the nationalists had little difficulty in putting to flight. The rebellions behind the lines held by the nationalists posed a greater problem, but these too were suppressed, often by militias. Circassians who supported the nationalists routed their fellow tribesmen loyal to the Sultan. Similarly, Kurdish tribes fought each other, and those which sided with the nationalists helped the weak national army to establish the authority of the National Assembly. Nevertheless Mustafa Kemal felt personally threatened when the feudal clan which dominated the district of Yozgat, just east of Ankara, rebelled against his authority. The army was unable to suppress the rising, and the nationalists' Circassian allies had to be rushed from their territory west of Ankara to do the job. Their leader, Edhem, commander of the 'mobile force' of horsemen, and patron of the Green Army, got ideas above his station and strutted around like a bully when he showed up in Ankara with his fighters. He got his comeuppance a few months later when the new regular national army took over the command of militias. Refusing to submit to the discipline of the new nationalist regime, Edhem and the remnant of his forces sought refuge with the Greeks. He ended up in Transjordan, where fellow Circassians provided the guard of Abdullah, whom the British had installed as emir.
On the ground, the military situation remained frozen for a year after the Greek occupation of İzmir and the surrounding area in May 1919. But while the wheels of diplomacy slowly ground forward, the Allies demobilised in response to domestic discontent. When the Paris Peace Conference opened, Lloyd George made much of the fact that there were more than 1 million British troops occupying Ottoman territory. A few months later their numbers fell to little over 300,000, and these were fully occupied holding Mesopotamia and Palestine, with only a weak force guarding the Turkish Straits and occupying Istanbul. This led to the next step in the destruction of Anatolia.
On the night of 14/15 June 1920, Turkish nationalist detachments outside İzmit (Nicomedia) clashed with a weak British force guarding the town, which controlled access to Istanbul from the east. The British commander, General George Milne, asked London for reinforcements. None were available, and the Chief of the Imperial General Staff proposed that a Greek division should be used to defend the Ottoman capital. The Greek Prime Minister Venizelos was only too ready to oblige with a division stationed in western Thrace. His reward was permission for Greek troops to occupy eastern Thrace, including Edirne (Adrianople), and to cross the Milne Line to seize the whole of western Anatolia, south of the Sea of Marmara.
The first steps leading to the disastrous decision to impose draconian peace terms on Turkey were taken at Allied consultations in London between 12 February and 10 March 1920. At a meeting on 16 February, Venizelos pressed his claims to İzmir and the surrounding area on the basis of population statistics, which exaggerated the number of Greeks and undercounted the Turks. He was supported by Lloyd George. The London conference was followed by the extension of British military control in Istanbul on 16 March, but not before the British High Commissioner in the Ottoman capital had outlined his fears. 'The terms are such that no Turks... can very well accept,' wrote Admiral de Robeck. He warned that the Allies would have to be prepared 'for a resumption of general warfare'. Moreover, they would 'do violence to their own declared and cherished principles... and perpetuate bloodshed indefinitely in the Near East'.
The French had similar reservations. On 12 February 1920, the day that the London conference opened, their troops had been forced by a local uprising to evacuate Maraş in southern Turkey. The uprising was led by an imam, known as 'the Milkman'. The memory of this episode has been kept alive. Today, the town is known officially as Kahramanmaraş (Maraş the Heroic), and it boasts of the University of the Milkman Imam. Some of the Armenians who had accompanied the French troops were killed during the evacuation, giving rise to reports of an Armenian massacre. Having experienced Turkish resistance, the new French Prime Minister Alexandre Millerand persuaded the Allies to commission a report from the military commission chaired in Versailles by Marshal Ferdinand Foch, the victorious commander on the Western Front. Foch concluded that no less than 27 divisions would be required to impose the terms demanded by Lloyd George and his protégé Venizelos. Although he was warned by Lloyd George that he could expect no help, Venizelos promised rashly that his army could do it alone. The Italians, who had been cheated out of their main prize, expressed their doubts. Nevertheless, the final plan to partition Turkey was agreed at the San Remo Conference, just as Mustafa Kemal's nationalist government was taking shape in Ankara. There was only one way of enforcing the Allied peace terms. On 21 June at a meeting in Boulogne, the Allied leaders allowed the Greek army to occupy eastern Thrace and the whole of western Anatolia.
An Ottoman delegation was summoned to Paris to sign the peace treaty. It was led by the elderly Tevfik Pasha, the Sultan's man for all seasons. On 25 June, the Ottoman delegation submitted its reply to the partition project on which the Allies had agreed at San Remo. Tevfik Pasha had already advised his government that the Allied peace terms were incompatible with the continued existence of an independent Ottoman state. This was strongly argued in the Ottoman reply, which made the point that the Allied peace settlement imposed on the Ottoman government obligations while depriving it of the means to carry them out. The desire to tie down the Turks had been pushed to absurd lengths. Under the Allied plan, there would be eight separate jurisdictions in Istanbul: the Sultan's government, the proposed Straits Commission (with its own flag), the military authorities of the Allied occupation forces, the political authority of the High Commissioners of Britain, France and Italy, the Allied commission for supervision and organisation, the international financial commission, the board of the foreign-owned Ottoman public debt and foreign consular courts applying their own laws. But the Allies were in no mood to listen to reason. Rather than wait for their response, which he could guess in advance, Tevfik turned to the Grand Vizier Damad Ferid, who had joined the delegation, much to the displeasure of the other members, and said, 'There is no point in staying on for there is nothing more we can do. Let us at least save money by returning home and leaving our junior colleagues here.'
On 11 July the Allied leaders met in Spa in Belgium, where the Kaiser had his headquarters during the First World War. Millerand, Curzon, the Italian representative Count Sforza, Viscount Chinda of Japan and Venizelos were there. Sforza was an ironic observer; the Japanese were not really interested; Curzon stuck to Lloyd George's line, in spite of his reservations; and Venizelos made sure that a crushing reply was sent to the Ottoman government. He succeeded. Whatever they might think in private, the Principal Allies agreed on a text that was both uncompromising and insulting.
The Ottoman decision to enter the war on the side of Germany, they declared, was an act of treachery. It prolonged the war by two years and caused the Allies the loss of millions of men and billions in money. After 1914, the reply thundered, the Ottomans had murdered 800,000 Armenians, and deported another 100,000 as well as 200,000 Greeks. The Allies had to guard against further treachery in deciding the regime of the Straits. The accusations led to a final threat: if the Ottoman government did not sign the Treaty, or if it was unable to impose its authority in Anatolia, the Allies reserved the right to review their terms and drive the Turks out of Europe for ever. The Ottoman government was given ten days until 27 July to reply to this ultimatum. Prejudice against Turks could go no further. In Britain today this forgotten text would fall foul of the Race Relations Act. But in Turkey it is remembered as the expression of abiding anti-Turkish prejudice, and it has left a mark on attitudes to the outside world.
By the time the Allied ultimatum was received in Istanbul, the whole of coastal Anatolia, with the exception of the shores of the Black Sea, was under foreign occupation. Turkish troops on the ground were too weak to prevent the advance of the Greek army. Isolated in eastern Thrace they had no option but to surrender. In Anatolia, the Greeks swept north and west out of their enclave round İzmir. On 8 July 1920, they occupied Bursa, the second capital of the Ottomans, at the centre of the rich Bithynian plain south of the Sea of Marmara. This was a bitter blow to the Turks, for whom Bursa, like Edirne (Adrianople), symbolised the glories of the Ottoman Empire. As a sign of mourning, the rostrum of the National Assembly in Ankara was draped in black.
Arnold Toynbee, who had earlier worked for the government and helped compile the British _Blue Book_ designed to rally the American public to the Allied cause, with stories of Armenian atrocities, took time away from his duties as Professor of Medieval and Modern Greek at King's College, London in order to report for the _Manchester Guardian_ , then as now the voice of British liberalism, on the progress of the Greek occupation of Anatolia. From the eastern approaches of Istanbul, he could see the flames of Turkish villages torched by the Greeks on the eastern shores of the Gulf of İzmit. The experience changed his outlook. In _The Western Question in Greece and Turkey_ , the book he published in 1922, he came to the conclusion that Greece was 'as incapable as Turkey (or for that matter any Western country) of governing well a mixed population containing an alien majority and a minority of her own nationality'. The Greek shipowners who had funded the chair at King's College were furious. Toynbee was forced to leave. He devoted himself to the development of the Royal Institute of International Affairs and to writing his ten-volume _Study of History_ , in which his pessimistic view of Western civilisation found expression in the theory that all civilisations arise as a challenge to a response and that they are all destined to die. Historical, and generally cultural, relativism was a response to Allied triumphalism at the end of the First World War. Eventually, Toynbee gained the admiration of Turks who, unlike him, had no doubts about the values of Western civilisation, whatever the misdeeds committed in its name.
The Allied threat to drive the Turks out of Europe forever cut no ice with the Turkish nationalists who had, in any case, left European Turkey to carry on the fight in Anatolia. But the Sultan was determined not to compromise the prospect of staying on in Istanbul, as a shadowy sovereign claiming to be Caliph of all Muslims. Even so, he decided to summon a council of the throne before agreeing to the Allied demands. His Grand Vizier, Damad Ferid, argued that to reject the terms would be equivalent to committing the sin of suicide. The Ottoman dynasty was like an ancient tree. So long as its roots remained in its native soil, it was capable of new growth. Summoned to choose between a shadowy survival and extinction, the grandees summoned to the council voted in favour of accepting the peace settlement in spite of its 'terrible conditions'. There was only one dissenting vote. It was cast by Rıza Pasha, a retired artillery general.
Armed with the authority of the throne council, an Ottoman delegation went to Paris to sign the peace treaty imposed by the Allies. Two of its members – a diplomat and a senator – were inconspicuous. But the third had a considerable, although controversial, reputation. He was the poet Rıza Tevfik, known as 'the philosopher', philosophy being the subject he taught at the university of Istanbul. He had been a member of the CUP before joining Damad Ferid in the Liberal Union. A liberal and a patriot after his fashion, who believed in the doomed ideal of 'the union of all elements' (the peaceful co-existence of the constituent communities of the Ottoman state), he was listed among the 150 opponents of the nationalists who were exiled after 1923. Together with the surviving exiles, he was pardoned in 1938 and returned to Turkey where he is remembered as an eccentric idealist out of tune with the times.
On 10 August 1920, the Ottoman delegation signed the peace treaty at Sèvres, outside Paris. Critics were not slow to observe that the Treaty was as brittle as the porcelain made there for the French court. But it was certainly nothing like as beautiful. On the same day, Britain, France and Italy signed a pact on their respective zones of influence in what remained of Turkey. The Italians were to enjoy preferential treatment in south-western Anatolia, the French in the south and the British in the extreme south-east, north of Iraq. The pact was a British sop to the French, who had given up Mosul, promised to them in the Sykes-Picot Agreement, and particularly to the Italians, who lost İzmir and who did not add to their territorial gains – the Dodecanese and Libya – acquired on the eve of the war. But the Italians were not satisfied, and became the first Allies to befriend the Turkish nationalists. The French preferred to wait on events before making their own arrangements. Thus, right from the beginning, two of the Principal Allies did not share Lloyd George's enthusiasm for the Treaty of Sèvres. Even Curzon had misgivings. He asked Lloyd George to 'think seriously' about Anatolia and the Greeks. He was, he said, 'the last man to wish to do a good turn to the Turks', but he wanted to achieve 'something like peace in Asia Minor, which was impossible so long as the Greeks were marching about inside it'.
The Treaty of Sèvres died 'intact, though dead, whole though unratified' in the words of Andrew Ryan, the Dragoman at the British embassy in Istanbul. Greece was, in fact, the only signatory to ratify it. Six months after the signature of the Treaty, a conference had to be arranged in London to amend its more outrageous provisions. But this proved impossible.
Under the Treaty of Sèvres, the Ottoman state was to lose eastern Thrace to Greece, the territory of which would extend right up to the suburbs of Istanbul. Istanbul would remain nominally under Ottoman sovereignty, but as the Ottoman delegates had already pointed out, this would be diluted to vanishing point. The area around İzmir, known to Greek nationalists and Western Philhellenes by the classical name of Ionia, would also remain under nominal Ottoman sovereignty, but only for five years, after which its fate would be decided by a referendum. The deportation and flight of Turks which followed the Greek occupation had made certain in advance that the referendum would result in the annexation of Ionia to Greece. In the south, French-Mandated Syria would gain a large slice of adjacent Turkish territory. In the east, the Kurds would gain autonomy immediately and independence if they opted for it a year later and the Council of the League of Nations thought they had the capacity for it. Further north, there would be a greater independent Armenia with access to the sea, within borders which were to be decided by President Wilson. Wilson announced his award on 22 November 1920, in the dying days of his administration after Congress had refused to ratify the Covenant of the League of Nations. The outgoing president generously gave the Armenians the port city of Trabzon, the fortress town of Erzurum, and all the country round Lake Van. Wilson's letter announcing his decision was touching in its optimism. 'It is my confident expectation,' he wrote that:
the Armenian refugees and their leaders... will by refraining from any and all form of reprisals give the world an example of that high moral courage which must always be the foundation of national strength... surpassing in the liberality of their administrative arrangements... even the ample provisions for non-Armenian racial and religious groups embodied in the Minorities Treaty.
Woodrow Wilson's faith was misplaced. When the newly established Armenian republic took over the frontier provinces of Russian Transcaucasia from the British, which Turkish troops had evacuated after the armistice, Muslim villages were torched and many of their inhabitants killed. In September 1920, a month after the signature of the Treaty of Sèvres, the nationalist government in Ankara authorised Karabekir to cross the old Tsarist frontier. On 30 October he captured the fortress of Kars. This time Armenian civilians fled or were killed. It was the fourth wave of human wretchedness washing over the eastern Anatolian plateau since 1914: Muslim Turks and Kurds escaping the advancing Russians in 1915, while Armenians were being deported and killed in the Turkish rear; Turks fleeing from Armenians who took over from the Russians in February 1917; Armenians escaping from advancing Turks later the same year; and, finally, the two rounds of ethnic cleansing in 1919–20, with Muslims suffering first and Armenians second. No Armenians were left thereafter on the Turkish side of the frontier except for those who sought refuge with their Muslim neighbours and converted to Islam. On the Russian side, ethnic cleansing stopped and was replaced by the cleansing of class enemies with the advent of the Bolsheviks, and then resumed and was completed after the dissolution of the Soviet Union some 70 years later.
As its army collapsed, the Armenian government sued for an armistice. On 2 December 1920 the government of the Grand National Assembly signed a peace treaty with Armenia, and Turkey regained the three frontier provinces which it had lost to the Russians in 1878. Soon afterwards the Bolsheviks took over in what remained of Armenia, which was thereafter ruled from Moscow as the Armenian Soviet Socialist Republic. Its coat of arms showed Mount Ararat (Ağrı Dağ in Turkish), but the mountain now lay in Turkish territory. It did not take long for Wilson's award to be mocked by history. Armenian nationalists are still hoping that somehow or other they will regain what Wilson had given them. But if there is, in their eyes, an unredeemed Armenia, there are no unredeemed Armenians, and they are finding it difficult enough as it is to repopulate the territory which they seized from Azerbaijan and ethnically cleansed in the 1980s.
Neither Sultan Vahdettin nor his hated Grand Vizier Damad Ferid signed the Treaty of Sèvres. Forgetting conveniently that he had done his best to stifle opposition to the Treaty, the Sultan claimed later that his only motive was to gain time until the balance of external forces moved in Turkey's favour. In Ankara, the Grand National Assembly, under Mustafa Kemal's determined leadership, did not prevaricate. On 19 August, nine days after the signature of the Treaty, it declared that the Ottoman signatories and all those in the throne council who had voted in favour of signing were guilty of high treason.
Ineffective as it was, the Treaty of Sèvres left a legacy of bitterness which persists to this day. Its authors looked down on the Turks as a people incapable of progress who had to be civilised by external force. They had to make sure that the brakes on their railway carriages were in order (Article 358), that only qualified archaeologists were allowed to dig for antiquities (Article 421, add.7), that the white slave trade was effectively banned (Article 273/6), that obscene publications were banned (Article 273/7) and that birds useful to agriculture were protected (Article 273/11). If to this day it is a criminal offence in Turkey to denigrate 'Turkishness', the reason should be sought in the memory left by the Treaty of Sèvres.
The impact of San Remo and Sèvres
These events of 1919–20, which culminated in the Treaty of Sèvres, had attempted to set a new path for the Middle East based on the ambitions of the victors, and for a time they seemed to have succeeded. It was now clear that the centuries-old Turkish dominance of the Arab lands was at an end. In its place were four new entities under Anglo-French Mandates, Palestine, Iraq, Lebanon and Syria, within boundaries which were to remain in place even though they took little account of the wishes of the inhabitants at the time, let alone established economic patterns or geographical realities. These Mandates confirmed the ambitions of the British and French to replace the Turks, which had emerged by 1916 in the Sykes-Picot Agreement. The Zionists, guided by Weizmann, had secured their major objective of having Palestine placed under a British Mandate, with Britain charged with implementing the Balfour Declaration. They had the added bonus, or so it seemed, of having Samuel as first High Commissioner. By any reckoning it was a triumph for the strategy Weizmann had been pursuing, even though he had his critics within the Zionist movement, both in Palestine and the United States. Feisal's dream of a Hashemite Arab kingdom based upon Damascus had perished on the altar of France's colonial ambition which the British were willing to indulge, despite the fact that the French had contributed virtually nothing to Allenby's victories. Both the British and the Zionists were coming to realise, however, that Arab nationalism was a growing force as disturbances across the Middle East, not least in Palestine, were showing all too clearly. Even more of an immediate challenge to the victorious powers was the fast-emerging Turkish nationalism, which had found its voice in 1919–20, and its leader in Mustafa Kemal. If the Treaty of Sèvres had humiliated Turkey, as it clearly did, those who imposed it had not reckoned with Mustafa Kemal and the strength of the forces he was now leading.
5
# The Middle East Rebels and the Peace Settlement Revisited
The consolidation of Kemal's authority
The Treaty of Sèvres was buried on the battlefields of western Turkey. The casualties suffered by the new regular Turkish army in these battles were comparatively light – 13,000 men killed and 35,000 wounded. The combined losses of the Greek and Armenian armies were much heavier – more than twice as many. But it was the civilian population which suffered most, with hundreds of thousands dying and some 3 million uprooted. It took a generation before these losses were made good, and when they were, another mistaken assumption which underlay the rickety edifice designed at Sèvres was made manifest. The Greek territorial claims put forward by Venizelos and the Armenian claims accepted by President Wilson were both based on demographic projections which assumed that the Greek and Armenian population would increase fast enough to fill the territories wrenched from Turkey, and faster in any case than the Turkish population. This was the case when Greeks and Armenians were more prosperous and, therefore, healthier than their Turkish neighbours. But peace and medical services reversed the trend. Today the population of Turkey is five times larger than that of Greece and Armenia combined, and there are not enough Greeks and Armenians to realise the dreams of such unreconstructed nationalists as survive in their midst.
Diplomacy and armed resistance went hand in hand under Mustafa Kemal's guidance. The immediate task after Sèvres was to suppress the risings in the Turkish nationalist rear fomented by the Sultan's government in Istanbul. This was done between August and December 1920. Faced with the failure of his attempts to liquidate the nationalist movement in Anatolia, Damad Ferid resigned on 17 October, and left the country for a rest cure in the spa of Karlsbad (now Karlovy Vary in the Czech Republic). He was to return to Istanbul once only, very briefly in September 1922 when he collected his wife Mediha (the Sultan's sister), other members of the family and such belongings as he could carry away, and slipped off to permanent exile in France. Sultan Vahdettin, who was himself about to follow him, was informed in an impersonal note which read: 'At her husband's insistence, the Princess Mediha left for Europe for treatment two hours ago, as her rheumatism was getting worse here.' Put out, the Sultan remarked pathetically, 'The naughty boy! He got the State into this mess and then walked away.' Vahdettin was, of course, himself responsible for bringing the 'naughty boy' to power over and over again. When he had appointed Damad Ferid for the last time after the signature of the Treaty of Sèvres, he was warned by the former Deputy Speaker of Parliament that the appointment would be calamitous for the country and the dynasty. Vahdettin was not dissuaded. 'If I so desired,' he said, 'I could name as Grand Vizier the Greek or Armenian Patriarch or even the Chief Rabbi.' 'You could, Sir,' the Deputy Speaker replied, 'but it wouldn't do you any good.' After Damad Ferid's precipitate final departure, his name never again passed the lips of his exiled sovereign.
Damad Ferid was succeeded once again by the veteran statesman Tevfik Pasha, who was to be the last Grand Vizier of the Ottoman Empire. Tevfik's son was married to the Sultan's daughter, and he was, therefore, trusted as a relative. Nevertheless, in the proclamation which he issued from exile in Mecca in order to exculpate himself, Vahdettin claimed that his actions had always been guided by public opinion or by other 'considerations which could not be resisted', and went on, 'The best proof is that I kept Tevfik Pasha in power for more than two years, solely because public opinion was not opposed to him, even although he allowed Kemalists, whose bad intentions towards my person and my position were manifest, to establish their influence in Istanbul.'
The Soviet dimension
In July 1920, a month before the signature of the Treaty of Sèvres, Mustafa Kemal had dispatched to Moscow his Foreign Minister Bekir Sami (a Turkish nationalist of Caucasian stock). But, just like their Western foes, the Bolsheviks were loath to put their money on Mustafa Kemal before they could see his form. At first they offered unacceptable odds, demanding a slice of eastern Turkey for the Armenians as the price of their support. In any case, there were other Turkish competitors for Moscow gold.
The CUP war leader Enver, who had sought refuge in Germany at the end of the war, managed to get to Moscow with the help of his German friends and canvassed Bolshevik support for a plan to mobilise Muslims worldwide against the British. He was opposed by Turkish Communists subservient to Moscow. Their leader was a Paris-trained radical journalist, Mustafa Suphi. An opponent of the German alliance, he had sought refuge in Russia where he was detained as an enemy alien. Set free after the Bolshevik Revolution, he recruited Turkish prisoners of war in Russian camps to help the Red Army, and formed the Turkish Communist Party which was admitted to the Communist International. The three groups contending for Bolshevik support – the delegates of the government of the Grand National Assembly in Ankara, Enver and his fellow exiles and Mustafa Suphi and his Moscow-line Turkish Communists came face to face at the First Congress of the Peoples of the East which opened in Baku on 1 September 1920.
In April that year the Red Army had invaded Azerbaijan, which became a Soviet Socialist Republic. But while the short-lived nationalist government of Azerbaijan was thus removed from power in Baku, 'bourgeois' nationalists were still in control of Armenia and Georgia to the west. Moreover, Bolshevik control was incomplete elsewhere in the Tsar's former possessions in Asia. The collapse of the Tsarist regime had brought to the fore indigenous revolutionaries in non-Russian communities. But these tended to be National Communists – nationalists first, Communists second. In the eyes of Moscow they were useful idiots, like Western apologists for the Bolsheviks, who could be liquidated at a later date. The purpose of the Baku congress was to form an Eastern popular front of Moscow-line Communists, National Communists, radicals and anti-imperialists of various persuasions, in order to further the aims of the Bolsheviks.
The three competing groups of Turkish delegates kept in touch with each other, while eyeing each other with suspicion. Enver, who had formed a shadowy League of Islamic Revolutionaries, which existed largely in his imagination, took part as the self-appointed representative of the Muslims of north Africa. He had prepared a speech in which he argued that, had the Soviets been in power in 1914, he would have made common cause with them rather than with the Kaiser's Germany, but that, in any case, he had hastened the advent of the Russian Revolution by closing the Straits to the Allies in the First World War. However, Turkish Communists prevented Enver from reading his own speech, shouting, 'His place is not on the rostrum, but in the dock of a people's tribunal.' More realistically, Mustafa Kemal warned Enver against frightening the Bolsheviks with the spectre of pan-Islam.
Mustafa Kemal had to tread delicately to achieve his objective. He wanted to win material support from the Bolsheviks, while keeping them out of his country, and at the same time regain territory lost to the Russians in 1878, which the Bolsheviks wanted for themselves. What he offered in return was Turkish acquiescence in the establishment of Soviet power in Azerbaijan, whatever was left of Armenia and a slightly reduced Georgia. To pacify the Bolsheviks further and pre-empt Turkey's own Marxist revolutionaries, he went through the motions of creating a 'people's government' in Ankara. In Marxist jargon, a 'people's republic' is an acceptable stage in the transition from capitalism to socialism. Having opened the National Assembly with elaborate Islamic ritual and proclaimed the nationalists' loyalty to the Sultan, Mustafa Kemal presented to his deputies the programme of the 'people's government', as he called his government on that occasion only – and then never again. The programme, which set out the objective of 'liberating the Turkish nation from the domination of imperialism and capitalism... with the help of God', was endorsed unanimously and enthusiastically by the National Assembly on 18 October 1920. It was, of course, never implemented, but it served its purpose domestically and internationally, and it has left some traces.
At home, the 'people's programme' helped Mustafa Kemal establish control over the People's Group, which consisted of some 60–70 Assembly members, and was the political wing of the Green Army. When the time came for Mustafa Kemal to form his own party, he called it the People's Party. After the proclamation of the republic, it became the Republican People's Party, a name which it has retained to this day. For a long time, it ruled the country single-handed, but it has never achieved power single-handed in a free election. Abroad, there was of course no question of pulling the wool over the eyes of the Bolsheviks, but Mustafa Kemal's dealings with Moscow frightened the Principal Allies with the spectre of Communism.
Kâzım Karabekir, the nationalist commander in eastern Turkey, wrote in his memoirs that when he took up his command in May 1919, the British control officer, Colonel Alfred Rawlinson, confided in him that the Allies were in no position to stop the spread of Bolshevism by military means, for that would require calling up once again men who had just been demobilised. Karabekir thought that Rawlinson wanted him to provide an anti-Communist barrier in the Caucasus. In the event Mustafa Kemal wrote off the Caucasus, while preventing the spread of Communism to Turkey.
In December 1920, after the Turkish nationalists and the Bolsheviks had partitioned the territory claimed by Armenian nationalists, Mustafa Suphi, the leader of Turkish Communists loyal to Moscow, left Baku for Turkey. As Karabekir did not allow him to enter Erzurum, he made his way to Trabzon (Trebizond). Harassed on the way and despairing of success, he found a boat for the return voyage to Bolshevik territory. He never made it. Thugs, organised by the Unionist boss of the guild of boatmen, embarked with him. Off the Turkish coast, they murdered Mustafa Suphi, his wife and 13 companions and threw their bodies overboard. Some time later, the perpetrators of the crime were themselves killed by the nationalist authorities. Ankara's relations with Moscow were not affected.
Kemal and the Greeks
Just as Mustafa Kemal's diplomatic position was beginning to improve, the position of Greece weakened dramatically. Venizelos had sought to capitalise on his illusory gains at Sèvres by calling a general election. On the eve of the election, on 25 October 1920, King Alexander of Greece died of blood-poisoning after being bitten by a monkey in the palace grounds. Alexander had been brought to the throne as the unwilling successor to his father Constantine, an opponent of Greek entry into the war on the side of the Allies. Greeks living within the country's pre-war boundaries were war-weary. Venizelos, who knew this, employed questionable tactics to win the election. Greeks in the newly acquired province of eastern Thrace, who were Venizelist to a man, were given the vote; so, too, were the armed forces, where Venizelist officers not only put pressure on their comrades, but falsified results. An opposition leader was murdered in Athens. Constantine's policy of neutrality appeared attractive in retrospect. Accused of tyranny, Venizelos was roundly beaten on 14 November by supporters of Constantine. On 2 December 1920, at French prompting, Britain, France and Italy issued a joint warning that 'the restoration to the throne of Greece of a King, whose disloyal attitude... towards the Allies during the war caused them great embarrassment and loss, could only be regarded by them as a ratification by Greece of his hostile acts'. In spite of this warning, the referendum held in Greece three days later yielded a massive vote for Constantine's return.
Regime change could, at least in theory, have given Greece the opportunity to withdraw from Anatolia while trying to hang on to eastern Thrace. But withdrawal was not an easy option. Greeks who had been Ottoman subjects had compromised their position by siding with their country's enemies. What is more, Venizelos had convinced most metropolitan Greeks that he had settled 'the national question' – in other words that the annexation of 'Ionia' (western Anatolia) to Greece was an accomplished fact. Swayed by this unfounded belief, the new regime lost the opportunity to go for half a loaf. It was not the monkey's bite that changed the course of history. It was rather the decision of the new Greek regime under King Constantine to outbid Venizelos in expansionist zeal. Before long, the risks they had taken became clear on the ground.
The defeat of the Armenians and the understanding with Moscow allowed Mustafa Kemal to concentrate his forces on the western front against the Greeks. Karabekir stayed on in Erzurum, while the western front was entrusted to Colonel İsmet. In January 1921, Greek troops made a first attempt to move inland from the coastal areas they had occupied. Their main thrust was from the Bithynian plain, centred on Bursa, towards the town of Eskişehir, lying on the railway line between Istanbul and Ankara. On the edge of the Anatolian escarpment, near the small railway station of İnönü, they were met by İsmet's newly assembled troops and thrown back. As a reward for his victory, İsmet was promoted to brigadier by the National Assembly. The rank of one-star general carried with it the title of Pasha.
The Greeks claimed that their advance had been a probing manoeuvre rather than an offensive to defeat Turkish nationalists. Nevertheless, the setback had immediate political consequences. The Principal Allies called a conference in London to discuss a mutually acceptable revision of the Treaty of Sèvres concluded four months earlier. They invited to it both the Istanbul and the Ankara governments, thus conferring a measure of recognition on the latter. As soon as the conference opened on 21 February 1921, the chief Ottoman delegate, Grand Vizier Tevfik Pasha, withdrew to the background, saying that the Turkish case would be presented by Bekir Sami, the Foreign Minister of the Ankara government. Predictably, the conference failed: the Greeks stood out for all their gains at Sèvres, Bekir Sami insisted on the National Pact – the integrity of Turkey within the 1918 armistice boundaries. But while the conference produced no results, on its margins Bekir Sami struck separate bargains with the Principal Allies, tempting them with economic concessions if they came to an agreement with Ankara. After his return, the bargains were repudiated by the Turkish National Assembly, and Bekir Sami resigned. But they widened the cracks in the laboriously constructed Allied united front.
While Bekir Sami was holding off and then tempting the Western Allies in London, another Turkish nationalist delegation was negotiating in Moscow. On 16 March, four days after the London conference had broken down, a Turkish-Soviet friendship agreement was signed in Moscow. A few months later, it was supplemented by a friendship agreement between Turkey, on the one hand, and, on the other, Georgia, Armenia and Azerbaijan, which had all become Soviet Socialist Republics. Turkey regained its pre-1878 eastern frontier, with the exception of the port of Batum which became the chief town of Ajaria (or Adjara), theoretically an autonomous republic within Georgia. Apart from fixing the eastern frontier of the Turkish state, the agreement also provided for Soviet aid in gold and weapons. It was to prove crucial in sustaining the military capacity of Turkish nationalists.
The first shipment of 1.5 million gold roubles arrived in December 1920. Others followed at regular intervals: another 4 million gold roubles, more than 33,000 rifles, 50 heavy guns (some left by the British), 300 machine-guns, etc. Characteristically, the shipments came after a second Turkish military success. On 23 March 1921, the Greeks returned in force, trying once again to scale the escarpment near İnönü. At first they succeeded in storming some commanding heights. But a Turkish counter-attack on 31 March dislodged them from their gains. İsmet gave the news to Mustafa Kemal. From the peak of Metristepe, he reported, he could see the Greeks fleeing to the plain below. Turkish history records the victory as 'the second Battle of İnönü'. Mustafa Kemal congratulated İsmet with a Churchillian phrase which every Turkish schoolboy is meant to know by heart: 'You have vanquished not just the enemy but also the ill fortune of our nation.' Yet the country's destiny had to take another knock before it triumphed over adversity.
The Hashemite revival: Iraq and Transjordan
After the debacle in Syria, it would not have been any great surprise if the world had never heard of Feisal again. However, within a year, the British government had come to the conclusion that he was the only possible candidate to be ruler of strife-torn Iraq and his election as Iraqi king was arranged. This astonishing change of fortune was driven by the necessity of the British to create ruling structures in Iraq that would allow Britain to retain its influence there but at a much lower cost. More or less at the same time, Abdullah was allowed to establish himself as Emir of Transjordan. This occurred because of the same financial constraints on the British and the need to have some plan for the desert territory east of the Jordan that the British appear to have envisaged as forming part of Feisal's kingdom in Syria. By the mid-1920s, Feisal and Abdullah were firmly established as rulers in the British Mandates of Iraq and Transjordan. Hussein, however, who maintained lingering hopes that he would be ruler of a wider Arab entity in the Middle East was to lose the kingdom he had established in the Hejaz and was to end his life in bitter exile in Cyprus.
In October 1916, the _ulema_ , the leading Muslim scholars, in Mecca had declared Hussein King of the Arab Nation and religious chief until Muslims were of one opinion concerning the fate of the Islamic Caliphate. Hussein's claim for leadership of all Arabs was not widely accepted by many Arabs, nor, indeed by his main sponsor, the British government. The British were disturbed by the hubris of his claims and would only recognise Hussein as King of the Hejaz.
During the Arab Revolt, power had begun to drain away from Hussein to Feisal, of whose successes Hussein became increasingly jealous. In August 1918 a furious row had broken out between them, with Feisal threatening to resign as military commander, and only Lawrence's mediation prevented this from developing into a full-blown crisis. During the Syrian crisis of early 1920, Hussein had undermined Feisal's attempts to compromise with the French, seemingly oblivious to the realities of the situation.
Within the Hejaz itself, Hussein's position was not that strong. His other rivals in the Arabian peninsula, especially 'Abd al-'Aziz Ibn Saud, had also been strengthened by the war. Ibn Saud had risen to prominence in 1902 when a force he led captured the city of Riyadh in central Arabia from Ibn Rashid. This success allowed him to make himself Emir of Nejd. He had continued to expand his territory and by 1914 he was the most significant power in Central Arabia and was essentially independent of the Ottomans. Ibn Saud was an adherent to the particularly austere Wahhabi sect of Sunni Islam, which was founded in the 18th century by Muhammad ibn 'Abd al-Wahhab (1703–92), who formed an alliance with the Sauds. By 1806, most of the Arabian Peninsula including Mecca and Medina had been conquered. Eventually forces from Egypt crushed the Sauds and the Wahhabis. The family's fortunes did not recover until the early 20th century when Ibn Saud launched his wave of conquest.
The religious zeal of the Wahhabis provided considerable societal cohesion in the Nejd. Any sort of cohesion, other than a universal willingness to accept Hussein's subsidies and bribes, was singularly absent in the Hejaz. Ibn Saud also forged a new instrument of state-building and military power with his creation of the quasi-military religious brotherhood called the _Ikhwan_. The _Ikhwan_ , mostly former nomads, established settlements in the Nejd in which they founded _madrasahs_ (religious schools) and cultivated land. However, they could quickly be mobilised to terrorise Ibn Saud's internal and external enemies. Hussein and Abdullah were both well aware of the growing threat of Saud. While Ibn Saud had carefully husbanded the British subsidy he had received during the war, Hussein had lavished his on both the Arab Revolt and on bribing tribes to stay out of Ibn Saud's orbit. Abdullah's lack of participation in the Arab Revolt is partly explained by his fear that Ibn Saud would take advantage of Hussein's commitment to it to further his power.
The Khurma dispute and the decline of Hussein
In 1914, Emir Khalid of the Utayba tribe in the Khurma region, to the east of Jeddah, had converted to Wahhabism. He had remained under Hussein's political influence and had participated in the Arab Revolt. However, in 1917 Khalid had fallen out with Abdullah and begun to assert his independence by refusing to fight any more or pay taxes. He also sought aid from Ibn Saud, though Saud demurred from providing it. Hussein had also become increasingly concerned about British encouragement of Ibn Saud to attack the Ottoman supporter Ibn Rashid, which he saw as a threat to his pre-eminent position among the Arabs. At the root of it all was Hussein's desire to have Ibn Saud excluded from the war effort against the Ottomans. He wanted the British to be overwhelmingly dependent on him, but they, while leaning towards Hussein, also wanted to keep Ibn Saud as an ally and continued to cultivate him.
Hussein was determined to enforce his will in Khurma by military force. His first attempt to do so was rebuffed by Khalid and local forces in July 1918. _Ikhwan_ warriors began to move into Khurma to aid their co-religionists and Ibn Saud became increasingly committed to supporting its independence from Hussein. Leadership in the Arabian Peninsula in the early 20th century grew out of the barrel of a gun. If he could not suppress recalcitrant tribes such as the Utayba in Khurma, Hussein's claims to primacy would inevitably fail.
In May 1919, following the long-delayed surrender of the Ottoman garrison at Medina, Abdullah was sent with a Hejazi army to try to suppress Khurma once more. Abdullah had not gone north to Syria with Feisal because he viewed Hashemite ambitions in the Arabian Peninsula as more important than those in Syria and Mesopotamia. He had concluded that the end of hostilities with the Ottomans was merely a pause before a future conflict with Ibn Saud for supremacy in the Arabian Peninsula. However, on 25 May 1919, Abdullah's better armed and equipped army of 3,000 men was surprised by a night attack on their camp at Turaba spearheaded by _Ikhwan_ warriors. The army, including its heavy equipment, was virtually destroyed; Abdullah only just escaped with his life.
Hussein's power in the Arabian Peninsula was now severely diminished. Only British pressure on Ibn Saud prevented him pressing home his advantage. The British went so far as to prepare contingency plans to intervene. Ibn Saud, as usual, demonstrated commendable restraint and did not push his military advantage to its obvious conclusion. He remained anxious to remain on good terms with the British. As a British government memorandum written a couple of years later noted 'there is no doubt had he so desired, Ibn Saud could have taken Mecca and overrun the Hejaz'. Feisal, in control of Syria at this time, fearful that France would take the opportunity to attack should he rush to his father's aid, was unable to help. Hussein, however, became ever more anxious after Turaba that Syria should be linked to the Hejaz, as the viability of the Hejaz as an independent kingdom was always doubtful. The limitations of Hashemite power and Hussein's lack of leadership skills had been all too evident in the Khurma affair.
The British government considered that Hussein had been the cause of most of his own troubles by failing to parley with Ibn Saud. Lord Curzon now saw Britain's erstwhile ally as 'a pampered and querulous nuisance'. Hussein's sons, particularly Abdullah and Feisal, were estranged from him; Feisal, because of his success, and Abdullah as a result of the disaster at Turaba. His eldest son Ali, who remained at his father's side in Mecca, believed that the temperamental behaviour of his father was isolating him and was increasingly dangerous to the Arab cause.
The consequences of the defeat at Turaba were exacerbated by a growing financial crisis for Hussein. Since 1916, Hussein had become utterly dependent on the British financial subsidy. The subsidy proved to be an additional Achilles heel for him, however, for such was the lavishness with which he bribed tribes, he created the expectation that such largesse would continue for ever. The bribes also only bought temporary loyalty. When the British government began to reduce the subsidy, Hussein found his ability to maintain tribal influence in the Hejaz and neighbouring parts of Arabia severely diminished. Indeed, the financial crisis cost him support in the Hejaz as he was forced to tax the merchants and traders of Jeddah and Mecca in order to fund himself. The people of the Hejaz were used to receiving money from the Ottomans, not having to pay it out. By mid-1920 Hussein was receiving only £30,000 in gold a month from the British as opposed to over £200,000 at the height of the war.
In August 1920, the British requested that Hussein sign up to the Treaty of Versailles and the arrangements agreed at San Remo the previous April in return for further funding. Hussein adamantly refused. The British spent the next four years attempting to formalise their relationship with Hussein by means of a bilateral treaty. Lawrence met him in July and August 1921, tasked with persuading him to accept British terms. Hussein was his usual contradictory self. Lawrence commented: 'The old man is conceited to a degree, greedy and stupid, but very friendly, and protests devotion to our interests.' The fact was that Hussein had become increasingly convinced that the British had let him down over the post-war settlement and in his conflict with Ibn Saud. Despite Lawrence's entreaties, he refused to sign any treaty until the British recognised his kingship of Palestine and Iraq and priority over all rulers in Arabia. Lawrence eventually left.
The refusal to agree a treaty prevented Hussein receiving any further British support. It was a foolish decision and a fatal error. While Ibn Saud had created a socially and militarily cohesive state in central Arabia, Hussein had relied for legitimacy on his diplomatic skill and ability to win international support. The combination of military failure, incompetent governance and the rejection of overtures from Britain, his main sponsor, left his kingdom extremely vulnerable to further attack from his great enemy, Ibn Saud.
Revolts in Egypt and Iraq
Because of its strategic importance for their imperial communications, Egypt had been of vital concern to the British since the opening of the Suez Canal in 1869. From 1882 until the outbreak of war, Britain had _de facto_ ruled the country under the formula that it was there to give advice to an Egyptian government under the nominal suzerainty of the Sultan in Istanbul. With the outbreak of war in 1914 this fiction was swept aside and the country was unilaterally declared to be a British protectorate. But national sentiment had long been gathering strength and at the end of the war it found its voice in the _Wafd_ or 'Delegation' Party led by Saad Zaghlul Pasha, who had served as Minister of Justice and Minister of Education in pre-war governments as well as Vice-President of the Legislative Assembly. Denied a request to put the country's case in Paris, in contrast to Feisal, Zaghlul led a campaign of protest which led to his arrest and deportation on 8 March 1919 together with three of his colleagues. This action only spread the protests across Egypt, uniting city and country, Muslim and Copt and attracting the participation of women. Allenby, who was attending the Peace Conference, hastened back to take control of events. He quickly realised that there had to be a political as well as a military response, releasing Zaghlul and his colleagues on 31 March. By the time that the disturbances ended some 1,000 Egyptians and 75 British had been killed.
The government then set up a commission under Lord Milner to investigate the protectorate. The key seemed to be to find a formula which would secure Britain's strategic interests whilst recognising the reality of Egyptian national aspirations, and this lay behind the negotiations which Lord Milner conducted with nationalist leaders in the summer of 1920. Progress proved difficult, however, and in February 1922 the British government issued a unilateral declaration of Egyptian independence, but retained control of the country's defence and foreign affairs. Egyptian resentment continued, confirmed by the assassination in Cairo in 1924 of Sir Lee Stack, Governor-General of the Sudan. Attempts to negotiate a treaty between the two countries in 1928 and 1930 were unsuccessful, and the state of Anglo-Egyptian relations continued to be unsatisfactory.
The situation in Mesopotamia, as it was still termed, was, if anything, even more volatile. The award of the Mandate to Britain at the San Remo Conference was followed by a widespread revolt which broke out in July 1920. The reasons for this outbreak were a matter of some controversy at the time. The Acting Civil Commissioner, the gifted but imperious Arnold T Wilson, viewed what happened in part as the result of incitement from Feisal's government in Damascus, although even he could not disguise the fact of opposition to the Mandate. In fairness to Wilson, he was doubtful whether the Shia Arabs or the Kurds could come to terms with a government dominated by Sunni Arabs, the issue which has been at the heart of the country's problems ever since. Lawrence, on the other hand, put the matter with stark simplicity in a letter published in _The Times_ on 23 July. The Arabs, he pointed out, had not fought the Turks simply to change masters, but for their independence. The insurrection, which lasted into 1921, claimed an estimated 8,450 Iraqi lives. It was a severe strain on the British and Indian Armies, overstretched as they were. At the outbreak of the rebellion, there were 9,800 British and 25,000 Indian soldiers, but over the summer of 1920 a further 20 battalions had to be sent from India. British and Indian Army casualties were 426 killed, 1,228 wounded, and 615 missing or prisoners. The Mandate for Iraq was proving a poisoned chalice.
The pressure to cut military expenditure in Mesopotamia now required a reversal of policy. Direct rule from London or Delhi was no longer a feasible strategy and there was an urgent need to install a reliable Arab regime that would limit British expenditure in the country. At the end of December 1920, the Cabinet discussed a proposal from Percy Cox, who had resumed his old job as High Commissioner in Mesopotamia, that Feisal be proposed as king of Mesopotamia to sate nationalist sentiment and allow a significant reduction in the British garrison. Despite the disaster in Syria, Feisal still had considerable respect and numerous supporters within the upper echelons of the British government including the Prime Minister, Curzon and Hardinge, the Permanent Under-Secretary at the Foreign Office. Indeed Curzon would have activated the 'Feisal as King of Mesopotamia' option sooner had it not been for French objections.
The alternative to this strategy was far more unpalatable. This was to withdraw British forces to Basra and leave the rest of Mesopotamia to Mustafa Kemal's Turkish nationalists or even anarchy. Churchill's alternative strategy for reducing expenditure was to use air power. He succeeded in persuading Lloyd George that prescriptive (or perhaps more accurately, terror) bombing of recalcitrant Mesopotamian villages would allow significant savings in the number of troops required to hold the region. Combined with Cox's political strategy to provide an Arab government that would command the loyalty of the population and reduce the requirement for troops, massive expenditure savings could be made.
Churchill's coherent cost-saving strategy in Mesopotamia made him an obvious choice to deal with the crisis in the British Mandates in the Middle East. Therefore, when Milner indicated his desire to be relieved of the Colonial Office, Lloyd George decided to replace him with Churchill in January 1921. Churchill moved swiftly. He rapidly concluded that Feisal was the best man for the job of ruling Iraq. He also fast-tracked moves to streamline decision-making in the Middle East. Churchill was convinced that a single sub-department of the Colonial Office was the best solution, 'otherwise muddle, failure and discredit are certain'. Since 1917, the British had wrestled with how to run their policy in the Middle East, which according to Mark Sykes had some 18 different organisations and groups providing input. Now there was to be a single voice under the control of Churchill. While Curzon was irritated and suspected Churchill of a Middle Eastern power-grab, there must also have been a certain sense of relief that the troublesome area was now someone else's problem.
The Middle East Department of the Colonial Office came into being on 1 March 1921. It was given responsibility for the British Mandates, the Arabian Peninsula and Persia. The first Under-Secretary was John Shuckburgh, an India Office hand with significant experience of the Middle East. T E Lawrence agreed to be Churchill's Middle Eastern adviser. Both Lawrence and Hubert Young, the head of the political and administrative branch of the new department, were pro-Hashemite 'partisans'. However, their appointment reflected the need to have officials on board who would be able to woo the Hashemites and implement the new British strategy.
The key British link to Feisal remained, of course, Lawrence. He had been initially sceptical about helping the British government after what he felt was the betrayal of the Arabs at the Peace Conference. However, he met privately with Feisal to ascertain his views. The Emir was willing to work with the British though concerned that both Abdullah and his father might object. His strategy having some prospect of success, Churchill now decided to hold a conference in early March 1921 of all of the British Middle Eastern experts in Cairo that would focus on what to do with the Mesopotamian Mandate. The objectives were: to formally endorse a new Arab ruler; to formulate a timetable for the reduction in size of the British garrison to a more economical peacetime establishment; to calculate future financial aid for the Mandate; and to decide which parts of Mesopotamia were worth retaining. On his way to Cairo, Churchill met the French who reiterated their objections to Feisal being made king of Mesopotamia. However, the British no longer felt much beholden to the French on this issue.
The Cairo Conference
The venue for the conference was the Semiramis Hotel. Beginning on 12 March 1921, for 12 days over the course of more than 40 secret sessions, some 40 British Middle Eastern experts and policymakers – including all of the High Commissioners, the senior regional military commanders, the political residents, and governors of territories such as Somaliland – worked through an agenda that would shape the Middle East to the present day. It was rapidly agreed that for Mesopotamia, which was to be renamed Iraq, Feisal offered the best and most economical chance of success. Percy Cox and Gertrude Bell were both supportive but they proposed that Feisal should be seen to be the choice of the Iraqi people rather than be imposed. A formula was agreed that Feisal would announce his availability to serve as king of Iraq and the British government would state that it would not stand in his way.
The conference also considered the question of Palestine. Herbert Samuel, the High Commissioner, was still in favour of a Mandate encompassing all of Palestine and Transjordan, arguing that this was what the Balfour Declaration had stated and that the creation of a separate Mandate might lead to complications with the League of Nations. The question became more urgent when news reached the conference that Abdullah had advanced to Amman. It was now clear to Churchill that an agreement would have to be reached with him.
When Churchill and Lawrence went north to Jerusalem at the conclusion of the conference, a meeting was arranged with the Emir. Churchill told Abdullah that Transjordan would not be part of Palestine. Abdullah was offered a leadership role in Transjordan and a subsidy. In return he was to stop attacking the French. He would also receive British advisors and a promise of eventual progress towards independence. Abdullah was also persuaded to waive his claims to Iraq. There was also an intimation that if he behaved well, the French might approach him and give him a role in Damascus, although Antonius suggests that this was a trick to keep him quiet.
While in Jerusalem, Churchill addressed Arab and Zionist delegations on 30 March 1921. The Palestinians had already submitted a memorandum asking him to repudiate the Balfour Declaration and halt immigration. He made it clear to them that he had no intention of doing either. But of particular significance for the future was what he went on to say about the Balfour Declaration. Emphasising that Balfour had used the term a National Home rather than the National Home, he said that this did not mean a Jewish government that would dominate the Arabs. More ominously, from a Zionist perspective, he used the term 'national centre' when talking about the National Home, a term which was soon to take on some significance. Interestingly, this qualification did not feature in his response to the Zionist delegation. Rather he confirmed the British government's commitment to the Balfour Declaration, while emphasising this had to be undertaken without prejudice to the country's existing majority. He also warned them that the Arabs were very much afraid for their future. Just exactly how the Arabs felt would soon be revealed.
The most notable impact of the conference was that the 'Sherifian Solution' became the new British strategy for managing the Middle East. As Aaron Klieman notes, 'What had begun as an exercise in pragmatism had been expanded at Cairo into a principle to be applied wherever possible, beginning with Mesopotamia and then spreading to Arabia and Transjordan.'
Events now moved swiftly as the British sought to implement their plan. Lawrence told Feisal to make his way to the Middle East. On 15 April, they had a long conversation in which Feisal agreed that he would not attack the French in Syria, and would seek to compromise with Ibn Saud provided he did not attack his father in the Hejaz. He also fully acknowledged that he would need British advice and support in Iraq as the population there was not yet ready for self-government. The British agreed with him, Churchill envisaging that Iraq would be run 'much like an Indian state'. Percy Cox and Gertrude Bell prepared for Feisal's arrival. She organised everything from the Emir's travel arrangements to the design of a temporary flag for the new state. The main potential domestic opponent of Feisal was Sayid Talib, an ambitious former deputy in the Turkish parliament from a leading Basra family, who had spent the war in exile and was probably the most prominent nationalist in the country. After he was reported to have expressed displeasure at the turn of events, he was arrested and sent into permanent exile in Ceylon.
Feisal arrived in Baghdad on 23 June 1921. The Iraqi Council of Ministers, under Cox's direction, ratified Feisal as candidate and a plebiscite was arranged for August. Ninety-six per cent pronounced themselves in favour of Feisal, but there was no way that Feisal actually had that level of support. There were large numbers of pro-Turkish groupings who wanted close links with Mustafa Kemal, Shias who wanted a theocracy and Kurds who desired independence. However, Feisal was probably the least worse option. As Phoebe Marr notes, 'there is little doubt that no other candidate had his stature or could have received anywhere near the acclamation he did'. Feisal was crowned as Iraq's first monarch on 23 August 1921.
Tentions in the Zionist movement: Weizmann and Brandeis
While these events were unfolding in the Middle East, Weizmann briefly returned to Palestine prior to making his first visit to the United States in April 1921; the ostensible purpose of his trip to America was to stimulate interest in the Hebrew University, still a barren site on Mount Scopus, and to establish the Palestine Foundation Fund, the Keren Hayesod, in the country. Behind this journey, of course, lay his simmering feud with Brandeis and his supporters in the American Zionist movement, which had come into sharper focus at the annual congress of the Zionist Organization of America (ZOA) in November 1920. Here Brandeis's supporters had effectively downgraded the Keren Hayesod. Although he was, in a sense, entering the lions' den, Weizmann had brought with him a strong delegation, including Ussishkin, had enlisted the active support of Albert Einstein, and was welcomed on his arrival in the city by an ecstatic crowd of New York Jews.
It was not long before he locked horns with the ZOA's leadership. Even before he had disembarked, Judge Julian Mack, President of the ZOA, who came on board to meet him, handed him a memorandum setting out the views of Brandeis and his supporters. What it proposed amounted, in Weizmann's view, to nothing less than a disaggregation of the Zionist movement into its component parts. For his part, Weizmann was clear that a united Zionism was of the essence, and, as a result, he could not accept the terms of the memorandum. In not doing so, he was openly confronting the established leadership of the ZOA, Brandeis, Mack, Felix Frankfurter, Robert Szold, Jacob de Haas and Stephen Wise, as eminent a group of American Jews as could be imagined. In contrast, Weizmann's American supporters, such as Louis Lipsky, seemed lesser figures. But Weizmann's instincts told him that the sentiments of American Jewry were with him, and Ussishkin shared his view that they should not surrender to the American leadership.
Even so, attempts at a compromise were made, but they proved inconclusive. By the end of April, Brandeis was writing to his wife and to Frankfurter in bitter terms about Weizmann, whom he had evidently come to detest. For his part, Weizmann issued a statement as President of the World Zionist Organisation establishing the Keren Hayesod in the United States. This action brought the fraught relations between the two groups to a head, the confrontation coming at the 24th annual convention of the ZOA which met in the city of Cleveland from 5–8 June 1921. Weizmann and his delegation attended, but did not speak, although the deliberations and votes went decisively in their favour. Brandeis and Mack had been in contact prior to the convention about their positions should the decisions go against them, and they promptly resigned their offices, their main supporters leaving with them. On 19 June, Brandeis formally tendered his resignation as Honorary President of the World Zionist Organisation. Weizmann and his supporters within American Zionism were left in possession of the field, but at the cost of a bitter rift in the leadership of one of the world's most vibrant Jewish communities, the echoes of which would be heard for years to come.
Samuel, Arab resistance and British policy in Palestine
Churchill's warning about the nature of Arab fears was realised to an extent that put the outbreak of violence in 1920 into the shade. When Samuel had been in office just a week, he proclaimed an amnesty for those who had been involved in the spring disturbances, which included Jabotinsky, for whose release Weizmann had been vigorously campaigning. In August 1920, this amnesty was extended to the two principal Arab fugitives, Arif al-Arif and Amin al-Husayni, thus opening the way for the latter's entry into active Palestinian politics. His opportunity came in March 1921 with the death of the Grand Mufti of Jerusalem, his half-brother Kamil al-Husayni. Amin immediately campaigned to succeed him, apparently assuring the British of his good offices. Before this could happen, however, trouble broke out in a way that could hardly have been expected. On May Day, a quarrel occurred between communist and non-communist Jews in Jaffa, which, for reasons that are not entirely clear, sparked an Arab attack on the city's Jewish population, and then on five Jewish settlements. In the resulting violence, 47 Jews were killed and 146 wounded, while the police and troops killed 48 Arabs and wounded 73 others. In the aftermath, Amin al-Husayni was confirmed as Mufti, an appointment which saw him develop into one of Zionism's deadliest enemies.
While the Mufti's activism lay in the future, more serious from the perspective of Weizmann and the Zionists was both the scale of the violence and what it revealed about the state of Arab opinion. The official inquiry into what happened, chaired by the Chief Justice of Palestine, Sir Thomas Haycraft, left little doubt as to the latter. It identified the principal cause as hostility towards the Jews, linked to Jewish immigration and Arab perceptions of Zionist policies. Dismissing as superficial Zionist claims that the violence had really been directed against British rule, Haycraft identified the basic cause as the Arab fear that the increasing Jewish immigration would result in the loss of their economic and political position. He further pointed to the lifestyle of the young Jewish immigrants which jarred with the Arab way of life. Hostility to the Jews also cut across class barriers and the Muslim-Christian divide. By any reckoning, it was a sober analysis for the British and a disturbing one for the Zionists.
Samuel now turned to appease the Arabs. One of his first decisions following the outbreak of violence was to suspend immigration, an action which caused understandable consternation among the Jews. While he intended this to be temporary, Samuel indicated to Churchill that it should only be resumed if there were projects ready for the new immigrants. Part of his proposed solution was to create representative institutions through enlarging his Advisory Council with elected Muslim, Jewish and Christian members. He also confided in Churchill that the Zionist leaders had to recognise that their policies would not be possible in the face of the opposition of the greater part of the Palestinian population.
The high hopes that Weizmann and the Zionists had placed in Samuel at the time of the San Remo Conference were now turning sour. The appointment as Mufti of Haj Amin, whom they identified with the Jerusalem riots of the previous year, was distinctly unwelcome. The changing tone of British policy, already signalled in Samuel's letter to Churchill, could be clearly seen in his royal birthday speech in Jerusalem on 3 June 1921, in which he denied that Britain would countenance a Jewish government over the non-Jewish majority. He also introduced the concept of economic absorbability, which, he claimed, should govern immigration policy, and announced that the government was considering a partially elected legislative council.
Even before the Mandate had been formally endorsed by the League of Nations, qualifications of the Balfour Declaration were thus beginning to emerge. Given the fact that Churchill had been closely consulted on Samuel's speech, Weizmann was spurred into action. Clearly alarmed by the speech's content and tone, Weizmann attended a meeting at Balfour's house, during which he confided his fears in Lloyd George, Churchill and Maurice Hankey. That he had such access to the Prime Minister and Colonial Secretary was a clear answer to his critics in the Zionist movement, since neither Brandeis nor Ben-Gurion could have brought together such key figures at that time. After discussing his visit to the United States, Weizmann cut quickly to the point, castigating Samuel's speech as a negation of the Balfour Declaration. Challenged on the point by Churchill, he then compared the two documents, claiming that the speech would prevent the creation of a Jewish majority, which the Declaration had sanctioned. At this point Lloyd George and Balfour both interjected, reassuring Weizmann that the Declaration had anticipated an eventual Jewish state. Turning to the defence of the Jews, Weizmann apparently secured covert approval for bringing weapons into Palestine. He then turned to the legislative council proposal. While Churchill argued that this was being undertaken in Iraq and Transjordan, Weizmann responded, with some justice, that it was only being proposed for Palestine because the British had been forced into it. Lloyd George, Churchill and Balfour were inclined to agree. Weizmann then came to what was clearly his main concern; namely, that to set up representative government would mean abandoning Palestine, at which point Lloyd George told Churchill that the country must not be given representative government. The Colonial Secretary responded that he might have to bring this idea to the Cabinet, but that the establishment of the Jewish National Home would be excluded from any discussion. Weizmann denied that such a thing was possible.
The Palestinian delegation to London
Impressive though Weizmann's intervention in London was, it could not in itself halt the Arab offensive against Zionist aims. In May 1921, a Palestine Arab congress resolved to send a joint Muslim-Christian delegation, headed by Musa Kasim al-Husayn, of the powerful Jerusalem family, and the Christian Shibly al-Jamal, to Rome, where they were received by the Pope. The delegation then travelled to Paris, Geneva and London to lobby against the Balfour Declaration's incorporation into the proposed Mandate. In anticipation of their visit, Churchill felt the need to present his appreciation of the situation in Palestine to the Cabinet. His analysis was that the country was in ferment, with the Zionists' policies unpopular with everyone except themselves. He reported that elective institutions had been refused in deference to the Zionists, and that, as a result, the Arabs contrasted their situation in Palestine with that of Iraq. Nevertheless, Churchill said that if it were the wish of the Cabinet, he would implement the Balfour Declaration and the San Remo decisions. Reinforcing its chief's views, the Colonial Office advised that the Arabs objected to Zionist policy _per se_ , and that, as a result, the British government's aims in Palestine could only be achieved by showing that Jewish immigration would not undermine the Arabs' existing position. The tactic to be followed should be that of allowing gradual Jewish immigration linked to the ability of the country to absorb it.
The Palestinian delegation was in London for almost a year, in the course of which it became clear that the British government would not accede to their demands that it renounce the Balfour Declaration, end Jewish immigration, and grant self-government. A meeting with Weizmann, arranged by Churchill, was fruitless. Churchill's advice to the Cabinet was that there were two choices. It could revoke the Balfour Declaration, refer the Mandate to the League of Nations, set up an Arab government, and curtail or stop Jewish immigration. Alternatively, it could pursue existing policy and arm the Jews. A draft announcement by Weizmann to that effect failed to find support, however. This was an unpalatable choice, and it is hardly surprising that the ministers failed to make it. Discussion centred around two issues; namely, the fact that Britain had made a pledge in the Balfour Declaration, and the growing power of the Arabs in the territories around Palestine. While some argued that the Arabs had no right to Palestine since they had not developed it, others pointed to the inconsistency in the Balfour Declaration in promising support for a National Home while respecting the rights of the Arabs.
For his part, Samuel was increasingly worried by the situation in Palestine, especially given the pressure he was under to reduce the costs of its garrison. On 14 October 1921, he wrote to Churchill expressing his fears of repercussions should the Arab delegation to London return dissatisfied. In the first instance, he pressed for ratification of the Mandate, the delay in which he identified as contributing to his political, economic and financial difficulties. Secondly, he turned to the critical question of Arab-Jewish relations. What he was concerned to drive home was his belief that many Arabs would be prepared to accept the definition of the National Home which he had set out in his speech of 3 June, as long as this was held to be British policy. Again, however, he turned to Weizmann's Peace Conference statement that Palestine would become as Jewish as England is English, which, he said, was repeatedly quoted in the press in Palestine, as being inconsistent with the idea that Arabs and Jews could work together towards a common future. Samuel concluded by saying that the Arabs should stop asking for the abrogation of the Balfour Declaration, but also that, for their part, the Zionists should acknowledge that they were aiming to build a democratic commonwealth rather than a state in which they would be politically privileged, and that the statement about Palestine becoming as Jewish as England is English be amended to take into account that Palestine was a common home.
The evolution of the Churchill White Paper
Samuel's letter was poorly timed, since three days earlier negotiations for an Irish settlement had got under way in London, with Churchill as a key member of the British team. Compared with Ireland, Palestine was a peripheral British interest. Even after the treaty was signed on 6 December 1921, Churchill's involvement in Irish affairs increased since as a Dominion the emergent Irish Free State came under his portfolio as Colonial Secretary. When Sinn Fein split on 7 January 1922 between the supporters of Arthur Griffith and Michael Collins, who had signed the treaty, and those of Eamon de Valera, who rejected it, Irish affairs once again took on a dangerous dimension. With anti-Catholic riots in Belfast in the spring of 1922 and the outbreak of civil war in the Free State on 28 June, Ireland was never far from Churchill's mind. He was also engaged in a simmering, but increasingly acrimonious, dispute with Edwin Montagu over the rights of the Indian community in Kenya. While it would be going too far to say that Palestine was a distraction, its problems needed to be addressed.
If the purpose of the Arab delegation had been to seek a reversal of government policy, then they had clearly failed. What they had succeeded in doing was driving home that the Arabs of Palestine were adamantly opposed to British policies, something confirmed in November 1921 with the publication of the Haycraft Committee of Inquiry into the May disturbances. The measure of their success may be seen in a mounting campaign against the Balfour Declaration in sections of the British press, including those owned by the powerful newspaper barons Lords Northcliffe and Beaverbrook. Once again trying to square the circle, on 11 April 1922 John Shuckburgh wrote to the delegation on Churchill's behalf confirming that there would be no retreat from the Balfour Declaration, but that the government's purpose was to ensure that the section of the Declaration referring to the position of non-Jewish inhabitants was carried out.
With ratification of the Mandate now imminent, confirming this became the purpose of British policy, and in May Samuel came to London to assist in reaching a formula that would achieve it. Weizmann, meanwhile, allowed himself to be diverted into visiting Rome, since he believed the Vatican was a key opponent of the Balfour Declaration, as well as Berlin and Paris. On his return, he had to confront the uncomfortable fact that the House of Lords had voted to repeal the Balfour Declaration, although fortunately for the Zionists the House of Commons rejected a similar motion. While Balfour reassured Weizmann that the House of Lords vote was immaterial, it was yet another indication that British support could not necessarily be taken for granted. It stands repeating that this was a time when Irish affairs were consuming Churchill's attention with the seizure of the Pettigo-Belleek Triangle in County Fermanagh in Northern Ireland by Republican forces, and that Conservative support for the Lloyd George coalition was fast eroding – the House of Lords vote on the Balfour Declaration a clear symptom of this, whatever its author might say.
This highly febrile political situation saw the publication, on 3 June 1922, of the _Statement of British Policy in Palestine_ , commonly referred to as the Churchill White Paper. Here Weizmann's response to Lansing came back to bite him:
Unauthorised statements have been made to the effect that the purpose in view is to create a wholly Jewish Palestine. Phrases have been used such as that Palestine is to become 'as Jewish as England is English'. His Majesty's Government regard any such expectation as impracticable and have no such aim in view.
Referring to the fears which the Arab delegation had expressed, the Statement denied that there had ever been any intention of subordinating the Arabs, pointing out that the Balfour Declaration had made it clear that the National Home was to be founded 'in Palestine' rather than being the whole of the country. Addressing the Zionists, it confirmed that the Balfour Declaration was not up for negotiation, affirming the 'ancient historic connection' of the Jews to the National Home and that they were in Palestine 'as of right and not on sufferance'. It was the definition of the National Home that was problematic for Weizmann and the Zionists, however:
When it is asked what is meant by the development of the Jewish National Home in Palestine, it may be answered that it is not the imposition of a Jewish nationality upon the inhabitants of Palestine as a whole, but the further development of the existing Jewish community, with the assistance of Jews in other parts of the world, in order that it may become a centre in which the Jewish people as a whole may take, on grounds of religion and race, an interest and a pride.
Two other elements displeased and alarmed the Zionists. The first was the acceptance of the establishment of a legislative council, albeit gradually, which the Arabs had been demanding, but which the Zionists had opposed and which Weizmann had been given reason to believe Lloyd George had ruled out. The other was confirmation of the principle that immigration into Palestine should be dependant on its absorptive capacity, an unwelcome concept introduced by Samuel in his 3 July speech the previous year. To the Zionists it was a negation of their conviction that only through immigration could the economy of the National Home be developed.
Weizmann rightly regarded the terms of the announcement as a considerable retreat from the Balfour Declaration, but since he had been told that confirmation of the Mandate depended on Jewish acceptance of the White Paper, he was left with no alternative but to do so. He was even prepared to argue that the idea of economic absorbability could work to the Jews' advantage, though he later had to confess that this had not been the case. Even so, on 18 June 1922, Weizmann wrote on behalf of the Zionist Organisation, confirming acceptance of the new policy as set out in the _Statement_. The previous day, the Arabs had rejected it, as they were to do with so many initiatives in the future, usually to their disadvantage, as it turned out.
The way was now open for the Council of the League of Nations to confirm unanimously the Mandate, which it did on 24 July 1922. Weizmann's fear that the predominantly Catholic countries of Spain and Brazil would demur proved to be unfounded, and an attempt by the Papal Nuncio to defer the item was thwarted by the French. In many respects, the terms of the Mandate were what the Zionists had been working to secure and the Arabs had hoped to prevent. Crucially, the Preamble formally incorporated the Balfour Declaration into the Mandate, and, in a sense, went even further by recognising 'the historical connection of the Jewish people with Palestine and to the grounds for reconstituting their National Home in the country'. Under Article 2 of the Mandate, Britain was to place Palestine 'under such political, administrative and economic conditions as will secure the establishment of the Jewish National Home, as laid down in the preamble, and the development of self-governing institutions, and also for safeguarding the civil and religious rights of all the inhabitants of Palestine, irrespective of race and religion'. Articles 4 and 6 of the Mandate sanctioned the creation of a Jewish Agency, and charged the Mandatory with facilitating Jewish immigration, while making sure that the rights and positions of others were not prejudiced. Finally, Article 25 permitted the Mandatory to make separate provision for the land to the east of the river Jordan, which was confirmed by the League on 16 September. The campaign to secure the British Mandate for Palestine, which would include the implementation of the Balfour Declaration, was one which Weizmann had waged for five gruelling years. Now, at last, this key objective had been secured. But in the meantime events in Palestine and elsewhere in the Middle East had been gathering pace.
Turkey's war with Greece
As always, international politics were moving in response to the balance of forces on the ground. In May 1921, the British, French and Italian High Commissioners in Istanbul declared that the Straits would be treated as a neutral zone. Given that the Treaty of Sèvres had not been ratified, the Allies were officially still at war with the Ottoman state. But with their declaration of neutrality in the fighting between the armies of Constantine and those of Mustafa Kemal, the conflict which had started in 1914 between the Turks and the Allies was transformed into a Turkish-Greek war. This was underlined by the decision of the Italians in April and May to withdraw their occupation troops from Antalya and the area south of the Greek positions round İzmir. The Italians had arrived with supplies of food; they got on well with Turkish nationalists; and, finally, they left behind part of their equipment. The local Turkish population remembered them fondly.
The French were soon to follow suit. But, like the Bolsheviks, they wanted to see first whether the Turkish nationalists would hold their own in the war with the Greeks. However, even before the issue became clear on the western battlefields of Anatolia, the French commander in southern Turkey agreed to a 20-day armistice in May 1920. This was prompted by the capture by Turkish irregulars of a French detachment which had tried to hold a railway station in the Taurus mountains, north of Adana. As clashes resumed between Turkish militias, commanded by regular officers, and French forces trying to hold the territory awarded to France under the Treaty of Sèvres, the French government sent an unofficial envoy to Ankara to reach an understanding with the nationalist authorities. The envoy, Henri Franklin-Bouillon, chairman of the Senate Foreign Relations Committee, arrived in Ankara on 8 June 1921. He got on well with Mustafa Kemal, who guessed that France was willing to trade Turkish territory, north of the 1918 armistice lines, against Turkish acceptance of French rule in Syria. The French gave a preliminary sweetener by withdrawing their troops from Turkey's Black Sea coast where they were protecting French investments in Turkey's main coalfield. However, before a comprehensive deal was struck, France had to make sure that the Ankara government would survive the Greek onslaught in the west.
Rejecting the offer of mediation by Britain, France and Italy, the new Greek government reinforced its troops in Anatolia and launched a general offensive against the new and as yet untried Turkish army. Venizelos, who had moved to France after losing power in Athens, argued that by turning down the Allies' offer, his successors had led their country into diplomatic isolation. He had worked tirelessly, he said, to secure Britain's support for Greek territorial claims. Now that support had been compromised by Constantine's government.
At first this did not seem important, as the Greek army made spectacular gains. İsmet was out-manoeuvred. He expected the Greeks to renew their attack from the west. But the main thrust came from the south, and threatened to cut off his headquarters in Eskişahir. The morale of the Turkish troops was severely shaken and large numbers deserted. It was a critical moment for the Turkish nationalists. After visiting the crumbling front, Mustafa Kemal decided to sacrifice territory in order to save the core of his army, and ordered it to withdraw to the east bank of the river Sakarya, the last natural barrier before Ankara. The Greeks pressed on rapidly from Eskişehir, advancing deeper into the treeless Anatolian plateau in the heat of summer. On 23 August, they crossed a tributary of the Sakarya River and attacked Turkish positions on the heights overlooking the east bank.
In Ankara, the civil servants of the embryonic nationalist administration prepared to leave their ramshackle offices in the caravanserais and dilapidated private houses of their Anatolian capital, and move with their papers to Kayseri, the most considerable city to the east. The families of deputies in the National Assembly joined in the evacuation. Greek aircraft appeared in the sky and dropped bombs on Ankara's railway station. But for all its unruly and fractious nature, the Assembly stood firm. 'Have we come here to fight or to run away like women?' asked a bearded Kurdish tribal leader, whose loyalty to the Turkish resistance movement is remembered to this day. Faced with disaster, the deputies rallied round Mustafa Kemal. His place, they declared, was at the front in command of his troops. Mustafa Kemal agreed, but on condition that he was given extraordinary powers as commander-in-chief. It was a radical move, for under the Ottoman Constitution it was the Sultan who was commander-in-chief. Nevertheless, the powers were granted, but only for a term of three months, renewable at the National Assembly's discretion, and on condition that that they affected only the military conduct of the war and did not impinge on the Assembly's political prerogatives. These distinctions were lost to most Allied observers, who habitually referred to Mustafa Kemal as the nationalists' all-powerful 'generalissimo'.
Mustafa Kemal wasted no time in meeting the Greek threat. Promising the nation that the enemy would be 'throttled in the inner sanctuary of the fatherland', he ordered the requisitioning of supplies – food, horses, peasant carts, clothes – from an already impoverished population. Providentially, the first supplies of Soviet weapons arrived in the nationalist-held ports of the Black Sea in the nick of time. They were hauled by bullock-cart along dirt tracks to the front, often driven by peasant women. Turkish schoolchildren are taught to remember the heroic participation of Turkish women in their country's defence.
A few months earlier, the nationalists had organised officer training courses in Ankara. Freshly commissioned officers and cadets were thrown into the battle, which Mustafa Kemal directed from the small railway station of Polatlı, west of Ankara. Repeating their earlier successful manoeuvre, the Greeks tried to cut off Turkish forces by attacking them from the south, while keeping up the pressure from the west. They were better equipped than the Turks, but they were fighting in an inhospitable, alien environment. The arid plateau was ideal country for the cavalry, and the Turks made full use of it by harassing Greek lines of communications.
The Greek army fought well. It stormed the main heights commanding the battlefield and advanced to within 30 miles (48 kilometres) of Ankara. Explaining the setback to the National Assembly, Mustafa Kemal made the memorable statement: 'We are not defending a line, but an area – the area that encompasses the whole of the fatherland. Not an inch of it is to be surrendered until it is drenched with the blood of our citizens.' On 14 September he proclaimed a general mobilisation. This amounted to a final repudiation of the armistice agreement of 1918. Mustafa Kemal's strategy worked. The Greeks could not sustain their offensive. Sensing this, the Turkish army launched a counter-attack, forcing the Greek command to order a withdrawal to the west of the Sakarya River. Turkish troops were too exhausted to pursue them, and the Greeks returned to their starting point at Eskişehir, destroying everything in their path: villages, bridges, and the railway line to Ankara. It was a foretaste of what was to happen in much of western Turkey.
The Battle of Sakarya
On 17 September it became clear that the Turks had succeeded in throwing back the Greek offensive. The following day, Mustafa Kemal returned to Ankara. On 19 September a grateful Assembly promoted him to the rank of field marshal, and awarded him the title of Gazi. Its literal meaning is 'warrior for the faith (of Islam)', while in current usage it designates old combatants in general (soldiers who are killed are remembered as _şehit_ , or martyrs), and heroic commanders, in particular.
The Battle of Sakarya is remembered in Turkey as 'the officers' battle'. The army of the National Assembly had some 5,000 officers in all. Of them 300 were killed and 1,000 wounded in the battle, as they led soldiers demoralised by the retreat from Eskişehir and raw peasant recruits who had just joined the ranks. Total Turkish casualties of 3,700 dead and 18,000 wounded roughly matched the Greeks' losses. But Mustafa Kemal had greater reserves of manpower, and his fellow countrymen had their backs to the wall and pulled together, while Greek opinion was sharply divided on the wisdom of the invasion of Anatolia.
King Constantine had staked his throne on the success of the policy of waging war to the finish against the Ankara government. He had arrived in İzmir before the offensive began. It was not a successful visit: the Greek occupation authorities restricted his movements for fear of an attempt on his life; and the king was not impressed by the local Greeks who, he felt, expected their kinsmen from continental 'old' Greece to win the country for them. But Constantine's harshest remarks were reserved for the Turks. Moving to the newly occupied town of Eskişehir, where his younger brother Prince Andrew (the father of the Duke of Edinburgh) commanded an army corps, he wrote, 'It is extraordinary how little civilised the Turks are... It is high time they disappeared once more and went back into the interior of Asia whence they came.' But the Turks had no intention of disappearing, and, as far as civilisation was concerned, as Constantine had to admit himself, both sides fought each other with the greatest cruelty. The term 'ethnic cleansing' had not been invented at the time, but the reality was practised by both sides. Greeks drove Turks out of their villages in their zone of occupation; Turks deported Greeks from the coastlands they controlled. The shelling of Turkey's harbours on the Black Sea by Greek warships provided an excuse for the deportation of Black Sea Greeks, but the long-term aim of the deportation was to pre-empt Greek-Armenian plans to establish a Christian state of Pontus.
The deportation worried the representative of the area in the National Assembly in Ankara. Well-to-do Greeks and Turks lived side by side in some coastal towns. One deputy asked that Turkish property should be protected from the looting which inevitably followed the deportation of Greek householders. The practice of looting and then setting fire to the houses of the ethnic adversary was widespread during the long process of the dissolution of the Ottoman Empire. The deliberate destruction which the present generation has witnessed in former Yugoslavia had well-established historical precedents.
Militarily, Mustafa Kemal's success at the Battle of Sakarya was the turning point of the war. Unable to launch another offensive, the Greeks began to blame each other as they sought a way to cut short the conflict. It was a royalist, German-trained general, Ioannis Metaxas, the future dictator of Greece, who was the first to offer a realistic diagnosis:
It is only superficially a question of the Treaty of Sèvres. It is really a question of the dissolution of Turkey and the establishment of our state on Turkish soil... And the Turks realise what we want. If they had no national feeling, perhaps such a policy would be possible. But they have proved that they have, not a religious, but a national feeling. And they mean to fight for their freedom and independence.
Politically, success at Sakarya saved Mustafa Kemal's position both domestically and internationally. As the outcome was being decided, Enver waited on the Soviet side of the border in Batum, ready to bid for the leadership of Turkish resistance if Mustafa Kemal fell by the wayside. After Sakarya, Enver gave up any hope of returning and made for Central Asia. Instead of joining with the Bolsheviks against the British, he drifted – without realising what he was doing – into the ranks of the _Basmachi_ , or raiders, a disorganised popular movement of local Muslims who resisted the imposition of Soviet rule in Central Asia. It was his last adventure. He was killed in what is today the independent republic of Tajikistan, when the Red Army caught up with his band of irregulars and wiped it out. Having gambled with the lives of millions of his countrymen and lost, he gambled with his own life and lost again. Turks today remember his dashing courage and his patriotism, however wrong-headed. But for Mustafa Kemal he served as the counter-exemplar, who demonstrated the perils of adventurism.
Moscow understood that Mustafa Kemal had no time for pan-Islamic adventures, and caused him no difficulties when he got rid of Communists in his own country. Arrests of Communists in Anatolia began early in 1921 when Mustafa Kemal's army won its first successes at İnönü. After Sakarya, in October that year, Mustafa Kemal formed his own official Communist Party and ordered some of his generals to register as members. The official party was not admitted to the Communist International, but it served its purpose in weeding out such Turkish Communists as would not join it.
The most famous was Nazım Hikmet, Turkey's best-known and best-loved modern poet. Typically, he came from a family of high officials of Polish origin. He was greeted as a hero in Anatolia when he joined the nationalist movement in January 1921. But his romantic revolutionary zeal could not be accommodated in Ankara, and he was sent off to teach in a provincial school. Disappointed, Nazım Hikmet slipped off to Moscow where he moved in the circle of Mayakovsky, the leading poet of the Russian Revolution. He returned to Turkey after the nationalist victory in 1923, and was imprisoned time and again. He finally fled behind the Iron Curtain in 1951, just as Turkey became involved in the Cold War on the side of the West. Nazım Hikmet died in Moscow in 1963, leaving behind a body of work which has changed the course of Turkish poetry.
The most important diplomatic consequence of the Battle of Sakarya was the conclusion on 20 October 1921 of an agreement with France. Officially called an ' _accord_ ', it was in fact a preliminary separate peace treaty, which established the frontier between Turkey and French-ruled Syria. In exchange for French evacuation of southern Turkey, Turkey gave up – provisionally, as it happened – the district of İskenderun (Alexandretta). But the accord promised to establish a special administration there, which would protect the rights of its Turkish-speaking inhabitants. The Turkish government remained loyal to its implicit promise to desist from any interference in the internal affairs of Syria. Having frightened the French with the prospect of cooperation between Turkish and Arab nationalists, Mustafa Kemal turned away from the Arabs. As the last commander of Ottoman troops which had faced the disloyalty of Arab nationalists, he owed them nothing, and least of all the Hashemites, who had accepted British gold to harass the Turks. The French were to prove less meticulous than the Turks in carrying out their commitments. While anti-French Arab nationalists were denied facilities in Turkey, Kurdish exiles from Turkey, grouped round a tribal dynasty, were allowed to keep the feeble flame of Kurdish nationalism alive in Syria.
Apart from a free hand in Syria, France wanted to safeguard its network of schools, most of which were run by Catholic teaching orders in Istanbul. As ever, the promotion of French culture ranked high in French foreign policy. Kemal, who had been moulded by that culture, even if it was at second hand, did not object, for in his eyes, and in the eyes of most of his companions, France represented civilisation – not Western civilisation, but the one single civilisation of mankind. It followed that far from obstructing the development of an independent Turkey, French culture promoted it. However, Kemal resisted French pressure for economic privileges. France had been the major investor in the Ottoman Empire, including British-ruled Egypt, and it fought hard to keep the regime of capitulations, which allowed foreigners extraterritorial rights. The Ankara accord made no mention of the capitulations. They were left for the final peace treaty between Turkey and the Allies.
Lloyd George and the Greeks
The British were thus left as the sole defenders of the Greeks in Turkey. But cracks appeared in the British position too. While Lloyd George remained totally committed to the Greek nationalist cause, in spite of the fall from power in Athens of his fatal friend Venizelos, the Foreign Office under Curzon sought to lessen the damage done to British interests by Lloyd George's policy. The British High Commissioner in the Ottoman capital, Sir Horace Rumbold, believed that the future struggle for influence in Turkey would be fought between Britain and France. 'If this struggle comes,' he claimed, 'it will not be so much owing to any action taken by England but rather the direct result of French jealousy.' Doubts in London were reinforced by the stalwart opposition of the India Office to any step that might antagonise Indian Muslims and shake their loyalty to the British Raj.
While civilian politicians argued and intrigued among themselves, it was the military who acted to avoid the risk of a clash with Turkish nationalists. In July 1921, on the eve of the Turkish victory at Sakarya, the Allied Commander-in-Chief in Turkey, General Sir Charles ('Tim') Harington, agreed to meet Mustafa Kemal on board a British warship off the Turkish-held Black Sea port of İnebolu. The plan had been hatched by a demobilised British officer, Major James Henry, who was trying to win a mining concession in Anatolia. He suggested to the Turks that the British were keen on such a meeting, while telling the British military that the Turks wanted it. The intrigue fell through. Told that Harington was willing to meet him, Mustafa Kemal replied that he would come only if the British general agreed in advance to the complete liberation of the national territory and Turkey's unqualified independence in the political, financial, economic, judicial and religious spheres. Nevertheless, even if the initiative failed, it showed that the British military were ready to establish contact with Turkish nationalists.
In February 1922, the Ankara government sent its Foreign Minister Yusuf Kemal, who had succeeded Bekir Sami, to put its case directly to the French and British governments. On his way to France, Yusuf Kemal called on the British High Commissioner in Istanbul, and impressed him with his determination to accept nothing short of the sovereign independence of Turkey within the 1918 armistice lines. When Sir Horace Rumbold suggested that territorial concessions might be necessary, he replied that 'compromise must not always be at the expense of Turkey'. At the end of March, the British, French and Italian Foreign Ministers meeting in Paris proposed an immediate armistice, followed by negotiations for a new peace treaty. The proposal fell on deaf ears: the Turks demanded a full Greek withdrawal as soon as the armistice was concluded; the Greeks turned this down, believing that the Turks were incapable of turning them out of İzmir and eastern Thrace.
The Greeks sought desperately to avert the disaster threatening their Anatolian adventure. But their attempt to force the issue resulted in uniting all the Allies against them. In mid-July 1922, the Greeks threatened to march on Istanbul in the belief that possession of the Ottoman capital would give them the leverage to impose their terms on the Turks. Portraits of King Constantine appeared in the front windows of Greek shops in Istanbul, surmounted by the one word 'Erchetai!' – 'He is coming!'. But Constantine did not come to regain the city lost to the Turks by his namesake in 1453. For once, the Principal Allies acted in unison, and reinforced their warning to the Greeks to stay out of the neutral zone by assembling their troops and warships to resist a Greek march on Istanbul by force if necessary. The Greeks stopped in their tracks, having diverted to no purpose troops needed in western Anatolia for the final battle with the Turks.
Instead of counselling caution, Lloyd George hastened to undo the effect of the Allies' belated show of firmness. 'We are not allowing the Greeks to wage the war with their full strength,' he declared in the House of Commons on 4 August. 'We cannot allow that sort of thing to go on indefinitely, in the hope that the Kemalists entertain, that they will at last exhaust this little country, whose men have been under arms for ten or twelve years... and which has not indefinite resources.' But allow 'that sort of thing' was precisely what the Allies, including Britain, did. To paraphrase Henry Kissinger, one cannot expect a Great Power to commit suicide (or even to endanger its interests) in defence of an unwise ally.
As the Greek advance on Istanbul was being halted, the Greek proconsul in İzmir, Aristeidis Stergiadis, tried another way to lighten the burden. On 31 July he issued a proclamation saying that 'the work of liberation' would be continued 'by the liberating people itself', in other words by the locals and not by the Greek government. The administration of the area held by Greeks troops under the terms of the Treaty of Sèvres would be reorganised accordingly. But autonomy for Ionia made no sense. There were no Ionians, as there had been in classical antiquity, but only Greeks and Turks, and they were no longer able to live under the same roof. As the Greeks looked for outside help to hang on to their gains, the Turks took on 'the work of liberation' for themselves. The only effect of Stergiadis's initiative was to demoralise Greek troops even further, for in effect they were being asked to fight for territory which was about to be given up in any case.
Kemal's victory and the fate of Levanthine Smyrna
In Ankara, Mustafa Kemal came under increasing pressure to take the offensive. Nearly a year had passed since the Greeks had been stopped at the Battle of Sakarya. The Turkish national army had replenished its ranks with newly commissioned officers and recruits, and its arsenals with arms left behind by the French and the Italians, in addition to earlier shipments from Russia. What was the commander-in-chief waiting for? The answer was that Mustafa Kemal was keenly aware of the poverty of his domestic resources. His government controlled the most backward part of the country, without industry and with precious few skills. The new strength of the nationalists could easily be dissipated in an ill-planned operation. Mustafa Kemal wanted to be sure that he would be able to deliver a decisive blow, and before that to exhaust all possibilities of achieving his objective without further destruction and bloodshed. He proceeded cautiously. He inspected the front in July under cover of a football match between two army teams, which he watched in the company of his commanders. Having satisfied himself that his army was ready, he returned to Ankara and persuaded his ministers to minute their agreement with his decision to launch an offensive. Failure would have not only military but also political consequences. He tried to guard against both. To preserve complete secrecy, an announcement was put out that the commander-in-chief would be staying in Ankara to host a tea party at his residence. Then all communications were cut between Anatolia and the outside world.
An army of 225,000 Greeks were deployed against 208,000 Turks along a front which stretched from the shores of the Sea of Marmara in the north to the valley of the river Menderes (Great Meander), south of İzmir (Smyrna). Like other successful generals, Mustafa Kemal took the strategically sound risk of concentrating most of his forces on a narrow sector, leaving the rest of his front uncovered. It was the strategy of the single knock-out blow, which became known as the _blitzkrieg_. He targeted his offensive on the pivot of the Greek line, the peaks which dominated the town of Afyon on the main railway line from Istanbul. The Afyon salient was where the Greek front line changed direction from north-south to east-west, and was therefore open to attack from two sides. The main blow was delivered from the south to the right flank of the fortified mountain positions held by the Greeks. The intention was to cut them off from their rear base in İzmir, where the Greek commander-in-chief General George Hatzianestis had his headquarters on board a ship. Hatzianestis was an eccentric disciplinarian, who, it was rumoured, believed that his legs were made of glass and could break at any moment. But it was his army that broke.
The issue was decided in the sector chosen by Mustafa Kemal. On 25 August 1922, he joined his battle headquarters on the 6,000-foot (1,829-metre) high peak of Kocatepe. The following day, the Turks let loose an artillery barrage on the Greek positions on the peaks facing them. Then the Turkish troops advanced, climbing up the slopes against determined Greek resistance. The first day the Greek lines held. But Turkish determination was not dented. A Turkish colonel committed suicide because he could not keep his promise to capture a position as quickly as he had promised. 'It is not because I approve his action that I am telling you this', Mustafa Kemal said in his report to Parliament a few days later. 'Such behaviour is unacceptable. But I wanted to illustrate the spirit in which our officers and our commanders discharged their duty.'
The Turkish breakthrough came the following day, 27 August. Almost immediately, Greek morale collapsed. Their officers were bitterly divided into two rival camps, as Venizelists tried to undermine supporters of King Constantine. Troops had been exposed to Communist agitation about the imperialist nature of the war. Soldiers did not trust their officers, and the officers did not trust other ranks – or each other. Greek units retreating from their positions on the hills surrounding Afyon lost contact with each other. Many were surrounded. The retreat which started at Afyon extended to the whole front as far north as the Sea of Marmara. On 1 September, Mustafa Kemal issued his famous order: 'Armies, your immediate objective is the Mediterranean. Forward.' On 2/3 September, two Greek corps commanders surrendered when they found they had fallen into a trap. One of them, General Trikoupis, learned after his capture that he had been appointed commander of the entire front.
It took Turkish front-line troops six days to cover the 250 miles (400 kilometres) from Afyon to İzmir. As the Greeks fled to the coast, they set fire to towns and villages, destroying all that lay on their path. Units that managed to make it slipped through İzmir, leaving behind its terror-stricken Greek, Armenian and foreign citizens, and embarked on ships waiting off the Çeşme peninsula further west. On 9 September, Turkish troops entered İzmir. Mustafa Kemal made his official entry the following day. Three days later there was not a Greek soldier left anywhere in Anatolia, except for prisoners. A few days later there was almost nothing left of İzmir – or more accurately of Levantine Smyrna – and its non-Muslim inhabitants.
There were sporadic incidents of violence as Turkish troops advanced through the prosperous suburbs, where English and other European merchants had their villas, and entered the city. The troops were commanded by Nurettin Pasha, known as 'bearded Nurettin', who was notorious for his cruelty. He had been in command of the Ottoman troops which had besieged General Townshend's force in Kut in 1915 during the Mesopotamian campaign, but had been relieved of his command by von der Goltz, the German officer in overall command, before the British surrendered. At the end of the First World War, he was commander of the Turkish garrison in İzmir until the Allies insisted on his replacement just before the Greek landing. The Ankara government appointed him commander of the Central Army, whose task was to keep control of the nationalists' rear. It was this army which forced the Greek civilian population out of their homes along the Black Sea coast and then went on to suppress Kurdish risings. This was accompanied by so much bloodshed and destruction that the Grand National Assembly wanted to have Nurettin court martialled. But Mustafa Kemal was short of commanders and saved him from the wrath of the Assembly, transferring him to the command of the First Army under İsmet Pasha's overall command on the western front.
As commandant of a captured city, Nurettin had the duty of ensuring law and order in İzmir. But when the Greek Archbishop Chrysostom visited him to plead for the safety of his community, Nurettin handed him over to a mob of vengeful Muslims who tore the unfortunate prelate to pieces. Admittedly, it was difficult to restrain soldiers who had seen the destruction wrought by the retreating Greeks, and who found themselves in a prosperous city after years of hardship and grinding poverty. But no effort was made to prevent revenge killings and looting. And, as usual, once looting started fires followed, destroying the lives and property of ethnic adversaries.
The great fire of İzmir started in the Armenian quarter. In all, 20–25,000 buildings were burned down and an area of 2.4 million square yards (2.5 million square metres) was devastated. It was later claimed that the trouble was caused by Armenian resistance and by explosions of ammunition hidden in Armenian homes. Hatred between the Turks and the Armenians was intense, and only the strictest measures could have prevented a murderous confrontation. But instead of reining in ethnic hatred, Nurettin encouraged it. He did nothing to stop the killings and looting. The depleted city fire service was incapable of controlling the fire which engulfed the town right up to the waterfront. Only the poverty-stricken Turkish quarter on the heights round the citadel, the Jewish quarter and the immediate surroundings of the French consulate near the quayside were spared, suggesting that disloyal fellow subjects of the Sultan were deliberately targeted.
Terrified Greeks, Armenians and other Christians crowded the quays, begging to be taken on board Allied warships and transports anchored in the harbour. At first, Allied officers tried to restrict evacuation to their nationals, but as the harbour filled with the bodies of refugees who had thrown themselves on the mercy of Allied seamen, they had to accept on board civilians of any nationality, including Ottoman subjects. Within a few days 213,000 men, women and children were evacuated from the ruined city and carried to safety on board Allied warships and merchantmen. It was a remarkable achievement.
The Chanak Crisis
The occupation of İzmir by the Greeks had mobilised Turkish resistance to the partition plans of the Allies. The city was now to play an important part also in the consummation of the victory of Turkish nationalists. It was from İzmir that Mustafa Kemal decided to move Turkish troops north to press against the British-held perimeter of the neutral zone of the Straits.
During the four years which followed his return from the Syrian front at the end of the First World War, Mustafa Kemal had done his best to avoid a direct clash with the British, while he fought British protégés at home and abroad. He also encouraged contacts, however indirect and tentative, to convey his message that British policy towards his country was wrong-headed, and that if Britain accepted Turkey's full independence within the 1918 armistice lines, he would be only too happy to be its friend in the region and beyond. He had explained his position at a secret session of the National Assembly as early as 24 April 1920, the day after its official opening in Ankara:
Our nation is not opposed to the English. On the contrary it acknowledges and respects them as the greatest, the most just, most civilised and humane nation in the world . But after the armistice, the British entered our capital, and after establishing close contact with our people, they oversaw and backed the Greek occupation of the province of Aydın [İzmir] .So we said 'Do something to correct [your policy] and our nation will once again turn to you [in friendship]'.
Lloyd George was deaf to the message, but the British military were more receptive. And it was the attitude of the British (and Allied) commander-in-chief in Istanbul, General Harington, which prevented an armed clash between British and Turkish troops in September 1922.
Mustafa Kemal's aim in sending his troops to the perimeter of British positions at Çanakkale (Chanak), the fortress on the Asian side of the entrance to the Dardanelles, was to ensure that Istanbul and eastern Thrace up to the 1914 frontier came under the control of his government. With the exception of clashes with French occupation forces south of the Taurus mountains, officially attributed to popular resistance, he had succeeded from May 1919 onwards in achieving his objectives one by one without fighting British, French or Italian troops. Now, once again, he used the threat of force to avoid recourse to it. And once again the tactic worked. British policy changed in the way that Mustafa Kemal had suggested right at the beginning.
The painful, noisy and messy – but, in the last resort, effective – change in British policy was the essence of the Chanak Crisis, as it came to be called, which lasted for barely a month from mid-September to mid-October 1922. And it was not only British policy towards Turkey that changed. So, too, did the governments in London and Athens. The crisis affected also the relationship between London and the Dominions: the refusal of most of the Dominions to back a new conflict (New Zealand and Newfoundland were the two exceptions) marked the growing independence of the constituent parts of the British Empire. The change was bloodless for the British, bloody in Athens. But what came out of the Chanak Crisis was the birth of a new dispensation in that part of the Middle East, a dispensation which has lasted to this day. The peace treaty that was signed in Lausanne nine months later confirmed the outcome of the Chanak Crisis. Fortunately for the world, the crisis did not end, but merely interrupted, the career of one of the enemies of change, Winston Churchill.
Churchill was to describe his position with characteristic elegance:
Defeat is a nauseating draught, and that the victors in the greatest of all wars should gulp it down was not readily to be accepted. So having done my utmost for three years to procure a friendly peace with Mustapha Kemal and the withdrawal of the Greeks from Asia Minor, and having consistently opposed my friend the Prime Minister upon this issue, I now found myself wholeheartedly upon his side in resisting the consequences of the policy which I had condemned.
Churchill was an imperialist. He resisted the independence of India. He guided the British Empire through the perils of the Second World War and presided over its transformation into the Commonwealth. He believed in the benefits of empire for all its subjects, just as the French believed in their civilising mission in their empire and beyond. But Mustafa Kemal too had been a loyal servant of his empire, the Ottoman state, and had fought hard on three continents to defend its frontiers. He also believed passionately in the value of the civilisation which had developed in the West, and which Western empires were propagating throughout the world. His success in establishing a Turkish national state on the ruins of the Ottoman Empire, in the teeth of Western opposition, did not blind him to the merits of British or French administration for people who were as yet incapable of achieving and sustaining civilised self-rule.
It was natural to fear for the safety of Istanbul, the cosmopolitan capital of the Ottoman state, in the wake of the humanitarian disaster which had just stricken Levantine Smyrna (İzmir). Non-Muslims, particularly non-Muslim Ottoman subjects, as well as those Muslims who had sided with the Sultan and pinned their faith on the Allies, were terrified at the prospect of the forcible entry of the Turkish nationalist army into their city. But although Allied officials in Istanbul were keenly aware of these fears, the main concerns of the British government were different.
There was, of course, the prestige of the victors to be considered. But geopolitics was more important. Control of the Straits had been achieved at the cost of great sacrifices in the First World War. Freedom of navigation was important for the great trading powers of the West, although less important now that the Bolsheviks had seized control of Russia, which ceased to be a significant trading partner of the West. Now the pressing need was for a bulwark against Bolshevism. Mustafa Kemal had cooperated with the Bolsheviks, while Venizelos had sent Greek troops to Odessa to help the White Russian counter-revolutionaries. For the British government in particular, the rise of the Bolsheviks revived the fear of Russian expansion which had inspired the policy of supporting the Turks throughout the 19th century. That policy had been abandoned as the Kaiser's Germany came to present a greater threat to British (and French) interests, and, of course, as the Young Turks threw in their lot with the Germans. Lloyd George had been persuaded by Venizelos that Greece could replace Turkey as the defender of the northern frontier of the Middle East, an area long important to Britain as it lay across the route to India. Moreover, British and French rule newly established in the Arab lands had to be defended. But the defeat of the Greeks by Turkish nationalists had disproved the arguments of Venizelos. It was no use blaming the French, the Italians, the soldiers, the opposition and the press at home, as Lloyd George did, for the defeat of the Greeks and, consequently, of his policy. The policy had failed and an alternative had to be found.
When Turkish troops entered the neutral zone and pressed against the British positions round Çanakkale, the first reaction of the British government was to reinforce the troops on the ground and the warships patrolling the Straits. As there were no reserves available, appeals were sent to the Dominions to help guard the positions for which thousands of Anzacs had died. But Australia was unwilling to send its men back to Gallipoli. In fact none of the Allies was willing to fight the Turks.
This became clear when Curzon went to Paris to meet the French Prime Minister Raymond Poincaré. 'It was both a moral and physical impossibility for France to resist the Turks if they advanced,' Poincaré told Curzon, adding, 'French public opinion would not admit of a shot being fired against the Turk.' Curzon burst into tears, complaining: 'Never in my life have I had to endure such speeches.' It made no difference. On 23 September, ten days after the arrival of Turkish troops outside Çanakkale, Poincaré, Curzon and Count Sforza sent a joint note to Ankara which went a long way towards meeting Mustafa Kemal's objectives. The note declared that the Allies 'viewed with favour' the desire of Turkey to recover eastern Thrace, including Edirne (Adrianople), and the Turks could have Istanbul after the peace was signed. As a first step, they suggested a meeting between the Allied generals and Mustafa Kemal – at Mudanya, south of the Sea of Marmara, or İzmit on the eastern approaches to Istanbul.
The Mudanya armistice
Mustafa Kemal wanted – and needed – a more precise commitment. On 23 September, the same day that the Principal Allies sent their joint note to Mustafa Kemal, there was a military coup in Athens. King Constantine was forced to abdicate and a junta of Venizelist colonels seized power. Just as Constantine's return to the throne in 1920 had not halted the Greek invasion of Anatolia, but, on the contrary, had channelled more resources into it, so now the revolutionary colonels sought to prove their patriotic credentials by assembling troops in Thrace and hanging on at least to their country's gains in European Turkey. In the circumstances, the Allies' promise 'to look with favour' on the restoration of Turkey's 1914 frontier in Europe was not sufficient. What Mustafa Kemal wanted was for the Allies themselves to evict the Greeks. Urged by some nationalist politicians to extend the war to Europe, he replied that he would not sacrifice a single Turkish gendarme for an object he could achieve by peaceful means. Mustafa Kemal's popularity with his troops was well merited.
The Chanak Crisis showed also Mustafa Kemal's mastery of a very modern skill. Right from the beginning of his career, he had realised the importance of the press and made every effort to make friends of journalists. However, he also made sure that it was he and not the press who set the political agenda. During the First World War, Enver, the country's virtual military dictator, had deprived him of publicity. When Mustafa Kemal returned to Istanbul in November 1918 after the signature of the armistice, one of his first steps had been to start a newspaper that would propagate his fame and his views. The newspaper (which was managed by Fethi (Okyar), Mustafa Kemal's main political ally in the capital) was called _Minber_ ('The Pulpit'). It served Mustafa Kemal's purpose in presenting him as a safe candidate for his crucial appointment to Anatolia.
Almost immediately after his move to Ankara, Mustafa Kemal set up a press agency. Called the Anatolian Agency and staffed by professional journalists, it helped raise morale at home by disseminating news and comment which favoured the nationalists, and made their views known abroad. But securing the friendship of foreign correspondents was a more effective way of influencing public opinion in countries where they had greater credibility. Here Mustafa Kemal was fortunate in his choice of contacts. The French journalist Berthe Georges Gaulis visited him in Ankara and her friendly articles earned her the thanks of the Turkish National Assembly. Later her books made Mustafa Kemal's reforms known and appreciated in the West. But it was the attention that Mustafa Kemal had paid to a British correspondent, George Ward Price of the _Daily Mail_ , which was to prove particularly beneficial during the Chanak Crisis.
Ward Price had made his name as a war reporter when still in his mid-twenties during the Balkan Wars of 1912–13. Mustafa Kemal first met him in Istanbul in 1918 when he tried to persuade him of his friendly feelings towards Britain. Ward Price's reports from Turkey made him no friends among British officialdom: in the words of Neville Henderson, British Deputy High Commissioner in Istanbul, Ward Price 'dropped like a vulture from the sky' on a news story. But what mattered was the effect of his reports on the editorial policy of his paper. Even though Ward Price praised the mettle of British troops that faced the Turks at Chanak, the _Daily Mail_ concluded that Churchill's efforts to mobilise the Dominions against the Turks were 'bordering upon insanity'. On 21 September, the newspaper came out with the headline 'Get out of Chanak'.
Sir Horace Rumbold, the British High Commissioner, was enraged by the press which, he believed, had readily supported the Turkish nationalist cause. The _Daily Mail_ , he wrote, was 'beneath contempt'. The _Morning Post_ 'shuts its eyes to the bestialities of the Turks and slobbers over the French who don't deserve it'. As for the French press, it 'seems to be in the grip of the International financier or Jew who only cares for French financial interests and nothing else'. The self-righteous diplomat raged in vain. Mustafa Kemal's handling of the press helped him achieve his objectives.
On 29 September, General Harington was instructed to deliver an ultimatum to the Ankara government demanding that Turkish troops withdraw from the neutral zone immediately. If they did not, the British would attack them. Fortunately, General Harington was as determined as Mustafa Kemal to avoid a resumption of hostilities. Instead of delivering the ultimatum, he continued negotiations with the Turkish nationalists' representative in Istanbul. The Greek fleet, he said, had been withdrawn from the Sea of Marmara on 27 September 'under the strongest British pressure'. The French unofficial representative, the indefatigable Franklin Bouillon, reported that the Ankara government was prepared to negotiate an armistice leading to a peace settlement. Harington called him 'a perfect curse', but believed that if the Frenchman helped the two sides to sit round a conference table, he would have performed a useful service.
On 1 October, the Ankara government agreed to meet Allied representatives in Mudanya, the small port on the south shore of the Sea of Marmara which served the city of Bursa, now firmly under Turkish control. But Mustafa Kemal would not attend, just as he had earlier refused to meet Harington on board a British warship in the Black Sea, unless his terms were accepted in advance. The Turkish representative would be İsmet Pasha, the Turkish commander of the western front, and Mustafa Kemal's trusted lieutenant. Isolated politically at home and abroad, Lloyd George and Churchill gave way to the peace lobby, albeit with bad grace. Harington, who had earlier disobeyed instructions to confront the Turkish nationalists with an ultimatum, was instructed to be tough in the negotiations. He did not need advice from London to map out common ground for a satisfactory settlement.
The conference began on 3 October in a merchant's house on the waterfront, which had been used by the honorary Russian consul before the war. It was essentially a military meeting between equals: the British, French, Italian and Greek commanders in Istanbul on one side, and İsmet, the Turkish commander on the other. What was under discussion was the gradual transfer of Istanbul and of eastern Thrace to Turkish control. It was not an easy matter to arrange. The capital and its hinterland had a mixed population. Inter-communal relations had broken down, and the prospect of losing Allied protection terrified Christian communities, which had been led to believe that they would replace the Turks as rulers of the cosmopolitan heart of the Ottoman state. There were some 150,000 foreign nationals, most of them natives, who clung to their privileged status. As soon as they entered the First World War, the Young Turks had abrogated the capitulations, under which foreigners came under the jurisdiction of their own consular authorities. The Treaty of Sèvres had restored their extra-territorial status. It was no secret that the Ankara government was determined to abolish this privilege. Suspicions and fears were rife on all sides.
In the circumstances, the delegates could congratulate themselves on coming to an agreement after a week of tough bargaining. The terms signed on 11 October were simple. The Greeks were to evacuate their troops from eastern Thrace within 30 days, transferring civil authority to the Allies, who would also interpose themselves between Greeks and Turks on the frontier. The Allies would in turn hand over the administration to Turkish officials, who would be assisted by up to 8,000 Turkish gendarmes. Allied troops would remain in their present positions, i.e. would continue to occupy Istanbul and the Straits, until peace was signed.
The Greek delegate, General Mazarakis, saved face by absenting himself from the signing ceremony. But three days later, on 14 October, the Greek government announced that it would abide by the terms of the armistice. It had no other option. Fighting had ended in effect a month earlier when the last Greek soldier left Anatolia. Now, nearly four years after the defeat of the Ottoman state, and eight years after it had entered the First World War on the side of Germany, hostilities ceased officially. The armistice of Mudros, imposed on the defeated multi-national Ottoman Empire in November 1918, was replaced by an armistice negotiated with the victorious new Turkish national government. Mudros had not ended the fighting; Mudanya did so.
Within a month, all the Greeks – soldiers from the mainland and local civilians – had left eastern Thrace. Villagers loaded their belongings on carriages and carts and drove their cattle with them to the western bank of the Meriç (Maritza/Evros) River. The towns, including the frontier city of Edirne (Adrianople), took years to recover the loss of most of their skilled citizens. In Istanbul, Greeks who wanted to leave had longer to make their arrangements. Within a year some 150,000 had left, including the wealthiest members of the community. In 1914 there had been between 2 and 2.5 million Greek Orthodox residents in Turkey. By 1927, when the first official census was held in the Turkish Republic, the Greek community was reduced to 150,000, all of them in Istanbul. Today there are fewer than 5,000 Greeks in Turkey.
Eight days after the signing of the armistice at Mudanya, Lloyd George's coalition of Liberals and Conservatives fell apart. Meeting at the Carlton Club on 19 October the Conservatives decided to pull out of the government and fight the forthcoming general election as an independent party. Lloyd George resigned the following day and was replaced by the Conservative leader Bonar Law. Curzon deserted Lloyd George, whose interference in the conduct of foreign policy he had long resented, and stayed in charge at the Foreign Office. He kept his office when Bonar Law won the general election on 15 November. Lloyd George, unrepentant to the end, never saw office again. Churchill, who stood by him, put the leisure he had not sought to good use by writing his account of the war and much else besides, until his finest hour came in 1940.
In Greece accounts were settled in a more savage way. The junta court martialled the country's defeated leaders. After a travesty of a trial, six of them, including the Prime Minister Dimitrios Gounaris and the commander-in-chief General Hatzianestis, were sentenced to death on 28 November and shot without further ado. Prince Andrew escaped a similar fate thanks to British intervention. His sentence of exile was a lucky deliverance. Venizelos returned to the international scene, and became Greek representative at the Peace Conference in Lausanne.
If San Remo and Sèvres saw the imperial ambitions of the victorious powers touch their zenith, then the events of 1921–2 brought them back to earth. The Turks had demonstrated their ability to thwart the provisions of the Treaty of Sèvres, routing the Greeks and defying the British in the process. Lloyd George did not long survive the Chanak Crisis, and with him, of course, Weizmann and the Zionists lost one of their most consistent patrons. Nor could the Zionists be reassured by the drift of events in Palestine, Samuel's appointment as High Commissioner notwithstanding. The strength of Arab opposition saw Haj Amin al-Husayni, who was to emerge as a deadly enemy, ushered in as Grand Mufti of Jerusalem, while the Churchill White Paper was an unwelcome qualification of the terms of the Balfour Declaration. For their part, Arabs could take some comfort from the installation of Hashemite rulers in Baghdad and Amman. If this was not yet independence then, arguably, events were to prove, as was said in defence of the Irish treaty, that it provided the means of achieving it.
6
# From War to War
The Middle East had been at war, almost without a break, since 1911, the year the Italians invaded Libya. The First World War and the Turkish War of Independence, which followed, lasted eight years. But after the Turkish victory at the end of August 1922, the pace quickened. A fortnight later, the Greek army was out of Anatolia. A month after that an armistice was signed with the Allies. It then took another two weeks to sweep away the Ottoman monarchy, which had ruled the country for seven centuries. The Middle East now seemed set on a period of peace and reconstruction but while this became true for Turkey, once the Treaty of Lausanne had settled its future, for the rest of the region events were to be much less straightforward. The Arab world grew increasingly restive under the Mandates system, while the future of Palestine grew distinctly problematic as tensions grew between Arabs and Jews. Nor could the region be immune to the international tensions which steadily built up in Europe from 1933. The Middle East's critical importance as a strategic hub, as well as the need to have access to its oil, meant that it would not be left in isolation once hostilities broke out again in 1939. This time, however, Turkey was to be an exception, adhering to a clear policy of neutrality until virtually the end of the war. No such exception was to apply to the Jews of Europe, however, who were to become the victims of genocide.
The end of Ottoman rule
On 19 October 1922, a week after the signature of the armistice at Mudanya, General Re'fet (Bele), one of Mustafa Kemal's original companions in the War of Independence, arrived in Istanbul at the head of the force of Turkish gendarmes (in fact, soldiers in gendarmerie uniforms) that was to take over eastern Thrace. Turks in the Ottoman capital received him enthusiastically. The Ankara government had long had a representative in Istanbul with whom Allied High Commissioners dealt. But with Re'fet Pasha's arrival the relationship changed, as power in the old capital slipped out of the hands of the Allied authorities. Welcomed by the Sultan's ADC and the Grand Vizier, Re'fet made it clear that he recognised Vahdettin as Caliph only and not as temporal sovereign, and his government not at all. Mustafa Kemal had already decided to abolish the monarchy, even though the matter had not been debated in the National Assembly. Re'fet waited ten days before visiting Vahdettin in Yıldız Palace. The Sultan left this account of the audience:
This little man hid his true intention behind grand aspirations, and said that if I accepted a meaningless caliphate shorn of the constitutional sultanate, which we had all sworn to uphold, and if I sent a telegram to Ankara declaring that I recognised the law of fundamental organisation [the provisional Constitution voted by the National Assembly in 1921] and the Ankara government, I could save my person and position. I replied that I had to think it over. But the following day when I read Mustafa Kemal's insults against my person and our dynasty, the time came for a decision.
Re'fet was reported to have said later: 'I crossed my legs in front of the Sultan and leaned back so far that the tip of my shoes nearly touched his nose'. According to the Grand Vizier, Tevfik Pasha, Re'fet told the Sultan: 'Close the palace gates and don't allow anyone in. Unsuitable people are coming and going, and this leads to gossip. You can go to the mosque and nowhere else.' Nevertheless the Sultan received in audience two trusted advisers who were hated in Ankara – Mustafa Sabri, a clerical politician who had served Damad Ferid as Sheikh al-Islam, and the journalist Ali Kemal, who had infuriated the nationalists with his fiery articles denouncing the resistance movement in Anatolia.
It was not the Sultan, but the Allies who forced a decision. On 27 October, the Principal Allies – Britain, France and Italy – invited both the Istanbul government of Grand Vizier Tevfik Pasha and Mustafa Kemal's Ankara government to send delegations to a peace conference to be held at Lausanne in Switzerland. In response, Tevfik Pasha suggested to Mustafa Kemal that they should discuss the matter, but Kemal would have none of it. There was only one Turkish government, he insisted, the Ankara government formed by the National Assembly. He did not need the help or advice of Tevfik Pasha and his ministers. The Sultan's government was defunct and the time had come for him and his ministers to leave the stage.
On 30 October, Dr Rıza Nur, a maverick politician who had opposed the CUP before joining Mustafa Kemal in Ankara (and who was later to break with him and vilify him in his memoirs), tabled a bill in the Assembly, declaring that the Sultan's government had ceased to exist when the Allies forcibly closed down the Ottoman parliament on 16 March 1920. From that date, sovereignty, which had been appropriated by the Ottoman dynasty, had reverted to the Turkish nation. The Sultanate was now abolished, but the dynasty would continue to exercise the function of Caliphate at the discretion of the National Assembly. It was in Mustafa Kemal's mind a transitional arrangement, but he argued for it eloquently, saying:
On the one hand, the people of Turkey will become daily stronger as a modern and civilised state, and realise increasingly their humanity... and, on the other, the institution of the Caliphate will be exalted as the central link of the spirit, the conscience and the faith of the Islamic world.
Modernity and civilisation were synonymous.
Mustafa Kemal reminded his audience that there had been shadowy Caliphs between the 10th and the 16th century when temporal government was exercised by Sultans in the Islamic world. The two functions could, therefore, be separated. But the change of rhetoric was abrupt. When the National Assembly opened in Ankara on 23 April 1920, it had pledged loyalty to the Sultan and Caliph. Now it denounced the monarchy and praised a shadowy Caliphate. Inevitably, there was uneasiness in the ranks of the deputies. Could the wording of the bill perhaps be changed? Mustafa Kemal ended the argument the following day, when the matter came up in committee. In a speech in 1927 in which he gave his account of the genesis of the Turkish republic, Mustafa Kemal said that he stood on a bench in the committee room and told members:
Sovereignty and kingship are never decided by academic debate. They are seized by force. Now the Turkish nation has effectively gained possession of its sovereignty. This is an accomplished fact. If those assembled here see the matter in its natural light, we shall all agree. Otherwise, facts will prevail, but some heads may roll.
Thereupon, a member said, 'Sorry, we had approached the matter from a different angle. Now you have set us right.' On 1 November, the full Assembly passed the law abolishing the monarchy. There was only one dissenting vote.
The minutes of the committee have never been published, but whatever the exact words used by Mustafa Kemal, there was no doubt about his intentions. The Grand Vizier took the hint. On 4 November Tevfik Pasha submitted his resignation to the Sultan. Moving into his office, Re'fet informed the Allies that the administration of Istanbul was now in the hands of the Ankara government.
The first consequence was far from reassuring. The nationalists' hate figure, the journalist Ali Kemal (whose great-grandson Boris Johnson, also a polemical journalist and politician, was to be elected Mayor of London 85 years later) had tried to make amends by admitting that he had been wrong and the nationalists right. He had believed that salvation lay in cooperation with the Allies. The nationalists had proved that opposition to them was the right course. The tactics differed, but the objective was the same. The admission did not save him. He was kidnapped by nationalist agents in broad daylight in the European heart of Istanbul and taken to İzmit, where 'bearded Nurettin' now had his headquarters. After abusing him as a traitor, Nurettin handed Ali Kemal over to a lynch mob, which beat him to death. Mustafa Kemal made no secret of his disgust at the fate meted out to his opponent. Soon afterwards Nurettin fell into disgrace. He came out as a political opponent of Mustafa Kemal, who denounced him at length in his 1927 speech, and belittled his military career. Henceforth, repression was left to the courts.
News of Ali Kemal's murder terrified Turks who had cooperated with the Allies in Istanbul, and they hastened to seek refuge in the embassies and consulates of Allied states. The following year the peace treaty provided for a general amnesty for political offences. At the same time, the Turkish government undertook to draw up a list of no more than 150 political opponents who were to be exiled from the country. Prominent critics of the nationalist cause could thus make their way to safety abroad. Survivors among them were allowed back into the country in 1938. This act of reconciliation was one of Mustafa Kemal's last political decisions. He died later that year.
Fear of the new regime was keenest in the Sultan's palace at Yıldız. 'The philosopher' Rıza Tevfik, one of the Ottoman signatories of the Treaty of Sèvres, reports in his memoirs that rumours had reached the palace that 'Mustafa Kemal Pasha will come to depose the Sultan and have him executed. After all, this Turkish revolution is a replica of the great French Revolution. What the French did to Louis XVI, the Turks will do to Vahdettin. Revolutionaries have no other way.' The women and servants in the Sultan's private apartments were panic-stricken. 'Come what may, ensure the escape of our lord and master', they pleaded. But the Sultan had one more matter to settle.
It was a tradition that when the throne was vacated, every single person in the retinue of the late sovereign had to leave the palace. Women in the harem were either married off or entrusted to the care of their relatives. Only elderly servant women who knew the palace ceremonial were allowed to stay on. There had been 36 women in the harem of Vahdettin's brother and predecessor, Sultan Mehmed V (Mehmed Reşad). Vahdettin did not have a harem of his own before his accession, and he had allowed 12 women of his brother's harem to stay on. One of them was a young girl, called Nevzad, who celebrated her 19th birthday on 1 November 1922. Vahdettin married her before leaving the country. She was his third wife: the first had borne him two daughters, and the second his only son and heir, Mehmed Ertuğrul, who was ten years old in 1922, and was to die in Cairo in 1944. All three women joined Vahdettin in exile in Italy.
Vahdettin had always been fearful for his safety. Even before his accession to the throne he carried a handgun in his pocket, and he continued to do so to the end of his life. His audience was surprised one day when the gun fell noisily to the floor. Indecisive in most matters, he was, it seems, a good shot. But now safety had to be sought by other means. On 16 November Vahdettin wrote this letter to the Allied Commander-in-Chief, General Harington: 'I consider my life to be in danger in Istanbul, and I therefore take refuge with the noble British state and ask for transport from Istanbul to some other destination.' He signed it Mehmed Vahdettin, Caliph of the Muslims, and not Sultan. Forewarned, Harington had already been authorised to make the necessary arrangements. The following day at dawn an ambulance drew up at the gate of Yıldız palace. Vahdettin was smuggled on board. There was a delay on the way to the harbour as a tyre had to be changed. Eventually, Vahdettin, his son, and a suite of ten courtiers arrived at the quayside. It was raining heavily.
Harington was waiting to see off the last Ottoman Sultan. Vahdettin took out a gold cigarette case and lit a cigarette with trembling hands. Harington is said to have expected to be given the cigarette case as a souvenir. But retentive to the last, Vahdettin put it back in his pocket, as he asked Harington to make sure that his wives joined him abroad. He then embarked on the British battleship HMS _Malaya_ which was standing by in the harbour. Asked whether he would be happy to be taken to Malta, Vahdettin agreed. From Malta he made his way to Mecca, ruled precariously by the British protégé King Hussein, who had led the rebellion against the Ottoman state. Mecca, which was about to fall to Ibn Saud, did not provide an agreeable environment, and Vahdettin went on to take up residence in a villa at San Remo on the Italian Riviera. He died there in 1926, his young wife Nevzad at his bedside. It is said that the local Italian court took the unusual step of sequestering Vahdettin's coffin in an attempt to secure payments of his debts. Somehow a settlement was reached with his creditors, and the coffin was shipped to Damascus where Vahdettin was finally buried. HMS _Malaya_ was to make a return visit to Istanbul in 1938. On board was the British guard of honour which was to take part in Mustafa Kemal's funeral procession.
Superstitious observers noted that Vahdettin had brought ill fortune on himself. He suffered from rheumatism and walked with difficulty. When he entered the old palace at Topkapi for his accession ceremony in 1918, he had asked for his ebony walking stick. Told that it had been left behind, he exclaimed 'What a disaster!' This word of ill omen, uttered at the beginning of the reign, was bound to bring bad luck in the end. The ebony walking stick was the last object Vahdettin took with him when he left his palace for ever.
As soon as he left the country, Vahdettin issued a statement declaring 'I have not fled. I have migrated'. It was a reference to the Prophet Muhammad whose move from Mecca to Medina in CE 622, known as the _hijra_ , is the beginning of the Muslim era. Vahdettin insisted that he had not abdicated and that the Ottoman throne was still his by right. He pleaded in vain. On 18 November, the day after his escape, the chief cleric who acted as a minister of the Ankara government issued a fatwa ruling that it was lawful to depose the fugitive Sultan. The National Assembly immediately implemented the decision. It then proceeded to elect Vahdettin's cousin Abdülmecid, the heir apparent, to the newly defined position of Caliph.
Vahdettin had tried to rule as well as reign, like his eldest brother Abdülhamid II and unlike his other brother and predecessor Mehmed V. He claimed that he followed Abdülhamid's policy when he sought the friendship of Britain and France. Abdülhamid had in fact relied on Germany to offset Britain's political and France's economic power, and he used his title of Caliph to frighten European empires, worried about the loyalty of their Muslim subjects. The power equation had changed with the defeat of Germany and the triumph of Bolshevism in Russia. Britain and, to a lesser extent, France had a choice of Muslim puppets, and certainly by 1922 they had come to the conclusion that they could do without Vahdettin, either as Sultan or as nominal Caliph of all Muslims. True, the Ottoman Caliphate had supporters in India, but it was the survival of Turkey as an independent Muslim country rather than of the Ottoman dynasty that was the aim of the Khalifat movement in the subcontinent. That is why it sent money to the Turkish resistance movement, led by Mustafa Kemal, and opposed Lloyd George's design to partition the most important surviving independent Muslim country. After the First World War, decolonisation rather than pan-Islamism became the dominant ideology of elites among the Muslim subjects of European empires. Nostalgia was the only resource left to the Ottoman dynasty.
The shift in the ideological climate was beyond Vahdettin's grasp. He had trained himself in traditional Islamic culture during his long years of seclusion before his accession to the throne in 1918. The CUP had been modernist. Vahdettin turned away from the modern world. Abdülhamid II was interested in photography and had a photographic studio in his palace in Yıldız. Vahdettin's interest lay in Islamic calligraphy, classical Ottoman poetry and music. In all three he had ability, but not an outstanding talent. Abdülmecid, his successor as last Caliph, preferred Western arts. He composed Western palm court music, and was a competent portrait painter. Disregarding Islamic objections to the representation of the human form, he chose for his paintings subjects such as _Beethoven in the Harem_ and _Goethe in the Harem_ , as well as _Palace Concubine_. His interests did not endear him either to the elite or to the people. He practised Western arts, but thought of himself as a champion of Asia against Europe. One of his last political gestures in exile in German-occupied Paris was to send a telegram to the Japanese Emperor congratulating him on the success of his forces after Pearl Harbor. Bad judgement was characteristic of the last days of the Ottoman dynasty.
In spite of his tactical praise for the institution of a spiritual Caliphate, Mustafa Kemal was beginning to show his real feelings towards religion. On 2 October 1922, when he made his triumphal entry into Ankara to announce the victory of his armies, he was met at the door of the National Assembly by a uniformed imam, who started reciting a prayer of thanksgiving in Arabic. Mustafa Kemal pushed him aside. 'There is no need for this here,' he said. 'You can say your prayers in a mosque. We have won the war not with prayers, but with the blood of our soldiers.' He had mobilised Muslim religious sentiment at home and abroad to fight foreign invaders. He decided he could dispense with this now. But, at this stage, he took care not to confront Islam as such. In an off-the-record briefing he gave to leading Istanbul journalists in January 1923, he asked them not to describe the government as irreligious. That would be tantamount to an invitation to the public to attack him. The people, he explained, were not without a religion. They professed the Muslim faith. 'No one is rejecting religion, the way the Communists do', he said. Anyway, Communism was nonsense, and when Russia abandoned it, it would become stronger than it had been under the Tsars. When a journalist asked whether the government itself would be religious, he was vague. 'Will it or won't it? I don't know. There is nothing in the laws today to prevent it.' However, he indicated his own position when he added, 'If you insist, call the government materialist, but not irreligious.' He made no bones about his dislike of Muslim clerics, the hocas (pronounced hodjas). They were, he said, a worthless lot. The _madrasahs_ (religious schools), where they taught, had been a resort of draft-dodgers during the War of Independence. Talking to tradesmen in the southern city of Adana later that year, he made the claim that has dominated secularist discourse in Turkey to this day: 'The evils which have ruined and enslaved our nation have all been wrought in the name of religion', he said. There was no need to consult religious scholars ( _ulema_ ). 'Whatever is rational, whatever is in the interest of the nation and of the Muslim community, is also in conformity with religion. For if our religion had not been rational, it would not have been the perfect and the final religion.'
Mustafa Kemal had earlier addressed the faithful from the pulpit of a mosque in Balıkesir in western Anatolia. Preachers, he said, should use a language everyone understood, in other words, Turkish not Arabic. They should follow developments in science, politics, society and civilisation, and their sermons should be in conformity with scientific truths. Then, step by step, religion was banished from the public sphere altogether. Truth was to be found solely in contemporary scientific civilisation. If Islam equalled rationalism, then rationalism was sufficient.
However, the full secularisation of the state could wait a little longer. The immediate job after the conclusion of the armistice was to prepare for the Peace Conference in Lausanne. Mustafa Kemal was pleased with the way İsmet had brought the armistice negotiations at Mudanya to a successful conclusion, and decided to appoint him chief Turkish delegate in the final peace talks. True, İsmet was a soldier, not a diplomat. At Mudanya he had acted within his competence, as he faced Allied military commanders. At Lausanne he would have to argue with foreign ministers. İsmet himself was nervous about his qualifications. Mustafa Kemal brushed aside his reservations. İsmet was loyal and he fully shared his leader's vision. That was enough.
The Lausanne Conference
As the Lausanne Conference was held at foreign minister level, the first step was to appoint İsmet Foreign Minister, and then to choose his delegation. He was given two assistant delegates (one of them the sharp-tongued Rıza Nur) and 25 advisers. Some were members of the National Assembly, others career civil servants who had served the Ottoman government. Inevitably, the new civil service was recruited largely from among members of the Ottoman bureaucracy. One of the advisers was the former Unionist minister, Cavid Bey, an acknowledged expert in financial affairs. There was also one eccentric but astute choice – the Chief Rabbi Hayim Nahum. Unlike the Christians, the Jewish community had remained loyal to the Ottoman state, and Hayim Nahum could be relied upon to make use of his foreign contacts to advance the interests of the new government in Ankara. That he was a critic of Zionism was an additional advantage. It meant that his loyalty was not divided. Nahum was described as a teacher of French, the official language of the conference.
When İsmet arrived in Lausanne, he was told that the opening would be postponed for a few days to await the results of the British general election. Was this a British trick?, he wondered. The French hastened to reassure him. Prime Minister Poincaré invited him to Paris where he told İsmet that peace would definitely be concluded. In Britain, the Conservatives won the election on 15 November. Curzon, happy to be rid of the constant interference of Lloyd George, stayed on as Foreign Secretary under the new Prime Minister, Andrew Bonar Law. Before going to Lausanne, he, too, met Poincaré and the newly installed Italian dictator Benito Mussolini. But the united Allied front which Curzon wanted to form against the Turks was shaky.
The Conference was opened on 20 November by the Swiss President Robert Haab in the Mont Benon casino. İsmet thought that after the inaugural speech the meeting would break up until the first working session the following morning. But when Curzon insisted on speaking on behalf of the Allies, İsmet gave an impromptu reply in his schoolboy French (as he himself said). The Peace Conference was to be held between equals, not between a coalition of victors and a vanquished country. Sir Horace Rumbold, the British High Commissioner in Istanbul who had been summoned to Lausanne as Curzon's assistant, believed that İsmet had a great advantage. 'In the last resort,' he wrote, 'the Turks will not shrink from the use of force, while the mere thought of hostilities is repugnant to Bonar Law's mind.' Rumbold did not realise that Mustafa Kemal was just as averse to the resumption of hostilities. Both sides bluffed. But Mustafa Kemal had a clearer idea of his objective. This was the total independence of Turkey and, therefore, an end to foreign interference in Turkish internal affairs. The premise of the Treaty of Sèvres had been that the Turks were incapable of running their own state, whether in the management of the economy or in the administration of justice, or even in public health. Mustafa Kemal was determined that this judgment should be reversed at Lausanne. He was well aware of his country's backwardness, but he was convinced that his people had in them the capacity to run a successful state in the modern world.
The Peace Conference ranged far and wide. There were 12 national delegations – four host Allied countries (the fourth being Japan, which had little to say), five countries, including Turkey, invited to attend all sessions (one of them, the US, did not consider itself a party to the proceedings, while pursuing its own interests), the Soviet Union, invited to take part in the discussions of navigation through the Straits, and, for some reason, Belgium and Portugal (but not Spain, which had represented Greek interests in Istanbul in the absence of proper diplomatic relations). The last two were asked to state their views on some topics only.
Curzon was determined to dominate this unwieldy gathering. Poincaré and Mussolini left after the opening, and Curzon declared himself chairman on behalf of the Allied hosts. This might have encouraged the Greeks, reliant as ever on British support, to make impossible demands. But Venizelos, who was the chief Greek delegate, had learnt his lesson. In his heart of hearts he had always believed in disengagement between Greeks and Turks, in what a Turkish observer called 'divorce total'. He had been unable to get it on his own terms, but this did not mean that peace between the two peoples could not be secured in any other way. Greece had been defeated and was bankrupt. But Turkey, too, was in dire straits: many of its cities lay in ruins; it was poor and backward. Both countries had a common interest in peace.
Turkey's frontiers with the Soviet Union and French-Mandated Syria had already been fixed by bilateral treaties. For the rest, the usual practice of _uti possidetis_ prevailed: the final peace treaty was to legitimise facts on the ground. Eastern Thrace was already in Turkish hands; Mosul was occupied by the British as Mandatory Power in Iraq. The National Pact, voted by the last Ottoman parliament, had claimed İskenderun (Alexandretta) and the province of Mosul, and demanded referendums to determine the future of western Thrace and of the territory lost to Russia in the Caucasus in 1878. The treaties approved by the National Assembly during the War of Independence had already conceded İskenderun to the French, and Batum (but not the rest of the three districts originally lost to Russia) to the Soviet Union.
Mustafa Kemal was a realist: Turkish claims which were unlikely to succeed could be used as bargaining counters. But his political opponents in the National Assembly played the nationalist card and demanded that the Turkish delegation in Lausanne should insist on the full implementation of the National Pact. The opposition in the Assembly was joined by the Prime Minister Rauf (Orbay), the chief Ottoman signatory of the armistice signed at Mudros in 1918, and subsequently a principled nationalist supporter of Mustafa Kemal. Rauf had hoped to be the chief delegate in Lausanne, and was now determined to make İsmet's life difficult. İsmet played fair by asking the government's permission before departing in any way from the instructions he had been given. But he infuriated Rauf by copying his reports to Mustafa Kemal. He had other readers, unknown to him: the British had broken the code used by the Turkish delegation and were fully aware of his tactics. İsmet realised that there were leaks, but thought that these occurred in Ankara.
Frontiers were not the main issue of contention, as Britain and Turkey agreed to set aside the fate of Mosul for subsequent negotiations and, ultimately, for arbitration by the newly established League of Nations. Curzon's admirers attributed Turkish concessions to the British Foreign Secretary's encyclopaedic knowledge which allowed him to argue convincingly that Kurds, who were the majority in the province of Mosul, were ethnically distinct from the Turks. This, however, was hardly news to İsmet. His point was that Turks and Kurds formed a single community, united by common interests. Curzon did not dispose of the argument that sorting out Kurds from Turks would not serve the interests of either people.
The Kurds would rather be ruled by Turks than by Arabs. Their resistance to incorporation in an Arab Iraq was broken by British aerial bombing, accompanied by the promise that the British would stay on until Kurdish rights were secured. This is what happened in theory. In reality, the Kurds of Mosul were better off than their kinsmen in Turkey so long as British influence was paramount in Iraq. The moment that influence ceased, the Arabs tried to impose their rule on the Kurds, who resisted at great cost to themselves. The conflict continues to this day.
While the fate of Mosul was left in suspense at Lausanne, a settlement was agreed on the status of the Turkish Straits. The zone of the Straits was to be demilitarised, and free navigation was to be ensured under the supervision of an international commission. Soviet Russia wanted the Straits to be closed always to warships of countries which did not border on it. It was disappointed and did not sign the text which was eventually agreed. However, friendly relations between Moscow and Ankara were preserved, as both governments had other priorities.
After long and laborious negotiations, the political problems between Britain and Turkey were largely overcome. Now it was France, with which Turkey had already signed what amounted to a preliminary peace treaty, which delayed a final peace settlement. France stood out for the interests of its investors in the defunct Ottoman state. It believed that these could be safeguarded only if foreigners retained their extra-territorial privileges under the regime of capitulations. This meant setting a limit to Turkish sovereign independence. İsmet stood out for his country's untrammelled sovereignty. Special facilities could be granted to foreigners (and to non-Muslim communities in Turkey) only if they were reciprocated. Similarly, any settlement of economic claims should not impose impossible burdens on Turkey.
Mustafa Kemal probably overestimated the power of Britain, a country which he certainly admired, even though it had been his principal opponent. Like other Turks educated in the Western mould, he had a better understanding of the French, and this helped him to drive a wedge between the two Principal Allies. Curzon, bruised in earlier encounters with the French, tried his best to preserve a common Allied front. When İsmet refused to budge on capitulations, the settlement of Ottoman debt and compensation claims – where the French were particularly demanding – Curzon tried to twist his arm by appeals to self-interest. İsmet liked to tell the story that Curzon countered his insistence on Turkey's unconditional independence by saying:
We are not happy. We've been unable to have our way on any point. But all the proposals you have rejected are still in our pockets. You're taking over a ruined country. You'll certainly need money to build it up. You'll come and kneel before us to get that money. That's when I'll present to you one by one all the demands you're now rejecting.
Curzon may well have thought so, but he is unlikely to have been so crude. Whatever his exact words, İnönü's account enjoys universal credence in Turkey, and is frequently quoted by nationalists today as they denounce sales of Turkish assets to foreigners and the evils of globalisation.
Unable to make headway in the face of İsmet's stubborn resistance, Curzon issued what amounted to an ultimatum. On 30 January 1923, he asked İsmet to sign a text that, he argued, represented the final Allied position. But Curzon's stand was undermined by Poincaré who told the press that the Treaty, as it stood, formed only 'a basis for discussion' and no more. This made it easier for İsmet to refuse to sign. It was a dramatic moment. The British delegation had packed its bags, but the train which was to take them away was delayed in case İsmet changed his mind. He did not. There was no alternative to breaking off negotiations and adjourning the conference.
Curzon's superior airs were widely mocked behind his back. His discomfiture when his drunken valet stole all his trousers and hid them under his bed to cover up his hoard of empty bottles made the rounds of clubs in London. His assistant, Sir Horace Rumbold, was blimpish beyond parody. He thought that 'an uppish oriental' was 'an unpleasant animal', and was proud of the fact that he had never asked a Turk inside his house when he was High Commissioner in Istanbul. But his prejudices, which were shared by his colleagues, did not always impair his judgment. As the Lausanne Conference ground to a halt, he predicted in a private letter that the Turks would not sign the Treaty. He added that the French also were discontented with it, believing that it gave Britain what it wanted, but did not give France the economic benefits for which it had hoped. He was right, but he disregarded one other factor.
The Americans, who did not take part in the negotiations, nevertheless watched them carefully to make sure that the open-door principle giving all states equal access to international markets was respected, except where their own interests would be served by privileged treatment. They were particularly interested in a project originally formulated before the First World War by the retired US admiral Colby Chester. In its revived form, the Chester Concession provided for the construction by an American company of railways and harbours on a vast scale in eastern Turkey in exchange for the exclusive right to exploit mineral resources lying within 12½ miles (20 kilometres) either side of the new railways. The Kirkuk oilfield in the province of Mosul was the prize coveted by the Americans. Competition between the Americans and the British, who wanted to retain control of Mosul, suited the Turks in their effort to regain the area, and the National Assembly approved the deal on 9 April 1923. But eight months later it rescinded its decision, after the US had distanced itself from the Near Eastern peace settlement, and it had become clear that it was not going to intervene in the Mosul dispute.
While a mass of unfinished business was left on the table, Greece and Turkey signed two important agreements on 30 January, the day the Conference was adjourned. The first met an urgent humanitarian concern by providing for the exchange of prisoners of war and civilian detainees. As a result, thousands of Greek prisoners did not have to wait for the final peace settlement to regain their freedom. The second agreement had more profound long-term implications. It provided for an exchange of populations, covering all Ottoman subjects professing the Greek (Eastern) Orthodox faith in Turkey and all Muslims in Greece. There were two exceptions: Greeks in Istanbul and on two islands off the entrance to the Dardanelles – Imvros (later renamed Gökçeada) and Tenedhos (Bozcaada) – which reverted to Turkey could stay on, provided they had been resident there when the First World War started. The same provision applied to Muslims in western Thrace, which Greece had gained from Bulgaria – its only prize for its involvement in the war. The numbers of the two communities were roughly equal at 150–200,000.
The Greek Patriarchate could thus stay on in Istanbul. The Greek Patriarch is accepted by all Eastern Orthodox Christians as Ecumenical (in other words, universal) Patriarch, the most senior prelate in their church. However, as far as the Turks are concerned, the Patriarch is simply the religious leader of the Greek Orthodox community in the country. It was therefore agreed in Lausanne that he should be a Turkish citizen. This remains the official position of the Turkish government to this day. İsmet wanted the exchange of populations to be total, with no exceptions for Istanbul and western Thrace. This would have prevented much trouble in years to come. However, there was value also in preserving this most important link with the city's imperial (and, therefore, multi-ethnic) past. Life might have been simpler, but Istanbul would have been poorer without it. It was a reminder of the destiny of Istanbul as a world city. The preservation of some traces of its cosmopolitan past held the promise of a cosmopolitan future built on new foundations.
For the rest, most Greeks had already left Turkey, fleeing with the Greek army. But there were two Greek communities which had been cut off. Many of the Greeks who lived along the coast of the Black Sea had been deported to the interior, and for them resettlement in Greece came as a liberation. The other isolated community was made up of the Turkish-speaking Greeks of central Anatolia, an area known as Karaman (Caramania in Western literature) before the rise of the Ottoman state. These Caramanian Greeks ( _Karamanlı_ in Turkish; _Karamanlidhes_ in Greek) found it difficult to adapt to life in Greece, where they were mocked as Christians 'baptised in yoghurt'. They retaliated by referring to natives of Greece as 'Vlachs' – Romanian-speaking shepherds. Initial difficulties fostered survival techniques, and the descendants of the _Karamanlidhes_ gradually rose to prominence in their new homeland.
As for the Muslims who had lived in Greece during the centuries of Ottoman rule, many had migrated to Turkey before 1914, when independent Greece emerged in 1830 and then acquired Ottoman Thessaly in 1878, and most of Ottoman Macedonia in 1913. The exchange of populations of 1923 completed the process, except in western Thrace and for the small Turkish community in the Dodecanese islands, ruled by the Italians from 1911 to 1945.
The break in the Conference on 30 January 1923 was not an unmitigated disaster for the participants. But there were dangers, too. Rumbold, who returned to his post as High Commissioner in Istanbul, had to deal with fears that the Turks might seize the city by force. One contingency plan provided for the withdrawal of British troops from Istanbul to a fortified enclave in Gallipoli. In the fevered atmosphere of Istanbul, with its large population of panicky local Christians, British authorities found it hard to realise that Mustafa Kemal was a careful and patient statesman, averse to military adventures,
İsmet had his own difficulties, as critics in the National Assembly blamed him for making unnecessary concessions, which had not in the event saved the conference. Mustafa Kemal responded by touring the country to mobilise popular support. He returned to Ankara after he had outlined his reconstruction policy at the economic congress in İzmir, and made sure that the Assembly approved reasonable counter-proposals for the resumption of the Peace Conference.
As soon as the Allies agreed to send their delegates back to Lausanne, Mustafa Kemal prevailed on the Assembly to dissolve itself and fix a date for new elections. He then drew up a party manifesto and vetted all the candidates his embryonic party was to put forward. However, Rauf was still Prime Minister when the Peace Conference resumed in Lausanne on 23 April, exactly three years after the opening of the Turkish National Assembly in Ankara. Curzon, who had already secured all the main British interests, did not return to Lausanne, but left Rumbold in charge. İsmet went back to face French insistence on special treatment for its economic and cultural interests. The capitulations were again the most troublesome problem. Adamant that they should be abolished, İsmet advanced to his objective step by step. In his reminiscences he gives this account of his discussions with the French legal expert, Henri Fromageot:
His draft opened with the words 'To prepare the ground for the reform and abolition of the capitulations...'. 'No need,' I said, 'of preparing the ground... Why not say simply "the capitulations are abolished?"' 'You can't,' he replied, 'you must use legal language.' Well, I didn't master their legal language in nine months. Then one day Fromageot came to me with the same article. 'What do you want?' he asked. 'Write "the capitulations have been abolished, finished and done with"' I replied. 'All right,' he said. 'Have it your way.' 'What's happened to your legal language?' I asked. 'They have come to a decision to do away with the capitulations,' he replied. 'So they hadn't decided earlier? 'No they hadn't.'
One by one the other difficulties were disposed of. The French agreed that their bondholders should be repaid in francs at the current rate of exchange, and not in gold, as they had insisted earlier. The Ottoman public debt was apportioned among all the successor states. Letters were exchanged on conditions governing foreign schools, concessions granted earlier to foreigners, and so on. Now and then, İsmet made some temporary concessions: he agreed that Turkey would not increase its customs duties for five years, and that, also for five years, it would employ a few foreign advisers in the administration of justice and public health. Only one difficulty remained. It was clear to İsmet that there was no point in pressing Greece for reparations. The Greeks could not pay anyway. He offered to waive Turkish claims in exchange for a frontier rectification by which Turkey would gain Karaağaç, a suburb of Edirne (Adrianople), and the site of the city's railway station, which lay on the western (Greek) bank of the Meriç (Maritza/Evros) River. But back in Ankara, Rauf would not hear of it. Exasperated, İsmet threatened to break off negotiations and return to Ankara if the concessions he had made were not endorsed.
Mustafa Kemal, to whom he copied the telegram, knew that this was a subject open to demagogic exploitation. Rauf could say 'We cannot give up our claim of reparations against the Greeks who have wrecked our country. Not after our great victory.' He proceeded carefully to save Rauf's face, while İsmet waited impatiently for permission to sign the peace Treaty. Finally, on 19 July, Mustafa Kemal cabled to İsmet: 'I congratulate you most warmly on your success and await confirmation that the treaty has been signed.' Rauf did not associate himself with the congratulations. Nor did he meet İsmet when he returned to Ankara after the signing of the peace settlement. He resigned on 4 August. A week later, the newly elected Assembly held its first session and Mustafa Kemal's friend, Fethi (Okyar) became the new Prime Minister.
The Treaty of Lausanne was signed on 24 July 1923. It was an extraordinarily detailed document, running to 143 articles with 20 appendices and associated covenants. Agreement had not been easy, as Mustafa Kemal had realised from the start. 'The problems discussed round the peace table at Lausanne had not arisen during the last three or four years', he said. 'Centuries-old scores had to be settled.' But in the end the work was done solidly. Of all the treaties concluded after the First World War, the Treaty of Lausanne alone has survived. The Turkish insistence that it should be a treaty freely negotiated by all the parties has paid off. Even Greece, whose defeat it sealed, accepted it as the permanent basis for its relations with its neighbour, Turkey.
However, there were two absent parties at Lausanne, and these continued to nurse grievances against the Middle Eastern peace settlement. The first was Armenia, a signatory to the unratified Treaty of Sèvres. The Treaty of Lausanne made no mention of Armenia, whose frontier with Turkey had been decided by the 1921 Treaty of Kars. However, it would be Kurdish nationalism that posed the more serious threat to the Lausanne settlement.
The Middle East after Lausanne
The conclusion of the Treaty of Lausanne drew a certain line in the affairs of the Middle East. For the Turks it brought to an end the period of continuous warfare which had begun with the Italian aggression in Cyrenaica and Tripolitania in 1911. Their achievement should not be underestimated. Their only friend, Imperial Germany, had been defeated, and their fate had seemed to lie in the hands of their seemingly all-powerful enemies, all of which had ambitions at Turkey's expense. Out of these unpromising circumstances the Turks had through their own exertions and the clear-sighted leadership of Mustafa Kemal, successfully defended the integrity of their ancestral lands in Anatolia and eastern Thrace. As part of that transition they had acquiesced in the loss of their Arab subjects, but given the rising tempo of Arab nationalism they were none the worse for that, as the British were discovering. Able at last to pursue their own destiny, they were free to build a secular republic which would in time, Kemal believed, enable them to become the economic and social equals of the European states.
In May 1923, the British also recognised the Emirate of Transjordan as a national state being prepared for eventual independence, thus securing Abdullah's position. The signing of this agreement caused King Hussein to fly into one of his by-now characteristic rages. Already estranged from Feisal by his acceptance of the crown of Iraq and a truce with Ibn Saud, he now furiously denounced Abdullah. He believed Abdullah's deal with the British acknowledged Jewish claims in Palestine and more importantly, in his now extraordinarily egocentric view of the world, denied his own claims to rule Transjordan. Abdullah, unlike Feisal, was still strongly under the influence of his father and when he met him in January 1924 was so bullied and dominated by him that the British feared that the Emir might give up his claims in Transjordan in favour of Hussein. By now that was the last thing they wanted to see.
Hussein made one final blunder. In spite of his financial and military weakness, he took the opportunity provided by the abolition of the Caliphate by the Turkish National Assembly in March 1924 to declare himself Caliph. The action attracted support in Syria and in Transjordan where Abdullah canvassed on behalf of his father. However, in Iraq and Saudi Arabia, there was rejection and outrage. Ibn Saud's _Ikhwan_ warriors demanded that they be allowed to move against the Hejaz once and for all. In August 1924, Ibn Saud launched an offensive that rapidly took the towns of Taif and Mecca. Hussein abdicated in favour of his eldest son, Ali, though he continued to interfere from Akaba. Only Medina and Jeddah remained in Hashemite hands. Ibn Saud's forces blockaded Jeddah for more than a year. The foolishness of Hussein's decision to abandon his alliance with Britain was demonstrated when British military intervention routed an _Ikhwan_ raid aimed at toppling Abdullah in 1924. Ali might well have saved his regime, too. Instead, on 5 December 1925, Medina surrendered. This set off a mutiny amongst Ali's troops in Jeddah. Most of the Jeddah notables were by now willing to submit to Ibn Saud. Ali gave in to the inevitable and abdicated on 19 December 1925. The Kingdom of the Hejaz now ceased to exist. Ibn Saud and the _Ikhwan_ remained a threat to both Transjordan and Iraq. It was not until 1928 that Ibn Saud accepted the borders with Abdullah and suspicion and mistrust would continue down the years between the two leading dynasties of the Middle East.
Iraq under the Hashemites
The 1920s saw rapid political developments in Iraq after Feisal was finally confirmed on the throne. Britain was content to speed up the devolution of power, as it would reduce its financial commitment. The Anglo-Iraqi treaty of 1922 was followed by a supplementary agreement in 1924. The major external threat to the integrity of Iraq was Turkey's claim to the old Ottoman _vilayet_ of Mosul. However, in 1925, a League of Nations commission declared in favour of continued Iraqi control over the area and Turkey accepted this. The League of Nation's commission also recommended that the Kurds be granted limited self-rule. In the same year, an oil concession was granted to a consortium of British, Dutch, French and American oil companies to exploit the large discoveries around Mosul. Iraq received royalties for the oil that was extracted though its demand for an actual share of the company was rebuffed. This provided revenue to the government from the 1930s, reaching some £84.6 million a year by 1958.
Relations between the Iraqi leadership and Britain remained strained over the ending of the Mandate and over issues such as the introduction of conscription, especially between 1926 and 1929. The election of a Labour government in Britain in 1929 saw an increased appetite on the part of Britain to advance Iraqi independence. In 1930, a new Anglo-Iraqi treaty was signed. In return for rights to military bases and guarantees for economic and oil interests, the British government agreed to recommend the termination of the Mandate and to support Iraqi entry into the League of Nations. This was achieved in 1932 and Iraq became the first of the Mandates to achieve independence. British advisers were now employees of the Iraqi government and no longer able to veto government policy. The Prime Minister at the time of formal independence was Nuri al-Said. He proved to be the strong man of Hashemite Iraq. Right from the start he silenced opposition from those opposed to any continued British influence.
Feisal remained acutely aware of the underlying weakness of a regime that was dominated by Sunni Arabs in a land where they made up less than a quarter of the population. For this and for wider Arab nationalist reasons, Feisal continued to pursue wider pan-Arab ambitions. In short, he still wished to control Syria. If a union of the Fertile Crescent could be established with him at its head, the Shias and Kurds would be minorities in this wider entity. Furthermore, many of his key advisers and staff were Syrians who had come to Iraq. Perhaps the most important was the Yemenese-Syrian Sati al-Husri, who became Minister for Education. Part of the role of the embryonic school system of Iraq, which al-Husri developed, was to be 'a tool for nationalist indoctrination'. However, Feisal, well aware of previous setbacks, was careful not to push pan-Arabism too far. For instance, he was reticent about supporting the 1925 Druze-led revolt in Syria. Nonetheless, Feisal complained about provisions of the 1930 Anglo-Iraqi treaty because they seemed to preclude the unification of the Arab-speaking states of the Middle East. Feisal, the British High Commissioner Francis Humphrys noted in 1930, 'still hopes and works for the close federation under the rule of his House of all the Arab territories in Asia, and it seems that his intention is to endeavour to bring about first the union of Syria and Iraq'. The Sunni elite at the pinnacle of Iraqi politics envisaged Iraq as the Piedmont or Prussia of the Arab world which would drive forward the cause of pan-Arabism. One of the biggest political issues was conscription, which the king and the Sunni elite also viewed as a means of nation-building in their ethnically divided country. For this reason, the Shias and Kurdish populations were strongly opposed, as were the British who saw it as both financially and ethnically destablising.
There were other claimants for the mantle of 'leader of the Arab world'. Feisal's brother, Abdullah, who had consolidated his rule in Transjordan by the end of the 1920s, envisaged a role for himself in Syria. Indeed, as we have seen, he had stopped in Transjordan on his way to confront the French in Syria in 1920 and then hung on there in anticipation of being called to take the throne of Syria. He saw himself as the leader of any Hashemite restoration in Syria. His prospects were improved by the death of Feisal I of Iraq after a short illness in 1933. By then the Hashemite monarchy in Iraq was running into increasing difficulties, including sectarian problems with Shias, Kurds and the tiny Assyrian community. The last named were crushed with great brutality in a pogrom in 1933. The army was regularly called upon to put down tribal revolts in the Shia areas in the south of Iraq with the same heavy-handedness, especially after the introduction of conscription in 1933. This gave the army leadership increasing political influence.
In 1936, after Yasin al-Hashimi, the Prime Minister, began to demonstrate increasing authoritarian tendencies, General Bakr Sidqi, encouraged by al-Hashimi's enemies, staged a coup. King Ghazi, Feisal's young son and successor, did not especially object to the coup once the monarchy was not threatened. In any case, Ghazi tended to be in sympathy with the nationalist officer corps and lacked his father's political realism. Most importantly, the coup was a huge blow to constitutional rule in Iraq and signalled the beginning of violent faction-fighting among the Sunni elite. Sidqi was assassinated in August 1937 and the older establishment figures such as Nuri al-Said and Rashid Ali returned to positions of power. However, from 1937 until 1941, despite the holding of elections, the arbiter of power in Iraq was a nationalist army clique known as the 'Golden Square'. Civilian governments fell if they incurred the displeasure of this group, whose pro-Nazi and anti-British views were greatly heightened by the Arab revolt in Palestine between 1936 and 1939.
Atatürk and the new Turkey
Turkey's major setback at Lausanne had been the failure to gain Mosul with its important oilfield, which was retained in the British-Mandated country of Iraq, where it was to remain. Would Turkey have been better off if it had regained Mosul in 1923? Its budget would have benefited from the revenue of the Kirkuk oilfields. But it would have had to administer many more Kurds, as well as more Arabs. The Ottoman Empire had practised multiculturalism, but this had hastened its demise. None of the successor states of the Ottoman, Austro-Hungarian and Russian Empires in eastern Europe and the Balkans followed the sort of multicultural policies which are recommended today. Mustafa Kemal recognised the problem, but he had other priorities. The modernisation of Turkey came first, and for its sake he opted for good relations with all the Great Powers.
The failure of the Treaty of Lausanne to award Mosul to Turkey was the main objection raised by the opposition when the newly elected Assembly debated ratification on 23 August. But the opposition had been reduced to a handful of deputies, and the Treaty was overwhelmingly approved. The immediate need was to end the Allied occupation of Istanbul, which was to follow ratification. On 2 October Allied occupation troops left Istanbul. Four days later Turkish troops entered the city, while the last Allied soldiers left Gallipoli. On 13 October, the Assembly voted to move the capital of the Turkish state from Istanbul to Ankara.
The old Ottoman capital was demoted to the status of a provincial city. Civil servants had to move to Ankara. Trade suffered, as the transit of goods to and from Russia was reduced to a trickle after the Bolshevik revolution. The city was impoverished by the departure of many foreigners and indigenous non-Muslims. The new regime was not popular in Istanbul. Sensing this, Mustafa Kemal kept away from the old capital, which he had last seen in May 1919. It was only in June 1927, after he had consolidated his personal power, that he went back to Istanbul on the first of what became his regular summer trips to the city. By then the first statue to Mustafa Kemal had been erected on Seraglio Point at the entrance to the harbour.
The Treaty of Lausanne is the founding document of the Turkish national state. But the form, character and institutions of that state had yet to be decided when it was concluded. İsmet had signed it as the representative of the awkwardly named Government of the Grand National Assembly of Turkey. Soon the country was to acquire its new name. On 28 October 1923, Mustafa Kemal invited a group of supporters to dinner in his residence at Çankaya, on the outskirts of Ankara, and told them without further ado: 'Tomorrow we will proclaim the Republic.' The following day a bill to this effect was tabled and approved by the Assembly after a brief discussion. Elected first President of the Republic, Mustafa Kemal appointed İsmet as his Prime Minister, while Fethi moved over to become Speaker of Parliament. The citizens of Istanbul, including the government's representative Re'fet, learnt of the decision only when a 101-gun salute greeted the birth of the Republic on 29 October.
The circle of Mustafa Kemal's companions in the War of Independence gradually fell apart. Rauf was the first to move away when he was overridden over the terms of the Treaty of Lausanne. The sudden proclamation of the Republic cost the friendship of all those nationalist commanders who had not been consulted beforehand. They believed that they were joint authors of the victory in ' _Our_ War of Independence' – the title given to his memoirs by Kâzım Karabekir, the commander who first welcomed Mustafa Kemal in Anatolia and stood by him when he was dismissed by the Sultan. They wanted, therefore, a voice in the shaping and the government of the state, and they demanded this in the name of democracy. As an opposition journalist argued in Istanbul, the proclamation of a republic was not sufficient guarantee of the freedom of citizens. Republics could harbour dictators as in Latin America. Mustafa Kemal responded by hauling opposition journalists before a revolutionary court in Istanbul. They were acquitted, having been warned that criticism would not deflect Mustafa Kemal from the course he had chosen. In 1927 he offered this explanation for the defection of his original supporters: 'In the development of the nation's life which has led to today's republic and its laws, some of the travellers who had started together on the road of national struggle began to resist and oppose me as we crossed the limits of what they could comprehend or sympathise with.'
The radicalism of Mustafa Kemal's project was indeed hard for them to accept. The nationalist commanders who had sided with Mustafa Kemal had no particular love for the monarchy or for established religion. They were not reactionaries or backward-looking, as was claimed against them. They too admired the achievements of the West. But they were not prepared to sever all links with the past and alter their whole way of life. They were not democrats, but they wanted to have a voice in government. Mustafa Kemal was prepared to listen to other people's opinions. But he insisted that his decision should be final. Provided his will prevailed, he did not interfere with the administration. As a successful military commander, he knew how to choose subordinates capable of carrying out his orders, and how to delegate.
Mustafa Kemal's determination did not exclude prudence. Before proceeding with his cultural revolution in Turkey, he made sure that the army would remain loyal to him. The nation's will was sovereign, and the peasant, he declared, was the true master of the country. But power was in the barrel of a gun. Mustafa Kemal was lucky in that he found a respected professional soldier to whom he could entrust the command of the armed forces. Field Marshal Fevzi Çakmak was a German-trained battle-tried commander, who had started by opposing Mustafa Kemal, but having resolved to side with him, proved a totally loyal Chief of the General Staff during the War of Independence and then to the end of Kemal's life. The fact that he was a pious Muslim did not count against him. Fevzi Pasha was not an enthusiast; he professed the patriotic faith of regimental chaplains. When Mustafa Kemal died, opponents of İsmet's succession wanted to put him up as the candidate allegedly favoured by the first President. He declined, preferring to stay in command of the armed forces. But in the end Fevzi clashed with İsmet, objecting to being retired at the age of 68. He wanted to go on for ever.
On 15 February 1924, Mustafa Kemal and İsmet went to İzmir to watch army manoeuvres and meet military commanders. It was at this meeting that the decision was taken to abolish the Caliphate, just over a year after it had been set up as a separate institution. It had served its purpose of softening the blow of the abolition of the monarchy, and had no place in the new Republic, where it was bound to attract dissidents. A letter from the Aga Khan the previous November pleading for the preservation of the office was presented as an example of the foreign interference which it invited. But Mustafa Kemal had a wider purpose in mind. The presence of the Caliph in Istanbul was incompatible with the secularisation of the Turkish Republic which he was determined to introduce.
On 3 March 1924 a member of the Assembly who had received a clerical education was chosen to present a wide-ranging bill, going beyond the abolition of the Caliphate. Together with the Caliph Abdülmecid, all members of the Ottoman dynasty were to be exiled immediately. The bill was, of course, approved, and the same night the Caliph and his family were taken by car to a station outside Istanbul and put on a train to Europe. Any supporters he had in Istanbul were not given a chance to demonstrate. Abdülmecid was never to see the country again. He died in Paris in August 1944. Surviving members of the dynasty were allowed back after many years, princesses first in 1952, followed by male descendants in 1974. They enjoy social prestige, but do not attract political interest. The achievements of the Ottoman era, decried in the first years of the Republic, are now widely recognised. 'Ottomania' or Neo-Ottomanism is fashionable in the arts, architecture and cooking. But there never has been a movement favouring the restoration of the monarchy in Turkey.
The abolition of the Caliphate was accompanied by the removal of all religious influence on public policy and by the imposition of state control over religious practices. _Madrasahs_ were banned. Religious education in lay schools was restricted and discouraged until it disappeared altogether. The Ministry of Islamic Canonical Affairs and Pious Foundations, which had replaced the office of the Sheikh-al Islam, was abolished and replaced by a Department of Religious Affairs attached to the Office of the Prime Minister. This department employed and supervised mosque personnel, and laid down the law on practice and worship. The religious institution had always been under the control of the Ottoman state, but it used to enjoy some autonomy and could at times influence public policy. Now it was totally nationalised.
The nationalist commanders who were excluded from power found a popular cause in public disquiet at the unfolding cultural revolution. Forced to choose between politics and a military career, some of Mustafa Kemal's original companions resigned their commissions and formed an opposition party. They named it the Progressive Republican Party to emphasise that they were not counter-revolutionaries, reactionaries or monarchists. But the promise in the party programme that they would respect religious feelings and beliefs made plain their opposition to the radical transformation of society. In response, Mustafa Kemal adopted a somewhat softer approach. İsmet, known as a hard-line supporter of Mustafa Kemal's radical project, was replaced by the more conciliatory Fethi.
The let-up was short-lived. In February 1925, a Kurdish sheikh raised the standard of rebellion in the east. As the revolt spread, Fethi was seen as hesitant and ineffective. He was replaced by İsmet, who this time stayed in power for over a decade. The suppression of the Kurdish rebellion was followed by the banning of the opposition Progressive Republican Party, and by an acceleration of Mustafa Kemal's reform programme. All Dervish orders were banned and their shrines closed. Over the next few years, modernisation became synonymous with Westernisation. European laws were introduced wholesale: the Swiss civil code, which put an end to polygamy, German commercial law, the Italian penal code. In November 1925, the fez, which had been for over a century the distinctive head-gear of Muslim gentlemen, was banned, and Muslims were ordered to wear European-style hats or peaked caps, both of which are inconvenient when Muslims press their heads against the ground during prayers. A month later the European calendar and European time-keeping replaced the Muslim calendar.
Wilder opponents now took to plotting. In June 1926 an attempt to assassinate Mustafa Kemal in İzmir was narrowly averted when one of the conspirators gave the game away. The discovery led to a wave of repression. There was a loose connection between the conspirators and figures of the old CUP who had not accepted Mustafa Kemal's leadership. One such was Cavid, the wartime Ottoman Finance Minister who had advised the Turkish delegation at Lausanne. Critical as he was of Mustafa Kemal, he was not involved in the attempt on his life. Nevertheless, he was hanged along with the conspirators. It was the high point of state terror.
With all his opponents silenced and the country pacified, Mustafa Kemal could now give his account of the events which had led to the proclamation of the Republic and the subsequent cultural revolution. He did so in October 1927 in a speech to the convention of his Republican People's Party, by then the only party allowed in the country. The speech took six days to deliver. It started with the words, 'On the 19th day of May of the year 1919, I landed in Samsun.' Mustafa Kemal's life story had become the history of modern Turkey.
More radical changes followed. In April 1928, the reference to Islam as the official religion was dropped from the Constitution. In November that year the last important link with the Muslim Ottoman past was severed when the Latin alphabet replaced the Arabic one. The new alphabet was better suited to the phonetic structure of the Turkish language, and the change was made all the easier by the fact that the vast majority of the population was illiterate, so that most Turks learnt to read and write for the first time in the new script. Other changes were symbolic: Turkish women were given the vote, and some were elected or rather nominated town councillors and then Members of Parliament in uncontested elections. More importantly, the government encouraged career women. There had long been women teachers in girls' schools. Now there were women teaching in mixed schools and universities, practising medicine and law. The number of professional women grew gradually, although to this day the proportion of women employed outside the home in Turkey is low by European standards. Unlike the fez and clerical dress, the veiling of women was never banned. But it was discouraged and all but disappeared, the veil giving way to headscarves among older women in the cities and, more generally, in the countryside.
In 1934, after a law had been passed that all Turkish citizens should choose surnames in addition to the given Muslim names by which most of them were known, Mustafa Kemal was given the name of Atatürk, Father of the Turks, by the Assembly. The surname was restricted to him alone; it could not be used by his surviving sister or his adopted daughters. His marriage, which was dissolved in 1924, was childless.
Just as the reforms were being completed in Turkey, the settlement put in place after the First World War was beginning to break down in Europe. The first threat came from the Italian dictator Benito Mussolini. Then, in 1933, Hitler came to power in Germany. Proclaiming 'peace at home and peace in the world' as the principle of his foreign policy, Mustafa Kemal sided with the Western democracies in defence of the status quo. This allowed Turkey to win back two concessions it had made at Lausanne. In July 1936, a convention was signed at Montreux, abolishing the international commission of the Turkish Straits, allowing Turkish troops back into what had been the demilitarised zone of the Straits, and making Turkey responsible for applying rules for navigation through them. Then, on the eve of the Second World War, in exchange for a treaty of alliance with France and Britain, Turkish troops entered the district of İskenderun (Alexandretta), which had been administered as part of French-Mandated Syria. Renamed the province of Hatay (after Cathay, the area inhabited by Turkic tribes outside the Great Wall of China), the district became part of Turkey some six months after the death of Atatürk on 10 November 1938, at the age of 57. His work of laying the foundations of modern Turkey was complete. The country's subsequent history has shown that the foundations were solid.
The Palestine Mandate
With the formal confirmation of the League of Nations Mandate in 1922, the prospects for Zionism rested, above all, on how the National Home fared in Palestine. In 1922, the British estimated the population at 589,000 Muslims, 83,000 Jews and 71,000 Christians, who were mostly Arabs. By 1925, when Samuel's period as High Commissioner came to an end, the Jewish population had grown to 108,000, but this proved to be a boom year as far as immigration was concerned. That year some 33,801 Jews came into Palestine, while 2,151 left. Economic conditions in the country were far from easy, and in 1927 there were only 2,713 Jewish immigrants, whereas 5,071 left the country. Even so, the National Home was beginning to make progress. By 1929, the population of Tel Aviv had grown to 46,000, and it was acquiring critical mass as a Jewish city. Much of the organisation of the Jewish community turned on the powerful trade union movement, the Histadrut, or General Federation of Jewish Labour, which had been formed in 1920. Elected to its council in November 1921, Ben-Gurion became its driving force, rapidly emerging as the dominant personality in the _Yishuv_ , as the Jewish community in Palestine was called. As his stature grew, it became evident that in time he would come to rival, and possibly eclipse, Weizmann.
The highlight of this period for Weizmann undoubtedly came in April 1925 with the inauguration of the Hebrew University on Mount Scopus, the project he had lovingly nurtured for nearly a quarter of a century. The Weizmanns were accompanied to Palestine by Balfour, at the age of 77 and a poor sailor, paying his first visit to the country with which his name had come to be associated. The inauguration ceremony on 1 April was attended by many Jewish dignitaries, including Dr Judah Magnes, who was to be its first Chancellor and later President, but whose work on behalf of Arab-Jewish cooperation in the government of Palestine soon led to bitter recriminations by Weizmann, and alienated him from the mainstream of Zionism. Samuel and Allenby were also present, but inevitably the spotlight fell on Balfour. As expected, the author of the Declaration was rapturously received by a crowd of some 10,000, as he was in Tel Aviv and the Jewish settlements he visited. The Arabs of Palestine, on the other hand, greeted his arrival with a one-day strike, but much worse was to follow when he attempted a somewhat ill-advised visit to Damascus. A crowd of about 6,000 advanced on his hotel and had to be dispersed by the French army, leaving three dead. Balfour's visit to Syria ended almost as soon as it began. He was no better loved by the Arabs than he had been by the Irish, it seemed.
The comparative lull which settled on Palestine for much of the 1920s ended abruptly in 1928. Samuel's tenure as High Commissioner finished in 1925. He was succeeded by Field Marshal Lord Plumer of Messines, one of Britain's more successful commanders in the First World War. Between them, Samuel and Plumer managed to keep the political situation relatively calm, but political advance in Egypt, Iraq and Syria led to the Arabs of Palestine feeling left behind. Tension came to a head on 24 September 1928, Yom Kippur, the Jewish Day of Atonement, and it derived from the complex agreements and conventions which had come to surround the Western Wall. For centuries Jews had been allowed access to it, provided that nothing was erected on the pavement, and the British felt obliged to maintain this position. When the Jews put up a screen to separate men from women, the police forcibly took it down. In an atmosphere of increasing tension, each side protested to the League of Nations.
This incident, disturbing as it was, was but the portent of a much more serious sequence of events the following year. The immediate prelude, perhaps, was the culmination of negotiations Weizmann had been pursuing for a number of years, that is, the creation of an enlarged Jewish Agency, which had been provided for in the terms of the Mandate. This was at last agreed at the Sixteenth Zionist Congress in Zurich in the summer of 1929. The Jewish Agency was to be representative of both Zionist and non-Zionist Jews, with Weizmann as its President. In any other circumstances, this would have marked a new high point in his career, but within days any sense of satisfaction he might have felt was shattered by events in Palestine. On 15 August 1929, there was a Jewish procession to the Western Wall; the next day the Arabs followed suit. Then, from 23 to 29 August, there were attacks on Jews across Palestine. In all, 133 Jews were killed and 339 wounded, while 116 Arabs were killed and 232 wounded, most of them by the security forces. Particularly disturbing was the fact that these attacks took place in the ancient Jewish holy cities of Hebron, where some 60 people were killed, and Safed. Jews had lived there for generations, untouched.
The Commission of Inquiry into these events, chaired by Sir Walter Shaw, reported its findings on 31 March 1930, just days after Weizmann had mourned the death of Balfour. The subsequent report pointed to the fundamental differences in outlook between Arabs and Jews, but identified the basic reason behind the outbreak as being Arab fears over the level of Jewish immigration and the amount of land purchase. Shaw's recommendations were that the government should define what it meant by safeguarding the interests of the non-Jewish communities; revise the regulation of immigration, which he described as excessive; institute an inquiry into methods of cultivation and regulate land policy in the light of this; and emphasise once again that the Zionist Organisation could not take part in the government of Palestine.
Weizmann had for some time sensed the hostility of Ramsay MacDonald's Colonial Secretary, Lord Passfield, better known as Sydney Webb, a veteran socialist perhaps best remembered for his work in founding the London School of Economics, and who, with his wife, subsequently wrote a highly sympathetic account of Stalin's Russia. The conclusions of the commission did not, therefore, come as a complete surprise to Weizmann, unpalatable though they were. Receiving the report in advance, Weizmann arranged a meeting with MacDonald and Passfield, at which he was joined by three prominent colleagues, Lord Reading, the former Viceroy of India, Lord Melchett, formerly Sir Alfred Mond, and the American banker Felix Warburg. MacDonald apparently confided his belief that Shaw had exceeded his brief, promising to make a statement to the House of Commons reaffirming British commitment to the National Home, which he did, being supported by Baldwin on behalf of the Conservatives and Lloyd George for the Liberals. Weizmann was also in contact with Baldwin and Lloyd George, and, then, on 11 April the _Manchester Guardian_ published Weizmann's lengthy riposte to Shaw, written in his capacity as President of the Jewish Agency. Reasserting that the Jews were in Palestine as of right, he responded that to restrict immigration and land purchase would set at nought the creation of the National Home.
The government announced a further commission, under Sir John Hope Simpson, to carry forward the inquiry Shaw had recommended. Weizmann had hoped instead for the chairmanship of Smuts, whose sympathies he knew, and at a rather bitter meeting with MacDonald and Passfield he denounced the latter as a liar for reneging on a promise that he could meet Hope Simpson prior to his departure for Palestine. News that immigration into Palestine had been suspended was a further unwelcome indication of the drift of events, followed, as it was, by amendments to land legislation, and restrictions on the work of the Jewish Agency.
The best that Weizmann could do in the circumstances was try to anticipate through contacts with Passfield what the government's likely reaction might be. By the beginning of October he believed that there would be a five-year ban on land purchases, limits on Jewish immigration, and a loan to settle landless Arabs. His rather pessimistic conclusion was that Passfield, as he had recently done in Kenya with the Africans, would assert the rights of the Arabs as the indigenous population of the country. On 13 October, he wrote to Passfield and MacDonald protesting that any prohibition on land purchases would undermine the National Home, and acknowledge that the Arabs had the greater claim to Palestine. He argued that such a policy would run counter to the Balfour Declaration and the provisions of the Mandate.
Hope Simpson's report, published on 21 October and seen by Weizmann in advance, threatened to undermine one of the main planks of the Zionist platform; namely, that there was sufficient cultivable land to accommodate them without prejudice to the Arabs. Hope Simpson thought not, concluding that until there was further development of Jewish lands and better cultivation of Arabs lands, there was no room for any more settlers if the standard of living of the Arab cultivators were to be maintained. More optimistic from the Zionist perspective was his view that through development the countryside could not only sustain the present population, but accommodate at least an additional 20,000 families of settlers. The report was accompanied by a Statement of Policy which accepted Hope Simpson's figures and conclusions, but pointedly ignored his view that with development the land could absorb more Jewish immigrants. The Passfield White Paper, as it soon became known, came as a devastating blow to the Zionists, and to Weizmann in particular, for whom cooperation with Britain had been the sine qua non of Zionist strategy. His response was that the White Paper dealt a serious blow to prospects for the National Home, and was contrary to the policy set out in the 1922 White Paper. Complaining to Passfield that by issuing a Statement of Policy the government had precluded negotiations, he announced his resignation as President of the Zionist Organisation and the Jewish Agency. To MacDonald, more in sorrow than in anger, he lamented the failure of his policy of working in harmony with the British government.
Weizmann had long castigated the British administration in Palestine for being pro-Arab, but now he had to contend with the Colonial Office as well. As he began his lobbying campaign against the White Paper, he was probably correct in his suspicion that MacDonald was more sympathetic than Passfield. As well as mobilising support in Jewish circles, he enlisted his old friends Amery and Smuts, and the Conservatives Baldwin and Austen Chamberlain also joined in criticising the White Paper. MacDonald sought to defuse the issue by appointing a Cabinet Committee on Palestine, which would examine the question in consultation with the Jewish Agency. Despite his resignation as President, Weizmann co-operated fully throughout the winter of 1930/1, emphasising that the National Home could not be curtailed at its current level, and that the Jews had been the victims in 1929. His reward came on 13 February 1931 in the form of a letter addressed to him from MacDonald, which, while it did not rescind the White Paper, substantially qualified it. In his letter, MacDonald challenged the view that the White Paper 'foreshadows a policy which is inconsistent with the obligations of the Mandatory to the Jewish people'. Emphasising that the Mandate put obligations on Britain towards both Arabs and Jews, he denied that there was any intention to end Jewish land purchases. On the even more vexed question of immigration, he reiterated the long-standing policy of absorptive capacity, confirming that the government did 'not contemplate any stoppage or prohibition of Jewish immigration in any of its categories'. To the Arabs the White Paper had been replaced by the 'Black Letter'.
Once again, Weizmann had succeeded, but this time rather against the odds, and the whole episode had raised questions about his reliance on British good intentions. His critics, especially the Revisionists, the organisation Jabotinsky had formed after falling out with Weizmann in the 1920s, assailed him for accepting a letter rather than another White Paper. This accusation was as unjust as it was wrong-headed, since MacDonald's letter opened up the possibility of immigration into Palestine just as the Jews of Europe were to need it most. The sequel was that at the International Zionist Conference in Basle in July 1931, Weizmann's opponents managed to pass a motion of no confidence in him. It was the lowest point in his political career thus far.
After such a bitter rebuff, it is hardly surprising that Weizmann turned for consolation to the other passion of his life, chemistry. Although he did not cut himself off entirely from Zionism, he built a small laboratory in London, and then another opportunity to revive his scientific career presented itself. This opening was the Daniel Sieff Research Institute at Rehovoth, funded by Weizmann's friend Israel Sieff in memory of his son, and inaugurated in April 1934. Here the Weizmanns built their home in Palestine, a classic piece of modernist architecture, designed by Erich (later Eric) Mendelsohn, one of Germany's leading architects, who had recently left the country. After the tribulations he had just come through, this might have seemed an idyllic interlude in Weizmann's life when he could turn to domestic and scientific matters, except for the reason Mendelsohn had left Germany: the coming to power of Adolf Hitler on 30 January 1933.
The impact of Hitler and the Arab Revolt in Palestine
Adolf Hitler, an Austrian who had absorbed the anti-Semitic atmosphere of pre-1914 Vienna and who had harped on the so-called injustices of the Versailles settlement, was barely in power before he began the systematic exclusion of Jews, hitherto amongst the most patriotic of Germans, from national life. What followed hardly needs repetition: the Nuremberg Laws of 1935, the atrocities against the Viennese Jews which followed the Austrian _Anschluss_ in 1938, the _Reichskristallnacht_ of November 1938, culminating in Hitler's Reichstag speech of 30 January 1939 in which he foretold the fate of the Jews in the event of war, a conflict he was about to start. The result was an exodus of Jews from Germany and elsewhere in Europe. Since the United States was no longer an option for most of them as a result of the ethnic quotas imposed in the 1924 Immigration Act, Palestine was the obvious choice, made possible by Weizmann's recent intervention with MacDonald. The figures speak for themselves. By 1938, Jews numbered some 401,600 out of a total population of 1,415,700. Moreover, many of these immigrants were middle-class urban Jews who brought with them the cultural values of Central Europe. Tel Aviv was now a major urban centre of 150,000 people. Emblematic of the changing nature of the _Yishuv_ was the arrival in 1936 of the legendary Italian conductor Arturo Toscanini to conduct the fledgling Palestine Orchestra, which had recently been founded largely from musicians dismissed in Germany, and, as the Israel Philharmonic, would later become one of the world's leading orchestras. The concert was attended by Weizmann.
This transformation of the National Home provoked the Arabs into action. On 15 April 1936, a Jew was killed near Nablus and the Arab Revolt began. It lasted until 1939, tying down British forces just at the time when the ambitions of Germany, Italy and Japan were becoming increasingly ominous. The Arab Higher Committee was formed, led by Haj Amin al-Husayni, who was now clearly the leader of the Palestinians. The government's response was to send yet another commission of inquiry, chaired by Lord Peel, sadly ill with cancer, charged with making recommendations that might remove the grievances of both parties. Its most dynamic member was Reginald Coupland, Beit Professor of Colonial History at the University of Oxford, who had already analysed nationality problems in Ireland, Canada and South Africa. There then developed a fascinating dynamic between Coupland and Weizmann, who had returned to the presidency of the World Zionist Organisation in 1935. On 23 December 1936, when Weizmann was giving evidence on behalf of the Jewish Agency, Coupland threw out the suggestion of creating what he called two big areas in Palestine. Then, on 8 January 1937 he developed this concept by setting before Weizmann the idea of partition, which would lead in time to independent Arab and Jewish states. What underpinned Coupland's thinking was his conclusion that Arab civilisation was Asian, while that of the Jews was European, and, that, as a result, their national aspirations were incompatible. Weizmann grasped the significance of what Coupland was saying. What was being suggested was a state, not a National Home, albeit in part of Palestine. He was also aware that despite the growth in Jewish numbers, the Arab population was also expanding, and that the prospect of a Jewish majority was some way off. He also knew that partition would meet with resistance in Zionist ranks, especially since it was felt that the creation of Transjordan had already truncated the National Home.
At the end of January 1937, the two men consulted privately at the agricultural settlement of Nahalal, where Weizmann became convinced that partition offered the best way forward. When the Royal Commission reported on 7 July to the Colonial Secretary, none other than Weizmann's old friend Ormsby-Gore, it was in favour of partition. Rather like Caesar's Gaul, Palestine was to be in three parts: a Jewish state along much of the coast and Galilee; an Arab state in the interior; and Jerusalem retained as a British enclave with a corridor to the coast. This proposal was accepted by the Cabinet and in Parliament, though criticised in debate by the veteran pro-Zionist speakers Lloyd George, Churchill and Samuel, who saw partition as contrary to the Mandate. Their reservations were more than echoed in influential sections of the Zionist movement, as Weizmann had known from the start they would be.
The dispute within Zionism had unmistakable echoes of the 1903 'Uganda Offer' crisis, except that this time Weizmann was sitting in Herzl's seat, and it came to a head at the Zionist Congress in Zurich in August. Weizmann was supported by the bulk of European and Palestinian representatives, including Ben-Gurion, who had been initially opposed to partition. The opposition was spearheaded by Ussishkin, but the real threat came from the United States, whence Weizmann's old feud with Brandeis came back to bite him. Brandeis did not attend the Congress, but at a preparatory meeting with Felix Frankfurter, Rabbi Stephen Wise and the lawyer Robert Szold, partition was rejected. Wise, however, was not in Europe for long before the realities of the Jewish position in Palestine were impressed upon him, and his position changed. He was the prime architect of the compromise strategy that the Congress approved on 10 August 1937; namely, that the Zionists should reject the Peel Commission recommendations, but should negotiate with the British government for a more favourable scheme. While this formula left the door open for partition, it was a lukewarm endorsement, which was ultimately unhelpful to Weizmann, especially since on 11 September an Arab National Conference at Bludan in Syria totally rejected the scheme. It left the British government with the obvious question of whether they should press ahead with a partition plan neither side seemed really to want.
Buoyed up by an assurance from Ormsby-Gore that in a year's time he would be preparing for the establishment of a Jewish state, Weizmann left for Palestine, but the Colonial Office was a junior player compared with the Foreign Office. With war threatening in Europe and the Mediterranean, the last thing the Foreign Secretary, Anthony Eden, and his Prime Minister, Neville Chamberlain, wanted was a hostile Arab world. At a Cabinet meeting on 22 December 1937, it was decided to send a commission under Sir John Woodhead to explore the implementation of a partition scheme, but with a confidential letter to the effect that he was free to pronounce against it. His report duly did so on 9 November 1938, the day the _Reichskristallnacht_ was unleashed upon the Jews of Germany. All Weizmann's attempts to influence the commission came to nothing, his view that its purpose had been to justify a course of action already determined being quite correct.
If Weizmann felt that his relations with the British government had touched their nadir, much worse was to follow. In May 1938, Ormsby-Gore, whose pro-Zionism had become an inconvenience, was replaced at the Colonial Office by Malcolm MacDonald, son of the late Prime Minister. Even before Woodhead concluded his work, MacDonald had decided upon a conference to discuss the future of Palestine. The conference, held at St James's Palace, opened on 7 February 1939, and ended on 15 March, just as Hitler was taking over the rump of Czechoslovakia which Chamberlain thought he had saved at Munich the previous September. The conference was predictably inconclusive, but during its course, through, it seems, a clerical error, Weizmann became aware of what MacDonald was planning. There would be an independent Palestine, and limited Jewish immigration for the next five years, but after that immigrants would only be allowed with Arab consent. At the closing session, which Weizmann and Ben-Gurion did not attend, MacDonald outlined his proposal, which confirmed what Weizmann had already discovered, but in greater detail; namely, that Palestine would become independent in ten years, and that 75,000 Jews would be permitted to enter over the next five years, but after that only with Arab agreement. This meant, quite simply, that the Jews could only ever be a minority in the country. These, in essence, were the policies which MacDonald went on to unveil in his White Paper of 17 May 1939. They were rejected by the Palestinian Arabs, despite the extent to which the White Paper favoured them, but they proved enough to help Britain's friends, Abdullah of Transjordan, Ibn Saud of Saudi Arabia and Nuri al-Said in Iraq, keep the Arab world largely quiescent in the Second World War.
The Zionist Congress that convened in Geneva on 16 August 1939 as Europe teetered on the edge of war could not have been other than a bleak affair. While there was no question but that the Jews would support Britain in war, the Congress denounced the White Paper in anguished terms. As it ended on 24 August came news of the Nazi-Soviet Pact, the cynical agreement between two hitherto bitter ideological foes, which opened the way for Hitler's imminent attack on Poland. The German attack on 1 September triggered the Anglo-French declaration of war two days later, but this did nothing to save Poland or the millions of Polish Jews who were now at Hitler's mercy. Hitler's domination of the continent was extended with his successful campaign in western Europe the following year and then by his invasion of the Soviet Union on 22 June 1941. By the autumn of that year, Germany controlled what had been the Pale of Settlement, with the direst of consequences for its Jewish inhabitants.
The Middle East at war
Italy's entry into the war in June 1940 meant that the Middle East became an area of critical concern. It was, therefore, fortunate for the British that in August 1936 they had been able to conclude a treaty with Egypt which allowed them the use of key facilities in wartime, safeguarding strategic routes through the Suez Canal as well as access to oil supplies in the Gulf. By June 1942, German and Italian forces were a mere 60 miles (97 kilometres) from Alexandria, and were only halted by General Sir Claude Auchinleck at the First Battle of El Alamein. At the same time, the German advance into the Caucasus was threatening the British position in the Middle East from the north. Once American resources were fully deployed, the Persia-Iraq Command became a major Allied supply centre for the Soviet war effort, offering an alternative to the hazardous Arctic convoys. Before then, however, certain events in Iraq had to be played out.
In 1939 Ghazi died in a car crash. His successor was his young son, Faisal II. Abdulilah, son of Ali ibn Hussein the last King of the Hejaz, became regent. He was by instinct pro-British. Consequently, tensions between the royal family and the nationalist officers in the army grew from the outbreak of the Second World War. These were exacerbated by British demands for full Iraqi compliance with their obligations under the 1930 treaty, including the breaking of diplomatic relations with the Axis Powers. In the spring of 1941 Abdulilah was forced to flee after months of political infighting culminated in the seizing of power by the nationalist Rashid Ali, who enjoyed the confidence of the 'Golden Square'. The British, convinced of a German-Italian plot to drive them from the Middle East, decided to secure their positions in the region. In a matter of a few weeks in late April and May 1941, British forces landed at Basra and toppled the Rashid Ali regime. In June, they moved against Syria and expelled the Vichy Governor. A second British occupation of Iraq followed and a pro-British ruling group around the regent was re-installed. Those who had opposed the British, such as Rashid Ali, found themselves exiled and excluded from power. His supporters who stayed behind were executed or imprisoned. Nuri al-Said backed the British and became the dominant political figure in post-1941 Iraq. He viewed the British connection as an important support for the Hashemite monarchy in Iraq and its wider ambitions in the Middle East.
In sharp contrast to the hostilities being waged all around her, Turkey was at peace. On her borders were the British in Iraq, the Vichy French in Syria, Hitler's ally Bulgaria, the Soviet Union, and after the fall of Greece in 1941, the German army. Still emerging as a nation state, Turkey was in no military or economic position to match the combatant powers, especially after a devastating earthquake in December 1939. Even so, it was a major achievement of the President throughout the period, Atatürk's long-standing colleague İsmet İnönü (the surname he adopted to commemorate his victory over the Greeks near the village of that name), to steer the country's neutrality in the face of many pressures. His success was similar to that of Eamon de Valera in Ireland. In each case geographical realities meant pragmatic choices had to be made, and just as de Valera allowed British aircraft to fly over Irish territory, German military shipping passed through the Straits. Britain's desire to have Turkey's active participation in the war was signalled by Churchill's visit in January 1943, but İsmet İnönü played for time. The Turkish leader did not make de Valera's gesture of offering condolences on the death of Hitler. Instead, on 23 February 1945 Turkey declared war on Germany, thus ensuring its place at the forthcoming San Francisco conference which was to set up the United Nations Organization, and hence chart the diplomatic shape of the post-war world. Turkey thus emerged intact, unscathed, and on the winning side.
The Holocaust
The genocidal nature of Hitler's intentions towards the Jews became clear in the course of 1941, prior to which the Jews in occupied Poland, the General Government as it was called, had been confined to ghettos, principally in Warsaw, Cracow, Lodz and Lublin. On 31 July 1941 Hermann Goering, who had earlier been given responsibility for Jewish affairs, ordered Reinhard Heydrich of the SS to proceed to a 'final solution' of the Jewish question. That Hitler was behind the order, and certainly the actions which followed, need be in no doubt. Overall direction was held by the head of the SS, Heinrich Himmler. _Einzatsgruppen_ of his SS were already at work as the German army conquered much of the Soviet Union, and by the autumn of 1941 were engaging in the mass murder of Jews, some 34,000 in Kiev alone in September. Propaganda Minister Joseph Goebbels, who had been behind the 1938 _Kristallnacht_ pogrom, was determined to remove the Jews from Berlin, where he was _Gauleiter_. November 1941 saw the killing at Riga and Kaunas of Jews from Germany, as well as the first gassing of Polish Jews at Chelmno and Belzec. From his headquarters in Lublin, the former _Gauleiter_ of Vienna, SS police chief Odilo Globocnik, directed the extermination of the Jews in the General Government, killing around 1,700,000.
On 20 January 1942, Heydrich coordinated what was happening at a conference with other officials at Wannsee on the outskirts of Berlin. Jews from across Europe were to be divided into those fit or unfit for work, the latter to be killed, while the former were to be worked to death as forced labourers. Heydrich's subsequent assassination outside Prague made no difference to the course of events, which proceeded relentlessly under the supervision of the Austrian SS officer Adolf Eichmann. The camps at Chelmno, Belzec, Sobibor and Treblinka had no other function but extermination, while Maidanek outside Lublin and the vast Auschwitz-Birkenau complex near Cracow had a dual function, serving also as labour camps. It is estimated that over a million people were killed at the latter, most of them Jews. When the Allied victory brought the slaughter to an end, between 5,500,000 and 6,000,000 European Jews were dead. The death, at their own hands, of Hitler, Himmler, Goering, Goebbels and Globocnik was no consolation. Eichmann escaped the immediate fate of his superiors, finding refuge in Argentina until being spirited to Israel in 1960, tried and executed two years later.
Palestine in the war
The fate of the European Jews more than justified the worst fears of the Zionist leaders who had met in Geneva in August 1939. There was no doubt what course of action they would take. On 29 August, Weizmann wrote to Neville Chamberlain that the Jews would fight on the British side. He was true to his word, tragically so, since his younger son Michael, a pilot in the Royal Air Force, went missing over the Bay of Biscay in February 1942. By 1943, some 21,000 Palestinian Jews had reinforced the British in the Middle East, serving in such non-combat roles as transport and construction, although Jews were also allowed to enlist for fighting duties. Frustration at being largely confined to an auxiliary role fuelled the demand for the formation of active Jewish fighting units, but the British, fearful of Arab reaction, were slow to move. Sanction for a Jewish brigade was only given in September 1944, and after training it went into action on the Italian front the following March, rather late in the day as the result of British procrastination. Nevertheless, the scale of Jewish support for the Allied war effort contrasted with the position taken up by Haj Amin al-Husayni, who met Hitler and was photographed reviewing Bosnian Muslim recruits to the SS, actions which did nothing to help the Palestinian Arab position after the war.
Britain's tepid reaction to the Jewish army proposal reflected its determination to hold to the White Paper policy. As news of what was happening in Europe started to reach the Jews of Palestine and the United States, resentment mounted over Britain's handling of the immigration issue. Two incidents brought this into sharp focus. On 25 November 1940, the Patria, which was about to transport illegal refugees to Mauritius, blew up in Haifa harbour, killing 257. Then, in February 1942, the _Struma_ , which had arrived at Istanbul from Romania with 769 Jews on board, sank with the loss of almost all its passengers in the Black Sea after the British authorities had made it clear they would not be admitted to Palestine.
By 1942, when news of Nazi extermination policies was reaching the western Allies, the focus of Zionist activity had steadily moved to the United States. The Biltmore Conference, held in New York in May of that year, pledged the movement to making Palestine a Jewish commonwealth, an important revision of the original Basle Programme. Under the banner of the American Zionist Emergency Council, American Jews began to mobilise their political influence, to considerable effect after 1945. In Palestine itself right-wing sentiment, opposed to the policies of Weizmann and Ben-Gurion, saw the emergence of two underground organisations, the Irgun Zvai Leumi ('National Military Organisation') and the Leh'i ('Fighters for the Freedom of Israel'), often known as the Stern Gang after its founder, Avraham Stern. In 1942, Stern was killed by the police, but his mantle was taken up by Nathan Yellin-Mor. In November 1944, two of the organisation's members assassinated the British Minister in the Middle East, Lord Moyne. At their trial, they cited Britain's immigration policy as their reason. In February 1944, led by the young Polish Jew Menahem Begin, the Irgun set off bombs at the Department of Migration in Tel Aviv and Jerusalem. These activities were an ominous sign of what might develop after the war should the British still adhere to their White Paper immigration strategy.
7
# Conclusion: The Legacy
Unlike its predecessor, the Second World War was not followed by a peace conference. Germany had surrendered unconditionally, its immediate future lying with the military authorities of the United States, United Kingdom, France and the Soviet Union, each of which had its zone of occupation. The future shape of international relations found its focus in San Francisco in the spring of 1945 when the victorious powers came together to create the new United Nations Organization which was to ensure that the world would not have to endure another conflict, or so its founders hoped. President Franklin D Roosevelt had entertained the perhaps utopian, but certainly admirable, vision of a world in which peace would be guaranteed by the victorious powers cooperating through the United Nations. This was not to be. Instead, by 1949 East and West were locked into the Cold War, which lasted until the fall of Communism and collapse of the Soviet Union some four decades later. Although the peoples of the Middle East had their own concerns throughout this period, no part of the world could entirely escape the consequences of this seemingly intractable ideological conflict.
The war had finally set the clock ticking for European imperialism. Recovering as it was from four years of occupation, France was in no fit state to reassert its position in Lebanon and Syria. Whilst the Americans had always been clear that they were not fighting the war in order to restore the European empires, they were prepared to acknowledge the Middle East as a British sphere of influence. They did not, however, realise at first that Britain had been ruined financially and economically by the war. Their acknowledgement of the growing importance of the Middle East came in February 1945 when, on his return from the Yalta Conference, Roosevelt took the time to meet Ibn Saud in Egypt, assuring the Saudi king that 'he would do nothing to assist the Jews against the Arabs and would make no move hostile to the Arab people'. The meeting illustrated the importance that the future of Palestine was assuming. By the time the two men met, the Red Army's liberation of Auschwitz at the end of January had amply confirmed the appalling reality of the Holocaust. Jews were now resolved that statehood was the only means by which such a tragedy could never recur, and were determined to achieve it.
Turkey and the Western Alliance
A neighbour of the Soviet Union, Turkey controlled Moscow's access to the Mediterranean through the Straits. The Montreux Convention, signed in 1936, made Turkey responsible for implementing its provisions on navigation through the Straits. Enlisting Turkey's sympathy was, therefore, of vital importance for both East and West. This became clear as early as the Potsdam Conference in the summer of 1945 when Josef Stalin signalled the Soviet Union's interests in the Straits, including the possibility of a base. The basis of the Soviet case was that Axis ships had been allowed through during the war. The British and Americans were not initially unsympathetic to the Soviet Union's needs as a Black Sea power, but clearly the establishment of a base was a step too far. In addition, the Armenian and Georgian issues made a reappearance with a Soviet claim to the districts of Kars and Ardahan in north-eastern Anatolia. At all events, the Potsdam Conference had more urgent issues to hand, and the future of the Straits was postponed until another day.
Turkish-Soviet relations deteriorated in the winter of 1945/6 at a time when the Americans were annoyed by Moscow's failure to withdraw its troops from parts of Iranian territory where they had been stationed during the war. American fears were signalled by the decision in March 1946 to return the body of the deceased Turkish Ambassador to Washington on board the USS _Missouri_ , the battleship on which the Japanese surrender had been signed the previous year. The presence of this powerful vessel with her nine 16-inch guns reflected the deterioration of relations between Washington and Moscow, and symbolised American power in an area which had hitherto been a British preserve. By the summer of 1946, relations between Ankara and Moscow were so bad, with reports of major Soviet troop build-ups along the Caucasus and in Bulgaria, that Turkey began a general mobilisation. On 15 August, President Harry S Truman convened a meeting of senior advisers, including the chiefs-of-staff, to review American policy on the Straits. The Department of State's advice was that Soviet pressure on Greece and Turkey was designed to dominate the eastern Mediterranean. Such pressure should be resisted, even at the risk of hostilities. Considering also the civil war between Nationalists and Communists in China, Truman agreed that it was time for America to test Soviet intentions. It was decided to reinforce the _Missouri_ , which was still in Istanbul, with the navy's newest and most powerful aircraft carrier, the USS _Franklin D. Roosevelt_ , and to make clear both support for Turkish sovereignty, and that responsibility for the defence of the Straits rested exclusively with the Turks.
Since 1945, Britain had provided the main economic support to Turkey, and to Greece, but this proved to be too much of a financial burden on its depleted resources. On 21 February 1947, Washington was informed that Britain could no longer continue its aid to the two countries. This decision, coming at a time when East-West relations were already coming under severe strain, led to a major statement by Truman, which set American foreign policy on a new course. Addressing Congress on 12 March 1947, while asking for $400 million in aid for Greece and Turkey, Truman also announced that America would support free peoples, a speech which became known as the 'Truman Doctrine'. Turkey's strategic importance in the fast-deteriorating relationship between Washington and Moscow was clear.
From then on, the country moved steadily, but decisively, into the American and Western orbit. An American military mission arrived in May 1947 to advise on the modernisation of Turkish armed forces. In July 1948, the economic assistance provided under the European Recovery Program, commonly known as the Marshall Plan, was extended to Turkey. By 1950, the United States had provided $108 million in direct and $75 million in indirect aid, as well as military assistance amounting to some $200 million. The next logical step for Turkey was to be admitted to the North Atlantic Treaty Organization (NATO), formed in April 1949. Turkey was hardly on the North Atlantic, but then neither was Italy, one of the original signatories. The geography was ignored. Two things paved the way for Turkey's entry. On 14 May 1950, free elections, based upon a secret ballot, were held, bringing to power a new government under Adnan Menderes. Then, in the Korean War which broke out a few weeks later, Menderes committed a Turkish brigade to the United Nations forces, under American command. In February 1952, Turkey became a full member of NATO, the cornerstone of American defence and foreign policy. It was now a fully-fledged member of the Western defence community, bringing to an end the non-alignment which had marked its foreign policy since Lausanne, but which had been increasingly difficult to sustain since 1945.
The Arabs in the post-war world
During the war, the Free French under General Charles de Gaulle promised independence to Syria and Lebanon subject to the conclusion of an acceptable treaty, but France's power in the region was in tatters. Britain and the United States now wielded increasing and decisive influence and they saw little gain for the West in the continuation of French rule. In 1943, the nationalists in Syria won elections called by the Free French administration under huge pressure from the British and the United States. Shukri al-Quwwatli, a radical pan-Arab, became President. France still controlled the _les Troupes Spéciales_ , the locally recruited paramilitary force which they had used to try to prevent independence until French interests were guaranteed. Its refusal to withdraw culminated in May 1945 in the outbreak of anti-French riots. Subsequent attempts to restore order and control were strongly criticised by the British, who demanded France withdraw its forces. Bowing to international pressure, France finally conceded defeat and withdrew its forces in April 1946.
Lebanon's path to independence was no less troubled. The French arrested much of the Lebanese government after elections in 1943 brought anti-French groups to power. As in Syria, this was a forlorn attempt to maintain control and the British forced the French to retreat. In 1946, France withdrew its forces and Lebanon became independent under President Bishara al-Khouri. However, gaining independence was only part of Lebanon's political problems. The country's population was divided virtually 50/50 between various Christians sects (the most significant being Maronite Christians) and Muslims. Muslims were again split between Sunnis and Shias, with a substantial Druze minority. Muslims were generally sympathetic to union with Syria. An unwritten grand political compromise, called the National Pact, was agreed between the Christian leaders and Muslims in 1943. This provided for a permanent division of political spoils between Christians, who received the Presidency in perpetuity, and Muslims who were guaranteed the office of Prime Minister. A ratio of six Christians to five Muslim members of parliament was also enshrined. The Christians compromised by accepting that Lebanon would be an Arab state.
A strong supporter of the British reconquest of the Middle East during the Second World War was Emir Abdullah of Transjordan, who provided military backing with his British-trained Arab Legion. Abdullah, by default, was now de facto leader of the Hashemite family. However, he ruled the weakest of the Arab states and the one most dependent on British support. Transjordan remained desperately poor and underdeveloped. With a tiny population, lacking oil or other natural resources, Abdullah, even more so than his relatives in Iraq, considered it necessary to further his ambitions by merging Transjordan in a wider Arab entity. For one thing, it would allow him to throw off the shackles of the British. He was anxious that he should have a leading role in the post-war settlement of the Middle East when it was assumed that the Mandate system would come to an end. Abdullah, and virtually all pan-Arabists, believed that this would presage the union of all of the Arab countries in the Fertile Crescent (Iraq, Syria, Transjordan and Palestine).
Anxious that talks on Arab unity should take place before Transjordan, Syria, Palestine and Lebanon became independent, and fearful that he would be too weak to achieve union on his own, Abdullah had decided that his best chance of success was to co-operate with the British in the hope that they would use their enhanced influence in Syria after 1941 to get him the throne there. His big plan was to create a Greater Syria, essentially a Syrian-Jordanian federation. However, he was mistrusted by much nationalist opinion in the Arab world as a British stooge. Syrian nationalist leaders such as Faris al-Khouri were reluctant to commit themselves while vestiges of French influence remained. Shukri al-Quwwatli, the President of Syria, rejected Abdullah's overtures decisively in 1946 and the creation of the Arab League, formed by Egypt, Syria, Lebanon Jordan, Iraq and Saudi Arabia, in March 1945 gave Egypt an increasingly important role in Arab unity discussions. Neither did the British themselves have much interest in backing Abdullah in Syria. While they had come to the view that Abdullah was one of Britain's most useful Middle Eastern allies, they were sceptical about his wider regional ambitions. Reward for his loyalty came in 1946 when Transjordan was granted formal independence and renamed the Hashemite Kingdom of Jordan; Emir Abdullah became King Abdullah. By then, however, it was clear that the future of Palestine was the most burning issue in the Middle East.
Palestine: the Jewish Revolt
When the war ended, Weizmann's long-standing dominance of Zionist affairs began to ebb. British policy under the Labour government, which came into office in the summer of 1945, adhered stubbornly to the terms of the 1939 White Paper, the Foreign Secretary, Ernest Bevin, and his principal adviser on Palestine, Harold Beeley, incurring Jewish opprobrium as a result. With Hitler's atrocities now fully revealed, Jews were determined to secure their state, and were in no mood to indulge the British. In the circumstances, Weizmann's reliance on Britain seemed to belong to another age. On 1 October 1945 three Jewish groups in Palestine, the Haganah, the Irgun and Leh'i, began the Jewish Revolt against the Mandate. On the political front, Weizmann seemed a spent force. His relations with Ben-Gurion had become increasingly uneasy since 1942, and he now had a new adversary in Rabbi Abba Hillel Silver, a rising star in American Zionism. His support for partition was not dead, however. At a Zionist Executive in Basle in July 1946, it was agreed that partition could be the basis of a solution. Frustrated by the continuing crisis in Palestine, the British announced plans for a conference in London.
The simmering crisis within Zionism came to a head at the Twenty-Second Zionist Congress, held at Basle from 9–24 December 1946. It was the first since 1939, and in his presidential address Weizmann mourned the 6 million fellow Jews who had been murdered. Castigating the 1939 White Paper, he expressed understanding for the temper of the young Palestinian Jews, but still condemned violence as something alien to Zionism, and pleaded for restraint. The only way forward, he argued, was the establishment of a Jewish state. But the times were not with him. Now dominated by the representatives of Palestinian and American Zionism, the Congress voted to boycott the London conference, which had already got under way in September without them, or, indeed, the Arabs. Weizmann, who had advocated taking part, took this as a vote of no confidence and resigned the presidency. He never again attended a Zionist Congress.
Despite spurning him, Zionism had not finished with Weizmann. When the London conference reconvened in January 1947, the Palestinian Arabs attended, and the Jewish Agency, despite the December vote, came for what, with some sophistry, it called informal talks. Partition was now top of the agenda, but the Arabs were adamantly opposed, as always, and the Jewish Agency was too Delphic in its attitude for the British to proceed along this path. Unable to see a way forward, in February, the British government agreed to hand over the future of Palestine to the United Nations. On 15 May, the United Nations Special Committee on Palestine (UNSCOP) was established. Consisting of representatives of Guatemala, Uruguay, Peru, Australia, Canada, Sweden, the Netherlands, Czechoslovakia, Yugoslavia, India and Iran, it was charged with making recommendations for the future of Palestine by 1 September. The Arabs decided to boycott its proceedings, but the Jews made no such mistake. The first task confronting the Zionist leaders was to convince UNSCOP that the British Mandate should end. This was brilliantly accomplished when the refugee ship _Exodus 1947_ was intercepted by the Royal Navy on 17 July. Two days later, two members of UNSCOP watched its passengers disembarking at Haifa prior to their return to Germany.
On the more crucial question of the future of Palestine, the Zionist movement was still committed to the 1942 Biltmore Program, but privately Ben-Gurion had concluded that partition was the more realistic option. Weizmann, of course, had been its advocate since 1937. When Ben-Gurion presented the Jewish Agency's case before UNSCOP in Jerusalem, he did not mention partition. This task was left to Weizmann, who testified on 8 July 1947. Arguing that partition would mean a sacrifice for the Zionists, he conceded that they knew they could not have the whole of Palestine. He appealed for a more generous line than the one offered in the Peel Commission report by including the Negev Desert in a Jewish state. It was a clear signal to UNSCOP of what the Zionists would accept. Recalled before the committee, Ben-Gurion confirmed that they would consider a Jewish state in an area less than the whole of Palestine; privately, he assured them that he would support partition provided he got the Negev.
When UNSCOP reported on 1 September, its members recommended termination of the Mandate. On the future of Palestine, there was less agreement. The Indian, Iranian and Yugoslav members supported a bi-national federal state, the Australian could not support any scheme, while the majority ruled in favour of partition. There was to be an Arab state, a Jewish state, a _corpus separatum_ for Jerusalem, and economic unity. The Jewish state was to include the Negev, as Weizmann had argued. The Arabs, backed by the British, rejected partition, while the Jews, strongly supported by the Americans, worked assiduously to achieve it. The Americans, however, were concerned that the projected Jewish state contained too many Arabs, and the obvious way to reduce this was to exclude the Negev with its Bedouin population. Faced with this prospect, the Zionists turned again to their old warhorse.
On 19 November, Weizmann met President Truman at the White House. Persuaded by Weizmann that the Negev was vital to the Jewish state, Truman issued immediate instructions to his delegation at the United Nations that it should not be assigned to the Arab state. Not only was this an important intervention, but the impression Weizmann had made on Truman was to prove even more invaluable the following year. When the Ad Hoc Committee on the Palestinian Question took the vote on partition on 25 November 1947, it was supported by 25 votes to 13, with 17 abstentions and 2 absentees. This vote was some way short of the two-thirds majority needed to make it a formal recommendation of the General Assembly, where the vote was due to be taken on the 29th. Once again, Weizmann was brought into action, successfully telegraphing his friend Leon Blum to get France's vote changed to one of support for partition. In fact, it took direct action from the White House to secure a change in intention by enough states, so that when the vote was held, partition passed by the necessary majority of 33 votes to 13, with 10 abstentions. Exactly 50 years after the First Zionist Congress, sanction had been given for a Jewish state, and Weizmann was given a rapturous reception at a rally in New York.
His services were not yet at an end, however. With the Arabs resolutely opposed to partition, and the British determined not to implement it, the situation in Palestine deteriorated dramatically. While partition had been strongly supported by Truman and his advisers, this was far from the case amongst key officials in the Department of State, and events in Palestine in early 1948 enabled them to mount a campaign against it. What they recommended was that if the United Nations resolution could not be implemented, then the question of Palestine should be referred back to the General Assembly. Truman agreed to this in principle, though with the caveat that he should see the final draft of any speech. Irritated as he was by the amount of lobbying he had been subjected to on the issue of Palestine, he gave instructions that no more Zionist leaders were to see him, and that included Weizmann.
Knowing nothing of the State Department's campaign against partition, but sensing the coldness coming from the White House, the Zionist leaders searched for a way through the embargo. The key proved to be Eddie Jacobson, Truman's old army comrade and business partner from Kansas City. On 13 March 1948, Jacobson saw Truman at the White House. He persuaded an initially reluctant President to meet Weizmann, whom he compared with Truman's political hero, Andrew Jackson. The subsequent meeting on 19 March, at which no minutes were kept, proved crucial, with Truman reassuring Weizmann that he still supported partition. The following day, unaware of this development, Warren Austin made a speech to the Security Council in which the United States repudiated partition, casting doubt on the prospects for a Jewish state. Jewish opinion, equally ignorant of the White House meeting, was outraged, but as the controversy swirled around the White House, Weizmann kept silent, trusting in Truman's good faith, and earning the President's goodwill in the process. It was not the least of Weizmann's services to Zionism.
The State of Israel: Weizmann as President
When the British Mandate for Palestine ended on 14 May 1948, Ben-Gurion proclaimed the establishment of the State of Israel in the Tel Aviv museum; 11 minutes later it was accorded _de facto_ recognition by Truman. Still in New York, Weizmann was not present at these historic events. On 17 May, he received the news that the Provisional Council of State led by Ben-Gurion had elected him President, and this was subsequently confirmed in Israel's first election in January 1949. To become the first President of the State of Israel should have been the triumphant finale to Weizmann's career, but it proved instead to be a coda played out in a minor key. Before returning to Israel, he performed one last service. At an official meeting with Truman on 23 May, Weizmann learned that the United States was willing to make a loan of $100 million to the new state. But he was not long home when the picture darkened.
Now in his mid-70s and in declining health, Weizmann still hoped to play an active part in affairs as President, along the lines of certain continental European countries. Ben-Gurion, for his part, was determined that the role of the President should, like that of the British monarch, be purely symbolic, precisely the word Foreign Minister Moshe Sharett used, with rather insulting honesty, when describing its functions to Weizmann. He was not consulted by Ben-Gurion's government on affairs of state, nor was his request to receive Cabinet minutes granted. Of particular chagrin was the omission of his signature from the Declaration of the Establishment of the State of Israel. He had, of course, not been present in Tel Aviv at the time, but it galled him that there were 34 signatories to the historic document, and that space had been left for three others who had been absent, but not for him. At best, it seemed a curious omission of the man who had guided Zionism through its pivotal phase, and who was the first President of the State. He was honoured, of course, but that was not what he had wanted. He made one final visit to the United States in 1949 on behalf of his beloved research institute, now named after him, but it was as 'The Prisoner of Rehovoth' that he now saw himself. For the final year of his life, Weizmann was almost entirely confined to his bed. On 9 November 1952, he died.
The First Arab-Israeli War and the Palestinian _al-Nakba_
The day after Ben-Gurion proclaimed the State of Israel, it was attacked by armies from the Arab League, Egypt, Syria, Lebanon, Jordan, Iraq and Saudi Arabia, beginning a war which was to end in February 1949 with Israel's victory. The Israelis were fighting on interior lines against forces from six Arab countries, but which lacked modern weapons and were far from united in their purpose. The armistice agreements of 1949, which brought hostilities to an end, left Israel with borders more extensive and rather more secure than those which had been set out in the UNSCOP plan. Israel now compromised some 78 per cent of pre-1948 Palestine. Even so, the coastal plain was narrow, and the towns and cities still potentially vulnerable to attack, since the armistice agreements did not end the state of war. Rather the contrary, since defeat generated radicalism in the Arab world. In 1952, the Free Officers movement overthrew the monarchy in Egypt. The leading revolutionary, Colonel Gamal Abdul Nasser, became President in 1954, and was to become the charismatic voice of a new Arab nationalism at odds with the West and with Israel. Security, or rather the lack of it, would be an abiding Israeli concern. Israel also secured west Jerusalem, but not the Old City which held the Western Wall, a source of bitter regret.
With Weizmann's old colleague and sometime rival Ben-Gurion as Prime Minister, Israel could now proceed with the business of nation building. By the mid- 1960s, aided by reparations from West Germany, its economy had reached a level comparable with that of southern Europe. The new state had absorbed large numbers of Jews, mainly from the Middle East and north Africa. The arrival of immigrants from these areas altered the nature of Israel's population, hitherto almost entirely European in origin. Because of Hitler's genocide, substantial immigration from Europe was no longer possible, although the country was able to take in survivors from the Holocaust. Relations between the Ashkenazim, Jews of European origin, and the Sephardim from the Middle East and north Africa, were not always easy. The country also experienced tensions between secular and religious Jews, but whatever their differences the overwhelming bulk of Israelis were united behind the ideal of a Jewish state, and took pride in its achievements.
The Palestinians were the principal losers in all of these events. Although they had vehemently rejected partition in 1947, no Palestinian political entity came into being. Instead, the remaining 22 per cent of Mandated Palestine fell into two parts. The area which became known as the West Bank, including east Jerusalem, was held by Abdullah's Arab Legion, and was formally annexed by him in 1950. Abdullah viewed the creation of Israel more phlegmatically than did the other Arab states, and Jordanian and Israeli negotiators maintained discreet contact after the war. These negotiations included proposals for a final partition of Palestine that would include a Jordanian corridor to the Mediterranean and a non-aggression pact. However, there was strong opposition within Abdullah's government and in the wider Arab world. Israel was also unwilling to make the necessary territorial concessions to make an agreement work. These talks came to an abrupt conclusion with the assassination of Abdullah by an extremist Muslim outside the al-Agsa Mosque in Jerusalem on 20 July 1951. After a brief interval, he was succeeded by his 17-year-old grandson Hussein, who proved to be one of the most durable leaders in the region, dying of cancer in 1999, by which time he had steered the Hashemite dynasty through many challenges.
The Gaza coastal strip, which had been bitterly contested by the Israeli and Egyptian forces in 1948–9, remained occupied and administered, but not annexed, by Egypt. Its fate was lamentable, and prospects dim. Much of it comprised sand dunes, it had no resources worth the name, and its farmlands and groves were divided by the armistice lines. A pre-1948 population of 70,000 was swollen by 200,000 refugees. The total number of Palestinian refugees by 1949 was around 750,000. Some had fled, others been expelled in the course of the fighting. Without homes, businesses or land, consigned to refugee camps in Jordan, Gaza, Lebanon, Syria, Iraq and Israel itself, they had to rely for support in the decades to come on the United Relief and Works Agency for Palestine Refugees (UNWRA), established in December 1949. The events of 1948–9 were for the Palestinians al-Nakba, 'the catastrophe'. The future of the Palestinian refugees became one of the great unanswered questions of the Middle East, their numbers growing appreciably over the years.
The Arab-Israeli Wars
The war of 1948–9 was the first of many. In February 1955, Palestinian raids into Israel resulted in a major incursion into Gaza. On 29 October 1956, Israel attacked Egypt in the Sinai Desert as part of a plan secretly agreed with Britain and France, which had been building up their forces in response to Nasser's nationalisation of the Suez Canal Company. The ill-conceived Anglo-French military landing at Port Said on 5–6 November was brought to a swift stop by an irate President Dwight D Eisenhower. The United Nations Emergency Force (UNEF) was put in place.
The 'Suez Crisis', as it was known, signalled the end of Britain's role in the Middle East, and confirmed America's predominance, which was to grow in the decades ahead. In June 1967, Egypt and Syria began to mass their forces in response to an ill-founded Soviet message that Israel was planning to attack the latter. When Nasser demanded the withdrawal of UNEF and then announced a blockade of the Straits of Tiran, something which Israel had said would constitute a _casus belli_ , the crisis assumed critical proportions. Israel reacted with a lightning campaign, which in a matter of days saw her forces advance to the Suez Canal and capture the strategic Golan Heights from Syria. King Hussein rallied to the Arab cause, losing east Jerusalem and the West Bank as a result. After one of the most dramatic military victories of the post-war world, Israel now occupied all of pre-1948 Palestine, as well as extensive Egyptian and Syrian territory.
On 6 October 1973, Egypt's President Anwar al-Sadat and Syria's President Hafez al-Asad, seemingly frustrated by the lack of diplomatic progress, launched a surprise attack on Israeli positions along the Suez Canal and on the Golan Heights. After initial Egyptian and Syrian successes along the Suez Canal and on Mount Hermon, the Israelis counter-attacked, aided by a massive American resupply operation. When hostilities ended, largely as the result of American Secretary of State Henry Kissinger's diplomacy, the Israeli army was deployed on the western bank of the southern part of the Suez Canal, surrounding the Egyptian Third Army, and also threatening Damascus after successful operations on the Golan front. The result of the war was far from clear-cut. The Israeli forces had recovered well after their initial reverses. Critically, however, Egyptian and Syrian military pride and confidence had been restored, opening the way for diplomatic moves, as Sadat had certainly hoped. With his success in negotiating a ceasefire behind him, Kissinger was well placed to begin the process.
Iraq: the end of the Hashemite monarchy
In contrast with Abdullah's willingness to seek peace with Israel, Iraq, despite its pro-Western orientation, was militantly opposed to any compromise with the new state. The year 1948 was a very unsettled year for the country. Severe riots erupted over the Palestine conflict and over the new Anglo-Iraqi agreement, the Treaty of Portsmouth. The former were aimed at the large Jewish population in Baghdad, who soon concluded they had no future in Iraq and the vast majority of them left, abandoning most of their property, in the early 1950s. Nuri, now the dominant figure in Iraqi ruling circles, took the opportunity offered by the death of Abdullah I of Jordan to reclaim Iraqi leadership of schemes for unity in the Fertile Crescent. However, with the coming to power in 1952 of the new military regime in Egypt, he now faced a rival for regional leadership. Nasser's earliest achievement was to sign an agreement that ended British base rights in peacetime in Egypt. This contrasted with Nuri and the Iraqi royal family's continued advocacy of the British connection and the maintenance of British bases. Britain would retain air bases and military facilities and rights in Iraq until after the 1958 revolution.
Moreover, Nuri, influenced by a deep distrust of the Russians dating back to his days in the Ottoman army, was deeply committed to bringing Iraq firmly into the Western Alliance. To this end, in early 1955 he orchestrated the creation of a regional defence organisation, the Baghdad Pact, which included Britain, Iran, Turkey and Pakistan. Nuri eventually hoped to bring other Arab states, including Jordan and Syria, into the alliance. The Baghdad Pact provoked fierce opposition from Nasser, who saw it as a challenge to his own preference for Arab states to be neutral in the Cold War and a block to his own ambitions for regional leadership. The Egyptian leader directed the full weight of an increasingly powerful propaganda machine against the Iraqi leadership. Jordan decided not to join after Egyptian-inspired riots, and Syria became increasingly entranced by Nasser's brand of Arab nationalism. The Hashemites faced increasing isolation – a situation only exacerbated by the Anglo-French-Israeli invasion of Suez. An international crisis over Syria in the summer and autumn of 1957, in which, with British encouragement, Nuri floated a number of schemes for Iraqi intervention, only strengthened Egyptian influence. This culminated in a union of Egypt and Syria, called the United Arab Republic, under Nasser's leadership in February 1958. Nuri, in desperation, floated a counter-proposal – the Arab Union – made up of Iraq and Jordan, but it had little popular support.
Domestically the regime remained unstable. Iraq had huge social divisions between the peasant masses that saw little benefit from increased oil revenues and the landlord classes that grew ever more prosperous. The landed classes also excluded a growing middle class from the levers of power. A Development Board tasked with spending the oil revenues was the subject of criticism for moving too slowly. Nasserite propaganda over the Baghdad Pact tapped into widespread political disquiet about Iraq's pro-Western foreign policy. The government treated even mild political opposition as subversion, leaving little opportunity for legitimate political opposition.
Within the army the wider political discontent was reflected in the growth of groups in the officer class modelled on the Egyptian Free Officers. They became increasingly determined to end the regime. The opportunity arose in July 1958, when Iraqi troops were ordered to Jordan to bolster the regime there. Instead they marched on Baghdad and seized power. In appalling scenes, the royal family, including the youthful king and the former regent Abdulilah, were slain. Nuri was captured attempting to reach a friendly foreign embassy, allegedly disguised in women's clothes, and murdered. Iraq was proclaimed a republic under Brigadier General Abd al-Karim Qasim.
Fatah and the PLO
It took the Palestinians fully a decade to rally politically after the events of 1948–9. When they did so, the key figure was an engineer from Gaza who had fought in the war, Yasser Arafat. In 1959, with a small group of friends, he formed Fatah, 'The Movement for the Liberation of Palestine'. Its moment came after the 1967 war when its fighters challenged the Israeli army at Karameh in Jordan, and established networks in the West Bank. In 1968–9, the Palestine Liberation Organization (PLO), a hitherto largely ineffectual body which had been created in 1964, was restructured under Fatah's leadership with Arafat as chairman, a position he was to hold until his death in November 2004.
Armed Palestinian resistance to the Israeli occupation took several forms. While Fatah mounted conventional raids inside the West Bank, the Popular Front for the Liberation of Palestine (PFLP) targeted airliners, ensuring that the Palestinian issue was never far from the world's headlines. This phase reached a climax in September 1970 when the hijacking of three airliners to Jordan led King Hussein, in an operation which became known as 'Black September', to strike at the Palestinian bases in his country. The term 'Black September' reappeared at the 1972 Munich Olympics when an organisation of that name killed eleven Israeli athletes.
In the period after the 1973 war, the PLO increasingly followed a political path, never likely to be easy since the Israelis understandably regarded it with deep hostility and Fatah was only one of a number of groups within it. Its high point came when Arafat addressed the General Assembly of the United Nations in New York in November 1974, but this momentum could not be sustained, not least since the Palestinians became caught up in the crisis which developed in Lebanon the following year, leading to a prolonged civil war in the country.
Until the 1970s, Lebanon was the financial centre of the Middle East and appeared to be the most successful of the Arab states. However, beneath the surface of calm and prosperity lay substantial communal tensions. The country also found itself drawn into the inter-Arab disputes of the 1950s, the Israel-Palestine conflict owing to the presence on its soil of a sizeable population of Palestinian refugees, as well as the wider world struggle between the United States and the Soviet Union. Lebanon's National Pact held until the late 1950s when the tensions caused by the intra-Arab struggle and the growing internal troubles of a divided communal society led to a brief civil war. From the late 1960s Lebanon-based Palestinian guerrilla attacks on Israel provoked ever greater Israeli reprisals that destabilised relations between the Christian and Muslim communities. In 1975, full-scale fighting broke out between Christians and Palestinians. This widened into a Muslim-Christian civil war, which lasted until 1989, eventually involving, in various capacities, Syria, Israel, the United States, France, Italy and the United Kingdom.
Attempts at an Arab-Israeli peace settlement
Attempts at a diplomatic settlement began almost as soon as the 1967 war ended, the key document being United Nations Security Council Resolution 242 of 22 November, which served as the basis of negotiations thereafter. At its heart was the provision that Israel armed forces should withdraw from territories occupied in the recent conflict, a condition that could be, and was, interpreted in different ways. It did, nevertheless, acknowledge the sovereignty of every state in the area. Accepted by Egypt and Jordan, this carried their implicit recognition of Israel. The resolution also called for a just settlement of the refugee problem, but this was not a description the Palestinians accepted. Two years later, American Secretary of State William Rogers announced an ill-fated peace plan, but it took the 1973 war for any progress to be made. In 1974–5, Henry Kissinger negotiated important disengagement agreements between Israel and its two major antagonists, Egypt and Syria, which defused much of the immediate danger. A ceasefire line along the Golan Heights was agreed, and both banks of the Suez Canal were restored to Egypt. In return, Sadat announced that Israeli cargoes would be allowed through the Suez Canal.
The next major move was made by President Sadat, who, to universal surprise, addressed the Knesset in Jerusalem in November 1977 with a plea for a peace settlement, which would include not just a peace agreement between Egypt and Israel but a settlement for the Palestinians. In the meantime, the Labour Party, which had dominated Israeli politics since the foundation of the state, had lost power to the right-wing Likud led by former Irgun leader Menaham Begin and General Ariel Sharon, who had commanded the Israeli crossing of the Suez Canal in 1973. Their victory reflected in part the growing power of Jews of Middle Eastern origin.
Despite Sadat's dramatic intervention, it took the determined intervention of US President Jimmy Carter for progress to be made. Two Frameworks were agreed between Egypt and Israel at the Camp David summit which he convened in September 1978. The first provided for a peace treaty between the two countries, which was signed on 26 March the following year, and survived Sadat's assassination in October 1981. In return for giving back the Sinai Desert, Israel had removed the threat from its most powerful Arab adversary. The second Framework, which sought to address the future of the West Bank and Gaza, failed in its purpose. This was to provide 'full autonomy' for the inhabitants of the West Bank and Gaza, but it proved impossible to agree what this meant.
The war in Lebanon and the Intifada
On 6 June 1982, 'Operation Peace for Galilee' began when Israeli troops invaded Lebanon and within days were on the outskirts of Beirut, close to Muslim areas of the city and Palestinian refugee camps. It was a controversial war, even within Israel itself, and sustained bombardment of parts of the city bought intense pressure from President Ronald Reagan for a resolution. As a result, a joint American, French and Italian Multinational Force oversaw the evacuation of Yasser Arafat and his PLO forces from the city. President Reagan followed this with a new peace plan, which within days was overtaken by events when the Maronite leader, Bashir Gemayel, on whom Israel had placed considerable hopes, was assassinated. Lebanese supporters of the slain leader massacred hundreds of Palestinians in the Sabra and Shatila refugee camps, in an area of west Beirut which the Israelis had occupied in the aftermath of Gemayel's murder. A new Multinational Force of American, French, Italian and British soldiers was sent to Beirut, but its mission became inseparable from the passions of the Lebanese conflict. The crisis came on 23 October 1983 when suicide bombers killed 241 American marines and 78 French soldiers. By the following spring, the Multinational Force had been withdrawn.
The focus of events then moved to the West Bank and Gaza where there had been mounting frustration at the lack of diplomatic progress, and anger over Israeli settlement activities, which had steadily built up in the course of the 1980s. The Intifada, or Uprising, which began in Gaza in December 1987 and then spread to the West Bank, was an unprecedented and widespread challenge to the Israeli occupation. Out of the Intifada came a new movement which in time was to challenge not just Israel but Fatah. This was Hamas, the Islamic Resistance Movement, founded by Sheikh Ahmed Yassin. The movement combined social work and an intense Islamic commitment with a military wing, the Izz al-Din al-Qassam Brigade. Hamas was destined to grow in opposition to the secular Fatah.
Iraq after the Hashemites
The Iraqi Republic which emerged from the ruins of the Hashemite monarchy was prey to conflicting political ambitions and ideologies, Qasim himself being overthrown and shot in 1963. In July 1979, Saddam Hussein, a leading member of the Ba'th Party which had built up a strong power base in the security services, became President, inaugurating his rule with a ruthless purge of party rivals. He soon had his country in a firm grip, his power based in the Sunni heartland, the Ba'th Party and the armed forces, and began an adventurous foreign policy. While Saddam Hussein's regime was secular, Sunni Arabs had been the dominant element in the country since its creation. Shia Iran, where the Shah was overthrown in 1979 and which was in the process of establishing an Islamic republic, was Saddam Hussein's first target. The Shatt al-Arab waterway, Iraq's sole maritime outlet, had long been an issue between the two countries, and the upheaval caused by the revolution in Iran seemed to present a unique opportunity for action. In September 1980, Iraq began a series of attacks on Iranian territory. Revolutionary Iran proved to be a stern opponent, however. The war dragged on until 1988, leaving Iraq with massive debts, and no gains.
The war with Iran was not Saddam Hussein's last misreading of the international situation. His next target was Kuwait. Here, too, there were long-standing border disputes, as well as a debt of $30 billion resulting from the war with Iran. On 2 August 1990, the Iraqi army invaded. Kuwait was in no position to resist, but Saddam Hussein seriously misjudged the effect his conquest would have in the rest of the Middle East, and in Washington. On 5 August, President George Bush announced that the aggression would not stand unopposed. Saudi Arabia gave its permission for American troops to enter its territory, while Britain and France announced their support. They were joined by troops from a number of countries, most notably Egypt and Syria, an indication of how the Iraqi leader's ambitions were seen elsewhere in the Middle East. Turkish opinion was divided. Turkish troops did not take part, but permission was given for operations from the NATO air base at Incirlik in southern Turkey. On 29 November 1990, the United Nations Security Council passed a resolution demanding Iraqi withdrawal from Kuwait by 15 January. When this deadline expired, air attacks on Iraq began. The coalition's ground assault was launched on 24 February 1991, liberating Kuwait in three days. The Security Council had not sanctioned further action, and certainly not an advance on Baghdad. Hopes that defeat would lead to Saddam Hussein's overthrow were confounded, since he had carefully husbanded his Republican Guard, an essential prop of his government. Risings in the Shia south and Kurdish north were ruthlessly suppressed, and although Iraq was subject to United Nations sanctions, his power remained intact.
After the 9/11 attacks of 2001 on New York and Washington by al-Qaeda, the United States decided to remove Saddam Hussein. While his regime was swiftly removed in the spring of 2003, the ensuing years saw a violent insurgency and widespread destruction. Tens of thousands of Iraqis died in the conflict. American forces captured Saddam Hussein in December 2003. Put on trial in 2005 for the murder of 148 Shia villagers, he was found guilty, and was executed on 30 December 2006. In the meantime, a new government under Nuri al-Maliki, leader of the Da'wa Party, had been formed in May, following elections in December 2005. Elections for the 325-member Council of Representatives on 7 March 2010 were less decisive, however, leaving Maliki's State of Law Coalition with 89 seats and the opposing Iraqi National Movement led by former premier Iyad al-Allawi with 91. The political future of Iraq was beginning to emerge, however tentatively, and in the face of many challenges, which before long came to the surface once again.
An uncertain peace process
In the course of 1993, a highly secret dialogue between key Israeli and PLO representatives had been maturing in Norway, culminating in an historic exchange of letters, the Declaration of Principles, on 9 September. In this dramatic development, the PLO recognised Israel's right to exist and renounced terrorism, while Israel promised to withdraw from Gaza and the city of Jericho on the West Bank. There were to be elections for a Palestinian Council, which was to administer the West Bank and Gaza for five years, while a final settlement was being negotiated. In a ceremony at the White House on 13 September, presided over by President Bill Clinton, Arafat and Israeli premier Yitzhak Rabin shook hands and signed the agreement. A meeting in Cairo in May 1994 paved the way for the creation of a Palestinian Authority with Arafat as President. It was followed by a peace treaty between Israel and Jordan in October. Even so, the Oslo peace process had its opponents on both sides. Hamas waged a campaign against it, while Rabin was assassinated at a rally in Tel Aviv on 4 November 1994 by a young Israeli. Suicide bombers undermined Israeli support.
Despite the iconic handshake in the Rose Garden of the White House, the peace process did not flourish, defying the best efforts of the Clinton administration. Suicide bomb attacks in Israel and continuing Israeli settlement activity in the West Bank did not encourage goodwill, quite the reverse. Elections for the Palestinian Council took place in January 1996. The Council was addressed by Clinton after the Nye Valley conference in 1998 arranged for 40 per cent of the West Bank to be placed under its control and provided that the Palestinians would implement security measures. In July 2000, Clinton made a valiant and imaginative attempt to bring Arafat and Israeli premier Ehud Barak to a settlement at a summit at Camp David. At issue was the prospect of a Palestinian state within the 1967 borders, but with territorial adjustments that would transfer most of the Jewish settlements to Israel, while compensating the Palestinians with some Israeli territory. The Palestinians would have full sovereignty in parts of east Jerusalem and custodial rights on the Haram al-Sharif shrine in the city. It seems that Barak was prepared to concede to the Palestinians 91 per cent of the West Bank, as well as custodianship over the Haram al-Sharif/Temple Mount, sovereignty in part of Jerusalem, and a solution for the refugees. Arafat could not agree.
The collapse of the summit was quickly followed by a return to violence. The occasion, if not the actual cause, of the outbreak was the visit to the Haram al-Sharif Temple Mount on 28 September 2000 by Israeli opposition Likud leader Ariel Sharon, an object of particular dislike to Palestinians. When Palestinian protesters were fired on by police the following day, killing four people, what came to be called the al-Agsa Intifada began. It was more violent than the first Intifada, with suicide bomb attacks provoking Israeli retaliation with tanks and helicopter gunships. In January 2001, at the very end of his presidency, Clinton made a final attempt to reach a settlement, but again Arafat could not be persuaded, his sticking points being the Old City of Jerusalem and the right of return of the Palestinian refugees. The Israeli election which immediately followed was won by Sharon.
By 2002, Israeli-Palestinian relations had deteriorated into a depressing and bloody spiral of suicide bombings and Israeli retaliation. On 27 March, a suicide bomb at a Passover celebration in Netanya killed 28 and injured 140. In response, Sharon launched 'Operation Defensive Shield' across the West Bank, effectively isolating Arafat in his Ramallah headquarters. Casualties as the result of operations in the Jenin refugee camp were particularly controversial. On 30 April 2003, following the fall of Baghdad, President George W Bush announced a 'Performance-Based Roadmap to a Permanent Two-State Solution to the Israeli-Palestinian Conflict', which was to see a final settlement by 2005. This proved no more successful than its predecessors, although the American commitment to the pursuit of a two-state solution was in itself significant.
There were critical developments affecting the West Bank and Gaza. In the former the Israelis began the construction of a security fence intended as a barrier against suicide attacks. It was a formidable affair which in Jerusalem took the form of a concrete wall. Palestinians viewed it as a wall of annexation, since it took in settlement blocks beyond the 1967 border and impacted adversely on a number of communities, notably Bethlehem whose economy depended on the tourist trade. In Gaza, continuing suicide attacks led the Israelis to target the Hamas leadership. On 22 March 2004, the movement's founder, Sheikh Ahmed Yassin, was killed by a missile, to be followed a month later by his successor in the leadership. These strikes did not inhibit the movement's growth. In Ramallah, Arafat's health had been declining. Flown to France for treatment, he died on 11 November, his burial at his Ramallah headquarters being the occasion for widespread mourning amongst Palestinians for whom he had long embodied their cause.
Sharon had the capacity to surprise. Despite strong opposition in his party, he forged ahead with a disengagement plan for Gaza. By September 2005, all settlements and military units had been withdrawn. This disengagement was followed by a dramatic political move. In November, Sharon resigned from Likud, forming a new centrist party, Kadima, or 'Forward'. While committed to Israel's security, the party promised to pursue the peace process based upon two states. How Kadima would have developed under Sharon's leadership was never put to the test, since the following January he was struck down by a cerebral attack. In the Israeli election of March 2006, now led by former Jerusalem mayor Ehud Olmert, Kadima emerged as the largest party, and was able to form a coalition government with Labour. Olmert's government had to confront new realities, since in the Palestinian elections in January, Fatah was eclipsed by Hamas. In March, Hamas's Ismail Haniya became Prime Minister of the Palestinian Authority.
As tensions between the two new governments rose, in July 2006 serious fighting broke out on Israel's border with Lebanon, where the Islamic militia Hezbollah mounted a raid killing eight Israelis. In the subsequent large-scale fighting northern Israel was hit by some 4,000 rockets, while 144 Israelis and over 1,000 Lebanese are believed to have been killed. Israel was also being attacked by rockets from Gaza, where tensions between Hamas and Fatah were coming to a head. In June 2007, bitter fighting between them left Hamas in firm control of Gaza and Fatah holding on to the West Bank.
This _de facto_ fragmentation of the Palestinian Authority did not bode well for the success of a major conference presided over by President Bush at Annapolis on 27 November, at which the parties committed themselves to strive for an agreement based on two states by the end of 2008. This did not happen. Instead, Israel's increasingly bitter relations with Gaza held the stage. Continuing rocket attacks led to an Israeli closure of the border crossings in January 2008. As the situation in Gaza deteriorated, gaps were blown in the border fence with Egypt, leading thousands of Palestinians to cross into Egyptian territory. In June a ceasefire was arranged by the Egyptians, but this collapsed in December as a result of Israeli operations against the tunnels connecting Gaza with Egypt. When rocket attacks on Israel resumed, on 27 December 2008 the Israelis launched air attacks. 'Operation Cast Lead' soon involved major ground operations, lasting until 18 January. As it drew to a close and the scale of the conflict and of the casualties began to emerge, it was believed that over 1,000 Palestinians, including many civilians, had been killed, while Israel had lost thirteen. Southern Israel continued to be vulnerable to rocket attacks, while Gaza remained subject to border restrictions which impeded attempts at reconstruction.
Modern Turkey
Post-war Turkey continued to present a paradox. It was firmly linked to the West through NATO membership, but its relations with its neighbour and fellow alliance member, Greece, were frequently acrimonious. There were disputes over Aegean islands, but the principal source of friction was Cyprus, which Britain had acquired from the Ottomans in 1878, but where Turks were only some 20 per cent of the population. The Greek Cypriot campaign in the 1950s for _Enosis_ , union with Greece, raised fears in the predominantly Turkish north of the island. The island became independent in 1960 with Archbishop Makarios as President. In 1974, the National Guard mounted a coup against him with a view to securing union with Greece, but this provoked a Turkish military landing, leading to the creation of the Turkish Republic of North Cyprus, effectively partitioning the island. The unresolved future of Cyprus was to complicate Turkey's foreign relations, not least its bid to join the European Union, especially since the (Greek) Republic of Cyprus became a full member in 2004.
Membership of NATO meant that relations with Washington were central to Turkey's foreign policy for much of the period, its security powerfully guaranteed by the American Sixth Fleet in the Mediterranean. In 1954, the United States acquired a major military asset with the construction of the Incirlik air base in south-eastern Turkey. This substantial facility enabled NATO to threaten the Soviet Union on its southern flank. In 1980, the Defense and Economic Cooperation Agreement between the two countries set the terms for the base's use. With the ending of the Cold War, its function changed, placing American aircraft significantly closer to the Middle East than did the Rhein-Main air base in Germany. In 1962, loyal NATO membership also allowed the United States to base 17 Jupiter missiles targeted on the Soviet Union on Turkish territory. This deployment presented a significant threat to the Soviets, but in October President Kennedy agreed to withdraw the Jupiters as part of the resolution of the Cuban Missile Crisis. Agreement with Moscow was negotiated, it seems, over the head of the Turkish government. Such was the _realpolitik_ of the time.
The Iranian revolution of 1979 reinforced Turkey's importance for the United States, which had seen its most powerful ally in the Middle East suddenly turn bitterly hostile. During the first Gulf crisis of 1991, Turkey permitted the use of the Incirlik air base, but the Second Gulf War of 2003 provoked a major crisis in its relations with the American administration. In its planning, the Pentagon had hoped to mount a two-pronged invasion of Iraq, with a northern attack mounted from Turkey. On 1 March, however, the Turkish parliament voted against the American troop deployment.
The military remained a powerful force in national life and politics, seeing itself as the heir to, and principal buttress of, the secular republic Atatürk had created. Under the banner of the National Unity Committee, in May 1960 a group of officers overthrew the Menderes government. The following year, the ousted premier and two of his ministers were executed. He has since been rehabilitated to the extent that the thousands of holidaymakers who visit the flourishing resorts of the Aegean coast, and those who come to appreciate the glories of the region's classical heritage at Ephesus and Bergama, pass through Izmir's Adnan Menderes airport, possibly unaware of how it came to be named.
The tension long inherent in the maintenance of a secular state in a country which remained 99.8 per cent Muslim began to surface in November 2002 with the coming to power of the Justice and Development Party (AKP), which had only been founded the previous year, led by Recep Tayyip Erdogan, a former mayor of Istanbul. The party, while pledging loyalty to the secular state, had a broadly conservative ethos. In 2007, its Foreign Minister, Abdullah Gul, a trained economist, was elected President, reinforcing the party's position. The fears of secularist supporters surfaced the following year when the government introduced constitutional amendments to remove the long-standing ban on the wearing of headscarves by women in the universities. The amendment was invalidated by the Constitutional Court, which, however, rejected a petition to have the AKP banned.
A more immediate threat to the stability of the Turkish state was Kurdish nationalism. The Treaty of Sèvres had provided for an independent Kurdistan, to be carved out of Turkey, should the Kurds want it and prove capable of sustaining it. Turkish Kurdistan could then link up with the Kurdish areas of the Iraqi province of Mosul. The Treaty of Lausanne did not mention the Kurds. But their cultural rights were covered obliquely by Article 39. This provided that:
... no restrictions shall be imposed on the free use by any Turkish national of any language in private intercourse, in commerce, religion, in the press, or in publications of any kind or at public meetings. Notwithstanding the existence of the official language, adequate facilities shall be given to Turkish nationals of non-Turkish speech for the oral use of their own language before the Courts.
This provision awaits implementation to this day. Restrictions placed on the use of the Kurdish language (or rather languages) in Turkey were resented by all Turkish citizens of Kurdish origin. Nationalists among them wanted more, their demands ranging from autonomy to full independence. In 1984, the Kurdistan Workers' Party (PKK) launched a guerrilla campaign, which increased in intensity after the 1991 Gulf War, as the movement had established bases in northern Iraq, from which Saddam Hussein's forces were excluded after the first Gulf War. By 1999, the insurrection had been largely suppressed, following the arrest of its leader Abdullah Öcalan, but the demand for some from of Kurdish autonomy remained.
In foreign affairs, Turkey engaged on a process of active engagement with its neighbours in the region. This included a dialogue with Iran, which lay under a blanket of international disapproval as a result of its nuclear enrichment programme. Fears over Iran's possible intentions were of particular concern to the United States and Israel, but Turkey maintained that the country was entitled to have a peaceful nuclear energy programme.
At the same time that Ankara was pursuing this policy, Turkish relations with Israel went into sharp decline. The two countries had long enjoyed a positive relationship, not least in military cooperation, but a series of events associated with Israeli policies towards Gaza changed this. This was dramatically symbolised in January 2009 by Prime Minister Erdogan leaving the stage when Israeli President Shimon Peres defended 'Operation Cast Lead' at the World Economic Forum. The blockade of Gaza led to a number of attempts to send supply ships, which Israel diverted to Ashdod, where the cargoes were first inspected before being sent on. In May 2010, six ships, including the Turkish vessel MV _Mavi Marmara_ sailed for Gaza, refusing to make for Ashdod. On 31 May, they were intercepted by Israeli commandos. Fighting on the _Mavi Marmara_ resulted in the death of eight Turks and one Turkish-American. Turkish opinion was outraged, and the Ambassador to Israel was recalled.
Active engagement with Turkey's Middle Eastern neighbours went alongside the country's long-standing ambition to join the European Union. Membership of the Union was neither straightforward nor pre-ordained, as the British had learned to their cost. Applicants were required to meet the complex requirements of the 35 chapters of the acquis communautaire, and a final accession treaty had then to be ratified by all 27 member countries as well as the applicant. Turkey's path to membership was prolonged. An Association Agreement was signed as early as 1963. The country's first application to join was in 1987, but was put on hold since new applicants were not then being considered. Subsequently, however, the Union dramatically expanded to include most of the states of Central and Eastern Europe, as well as Malta and Cyprus, which left Turkey's position looking anomalous.
In October 2005, the European Union agreed to begin the negotiating process with Ankara. Opinion inside the Union was divided on the issue. The unresolved position of Cyprus was an obvious difficulty. With a population of nearly 78 million, almost all of them Muslims, Turkey would be the largest member state close behind Germany with just over 82 million, 2.4 per cent of whom were of Turkish origin. Supporters of the Turkish application pointed to the country's key strategic position. Turkish membership would give the Union an extensive frontier with states in the Middle East and the Caucasus, the merits of which could be argued either way. The Union would almost certainly become more closely involved with contentious areas and issues hitherto at some remove. Conversely, however, Turkey's powerful armed forces would add considerably to the Union's military potential. Membership of the Union would certainly send an important signal for the 21st century that Islam and Christianity could work in harmony.
On 12 September 2010, Turkish voters overwhelmingly endorsed a government-backed list of 26 amendments to the country's 1982 Constitution, which were designed to reinforce its bid to join the European Union, but which were strongly opposed by secularist parties. Areas of Europe across the Balkans and in Andalucia had an Islamic as well as Christian heritage, and Istanbul was declared European City of Culture for 2010. Perhaps the case for Turkey's admission into the European Union was put most eloquently by President Barack Obama before the Turkish Parliament on 6 April 2009 when he when he reminded his listeners that Turkey and Europe were united by more than the bridges across the Bosporus. Europe, he said, gained by diversity and this would be enhanced by Turkish membership.
Erdogan's AK P remained the dominant force in the country's politics, securing a convincing majority in the parliamentary elections of June 2011 with 49.8 per cent of the vote. Its main rival, the Republican People's Party, which had a more secular approach, came second with 26 per cent. While the AK P was clearly popular, it did have its critics. June 2013 saw substantial protests in Istanbul. On 1 July 2014, however, Erdogan announced that he would stand for president under the country's new directly elected system. The following month, he was elected, confirming him as Turkey's most influential politician.
No longer imperial, nor as cosmopolitan as it had been in Ottoman times, Istanbul remained one of the world's great cities, still uniquely embracing Europe and Asia across the narrow waters of the Bosphorus, a symbol for the future many hoped.
Envoi
The Middle East in 2010 was a region of promise and paradox. Long gone were the empires of the Ottomans, British and French, the last two never having been other than birds of passage. The major outside power was the United States, but the problems of Iraq after 2003 showed that even it had limitations, and 31 August 2010 was to see the end of an active American combat role in the country. Despite the problems of reconstruction, and the divisions between Shia and Sunni, Arab and Kurd, which had festered since its very creation, Iraq possessed one of the world's most important oil reserves, offering possibilities for the future. If the Hashemites were long gone from Baghdad, the family still ruled Jordan under King Abdullah II. Israel was a fully-fledged democracy with a sophisticated economy, but the security problems apparent since its victory in 1949 remained. American diplomacy had closely engaged with the Israeli-Palestinian conflict for decades, but had failed to resolve it. The Palestinians lacked statehood, and the two components of the fledgling Palestinian Authority were divided by a secular Fatah in the West Bank and an Islamic Hamas in Gaza. Turkey moved in international affairs as an increasingly confident regional power. In contrast with an ageing European Union, which it aspired to join, Turkey had a young population, as, indeed, had the Middle East in general.
The end of the Cold War did not diminish the Middle East's importance in world affairs, as two wars involving Iraq demonstrated. Failure to resolve the Israeli-Palestinian impasse had ramifications well beyond the region, as well as tragedies for those directly involved. It was significant that President Obama's first overseas trip after his inauguration included Turkey. Then, on 4 June 2009, he made a major speech at Cairo University in which he declared that he had come to look for a new beginning in the relationship between his country and the world's Muslims. In a wide-ranging review, in which he explored issues of extremism, nuclear weapons, democracy, religious freedom, women's rights and economic development, he stressed the need for an Israeli-Palestinian settlement.
Obama's choice of Cairo reflected Egypt's key position. In the decades since it had thrown off British tutelage the country had grown in population to over 80 million and enjoyed considerable natural wealth, as well as its invaluable tourist revenue. The Suez Canal retained its critical importance. Hosni Mubarak, Vice-President and veteran air force officer, had replaced the assassinated Sadat as President in 1981, ruling the country for the next three decades through his National Democratic Party, maintaining the peace treaty with Israel, and receiving substantial aid from Washington. On 25 January 2011, this apparent stability was shattered when thousands of protesters assembled in Cairo's central Tahrir Square, and then in other cities, demanding democratic reforms and an end to the existing regime. Clashes with the police and government supporters failed to quell or deter them. Faced with the scale of the protests, Mubarak announced that he would not seek re-election in the presidential election scheduled for September, and the government began negotiations with opposition groups. Even so, the protests maintained their intensity. On 10 February, the President made a television address. Confounding the hopes and expectations of the protesters, he made it clear that he would continue in office for the rest of his term. The following afternoon, as crowds massed across the country, Vice-President Omar Suleiman came on state television, and in a brief statement announced that Mubarak was stepping down from the office of President, putting the country's affairs in the hands of the high council of the armed forces. As normality started to return, the army confirmed its commitment to the country's international treaties and to the transfer of power to an elected civilian government.
The potential for a new era was there, but the subsequent course of events exposed dangerous divisions in the country's politics and society. After a transitional period, a democratic election in June 2012 saw a narrow victory for Dr Mohamed Morsi, of the Freedom and Justice Party, strongly linked to the Muslim Brotherhood. But economic problems and what many saw as the pursuit of an Islamist agenda worked against him. In June 2013 mass protest rallies against him took place in Cairo and elsewhere, and on 3 July the army intervened, overthrowing him. Despite large-scale protests by its supporters, in the course of which numbers of whom reportedly were killed, in September the Muslim Brotherhood was declared illegal. The Defence Minister, General (later Field Marshal) Abdel Fattah el-Sisi, emerged as the country's leading contender for power. Resigning from the army, in May 2014 he was elected President.
The dramatic events in Egypt in January and February 2011, and elsewhere in the Middle East where existing regimes were challenged in what came to be called the 'Arab Spring', triggered a similar response in Syria. In 2000 President Hafez al-Asad, who had led the country for three decades, died being succeeded by his son, Bashar al-Asad. Bashar al-Asad came from a medical background and, like his father, his origins were in the minority Alawite community, traditionally strong in the army. The basic problem that he faced, in common with much of the Arab world, was that of a rising youthful population, many of them well educated, whose aspirations could not be met by the country's sluggish economic growth. Protests began in March 2011 in the southern city of Daraa and were soon replicated elsewhere, even in parts of Damascus. As these protests escalated into a full-scale uprising, it became clear that the government could rely on certain key assets, its strong military and security apparatus, support amongst the country's minority communities and a powerful regional ally in Iran.
Ranged against the regime was a variety of sometimes competing groups, mostly drawn from the majority Sunni community. Although the term Free Syrian Army was used, there was no unified command for the tens of thousands of men under arms. Neither side seemed able to secure a clear military advantage. The sectarian dimension to the conflict may be seen from the contribution made to the government's campaign by Iraqi Shia fighters and Shia Hezbollah members from Lebanon, while by 2014 it was believed that thousands of foreign Sunnis were fighting with the opposition. The result has been an intractable civil war in which an estimated three million Syrians became refugees in surrounding countries and with a death toll which by the spring of 2014 was reportedly in excess of 150,000.
The travails of Syria were matched by increasing problems across the border in Iraq. The American military presence there had barely ended in December 2011 when the deeply embedded fault lines in the country reasserted themselves. During the period of active American involvement discontent amongst sections of the Sunni community against the new dispensation had continued to simmer, although not at the same level as before the American military 'surge' of 2007. In the course of 2012 there was a growing feeling amongst them of discrimination at the hands of the Shia-dominated coalition government in Baghdad. In the spring of 2013 tensions between Sunnis and Shias escalated into increasingly serious violence out of which a new force emerged which was to challenge the established order not just in Baghdad but also in Syria.
At the beginning of 2013 an emergent Sunni group known as the Islamic State of Iraq began a series of attacks in the country, while in April the formation of the Islamic State of Iraq and the Levant (ISIL), drawing on support in both Iraq and Syria, was announced. Calling itself the Islamic State, in June the organisation declared a caliphate. After an initial breakthrough in Iraq's Sunni heartland of Anbar Province, its fighters decisively defeated the Iraqi army to capture the country's second city of Mosul. Further advances brought them to within less than 40 miles of Baghdad, while in Syria Raqqa also became a stronghold.
President Obama, amongst others, castigated the movement. On 10 September he listed acts of violence with which it had become associated, including the murder of two American hostages. Two British hostages were also killed, as was another American. Two Japanese nationals and a Jordanian pilot were then killed in early 2015. On 7 August 2014 Obama had authorized air strikes against Islamic State targets in Iraq and then subsequently extended these operations to include Syria. The United States was joined by aircraft from a number of Middle Eastern countries, while the United Kingdom, together with some Western countries, also mounted air strikes in Iraq, but not in Syria. In the course of these events Prime Minister Maliki lost power to his Dawa Party colleague Haydar al-Abbadi, whose cabinet seemed to reflect the demand for greater inclusion. The military successes of the Islamic State in Iraq and Syria inevitably called into question the political shape of the region as it had emerged at the end of the First World War. The organisation's ability to win territory and attract adherents from amongst the Sunni populations of both countries, and beyond, cast a question mark against the boundaries that Britain and France had first posited in the 1916 Sykes-Picot Agreement and which were then with modifications embodied in the post-war Mandates.
The military successes of the Islamic State and its pursuit of a radical Islamic agenda carried serious implications for the region, deepening existing tensions between Sunni and Shia, Muslim and Christian, religious and secular, and Arab and Kurd, threatening to further destabilise Iraq and Syria in the process. Its ability to hold territory and win adherents in both of these countries also called into question the boundaries which had emerged at the end of the First World War. Sunni Turkey and Shia Iran could not ignore what was happening on their borders. In the United States there was seemingly little appetite to become enmeshed in a new ground war in the region. Could air strikes, a highly motivated Peshmerga, and a revived and re-equipped Iraqi army, not to mention the complex nature of the Syrian opposition groups, reverse Islamic State's gains was the question of the hour.
The kaleidoscope in the region was dramatically changing, but this dynamic did not seem to apply to the Israeli-Palestinian question. Although Bush's Annapolis process failed to yield results, the pursuit of a two-state solution was taken forward by the Obama administration with both his successive Secretaries of State, Hillary Rodham Clinton and John F Kerry, engaging in negotiations which could not bridge the distrust between the two parties. In July 2013, Kerry launched a new initiative, which, it was hoped, would bring about a final status agreement in nine months, but in April 2014 the talks were suspended amongst mutual recriminations. Immediately after this, serious violence returned.
On 12 June, three Israeli teenagers were abducted and murdered in the West Bank, followed by the murder of a young Palestinian. As the crisis deepened, rockets were launched into Israel from Gaza, many of which were successfully intercepted by Israel's Iron Dome anti-missile system. On 8 July, Israel launched 'Operation Protective Edge' aimed at Gaza's military infrastructure. A particular target was a complex network of tunnels which had been constructed. Initial air strikes were followed by ground operations. Many civilian casualties were reported. Although a number of temporary truces were negotiated, it was not until 26 August that the Egyptians succeeded in brokering a ceasefire, by which time it is estimated that over 2,000 Palestinians and 73 Israelis had been killed, while much of Gaza's infrastructure was in ruins. Israel's security concerns were matched by the Palestinians' resentment over continued occupation and by Israeli settlements on the West Bank. Jerusalem, the refugees and the nature of a possible border within a two-state solution remained core issues.
This book has analysed the ways in which these societies, Arab, Jewish and Turkish, emerged out of the complex series of events which affected the Middle East between 1914 and 1923. The war and the peace agreements which followed set new agendas for this historic and complex region. If the war of 1914–18 was the product of European rivalries and ambitions, not the least of its consequences was a transformed Middle East in which leaders of courage and imagination, notably Feisal, Weizmann and Mustafa Kemal Atatürk, were inspired to seize the moment, often against difficult odds. Their successes and failures have been traced in this book. Nine decades later, their legacy remains.
# Notes
Preface and Acknowledgements
1. H W V Temperley (ed), _A History of the Peace Conference of Paris_ , Vol VI, (Oxford University Press, London, New York, Toronto: 1924) Chapter 1, 'The Near and Middle East'.
2. See, for example, George Antonius, _The Arab Awakening_ (Hamish Hamilton, London: 1988) and Leonard Stein, _The Balfour Declaration_ (Vallentine, Mitchell & Co Ltd, London: 1961). For a discussion of Antonius's book, see Chapter 1.
The Birth of Nationalisms
1. Lord Kinross, _The Ottoman Centuries: The Rise and Fall of the Turkish Empire_ (Perennial edition, New York: 2002) Parts 1 and 2.
2. While European diplomats were accredited to Constantinople, the Turks themselves used Istanbul. For reasons of consistency, I have used the latter, which the Turks insisted upon after 1923.
3. See entry for 'Turkey' in _Encyclopaedia Britannica_ , 11th edition, Vol XX VII (Cambridge University Press, Cambridge: 1911) pp 426–7.
4. Charles Tripp, _A History of Iraq_ (Cambridge University Press, Cambridge: 2007) p 12.
5. 'Turkey', _Encyclopaedia Britannica_.
6. Justin McCarthy, _The Ottoman Peoples and the End of Empire_ (Arnold, London: 2004) p 51.
7. Alan Palmer, _The Decline and Fall of the Ottoman Empire_ (John Murray, London: 1992) p 214.
8. Andrew Mango, _Atatürk_ (John Murray, London: 1999) Chapters 1–7.
9. The expert was V A Gordelevski, a Russian Turcologist, in a rare Tsarist wartime publication.
10. McCarthy, _The Ottoman Peoples and the End of Empire_ , pp 171–92.
11. C Ernest Dawn, 'From Ottomanism to Arabism: The Origin of an Ideology', _The Review of Politics_ , Vol 23, No 3 (Jul 1961) p 378.
12. English Arabist, traveller and diplomat Gertrude Bell, cited in David Fromkin, _A Peace to End All Peace_ (Andre Deutsch, London: 1989) p 35.
13. Ira Lapidus, _A History of Islamic Societies_ (Cambridge University Press, Cambridge: 2002) p 535.
14. Characterised in Albert Hourani, 'Ottoman Reform and the Politics of Notables', in William R Polk and Richard L Chambers (eds), _Beginnings of Modernisation in the Middle East: The Nineteenth Century_ (University of Chicago Press, Chicago: 1968) pp 41–68.
15. Frank Adams, 'Palestine Agriculture', in _Palestine: A Decade of Development, The Annals of the American Academy of Political and Social Science_ (November 1932) pp 72–83.
16. Adams, 'Palestine Agriculture', pp 72–83.
17. Philip Mattar, _The Mufti of Jerusalem: Al Hajj Amin Al-Husayni and the Palestinian National Movement_ (Columbia University Press, New York: 1988) pp 6–7.
18. M E Yapp, _The Making of the Modern Near East, 1792–1923_ (Longman, Harlow: 1987) pp 132–3.
19. Dawn, 'From Ottomanism to Arabism', pp 10–11.
20. Among critical looks at Antonius are Sylvia G Haim, '"The Arab Awakening", A Source for the Historian?', _Die Welt des Islams_ , Vol 2, No 4 (1953), pp 237–50; Elie Kedourie, _England and the Middle East: The Destruction of the Ottoman Empire, 1914–1921_ (London, Boulder: 1987) pp 29–66, 107–41; Elie Kedourie, _In the Anglo- Arab Labyrinth: The McMahon-Husayn Correspondence and Its Interpretations 1914–1939_ (Cambridge University Press, Cambridge: 1976) pp 64–136, 266–9; Albert Hourani, '"The Arab Awakening", Forty Years Later', in Derek Hopwood (ed), _Studies in Arab History: The Antonius Lectures_ , 1978–87 (Macmillan, Basingstoke: 1990) pp 21–40.
21. Hourani, '" _The Arab Awakening_ ", Forty Years Later', p 26.
22. Antonius, _The Arab Awakening_ , pp 37, 80, 81; Zeine N Zeine, _Arab-Turkish Relations and the Emergence of Arab Nationalism_ (Khayat's, Beirut: 1958) pp 56, 57, 68.
23. See C Ernest Dawn, 'The Origins of Arab Nationalism', in Rashid Khalidi et al, _The Origins of Arab Nationalism_ (Columbia University Press, New York: 1991) pp 18–19.
24. Eliezer Tauber, _The Emergence of the Arab Movements_ (Frank Cass, London: 1993) p 406; C Ernest Dawn, _From Ottomanism to Arabism: Essays on the Origins of Arab Nationalism_ (University of Illinois Press, Urbana: 1973) pp 152–3, puts the figure at only 144.
25. Most notably, Efraim Karsh and Inari Karsh, _Empires of the Sand: The Struggle for Mastery in the Middle East, 1789–1923_ (Harvard University Press, Cambridge MA: 1999) are very hostile to what they consider the imperialist ambitions of Sherif Hussein and the Hasehemites.
26. A useful summation of Dawn's more than three decades of musing on the subject is in Dawn, 'The Origins of Arab Nationalism', pp 3–31.
27. Majid Khadduri, _Political Trends in the Arab World: The Role of Ideas and Ideals in Politics_ (Johns Hopkins Press, Baltimore: 1970) p 19.
28. Cited in Martin Kramer, _Arab Awakening and Islamic Revival: The Politics of Ideas in the Middle East_ (Transaction Publishers, New Brunswick: 1996) p 24.
29. Raymond A Hinnebusch, _Authoritarian Power and State Formation in Ba'thist Syria: Army, Party and Peasant_ (Westview Press, Boulder, CO: 1990) p 45.
30. W Ochsenwald, Religion, _Society and the State in Arabia: The Hijaz under Ottoman Control 1840–1908_ (Ohio State University Press, Columbus, OH: 1984) p 17.
31. Ochsenwald, Religion, _Society and the State in Arabia_ , p 220.
32. W Ochsenwald, 'Ironic origins: Arab nationalism in the Hijaz', in Khalidi et al, _The Origins of Arab Nationalism_ , p 190.
33. James Morris, _The Hashemite Kings_ (Faber and Faber, London: 1959) p 18.
34. Kedourie, _In the Anglo-Arab Labyrinth_ , p 11.
35. Cited in Tufan Buzpinar, 'Opposition to the Ottoman Caliphate in the Early Years of Abdülhamid II: 1877–1882', _Die Welt des Islams_ , New Series Vol 36, Issue I (Mar 1996) p 67.
36. See Elizabeth Monroe, _Britain's Moment in the Middle East 1914–1956_ (Methuen, London: 1963) pp 11–23.
37. Cited in Buzpinar, 'Opposition to the Ottoman Caliphate in the Early Years of Abdülhamid II', p 80.
38. What follows is substantially based on R Baker, _King Husain and the Kingdom of Hejaz_ (Oleander Press, Cambridge: 1979); Kedourie, _In the Anglo-Arab Labyrinth_ ; A Susser and A Shmuelevitz (eds), _The Hashemites in the Modern Arab World: Essays in Honour of the Late Professor Uriel Dann_ (Frank Cass, London: 1995); Morris, _The Hashemite Kings_ ; Joshua Teitelbaum, _The Rise and Fall of the Hashemite Kingdom of Arabia_ (Hurst, London: 2001); and Haifa Alangaria, _The Struggle for Power in Arabia: Ibn Saud, Hussein and Great Britain, 1914–1924_ (Ithaca Press, Reading: 1998).
39. Morris, _The Hashemite Kings_ , p 23.
40. T E Lawrence, _Seven Pillars of Wisdom_ (Wordsworth, London: 1997) p 84.
41. Lawrence, _Seven Pillars of Wisdom_ , p 86.
42. Morris, _The Hashemite Kings_ , pp 24–5.
43. Teitelbaum, _The Rise and Fall of the Hashemite Kingdom of Arabia_ , p 41.
44. Teitelbaum, _The Rise and Fall of the Hashemite Kingdom of Arabia_ , p 41.
45. Abdullah, _Memoirs of King Abdullah of Transjordan_ (Cape, London: 1950) p 70.
46. J Nevo, 'Abdullah's memoirs as historical source material', in Susser and Shmuelevitz, _The Hashemites in the Modern Arab World_ , p 166.
47. Sir Louis Mallet to Sir Edward Grey, 18 March 1914, in G P Gooch and Harold Temperley, _British Documents on the Origins of the War, 1898–1914_ , Vol X, Part II ( HMSO, London: 1938) p 827, hereafter _British Docs_.
48. Alangaria, _The Struggle for Power in Arabia_ , p 63.
49. See James Nicholson, 'The Hejaz Railway', _Asian Affairs_ , Vol 37, No 3 (2006) pp 320–36 for the story of the railway.
50. Teitelbaum, _The Rise and Fall of the Hashemite Kingdom of Arabia_ , p 69.
51. Teitelbaum, _The Rise and Fall of the Hashemite Kingdom of Arabia_ , pp 69–70.
52. A I Dawisha, _Arab Nationalism in the Twentieth Century: From Triumph to Despair_ (Princeton University Press, Princeton: 2003) p 35.
53. See Ochsenwald, 'Ironic Origins: Arab Nationalism in the Hijaz', pp 189–203.
54. For the history of Zionism, see Walter Laqueur, _A History of Zionism_ (Schocken Books, New York: 1972) and Nahum Sokolow, _History of Zionism 1600–1918_ , 2 Vols (Longmans, Green and Co, London: 1919).
55. Alex Bein, _Theodore Herzl_ (The Jewish Publication Society of America, Philadelphia: 1941) pp 112–16.
56. See Theodore Herzl, _The Jewish State: An Attempt at a Modern Solution of the Jewish Question_ (H Pordes, London: 1972, 6th edition, revised, with foreword by Israel Cohen; original edition 1896).
57. 'The Basle Declaration', in Walter Laqueur (ed), _The Israel-Arab Reader_ (Pelican Books, London: 1970) pp 28–9; Laqueur, _A History of Zionism_ , pp 103–8.
58. Sokolow, _History of Zionism_ , Vol I, p 287; Vol II, pp 81, 284.
59. Dr Yehuda Slutsky, 'Under Ottoman Rule (1880–1917)', in Israel Pocket Library, _History from 1880_ (Keter Publishing House, Jerusalem: 1973) p 17.
60. Chaim Weizmann, _Trial and Error: The Autobiography of Chaim Weizmann_ (Hamish Hamilton, London: 1949) pp 11–27; Jehuda Reinharz, _Chaim Weizmann: The Making of a Zionist Leader_ (Oxford University Press, New York and Oxford: 1985) p 7; Norman Rose, _Chaim Weizmann: A Biography_ (Weidenfeld and Nicolson, London: 1986) pp 16–18.
61. Weizmann, _Trial and Error_ , pp 13–14.
62. Weizmann to Shlomo Tsvi Sokolovsky, Motol, Summer 1885, in Leonard Stein (ed), _The Letters and Papers of Chaim Weizmann_ , Series A, Vol I, Summer 1885–29 October 1902 (Oxford University Press, London: 1968) pp 35–7; hereafter _LPCW_ , Vol I.
63. Weizmann, _Trial and Error_ , pp 34–5.
64. Weizmann, _Trial and Error_ , pp 38–40.
65. Reinharz, _Chaim Weizmann: The Making of a Zionist Leader_ , pp 35–6.
66. Weizmann, _Trial and Error_ , pp 44–50.
67. Weizmann, _Trial and Error_ , pp 69, 76; Reinharz, _Chaim Weizmann: The Making of a Zionist Leader_ , p 51; Rose, _Chaim Weizmann_ , p 44.
68. Weizmann, _Trial and Error_ , pp 51–2.
69. Stein, _The Balfour Declaration_ , pp 90–1.
70. Weizmann, _Trial and Error_ , pp 61–8.
71. Weizmann, _Trial and Error_ , pp 80–1.
72. Professor Hugo Bergmann, 'Dr Weizmann's conception of the Hebrew University', in Paul Goodman (ed), _Chaim Weizmann: A Tribute on his Seventieth Birthday_ (Victor Gollancz Ltd, London: 1945) p 94; Reinharz, _Chaim Weizmann: The Making of a Zionist Leader_ , pp 86–91.
73. Weizmann to Theodore Herlz, Vienna, 21 May 1902; Weizmann to Theodore Herzl, Vienna, 4 June 1902; Weizmann to Theodore Herzl, Vienna, 25 June 1902: _LPCW_ , Vol I, 204, 207, 209, pp 263–9.
74. Weizmann, _Trial and Error_ , pp 103–5.
75. Weizmann, _Trial and Error_ , p 145; Vera Weizmann, _The Impossible Takes Longer: Memoirs by the Wife of Israel's First President as Told to David Tutaev_ (Hamish Hamilton, London: 1967) pp 1–3, 12–13.
76. Bein, _Theodore Herzl_ , pp 439–41.
77. Weizmann, _Trial and Error_ , pp 110–17.
78. Bein, _Theodore Herzl_ , pp 453–503.
79. Weizmann, _Trial and Error_ , p 146.
80. Weizmann, _Trial and Error_ , pp 123–34.
81. Vera Weizmann, _The Impossible Takes Longer_ , pp 30–5; Rose, _Chaim Weizmann_ , p 113.
82. Blanche E C Dugdale, _Arthur James Balfour, First Earl of Balfour_ (Hutchinson, London: 1936) Vol I, pp 325–6; Weizmann, _Trial and Error_ , p 142.
83. Weizmann, _Trial and Error_ , pp 142–5; Dugdale, _Arthur James Balfour_ , Vol I, pp 326–7; 'Introduction by the Rt Hon A J Balfour, MP' 20 September 1918, in Sokolow, _History of Zionism_ , Vol I, pp xxix–xxxiv; Reinharz, _Chaim Weizmann: The Making of a Zionist Leader_ , pp 270–5.
84. Reinharz, _Chaim Weizmann: The Making of a Zionist Leader_ , pp 275–7.
85. Stein, _The Balfour Declaration_ , pp 80–1. Makers
86. Weizmann, _Trial and Error_ , pp 161–9; Reinharz, _Chaim Weizmann: The Making of a Zionist Leader_ , pp 316–17.
87. Weizmann, _Trial and Error_ , pp 173–4; Vera Weizmann, _The Impossible Takes Longer_ , p 39; Reinharz, _Chaim Weizmann: The Making of a Zionist Leader_ , pp 359–67; David Vital, _Zionism: The Crucial Phase_ (Clarendon Press, Oxford: 1987) pp 120–1.
88. For the history of the railway, see Sean McMeekin, _The Berlin–Baghdad Express: The Ottoman Empire and Germany's Bid for World Power 1898–1918_ (Allen Lane, London: 2010); A J P Taylor, _The Struggle for Mastery in Europe 1848–1918_ (Oxford University Press, London: 1954) pp 383–5.
89. Winston S Churchill, _The World Crisis 1911–1918_ (Odhams Press Ltd, London: 1938 edition), Vol I, pp 436–7.
90. Palmer, _The Decline and Fall of the Ottoman Empire_ , pp 170–1, 220–2.
91. W W Gottlieb, _Studies in Secret Diplomacy during the First World War_ (George Allen & Unwin Ltd, London: 1957) pp 19–22.
Wartime Promises and Expectations
1. General Friedrich von Bernhardi, _Germany and the Next War_ (Edward Arnold, London: 1914; original edition (Stuttgart: 1912) pp 95–6.
2. 'The Turco-German Treaty of Alliance, 2 August 1914', in M S Anderson, _The Great Powers and the Near East 1774–1923_ (Edward Arnold, London: 1970) p 157; Mango, _Atatürk_ , pp 132–4.
3. Viscount Grey of Fallodon, KG, _Twenty-Five Years 1892–1916_ (Hodder and Stoughton, London: 1925) Vol II, p 165.
4. Lt-Col J W B Merewether, CIE and Lt-Col Sir Frederick Smith, Bart, _The Indian Corps in France_ (John Murray, London: 1918).
5. Winston S Churchill, _The World Crisis, 1911–1918_ , Vol I, p 437; see also _Correspondence Leading to the Rupture of Relations with Turkey_ , Cmd. 7628: 1914, _The Times Documentary History of the War_ , Diplomatic, Part 3 (Printing House Square, London: 1919) Vol IX.
6. Mr Beaumont to Sir Edward Grey, Constantinople, 11 August 1914, _The Times Documentary History of the War_ , Vol IX, p 94.
7. The Rt Hon Viscount Samuel, _Memoirs_ (The Cresset Press, London: 1945) p 139.
8. Samuel, _Memoirs_ , pp 140–1; Vital, _Zionism: The Crucial Phase_ , pp 92–3.
9. Jonathan Schneer, _The Balfour Declaration: The Origins of the Arab-Israeli Conflict_ (Bloomsbury, London: 2010) p 116.
10. Weizmann, Trial and Error, pp 190–1; Weizmann to Ahad Ha'am, London, 12 November 1914; Weizmann to Charles P Scott, Manchester, 12 November 1914, in Leonard Stein (ed), _LPCW_ , Series A, Vol VII, August 1914–November 1917 (Oxford University Press, London and New York: 1975) 32, 33, pp 37–9; hereafter _LPCW_ , Vol VII.
11. Trevor Wilson (ed), _The Political Diaries of C.P. Scott 1911–1928_ (Collins, London: 1970) p 113.
12. Weizmann to Vera Weizmann, Manchester, 10 December 1914; Weizmann to Charles P Scott, Manchester, 13 December 1914, in _LPCW_ , Vol VII, 65, 67, pp 77–80.
13. Weizmann, _Trial and Error_ , pp 192–3; Reinharz, _Chaim Weizmann: The Making of a Statesman_ , pp 24–5.
14. Weizmann to Yehiel Tschlenow and Nahum Sokolow, London, 20 March 1915, _LPCW_ , Vol VII, 141, pp 178–9; Stein, _The Balfour Declaration_ , pp 107–11.
15. Weizmann to Charles P Scott, Manchester, 23 March 1915; Weizmann to Yehiel Tschlenow and Nahum Sokolow, London, 15 April 1915, _LPCW_ , Vol VII, 147, 154, pp 183–5, 190–1.
16. German officers seconded to the Ottoman army were promoted one rank. Hence Generals Liman von Sanders, Erich von Falkenhayn and Colmar von der Goltz were styled Field Marshal during their service in Turkey.
17. Justin McCarthy, _Muslims and Minorities: The Population of Ottoman Anatolia and the End of the Empire_ (New York University Press, New York: 1983) pp 50, 52.
18. Justin McCarthy et al, _The Armenian Rebellion at Van_ (University of Utah Press, Salt Lake City, UT, 2006) pp 162–4, 180–5.
19. See Justin McCarthy, _Death and Exile: The Ethnic Cleansing of Ottoman Muslims, 1821–1922_ (Darwin Press, Princeton: 1995). For the Circassians and other Muslim refugees from the Caucasus, see pp 32–6, 47–9.
20. Lord Kitchener to Sir Edward Grey, 6 February 1914 cited in _British Docs_ , Vol X, p 827. See also Kedourie, _In the Anglo-Arab Labyrinth_ , p 5.
21. Kitchener to Grey, 14 February 1914, _British Docs_ , Vol X, p 827.
22. Kedourie, _In the Anglo-Arab Labyrinth_ , p 7.
23. C Ernest Dawn, 'The Amir of Mecca Al-Husayn Ibn-'Ali and the Origin of the Arab Revolt', _Proceedings of the American Philosophical Society_ , Vol 104, No 1 (15 Feb 1960) p 22; Kedourie, _England and the Middle East_ , pp 19, 52.
24. Kedourie, _In the Anglo-Arab Labyrinth_ , pp 21–1.
25. Joshua Teitelbaum, 'Sherif Hussein ibn Ali and the Hashemite vision of the post- Ottoman order: from chieftaincy to suzerainty', _Middle Eastern Studies_ , Vol 34, No 1 (1998) p 106.
26. Kedourie, _In the Anglo-Arab Labyrinth_ , pp 20–5.
27. Kitchener's paper is cited in _Jukka Nevakivvi, Britain, France and the Arab Middle East 1914–1920_ (Athlone Press, London: 1969), p 18; Asquith is cited on p 17.
28. T G Fraser, 'The Middle East. Partition and reformation', in Seamus Dunn and T G Fraser (eds), _Europe and Ethnicity: The First World War and Contemporary Ethnic Conflict_ (Routledge, London: 1996) p 163.
29. Kedourie, _England and the Middle East_ , pp 48–56.
30. Dawn, 'Ottomanism to Arabism', p 28.
31. Antonius, _The Arab Awakening_ , p 79.
32. Fromkin, _A Peace to End All Peace_ , pp 174–6.
33. Dawn, 'The Amir of Mecca Al-Husayn Ibn-'Ali and the Origin of the Arab Revolt', p 24.
34. T E Lawrence, report, 13 May 1917, 'Notes on Hejaz Affairs', _Arab Bulletin_ (13 May 1917).
35. Mary C Wilson, 'The Hashemites, the Arab Revolt, and Arab Nationalism', in Khalidi et al, _The Origins of Arab Nationalism_ , p 214.
36. Efraim Karsh and Inari Karsh, 'Myth in the Desert, or not the Great Arab Revolt', _Middle Eastern Studies_ , Vol 33, No 2 (1997) p 267.
37. Amir Abdullah to Ronald Storrs, 14 July 1915. The correspondence can be found in Great Britain Parliamentary Papers, Misc. No. 3., 1939, Cmd 5957; hereafter Cmd 5957.
38. Ronald Storrs, _Orientations_ (Ivor Nicholson & Watson, London: 1939) pp 160–1.
39. The correspondence can be found in Cmd 5957 or in Antonius, _The Arab Awakening_ , Chapter 6.
40. The following draws on Kedourie, _In the Anglo-Arab Labyrinth_ , Chapter 2; Monroe, _Britain's Moment in the Middle East_ , Chapter 2; Isaiah Friedman, _The Question of Palestine 1914–1918: British-Jewish-Arab Relations_ (Routledge & Kegan Paul, London: 1973) Chapter 6; and Briton Cooper Busch, _Britain, India and the Arabs, 1914–1921_ (University of California Press, Berkeley: 1971) Chapter 2.
41. Kedourie, _In the Anglo-Arab Labyrinth_ , p 4.
42. Kedourie, _In the Anglo-Arab Labyrinth_ , p 120.
43. Sherif Hussein to McMahon, 9 September 1915, Cmd 5957.
44. Fromkin, _A Peace to End All Peace_ , pp 176–80.
45. Friedman, _The Question of Palestine 1914–1918_ , p 72.
46. Fromkin, _A Peace to End All Peace_ , pp 177–8.
47. McMahon to Sherif Hussein, 24 October 1915, Cmd 5957.
48. Sir Henry McMahon to Sir John Shuckburgh, 12 March 1922, in Martin Gilbert, _Winston S. Churchill_ , Companion Volume IV, Part 3: April 1921–November 1922 (Heinemann, London: 1977) p 1805, hereafter Gilbert, _Churchill Companion_ , IV, Part 3; Samuel, _Memoirs_ , pp 172–3.
49. Antonius, _The Arab Awakening_ , pp 168–79.
50. Fraser, 'The Middle East: Partition and reformation', p 166.
51. Fromkin, _A Peace to End All Peace_ , pp 218–9.
52. See Karsh and Karsh, 'Myth in the Desert', pp 295–7.
53. Karsh and Karsh, 'Myth in the Desert', pp 295–7.
54. Howard Morley Sachar, _The Emergence of the Middle East, 1914–1924_ (Allen Lane, Penguin Press, London: 1970) pp 134–5.
55. Bruce Westrate, _The Arab Bureau: British Policy in the Middle East, 1916–1920_ (Pennsylvania State University Press, University Park, PA: 1992) pp 6–9.
56. T E Lawrence to Lord Curzon, 27 September 1919, in David Garnett (ed), _The Letters of T E Lawrence_ (Jonathan Cape, London: 1938) pp 291–3.
57. Lawrence, _Seven Pillars of Wisdom_ , p 76.
58. See Lawrence, _Seven Pillars of Wisdom_ , p 51, which questions Abdullah's sincerity.
59. James Barr, _Setting the Desert on Fire: T E Lawrence and Britain's Secret War in Arabia, 1916–18_ (Bloomsbury, London: 2007) pp 102–3.
60. Lawrence, _Seven Pillars of Wisdom_ , pp 183–4.
61. Lawrence, _Seven Pillars of Wisdom_ , p 215.
62. Lawrence, _Seven Pillars of Wisdom_ , p 85.
63. Jeremy Wilson, _Lawrence of Arabia: The Authorized Biography of T E Lawrence_ (Heinemann, London: 1989) pp 361–2.
64. Two recent accounts of Lawrence and the Arab Revolt are Barr, _Setting the Desert on Fire_ , and Wilson, _Lawrence of Arabia_ , Chapters 13–26.
65. Slutsky, 'Under Ottoman Rule (1880–1917)', pp 24–7.
66. L S Amery, _My Political Life, Volume 2: War and Peace, 1914–1929_ (Hutchinson, London: 1953) pp 117–8; John Henry Patterson, _With the Zionists in Gallipoli_ (Hutchinson, London: 1916). Patterson is best known for _The Man-Eaters of Tsavo_ (Macmillan, London: 1907). His African adventures are vividly portrayed in the 1996 film _The Ghost and the Darkness_.
67. Avi Shlaim, _The Iron Wall: Israel and the Arab World_ (Penguin, London: 2000) p 11; Rose, _Chaim Weizmann_ , pp 131–3.
68. David Ben-Gurion, _Recollections_ , ed Thomas R Bransten (Macdonald Unit 75, London: 1970) pp 60–1.
69. David Lloyd George, _War Memoirs_ , 2 vols (Odhams Press Ltd, London: 1938) Vol I, pp 112–17.
70. Weizmann, _Trial and Error_ , pp 218–22; Wilson (ed), _The Political Diaries of C.P. Scott_ , p 128; Lloyd George, _War Memoirs_ , Vol I, pp 347–8; Reinharz, _Chaim Weizmann: The Making of a Statesman_ , pp 40–72; Rose, _Chaim Weizmann_ , pp 152–8.
71. Lloyd George, _War Memoirs_ , Vol I, p 349; The Rt Hon The Earl Lloyd George of Dwyfor, OM, 'Foreword', in Goodman, _Chaim Weizmann_ ; Reinharz, _Chaim Weizmann: The Making of a Statesman_ , pp 67–9.
72. Andrea Bosco and Alex May (eds), _The Round Table, the Empire/ Commonwealth and British Foreign Policy_ (Lothian Foundation Press, London: 1997) pp i–xv.
73. Weizmann, _Trial and Error_ , p 229.
74. For a discussion see Schneer, _The Balfour Declaration_ , p 366.
75. Stein, _The Balfour Declaration_ , pp 362–9.
76. Weizmann, _Trial and Error_ , pp 235–6; Stein, _The Balfour Declaration_ , pp 368–9.
77. Weizmann to Vladimir Jabotinsky, Hazeley Down, 8 February 1917; Weizmann to C P Scott, Manchester, 20 March 1917, _LPCW_ , Vol VII, 306, 321, pp 328–9; Weizmann, _Trial and Error_ , pp 238–40; Stein, _The Balfour Declaration_ , pp 370–4.
78. Weizmann to C P Scott, Manchester, 23 March 1917, LPCW, Vol VII, 323, pp 346–7; Weizmann, _Trial and Error_ , pp 240–1; Stein, _The Balfour Declaration_ , pp 378–85.
79. Cambon's letter of 4 June 1917 is cited in Sokolow, _History of Zionism_ , Vol II, p 53; Friedman, _The Question of Palestine 1914–1918_ , pp 161–2.
80. Note of Interview with Robert Cecil at the Foreign Office, 25 April 1917, _LPCW_ , Vol VII, pp 375–8; Weizmann, _Trial and Error_ , pp 241–2; Stein, _The Balfour Declaration_ , pp 392–3.
81. Weizmann to Louis D Brandeis, Washington, 23 April 1917, _LPCW_ , Vol VII, 351, pp 371–3; Dugdale, _Arthur James Balfour_ , Vol II, pp 169–70.
82. Weizmann, _Trial and Error_ , pp 246–51; Reinharz, _Chaim Weizmann: The Making of a Statesman_ , pp 153–71.
83. Weizmann to the Editor of _The Times_ , London, 27 May 1917, _LPCW_ , Vol VII, 405, pp 418–19.
84. Weizmann, _Trial and Error_ , pp 252–5; Stein, _The Balfour Declaration_ , pp 442–61.
85. Weizmann to Sir Ronald Graham, London, 13 June 1917, _LPCW_ , Vol VII, 432, pp 438–42.
86. Weizmann to Harry Sacher, Manchester, 20 June 1917, _LPCW_ , Vol VII, 435, pp 444–5.
87. Esco Foundation for Palestine, _Palestine: A Study of Jewish, Arab, and British Policies_ , 2 vols (Published for the Esco Foundation for Palestine, Inc, Yale University Press, New Haven: 1947) Vol I, pp 102–3 (hereafter Esco, _Palestine_ ). Herbert Sidebotham, _Great Britain and Palestine_ (Macmillan, London: 1937) p 65.
88. See Schneer, _The Balfour Declaration_ , pp 334–5.
89. Stein, _The Balfour Declaration_ , p 470.
90. Friedman, _The Question of Palestine 1914–1918_ , p 257.
91. War Cabinet 227, 3 September 1917, CAB 23/4, in Fraser, _The Middle East 1914–1979_ , pp 13–14.
92. Weizmann to Louis D Brandeis, Washington (?), 12 September 1917, _LPCW_ , Vol VII, 496, pp 505–6; Weizmann, _Trial and Error_ , pp 257–8; Stein, _The Balfour Declaration_ , pp 504–7; Friedman, _The Question of Palestine 1914–1918_ , pp 261–3.
93. Weizmann to Philip Kerr, London, 19 September 1917; Weizmann to Nahum Sokolow, Brighton, 30 September 1917: _LPCW_ , Vol VII, 507, 513, pp 516, 520.
94. Weizmann to Arthur J Balfour, London, 3 October 1917, _LPCW_ , Vol VII, 514, pp 521–2; Weizmann, _Trial and Error_ , pp 257–8.
95. War Cabinet 245, 4 October 1917, CAB 23/4, in Fraser, _The Middle East 1914–1979_ , pp 15–17; Amery, _My Political Life_ , Vol 2, pp 116–17.
96. Weizmann to Louis D Brandeis, Washington, 9 October 1917, _LPCW_ , Vol VII, 516, pp 530–1.
97. Brandeis to Jacob de Haas, 17 October 1917, in Melvin L Urofsky and David W Levy (eds), _Letters of Louis D Brandeis, Vol IV (1916–1921)_ (State University of New York Press, Albany: 1975) pp 318–9; Stein, _The Balfour Declaration_ , pp 528–32; Weizmann, _Trial and Error_ , p 261.
98. Stein, _The Balfour Declaration_ , p 274.
99. War Cabinet 261, 31 October 1917, CAB23/4, in Fraser, _The Middle East 1914–1979_ , pp 17–18; _Palestine Royal Commission Report_ , Cmd 5479 (London: 1937) p 22.
100. Weizmann to Lord Rothschild, Tring, 2 November 1917, _LPCW_ , Vol VII, pp 541–2.
101. Weizmann to Jacobus H Kann, The Hague, 6 December 1917, in Dvorah Barzilay and Barnet Litvinoff (eds), _LPCW_ , Series A, Vol VIII, November 1917– October 1918 (Transaction Books, Rutgers University, Israel Univerisities Press, Jerusalem: 1977) 21, pp 19–20, hereafter _LPCW_ , Vol VIII; Weizmann, _Trial and Error_ , p 262; Vera Weizmann, _The Impossible Takes Longer_ , p 78; Sir Charles Kingsley Webster, _The Founder of the National Home_ (Yad Chaim Weizmann, Rehovoth: 1955) pp 30–1.
102. Sokolow, _History of Zionism_ , Vol II, pp 127–8.
103. Matthew Hughes (ed), _Allenby in Palestine: The Middle East Correspondence of Field Marshal Viscount Allenby June 1917–October 1919_ (Sutton Publishing for the Army Records Society, Stroud: 2004) pp 7–11.
104. Gwynne Dyer, 'The Turkish Armistice of 1918', I, _Middle Eastern Studies_ , Vol 8, No 2 (May 1972) pp 144–6.
105. http://www.americanrhetoric.com/speeches/wilsonfourteen points.htm
106. Dyer, 'The Turkish Armistice of 1918', p 342, n 2.
107. Dyer, 'The Turkish Armistice of 1918', p 147.
108. Dyer, 'The Turkish Armistice of 1918', p 150.
109. Martin Gilbert, _Sir Horace Rumbold: Portrait of a Diplomat 1869–1941_ (Heinemann, London: 1973) p 249.
110. Dyer, 'The Turkish Armistice of 1918', p159.
111. Mahmud Kemal Inal, _Osmanli Devrinde Son Sadriazamlar_ , 2nd edition (Istanbul MEB: 1965) p 2004.
112. Dyer, 'The Turkish Armistice of 1918', pp 153–4.
113. Dyer, 'The Turkish Armistice of 1918', pp 154–6.
114. A J Barker, _The Neglected War: Mesopotamia 1914–1918_ (Faber and Faber, London: 1967) pp 266, 296. Of the original 9,300 Indian troops, 2,500 perished.
115. Dyer, 'The Turkish Armistice of 1918', p 161.
116. Dyer, 'The Turkish Armistice of 1918', p 166.
117. Mahmud Kemal Inal, _Osmanli Devrinde Son Sadriazamlar_ , p 2034.
118. Dyer, 'The Turkish Armistice of 1918', pp 166–7.
119. Dyer, 'The Turkish Armistice of 1918', p 167.
120. Dyer, 'The Turkish Armistice of 1918', pp 168–9.
121. Edward Erickson, _Ordered to Die: A History of the Ottoman Army in the First World War_ (Greenwood, Westport, Conn: 2001) pp 231–5.
122. Dyer, 'The Turkish Armistice of 1918', pp 336–41.
123. Dyer, 'The Turkish Armistice of 1918', p 337.
124. Cemal Kutay, _Osmanlidan Cumhuriyete: Yüzyılımızda bir Insanımız Hüseyin Rauf Orbay_ (1881–1964) Vol 3 (Kazanci, Isttanbul: 1992) p 174.
125. According to some reports they boarded a torpedo-boat the Germans had captured from the Russians. The date of their flight is given as 8/9 November in some sources. See Andrew Mango, _Atatürk_ , p 190, n 21.
Arabs and Zionists in Paris
1. Hughes (ed), _Allenby in Palestine_ , pp 13–14.
2. Weizmann to Jacob de Haas, New York, (12) December 1917; Weizmann to Sir Mark Sykes, London, 16 January 1918, _LPCW_ , Vol VIII, 23, 69, pp 20–1, 62–3; Weizmann, _Trial and Error_ , pp 266–7; Stein, _The Balfour Declaration_ , p 622.
3. Weizmann to Vera Weizmann, London, 24–6 March 1918, _LPCW_ , Vol VIII, 138, pp 106–9.
4. Weizmann to Vera Weizmann, London, 6 April 1918, _LPCW_ , Vol VIII, 151, pp 118–20.
5. Weizmann to William G A Ormsby-Gore, Tel Aviv, 16 April 1918, _LPCW_ , Vol VIII, 161, pp 128–30; Storrs, _Orientations_ , p 366.
6. Weizmann to William G A Ormsby-Gore, 16 April 1918, _LPCW_ , Vol VIII, 161, pp 128–30.
7. Weizmann to Vera Weizmann, London, 18 April 1918; Weizmann to Louis D Brandeis, Washington, 25 April 1918: _LPCW_ , Vol VIII, 163, 175, pp 131–3, 158–67.
8. Weizmann to Vera Weizmann, London, 17 June 1918; Weizmann to Louis D Brandeis, Washington, 23 June 1918: _LPCW_ , Vol VIII, 213, 215, pp 209–11, 212–3; Weizmann, _Trial and Error_ , pp 290–5.
9. Weizmann to Arthur J Balfour, London, 17 July 1918, _LPCW_ , Vol VIII, 232, pp 228–32; Weizmann, _Trial and Error_ , pp 290–5.
10. Weizmann to Vera Weizmann, 27 July 1918, _LPCW_ , Vol VIII, 236, 237–40; Weizmann, _Trial and Error_ , pp 295–7.
11. Antonius, _The Arab Awakening_ , p 269.
12. Kedourie, _In the Anglo-Arab Labyrinth_ , pp 190–1.
13. Friedman, _The Question of Palestine 1914–1918_ , p 328.
14. Fromkin, _A Peace to End All Peace_ , pp 288–9.
15. Teitelbaum, 'Sherif Husayn ibn Ali and the Hashemite vision of the post- Ottoman order', p 109.
16. Lawrence, _Seven Pillars of Wisdom_ , p 551.
17. Wilson, _Lawrence of Arabia_ , pp 469–70, 511–12.
18. Wilson, _Lawrence of Arabia_ , p 566.
19. See Wilson, _Lawrence of Arabia_ , pp 566–8.
20. War Cabinet Meeting, 3 October 1918, UK CAB 23181482, The National Archives, Kew, London, (hereafter TNA).
21. Fromkin, _A Peace to End All Peace_ , pp 338–9.
22. See John Fisher, 'Syria and Mesopotamia in British Middle Eastern Policy in 1919', _Middle Eastern Studies_ , Vol 34, No 2 (Apr 1998) p 130.
23. Fisher, 'Syria and Mesopotamia in British Middle Eastern Policy in 1919', p 131.
24. Meir Zamir, 'Faisal and the Lebanese Question, 1918–20', _Middle Eastern Studies_ , Vol 27, No 3 (Jul 1991) pp 404–26.
25. Zeine N Zeine, _The Struggle for Arab Independence: Western Diplomacy and the Rise and Fall of Faisal's Kingdom in Syria_ (Khayats, Beirut: 1960) p 33.
26. Zeine, _The Struggle for Arab Independence_ , pp 213–14.
27. James L Gelvin, _Divided Loyalties: Nationalism and Mass Politics in Syria at the Close of Empire_ (University of California Press, Berkeley: 1998) p 13.
28. M S Anderson, _The Eastern Question, 1774–1923_ (Macmillan, London: 1966) p 378.
29. Fromkin, _A Peace to End All Peace_ , p 341.
30. Cited in 'Report of a Committee Set Up to Consider Certain Correspondence between Sir Henry McMahon and the Sherif of Mecca in 1915 and 1916', 1939, Cmd 5974, pp 50–1.
31. Jukka Nevakivi, _Britain, France, and the Arab Middle East, 1914–1920_ (Athlone Press, London: 1969) p 82.
32. John Darwin, _Britain, Egypt and the Middle East: Imperial Policy in the Aftermath of War, 1918–1922_ (Macmillan, London: 1981) p 155.
33. Zeine, _The Struggle for Arab Independence_ , pp 49–51.
34. Wilson, _Lawrence of Arabia_ , p 586.
35. Kedourie, _In the Anglo-Arab Labyrinth_ , p 213.
36. Timothy J Paris, 'British Middle East Policy-Making after the First World War: the Lawrentian and Wilsonian Schools', _The Historical Journal_ , Vol 41, No 3 (Sep 1998) p 773.
37. See the discussions in Marian Kent, _Oil and Empire: British Policy and Mesopotamian Oil, 1900–1920_ (Macmillan, London: 1976) pp 124–6, and Darwin, Britain, _Egypt and the Middle East_ , pp 258–65.
38. There is no actual official government note of this conversation. See S W Roskill, _Hankey, Man of Secrets, Volume 2: 1919–1931_ (Collins, London: 1972) pp 28–9. In August 1919 Clemenceau relied on the meeting to accuse Britain of perfidy: E L Woodward and Rohan Butler (eds), _Documents on British Foreign Policy, 1919–1939_ , First Series, Volume IV (1919) (Her Majesty's Stationery Office, London: 1952) Doc 242, (hereafter _DBFP_ , Vol IV, references are to Document numbers). See also Lloyd George, _The Truth about the Peace Treaties_ (Victor Gollancz, London: 1938) p 1038.
39. Wilson, _Lawrence of Arabia_ , p 591.
40. Paris, 'British Middle East Policy-Making after the First World War', p 779. See also Timothy J Paris, _Britain, the Hashemites, and Arab Rule, 1920–1925: The Sherifian Solution_ (Frank Cass, London: 2003).
41. John Fisher, _Curzon and British Imperialism in the Middle East 1916–19_ (Frank Cass, London: 1999) p xv.
42. Wilson, _Lawrence of Arabia_ , pp 592–3.
43. Weizmann to Aaron Aaronson, Washington, (22–23) October 1918; Weizmann to Gilbert F Clayton, GHQ, Palestine, 27 November 1918, in Jehuda Reinharz (ed), _LPCW_ , Series A, Vol IX, October 1918–July 1920 (Transaction Books, Rutgers University; Israel Universities Press, Jerusalem: 1977) 1, 38, pp 1, 40–3; hereafter _LPCW_ , Vol IX.
44. Weizmann to Gilbert F Clayton, Palestine, 5 November 1918; Weizmann to David Eder, Tel Aviv-Jaffa, 5 November 1918: _LPCW_ , Vol IX, 7, 8, pp 9–20.
45. Weizmann to Louis D Brandeis, Washington, 29 October 1918; Weizmann to David Eder, Tel Aviv-Jaffa, 26 November 1918: _LPCW_ , Vol IX, 4, 37, pp 2–8, 39–40.
46. Weizmann to Louis D Brandeis, Washington, 11 November 1918; Weizmann to C P Scott, Manchester, 1918: _LPCW_ , Vol IX, 11, 18, pp 22, 26–7.
47. Weizmann to Lord Robert Cecil, London, 1 November 1918: Appendix 1: 'Proposals submitted by the Zionist Organisation to the Secretary of State for Foreign Affairs regarding matters affecting the Jewish population of Palestine during the Military occupation of that Country', _LPCW_ , Vol IX, 5, pp 8, 389–90.
48. Weizmann to David Eder, Tel Aviv–Jaffa, 4 December 1918; Weimann to Nahum Sokolow, Paris, 5 December 1918: _LPCW_ , Vol IX, 52, 53, pp 53–6.
49. Weizmann to Sir Eyre Crowe, London, 16 December 1918, _LPCW_ , Vol IX, 70, pp 69–71.
50. 'Feisal-Weizmann Agreement', 3 January 1919, _LPCW_ , Vol IX, between pp 86 and 87; Antonius, _The Arab Awakening_ , pp 437–9.
51. Rose, _Chaim Weizmann_ , p 200.
52. Weizmann to Vera Weizmann, London, 8 January 1919, _LPCW_ , Vol IX, 100, pp 92–4; Reinharz, _Chaim Weizmann: The Making of a Statesman_ , p 296.
53. Weizmann to Sir Arthur Wigram Money, London, 26 January 1919, _LPCW_ , Vol IX, pp 104–7.
54. 'Statement of the Zionist Organisation regarding Palestine', 3 February 1919, _LPCW_ , Vol IX, Appendix II, pp 391–402.
55. See Temperley, _A History of the Peace Conference of Paris_ , Vol I, pp 249–50.
56. Unless otherwise stated, what follows is based on _Papers Relating to the Foreign Relations of the United States, 1919: The Paris Peace Conference_ , 13 vols (Washington, DC: 1942–7), Vol 3, pp 889–94, hereafter _FRUS PPC_.
57. Sir James Headlam-Morley, _A Memoir of the Paris Peace Conference, 1919_ (Methuen, London: 1972) pp 30–1.
58. Lloyd George, _The Truth about the Peace Treaties_ , p 1038.
59. Stephen Bonsal, _Suitors and Supplicants: The Little Nations at Versailles_ (Prentice Hall Inc, New York: 1946) p 32.
60. Bonsal, _Suitors and Supplicants_ , p 33.
61. _FRUS PPC_ , Vol 3, pp 889–90.
62. _FRUS PPC_ , Vol 3, p 1016.
63. _FRUS PPC_ , Vol 3, pp 1024–38.
64. _FRUS PPC_ , Vol 3, p 1029.
65. _FRUS PPC_ , Vol 3, p 1030.
66. Meir Zamir, 'Faisal and the Lebanese Question, 1918–20', _Middle Eastern Studies_ , Vol 27, No 3 (Jul 1991) p 408.
67. See M MacMillan, _Peacemakers: the Paris Peace Conference of 1919 and its Attempt to End War_ (John Murray, London: 2001) p 402.
68. Bonsal, _Suitors and Supplicants_ , p 45.
69. Lloyd George, _The Truth about the Peace Treaties_ , pp 1048–9.
70. Weizmann to Vera Weizmann, London, 28 February 1919, _LPCW_ , Vol IX, 123, pp 116–19.
71. Weizmann, _Trial and Error_ , p 304.
72. M Dockrill (ed), _British Documents on Foreign Affairs: Reports and Papers from the Foreign Office Confidential Print, Part II: From the First to the Second World War, Series I, The Paris Peace Conference of 1919_ , General Editors Kenneth Bourne and D Cameron Watt, _Volume 2: Supreme Council_ Minutes, January–March 1919 (University Publications of America, Frederick, Maryland: 1989) pp 260–1, hereafter Dockrill, _Supreme Council Minutes_ ; Weizmann, _Trial and Error_ , p 304.
73. Dockrill, _Supreme Council Minutes_ , pp 261–2.
74. Dockrill, _Supreme Council Minutes_ , pp 262–4.
75. Weizmann, _Trial and Error_ , p 205.
76. Dockrill, _Supreme Council Minutes_ , pp 264–5.
77. Weizmann, _Trial and Error_ , p 205.
78. Weizmann to Vera Weizmann, London, 28 February 1919, _LPCW_ , Vol IX, 123, pp 116–19.
79. Esco, _Palestine_ , Vol I, pp 161–2.
80. 'At the Peace Conference', in Goodman, _Chaim Weizmann_ , pp 155–60.
81. 'At the Peace Conference', in Goodman, _Chaim Weizmann_ , pp 155–60.
82. This meeting is described in Lloyd George, _The Truth about the Peace Treaties_ , pp 1057–73 and _FRUS PPC_ , Vol 5, pp 1–14.
83. Christopher M Andrew and Alexander Sydney Kanya-Forstner, _France Overseas: The Great War and the Climax of French Imperial Expansion_ (Thames and Hudson, London: 1981) p 197.
84. _FRUS PPC_ , Vol 7, p 747.
85. Notes of a conversation between Colonel House and Emir Feisal, 29 March 1919, in Garnett, _The Letters of T E Lawrence_ , p 275.
86. P Mantoux, _The Deliberations of the Council of Four, March 24–June 28, 1919: Notes of the Official Interpreter, Paul Mantoux, Vol I: To the Delivery to the German Delegation of the Preliminaries of Peace, Vol II: From the Delivery of the Peace Terms to the German Delegation to the Signing of the Treaty of Versailles_ (Princeton University Press, Princeton, NJ: 1992) Vol I, pp 41–57.
87. Jan Karl Tanenbaum, 'France and the Middle East, 1914–1920', _Transactions of the American Philosophical Society_ , New Series, Vol 68, No 7 (1978) pp 29–30.
88. Colonel House Diary, 14 April 1919, in Woodrow Wilson and Arthur Stanley Link, _The Papers of Woodrow Wilson_ (Princeton University Press, Princeton, NJ: 1986–92) Vol 57, pp 334–5; hereafter _Wilson Papers_.
89. Westerman memo, c. 17 April 1919, in _Wilson Papers_ , Vol 57, p 444.
90. Weizmann to Arthur J Balfour, London, _LPCW_ , Vol IX, 135, pp 128–32, also footnotes 1, 2 and 3.
91. Weizmann to Israel Sieff, Manchester, 12 April 1919, _LPCW_ , Vol IX, 136, pp 132–4.
92. _DBFP_ , Vol IV, Doc 182.
93. _DBFP_ , Vol IV, Docs 183 and 196.
94. _DBFP_ , Vol IV, Doc. 253.
95. _DBFP_ , Vol IV, Chapter II Introductory Note, p 253.
96. _DBFP_ , Vol IV, Doc 173.
97. _DBFP_ , Vol IV, Doc 174.
98. _DBFP_ , Vol IV, Doc 183.
99. Political Officer Baghdad to High Commissioner Egypt, 30 May 1919, TNA F04I158 119130/3.
100. _DBFP_ , Vol IV, Doc 189, Annex B.
101. _DBFP_ , Vol IV, Doc 182, Enc I.
102. _DBFP_ , Vol IV, Doc 176.
103. James L Gelvin, 'The Ironic Legacy of the King-Crane Commission', in David W Lesch, _The Middle East and the United States: A Historical and Political Reassessment_ (Westview Press, Boulder, CO: 1996) p 16.
104. _DBFP_ , Vol IV, Doc 181.
105. _DBFP_ , Vol IV, Doc 192.
106. Gelvin, 'The Ironic Legacy of the King-Crane Commission', p 16.
107. The full itinerary is in _FRUS PPC_ , Vol 12, pp 753–4.
108. _DBFP_ , Vol IV, Doc 199.
109. Gelvin, _Divided Loyalties_ , p 35.
110. _Wilson Papers_ , Vol 61, p 442.
111. _FRUS PPC_ , Vol 12, p 749.
112. _FRUS PPC_ , Vol 12, p 750.
113. Karsh and Karsh, _Empires of the Sand_ , p 278.
114. See _DBFP_ , Vol IV, Doc 178, and Karsh and Karsh, _Empires of the Sand_ , p 279, who are critical of Feisal's illusions and the British role in encouraging them.
115. Esco, _Palestine_ , Vol I, pp 213–22; Antonius, _The Arab Awakening_ , pp 443–58.
116. _DBFP_ , Vol IV, Doc 197.
117. _DBFP_ , Vol IV, Doc 211.
118. _DBFP_ , Vol IV, Doc 213.
119. _DBFP_ , Vol IV, Doc 227.
120. _DBFP_ , Vol IV, Doc 236.
121. _DBFP_ , Vol IV, Doc 242.
122. Vera Weizmann, _The Impossible Takes Longer_ , pp 91–2.
123. Michael Llewellyn Smith, _Ionian Vision_ (Allen Lane, London: 1973) pp 89–110.
San Remo and Sèvres: the Flawed Peace
1. Kâzim Karabekir, _Istiklâl Harbimiz_ (Yapi Kredi, Istanbul: 2008) Vol I, p 24.
2. Karabekir, _Istiklâl Harbimiz_ , Vol I, p 21.
3. Mango, _Atatürk_ , p 216.
4. Murat Bardakçı, _Sahbaba_ (Pan Yaymcilik, Istanbul: 1998) p 449.
5. Dogu Ergil, _Milli Mücadelenin Sosyal Tarihi_ (Tarhan, Ankara: 1981) p 60.
6. Ergil, _Milli Mücadelenin Sosyal Tarihi_ , p 54.
7. Ergil, _Milli Mücadelenin Sosyal Tarihi_ , p 65.
8. Llewellyn Smith, _Ionian Vision_ , p 71.
9. McCarthy, _Muslims and Minorities_ , p 77.
10. Ergil, _Milli Mücadelenin Sosyal Tarihi_ , pp 94–5.
11. Mahmud Kemal Inal, _Osmanli Devrinde Son Sadriazamlar_ , p 2040.
12. Sina Aksin, _Istanbul Hükümetleri ve Millî Mücadele_ (Cem, Istanbul: 1992) Vol I, pp 396–402.
13. _Wilson Papers_ , Vol 64, p 27.
14. Harry N Howard, _The King-Crane Commission: An American Inquiry in the Middle East_ (Khayats, Beirut: 1963) p 258.
15. Darwin, Britain, _Egypt and the Middle East_ , p 171.
16. _DBFP_ , Vol IV, Doc 242.
17. _DBFP_ , Vol IV, Doc 236.
18. _DBFP_ , Vol IV, Doc 256.
19. _DBFP_ , Vol IV, Doc 265.
20. _DBFP_ , Vol IV, Doc 278.
21. _DBFP_ , Vol IV, Doc 283.
22. _DBFP_ , Vol IV, Doc 295.
23. _DBFP_ , Vol IV, Doc 334.
24. _DBFP_ , Vol IV, Doc 383.
25. Karsh and Karsh, _Empires of the Sand_ , p 281; Sachar, _The Emergence of the Middle East_ , pp 272–3.
26. _DBFP_ , Vol IV, Doc 412.
27. Gertrude Bell to Family, 12 Oct 1919. Gertrude Bell's Diaries and Letters have been digitized by the University of Newcastle and are available at http://www.gerty. ncl.ac.uk. All references to Bell's Diaries and Letters are to that source.
28. Bell Diary, 8 Oct 1919.
29. Gertrude Bell to Family, 12 October 1919.
30. Bell Diary, 13 Oct 1919.
31. 'Syria in October 1919', November 1919, TNA F0371/4152.
32. _DBFP_ , Vol VII, Doc 12.
33. Malcolm B Russell, _The First Modern Arab State: Syria Under Faysal, 1918–1920_ (Bibliotheca Islamica, Minneapolis: 1985) pp 166–8.
34. Rohan Butler and J P T Bury (eds), _Documents on British Foreign Policy 1919–1939_ , First Series, Vol VIII (Her Majesty's Stationery Office, London: 1958); hereafter _DBFP_ , Vol VIII, Doc 214.
35. _DBFP_ , Vol XIII, Doc 219.
36. _DBFP_ , Vol IV, Doc 221.
37. Martin Gilbert, _Winston S. Churchill, Companion Volume IV_ , Part 2: 1917–1922, (Heinemann, London: 1977) p 1050, hereafter Gilbert, _Churchill Companion_ , IV, Part 2; _DBFP_ , Vol XIII, Docs 217, 223, 224.
38. Russell, _The First Modern Arab State_ , pp 138–9.
39. Russell, _The First Modern Arab State_ , pp 142–6.
40. Weizmann to Robert Vansittart, London, 1 March 1920, _LPCW_ , Vol IX, 294, pp 320–2.
41. _Palestine Royal Commission Report_ , Cmd 5479, Chapter II, 'The War and the Mandate'.
42. Weizmann to the Zionist Executive, London, 25 March 1920, _LPCW_ , Vol IX, pp 325–30.
43. _Palestine Royal Commission Report_ , pp 50–1; Mattar, _The Mufti of Jerusalem_ , pp 15–18.
44. Weizmann to (Lady) Emma Caroline Schuster, Twyford, Montreux, 3 May 1920, _LPCW_ , Vol IX, 318, pp 343–4.
45. Weizmann, _Trial and Error_ , pp 318–21.
46. Weizmann to Vera Weizmann, Launay, 19 April 1920, _LPCW_ , Vol IX, 306, pp 336–7.
47. _DBFP_ , Vol VIII, Doc 15.
48. _DBFP_ , Vol VIII, Doc 16.
49. Weizmann to Vera Weizmann, London, 26 April 1920; Weizmann to the Zionist Bureau, London, 27 April 1920: _LPCW_ , Vol IX, 313, 315, pp 340–2; Weizmann, _Trial and Error_ , pp 324–5.
50. _DBFP_ , Vol XIII, Doc 251.
51. Dan Eldar, 'France in Syria: The Abolition of the Sharifian Government, April–July 1920', _Middle Eastern Studies_ , Vol 29, No 3 (Jul 1993) pp 487–504, esp pp 492–5.
52. Russell, _The First Modern Arab State_ , pp 179–80.
53. _DBFP_ , Vol XIII, Doc 284.
54. 'At the First International Zionist Conference after the San Remo Decision, held in London, July 7th, 1920', in Goodman, _Chaim Weizmann_ , pp 160–5.
55. Shabtai Teveth, _Ben-Gurion: The Burning Ground 1886–1948_ (Robert Hale Ltd, London: 1987) pp 161–4.
56. Weizmann, _Trial and Error_ , pp 326–8; Laqueur, _A History of Zionism_ , pp 458–9; Reinharz, _Chaim Weizmann: The Making of a Statesman_ , pp 327–33.
57. Samuel, _Memoirs_ , p 154; Storrs, _Orientations_ , p 349; Norman and Helen Bentwich, _Mandate Memories 1918–1948_ (The Hogarth Press, London: 1965) p 59.
58. Cited in Taha Akyol, _Ama Hangi Atatürk_ (Dogan Kitap, Istanbul: 2008) p 156.
59. Fromkin, _A Peace to End All Peace_ , p 385.
60. Llewellyn Smith, _Ionian Vision_ , pp 123–5.
61. Llewellyn Smith, _Ionian Vision_ , p 122.
62. Llewellyn Smith, _Ionian Vision_ , p 121.
63. Mahmud Kemal Inal, _Osmanli Devrinde Son Sadriazamlar_ , pp 1731–2; Baskin Oran, _Türkiye'nin Dıs Politikası_ , Vol I, pp 119–23.
64. Baskin Oran, _Türkiye'nin Dıs Politikası_ (Iletisim, Istanbul: 2001) Vol I, p 123.
65. Mango, _Atatürk_ , p 329.
66. David Gilmour, _Curzon_ (John Murray, London: 1994) p 532.
67. Andrew Ryan, _The Last of the Dragomans_ (Bles, London: 1951) p 173.
68. http://wilsonforarmenian.am/Report/007Letter.pdf, pp 10–11. It is not surprising that the full text of the Treaty of Sèvres should be available on the internet courtesy of the Hellenic resources network and the Wilson Award thanks to an organisation of Armenian nationalists, 'Wilson for Armenia'.
69. Examples given in Bardakçı, _Sahbaba_ , p 162.
The Middle East Rebels and the Peace Settlement Revisited
1. Mango, _Atatürk_ , p 345. A single battle – Enver's unsuccessful assault on the Russians in the winter of 1914/15 – cost the Ottoman army 110,000 casualties (Hikmet Özdemir, _The Ottoman Army 1914–1918_ (Utah University Press, Salt Lake City, UT: 2008) p 52).
2. Mahmud Kemal Inal, _Osmanli Devrinde Son Sadriazamlar_ , p 2067.
3. Mahmud Kemal Inal, _Osmanli Devrinde Son Sadriazamlar_ , p 2053.
4. Bardakçı, _Sahbaba_ , p 450.
5. Sevket Süreyya Aydemir, _Makedonya'dan Ortaasya'ya Enver Pasa_ (Remzi, Istanbul: 1972) Vol 3, pp 549, 574.
6. Taha Akyol, _Ama Hangi Atatürk_ (Dogan Kitap), Istanbul: 2008) pp 274–80.
7. Karabekir, _Istiklâl Harbimiz_ , Vol I, p 24.
8. Llewellyn Smith, _Ionian Vision_ , p 166.
9. Akyol, _Ama Hangi Atatürk_ , pp 289–90. Figures vary in different sources.
10. Mango, _Atatürk_ , p 311.
11. For background on Ibn Saud see Yapp, _The Making of the Modern Near East_ , p 60.
12. Teitelbaum, _The Rise and Fall of the Hashemite Kingdom of Arabia_ , p 103.
13. This section leans heavily on J Kostiner, 'Prologue of Hashemite Downfall and Saudi Ascendancy: A New Look at the Khurma dispute', in Susser and Shmuelevitz, _The Hasehemites in the Modern Arab World_ , pp 47–65.
14. Mary C Wilson, _King Abdullah, Britain, and the Making of Jordan_ , Cambridge Middle East Library (Cambridge University Press, Cambridge: 1987) p 37.
15. Paper on proposed kingdom of Mesopotamia and the advantages and disadvantages of making Emir Faisal first King, War Office 32/5619.
16. Busch, _Britain, India, and the Arabs, 1914–1921_ , p 333.
17. Teitelbaum, _The Rise and Fall of the Hashemite Kingdom of Arabia_ , p 198.
18. Teitelbaum, _The Rise and Fall of the Hashemite Kingdom of Arabia_ , p 166.
19. Wilson, _Lawrence of Arabia_ , p 656.
20. Wilson, _Lawrence of Arabia_ , p 656, 657–61.
21. Yapp, _The Making of the Modern Near East_ , pp 340–45; Hughes, _Allenby in Palestine_ , pp 13–15; T.G. Fraser, 'Egypt in 1919: founding year of the American University in Cairo', in Aran Byrne (ed), _East-West Divan. In Memory of Werner Mark Linz_ , The Gingko Library, London, 2014, pp 21–35.
22. Sir Arnold T Wilson, MP, _A Clash of Loyalties: Mesopotamia 1917–1920. A Personal and Historical Record_ (Oxford University Press, London: 1931) pp 310–14.
23. Keith Jeffery, _The British Army and the Crisis of Empire 1918–22_ (Manchester University Press, Manchester: 1984) pp 150–1; John Marlowe, _Late Victorian: The Life of Sir Arnold Wilson_ (The Cresset Press, London: 1967) pp 212–31.
24. Darwin, _Britain, Egypt and the Middle East_ , pp 39–40.
25. Gilbert, _Churchill Companion, IV_ , Part 2, p 1279.
26. Paris, 'British Middle East Policy-Making after the First World War', pp 773–93.
27. Darwin, _Britain, Egypt and the Middle East_ , pp 35–6.
28. Gilbert, _Churchill Companion, IV_ , Part 2, pp 1300, 1303–6.
29. Monroe, _Britain's Moment in the Middle East_ , pp 35–6.
30. Wilson, _Lawrence of Arabia_ , pp 641–2.
31. Karsh and Karsh, _Empires of the Sand_ , p 308.
32. Wilson, _Lawrence of Arabia_ , p 643.
33. Gilbert, _Churchill Companion, IV_ , Part 2, p 1334.
34. The best account remains Aaron S Klieman, _Foundations of British Policy in the Arab World: The Cairo Conference of 1921_ (Johns Hopkins Press, Baltimore: 1970).
35. Sachar, _The Emergence of the Middle East_ , p 378.
36. Sachar, _The Emergence of the Middle East_ , pp 402–3; Wilson, _Lawrence of Arabia_ , p 649; Fromkin, _A Peace to End All Peace_ , p 504.
37. Wilson, _King Abdullah, Britain, and the Making of Jordan_ , pp 52–3.
38. Gilbert, _Churchill Companion, IV_ , Part 2, pp 1419–22.
39. Klieman, _Foundations of British Policy in the Arab World_ , p 124.
40. Wilson, _Lawrence of Arabia_ , p 650.
41. Gilbert, _Churchill Companion, IV_ , Part 3, pp 1553–4.
42. See Wilson, _A Clash of Loyalties_ , pp 265–6.
43. Phoebe Marr, _The Modern History of Iraq_ (Westview Press, Boulder, CO: 2004) p 25.
44. Weizmann, _Trial and Error_ , pp 326–36; Brandeis to Felix Frankfurter, 26 April 1921; Brandeis to Julian William Mack, 3 June 1921; Brandeis to the Executive Council of the World Zionist Organisation, 19 June 1921, in Urofsky and Levy (eds), _Letters of Louis D Brandeis_ , Vol IV, pp 553–4, 562–3, 567–8; Reinharz, _Chaim Weizmann: The Making of a Statesman_ , pp 344–50.
45. Mattar, _The Mufti of Jerusalem_ , pp 21–7.
46. _Palestine Royal Commission Report_ , pp 51–2.
47. Gilbert, _Churchill Companion, IV_ , Part 3, pp 1459–93.
48. Weizmann, _Trial and Error_ , pp 342–3.
49. Esco, _Palestine_ , Vol I, pp 274–5.
50. Gilbert, _Churchill Companion, IV_ , Part 3, pp 1558–61.
51. Gilbert, _Churchill Companion, IV_ , Part 3, pp 1585–90.
52. Esco, _Palestine_ , Vol I, pp 277–9.
53. Gilbert, _Churchill Companion, IV_ , Part 3, p 1606.
54. Gilbert, _Churchill Companion, IV_ , Part 3, pp 1650–5.
55. Esco, _Palestine_ , Vol I, pp 279–80.
56. Weizmann, _Trial and Error_ , pp 350–60.
57. _Statement of British Policy in Palestine_ , 3 June 1922, Cmd 1700 (London: 1922).
58. Weizmann, _Trial and Error_ , pp 360–2; Esco, _Palestine_ , Vol I, pp 285–6.
59. Weizmann, _Trial and Error_ , pp 363–4.
60. _Palestine Royal Commission Report_ , pp 34–40.
61. Llewellyn Smith, _Ionian Vision_ , p 166.
62. http://www.tarihogretmeni.net/tarih/diyab-aga-t13218.html
63. Mango, _Atatürk_ , p 318.
64. Sami Özerdem, _Atatürk Devrimi Kronolojisi_ (Çankaya Belediyesi, Ankara: 1996) p 58.
65. Mango, _Atatürk_ , p 321.
66. Llewellyn Smith, _Ionian Vision_ , p 232.
67. Llewellyn Smith, _Ionian Vision_ , p 232.
68. Gilbert, _Sir Horace Rumbold_ , p 243.
69. Gilbert, _Sir Horace Rumbold_ , p 243.
70. Gilbert, _Sir Horace Rumbold_ , p 249.
71. Llewellyn Smith, _Ionian Vision_ , p 283.
72. Llewellyn Smith, _Ionian Vision_ , p 281.
73. Mango, _Atatürk_ , p 340.
74. Mango, _Atatürk_ , p 332.
75. Izmir Metropolitan Council, _The City that Rose from the Ashes_ (Izmir Council, Izmir: 2003) p 15.
76. David Walder, _The Chanak Affair_ (Hutchinson, London: 1969) p 177.
77. _Atatürk'un Butun Eserleri_ (Kaynak Yaymlari, Istanbul: 2002) Vol 8, p 83.
78. Cited in Walder, _The Chanak Affair_ , p 191.
79. Walder, _The Chanak Affair_ , pp 232, 235, 242.
80. Walder, _The Chanak Affair_ , p 176.
81. Gilbert, _Sir Horace Rumbold_ , p 278.
82. Walder, _The Chanak Affair_ , p 289.
83. Alexis Alexandris, _The Greek Minority of Istanbul and Greek-Turkish Relations 1918–1974_ (Centre for Asia Minor Studies, Athens: 1983) p 104.
84. There were some 1.8 million Greeks in Anatolia (McCarthy, _The Ottoman Peoples and the End of Empire_ , p 91). Greek sources put the number of Greeks in Istanbul in 1923 at 250,000 (Alexandris, _The Greek Minority in Istanbul_ , p 104), and a similar number of refugees from eastern Thrace resident in Greece in 1928 (McCarthy, _The Ottoman Peoples and the End of Empire_ , p 131).
85. Alexandris, _The Greek Minority of Istanbul and Greek-Turkish Relations_ , p 141.
From War to War
1. Bardakçı, _Sahbaba_ , p 231.
2. Mahmud Kemal Inal, _Osmanli Devrinde Son Sadriazamlar_ , pp 2097–8.
3. Mango, _Atatürk_ , p 364.
4. Mango, _Atatürk_ , p 364.
5. Falih Rifki Atay, _Çankaya_ (Bates¸, Istanbul: 1984) p 342.
6. Bardakçı, _Sahbaba_ , p 225.
7. Bardakçı, _Sahbaba_ , p 244
8. This account of Vahdettin's departure and the events leading to it is based on Bardakçı, _Sahbaba_ , pp 239–54.
9. Mahmud Kemal Inal, _Osmanli Devrinde Son Sadriazamlar_ , p 2103.
10. Bardakçı, _Sahbaba_ , p 241.
11. Philip Mansel, _Sultans in Splendour: The Last Years of the Ottoman World_ (Andre Deutsch, London: 1988) p 125a.
12. Taha Akyol, _Ama Hangi Atatürk_ , p 345.
13. Mustafa Kemal, _Eskisehir-Izmit Konusmaları (1923)_ (Kaynak Yayinlari, Istanbul: 1993) p 96.
14. Mustafa Kemal, _Eskisehir-Izmit Konusmaları_ , pp 136, 148.
15. Mustafa Kemal, _Eskisehir-Izmit Konusmaları_ , p 144.
16. _Atatürk'ün Söylev ve Demeçleri_ (Atatürk Arastirma Merkezi, Ankara: 1989) Vol 2, p 131.
17. _Atatürk'ün Söylev ve Demeçleri_ , Vol 2, p 98.
18. Ihan Turan (ed), _Ismet Inönü: Lozan Baris Konferansi_ (Atatürk Arastirma Merkezi, Ankara: 2003) p 301.
19. Gilbert, _Sir Horace Rumbold_ , p 281.
20. Kemal Atatürk, _Nutuk_ (Atatürk Arastirma Merkezi, Ankara: 1989) p 513.
21. Turan (ed), _Ismet Inönü_ , p 305.
22. Gilbert, _Sir Horace Rumbold_ , pp 282–3.
23. Turan (ed), _Ismet Inönü_ , p 305.
24. Kemal Atatürk, _Nutuk_ , p 524.
25. Kemal Atatürk, _Nutuk_ , p 466.
26. Kamal S Salibi, _The Modern History of Jordan_ (I B Tauris, London: 1993) p 88.
27. Avi Shlaim, _Lion of Jordan: The Life of King Hussein in War and Peace_ (Allen Lane, London: 2007) p 17.
28. The history of Iraq since independence is well served by the Hanna Batatu's seminal _Old Social Classes and the Revolutionary Movements of Iraq: A Study of Iraq's Old Landed and Commercial Classes and of Its Communists, Ba'thists, and Free Officers_ (Princeton University Press, Princeton, NJ: 1978). Two excellent general accounts are the aforementioned Marr, _The Modern History of Iraq_ and Tripp, _A History of Iraq_.
29. Marr, _The Modern History of Iraq_ , p 30.
30. William Roger Louis, _Ends of British Imperialism: the Scramble for Empire, Suez and Decolonization: Collected Essays_ (I B Tauris, London: 2006) p 862.
31. See Peter Sluglett, _Britain in Iraq: Contriving King and Country_ 2nd edition (I.B. Tauris, London: 2007) pp 108–20.
32. Marr, _The Modern History of Iraq_ , p 34.
33. Tripp, _A History of Iraq_ , pp 61–2.
34. Cited in Khaldun S Husry, 'King Faysal I and Arab Unity, 1930–33', _Journal of Contemporary History_ , Vol 10, No 2 (1975) p 324.
35. Sluglett, _Britain in Iraq_ , p 94; Tripp, _A History of Iraq_ , pp 61–2.
36. Marr, _The Modern History of Iraq_ , pp 44–6.
37. It was adjacent to the historic Topkapi Palace of the Ottomans.
38. Mango, _Atatürk_ , p 394.
39. Kemal Atatürk, _Nutuk_ , p 11.
40. _Palestine Royal Commission Report_ , pp 43, 46, 62.
41. Howard M Sachar, _A History of Israel: From the Rise of Zionism to Our Time_ (Basil Blackwell, Oxford: 1976) p 155.
42. Teveth, _Ben-Gurion_ , pp 187–8.
43. Weizmann to Felix M Warburg, New York, 24 November 1929, in Camillo Dresner (ed), _LPCW_ , Series A, Vol XIV, July 1929–October 1930 (Transaction Books, Rutgers University; Israel Universities Press, Jerusalem: 1978) 104, p 103.
44. Weizmann, _Trial and Error_ , pp 390–400; Dugdale, _Arthur James Balfour_ , Vol II, pp 267–72.
45. _Palestine Royal Commission Report_ , pp 65–7.
46. Weizmann to Gerald Balfour, Woking, 19 March 1930, _LPCW_ , Vol XIV, 225, p 252.
47. _Palestine Royal Commission Report_ , pp 67–71.
48. Weizmann to C P Scott, Manchester, 31 March 1930, _LPCW_ , Vol XIV, 233, pp 256–7.
49. Weizmann to the Editor of the Manchester Guardian, 11 April 1930, _LPCW_ , Vol XIV, 248, pp 266–8.
50. Weizmann to Vera Weizmann, Paris, 13 May 1930, _LPCW_ , Vol XIV, 269, pp 281–3.
51. Weizmann to James Ramsay MacDonald, London, 16 May 1930, _LPCW_ , Vol XIV, 275, pp 300–1.
52. Weizmann to Felix M Warburg, New York, 6 October 1930, _LPCW_ , Vol XIV, 357, pp 376–81.
53. Weizmann to Lord Passfield, London, 13 October 1930, _LPCW_ , Vol XIV, 359, pp 382–4.
54. _Palestine Royal Commission Report_ , pp 71–3.
55. Weizmann to Lord Passfield, London, 21 October 1930; Weizmann to James Ramsay MacDonald, London, 21 October 1930: _LPCW_ , Vol XIV, 364, 368, pp 387–9, 391.
56. Weizmann, _Trial and Error_ , pp 413–15.
57. J Ramsay MacDonald, House of Commons, 13 February 1931; _Palestine Royal Commission Report_ , pp 74–7.
58. Weizmann, _Trial and Error_ , pp 417–20; Rose, _Chaim Weizmann_ , pp 289–93.
59. Rose, _Chaim Weizmann_ , pp 294–300.
60. _Palestine Partition Committee Report_ , Cmd 5854 (Her Majesty's Stationery Office, London: 1938) p 23.
61. Sachar, _A History of Israel_ , p 586; Michael Jackson, ed Janet Jackson, _A Scottish Life: Sir John Martin, Churchill and Empire_ (The Radcliffe Press, London: 1999) p 89.
62. For a fuller discussion see T G Fraser, _Partition in Ireland, India and Palestine: theory and practice_ (Macmillan, London and Basingstoke: 1984) Chapter 6, 'Palestine: the Peel Commission'; and T G Fraser, 'A Crisis of Leadership: Weizmann and the Zionist Reactions to the Peel Commission's Proposals, 1937–8', _Journal of Contemporary History_ , Vol 23, No 4 (October 1988) pp 657–80.
63. Weizmann, _Trial and Error_ , pp 493–501; Rose, _Chaim Weizmann_ , pp 344–6.
64. Esco, _Palestine_ , Vol II, pp 928–31.
65. For the 1941 coup and its aftermath see Marr, _The Modern History of Iraq_ , pp 53–6, and Tripp, _A History of Iraq_ , pp 99–106.
66. Andrew Mango, _The Turks Today_ (John Murray, London: 2004) Chapter 1.
67. Books on the Holocaust are too numerous to list, and the following can only be indicative: Lucy S Dawidowicz, _The War Against the Jews 1933–1945_ (Holt, Rinehart and Winston, New York: 1975); Sybille Steinbacher, _Auschwitz: A History_ (Penguin, London: 2005); Christopher R Browning, _The Origins of the Final Solution: The Evolution of Nazi Jewish Policy 1939–1942_ (Arrow Books, University of Nebraska Press, Lincoln and Yad Vashem, Jerusalem: 2005); Richard J Evans, _The Third Reich at War: How the Nazis Led Germany from Conquest to Disaster_ (Allen Lane, London: 2008; Penguin, London: 2009), especially pp 217–318, 'The Final Solution'.
68. Evans, _The Third Reich at War_ , p 318.
69. 'Historicus, The Last Decade', in Paul Goodman, _The Jewish National Home: The Second November 1917–1942_ (J M Dent & Sons Ltd, London: 1943), p 90.
70. Esco, _Palestine_ , Vol II, pp 1020–35.
71. Mattar, _The Mufti of Jerusalem_ , pp 102–7.
72. Esco, _Palestine_ , Vol II, pp 945–8.
73. T G Fraser, _The Arab-Israeli Conflict_ , 3rd edition (Palgrave Macmillan, Basingstoke: 2007) pp 20–1.
74. Esco, _Palestine_ , Vol II, pp 1042–9.
75. Esco, _Palestine_ , Vol II, pp 1040–1.
Conclusion: The Legacy
1. T G Fraser, _The USA and the Middle East since World War 2_ (Macmillan, Basingstoke: 1989) p xi.
2. Walter Millis (ed), _The Forrestal Diaries_ (Viking Press, New York: 1951) p 192; Dean Acheson, _Present at the Creation: My Years in the State Department_ (W W Norton & Company, Inc, New York: 1969) pp 195–6.
3. T G Fraser and Donette Murray, _America and the World since 1945_ (Palgrave Macmillan, Basingstoke: 2002) pp 23–4.
4. George Kirk, _The Middle East 1945–1950_ (Oxford University Press, London: 1954) p 42.
5. Mango, _The Turks Today_ , pp 44–7.
6. Malcolm E Yapp, _The Near East Since the First World War: A History to 1995_ (Longman, Harlow: 2007) pp 96–7.
7. See Wilson, _King Abdullah, Britain, and the Making of Jordan_ , pp 129–68.
8. Fraser, _Partition in Ireland, India and Palestine_ , p 156.
9. Presidential Address by _Dr Chaim Weizmann, Twenty-Second Zionist Congress, Basle, 9th December 1946_ (The Jewish Agency for Palestine, London: nd); Weizmann, _Trial and Error_ , pp 543–4; Vera Weizmann, _The Impossible Takes Longer_ , pp 211–13; Getzel Kressel, 'Zionist Congresses', in _Zionism, Israel Pocket Library_ (Keter Publishing House, Jerusalem: 1973) p 253.
10. Fraser, _Partition in Ireland, India and Palestine_ , pp 162–3.
11. Fraser, _Partition in Ireland, India and Palestine_ , pp 179–82; Fraser, _The USA and the Middle East since World War 2_ , pp 31–4.
12. Fraser, _The USA and the Middle East since World War 2_ , pp 38–43.
13. Rose, _Chaim Weizmann_ , p 446
14. Weizmann, _Trial and Error_ , pp 585–9; Vera Weizmann, _The Impossible Takes Longer_ , pp 237–52; R H S Crossman, 'The Prisoner of Rehovoth', in Meyer W Weisgal and Joel Carmichael (eds), _Chaim Weizmann: A Biography by Several Hands_ (Weidenfeld and Nicolson, London: 1962) pp 325–6; Rose, _Chaim Weizmann_ , pp 445–59.
15. The discussion of the Arab-Israeli conflict in the following paragraphs is drawn from Fraser, _The Arab-Israeli Conflict, passim_.
16. Avi Shlaim, _The Iron Wall: Israel and the Arab World_ (Penguin, London: 2001) pp 62–8.
17. Fraser, _The Arab-Israeli Conflict_ , pp 46–7, 54–8, 201; Benny Morris, _The Birth of the Palestinian Refugee Problem, 1947–1949_ (Cambridge University Press, Cambridge: 1987) pp 203–12. A recent study is Ilan Pappe, _The Ethnic Cleansing of Palestine_ (Oneworld, Oxford: 2006)
18. Tripp, _A History of Iraq_ , pp 125–6.
19. See Robert McNamara, _Britain, Nasser and the Balance of Power in the Middle East_ (Cass, Portland: 2003) pp 42–6.
20. Louis, _Ends of British Imperialism_ , p 860.
21. Stephen Longrigg and Frank Stoakes, _Iraq_ (Praeger, New York: 1959) p 225.
22. See George Lawrence Harris, _Iraq: Its People, Its Society, Its Culture_ (HRAF Press, New Haven: 1958) p 83 and Longrigg and Stoakes, _Iraq_ , p 242.
23. See Beverley Milton-Edwards and Stephen Farrell, _Hamas_ (Polity Press, Cambridge: 2010).
24. Tripp, _A History of Iraq_ , pp 213–14.
25. Tripp, _A History of Iraq_ , pp 224–39.
26. Fraser and Murray, _America and the World since 1945_ , pp 248–54; Tripp, _A History of Iraq_ , pp 244–50; Mango, _The Turks Today_ , pp 90–1.
27. Tripp, _A History of Iraq_ , pp 303–8; 313–14; see also Kenneth Katzmann, _Iraq: Politics, Elections and Benchmarks_ (Congressional Research Service, The Library of Congress, Washington, DC: 24 August 2010) http://fpc.state.gov/documents/ organization/147288.pdf.
28. Clinton's efforts can be studied in Bill Clinton, _My Life_ (Hutchinson, London: 2004) pp 911–16 and Dennis Ross, _The Missing Peace: The Inside Story of the Fight for Middle East Peace_ (Farrar, Straus and Giroux, New York: 2004) pp 650–711.
29. George Mitchell, _Sharm El-Sheikh Fact-Finding Committee Report_ (Washington, DC: 30 April 2001) http://www.state.gov/p/nea/rls/ppt/3060.htm.
30. Fraser, _The Arab-Israeli Conflict_ , p 191.
31. See Jim Zanotti, Jeremy M Sharp, Carol Migdalovtz, Casey L Addis and Christopher M Blanchard, _Israel and Hamas: Conflict in Gaza (2008–2009)_ (Congressional Research Service, Library of Congress, Washington, DC: 15 January 2009) p12, http://fpc.state.gov/documents/organization/116003.pdf.
32. Carol Migdalovitz, _Turkey: Selected Foreign Policy Issues and U.S. Views_ (Congressional Research Service, Library of Congress, Washington, DC: 29 August 2008) pp 16–17, http://fpc.state.gov/documents/organization/110398.pdf.
33. Robert Dallek, _John F. Kennedy: An Unfinished Life 1917–1963_ (Allen Lane, London: 2003) p 536.
34. Feroz Ahmad, _Turkey: The Quest for Identity_ (Oneworld Publications, Oxford: 2005) pp 145–6.
35. Jim Muir, 'The Northern Front and the Kurds' Endgame', in Sara Beck and Malcolm Dowling (eds), _The Battle for Iraq: BBC News Correspondents on the War against Saddam and a New World Agenda_ (BBC Worldwide Ltd, London: 2003) p 158–69.
36. Ahmad, _Turkey_ , pp 181–2; Carol Migdalovitz, _Turkey: Update on Crisis of Identity and Power_ (Congressional Research Service, Library of Congress, Washington, DC: 2 September 2008) http://fpc.state.gov/documents/ organization/110367.pdf.
37. http://www.hri.org/docs/lausanne/part1.html.
38. Carol Migdalovitz, _Iraq: The Turkish Factor_ (Congressional Research Service, Library of Congress, Washington, DC: 31 October 2002) pp 2–3, http://fpc.state. gov/documents/organization/14957.pdf; Carol Migdalovitz, _Turkey: Selected Foreign Policy Issues and U.S. Views_ , pp 4–5; Mango, _The Turks Today_ , pp 214–25.
39. See Carol Migdalovitz, _Israel's Blockade of Gaza, the Mavi Marmara Incident, and its Aftermath_ (Congressional Research Service, Washington, DC: 23 June 2010), http://fpc.state.gov/documents/organization/145581.pdf.
40. Commission of the European Communities, _Commission Staff Working Document. Issues Arising from Turkey's Membership Perspective_ (COM: 2004, 656 Final, Brussels: 6 October 2004) http://ec.europe.eu/enlargement/archives/pdf/key_ documents/2004/issues_paper_en.pdf; CIA, _The World Factbook: Turkey_ , https:// www.cia.gov/library/publications/the-world-factbook/geos/tu.html; CIA, _The World Factbook: Germany_ , https://www.cia.gov/library/publications/the-world-factbook/ geos/gm.html.
41. 'Remarks by President Obama to the Turkish Parliament', 6 April 2009, http:// www.whitehouse.gov/the-press-office/remarks-president-obama-turkish-parliament
42. Useful statistics may be found at: CIA, _The World Factbook, Egypt_ , https:// www.cia.gov/library/publications/the-world-factbook/geos/eg.html; Jim Zanotti, _Turkey: Background and U.S. Relations_ (Congressional Research Service, Library of Congress, Washington DC: 1 August 2014) http://fpc.state.gov/documents/ organization/230747.pdf
43. 'Egypt protests: Key moments in unrest', http://www.bbc.co.uk/news/ world-middle-east-12425375 "Source – BBC News/bbc.co.uk – © 2011 BBC". "BBC Credit": See: Jeremy M. Sharp, _Egypt: Background and U.S. Relations_ (Congressional Research Service: Library of Congress, Washington, DC, 10 January 2014, and 15 September 2014), http://fpc.state.gov/documents/organization/221319. pdf and 227629.pdf.
44. John McHugo, _Syria. From the Great War to Civil War_ , Saqi Books, 2014, pp 203–36.
45. Statement by the President on Iraq, 9 August 2014, The White House, www. whitehouse.gov/the-press-office/2014/08/09/statement-president-iraq; Statement by the President on ISIL, 10 September 2014, The White House, www.whitehouse. gov/the-press-office/2014/09/10/statement-president-isil-1; Kenneth Katzman, Christopher M Blanchard, Carla E Humud, Rhoda Margesson, Alex Tiersky, Matthew C Weed, _The "Islamic State" Crisis and U.S. Policy_ , (Congressional Research Service, Library of Congress, Washington, DC, 12 November 2014) http://fpc.state.gov/documents/organization/234351.pdf; Patrick Cockburn, _The Rise of Islamic State: ISIS and the New Sunni Revolution_ (Verso, London, New York: 2015) passim; Kenneth Katzman, _Iraq: Politics, Governance, and Human Rights_ (Congressional Research Service, Library of Congress, Washington, DC: 15 September 2014) http//fpc.state.gov/documents/organization/232510.pdf.
46. Jim Zanotti, _Israel and Hamas: Another Round of Conflict_ , CRS Insights (Congressional Research Service, Library of Congress, Washington, DC, 18 July 2014) http://fpc.state.gov/documents/organization/22981.pdf
# Further Reading
The First World War, the Peace settlements and their legacy
The subject of the First World War, the Peace settlement and its aftermath in the Middle East has generated a vast bibliography of popular and academic studies. This note only refers to those the authors have found most useful in preparing this book. The most recent concise history of the First World War is Norman Stone's _World War I: A Short History_ (Allen Lane, London: 2007). The context of the Peace Conference for the region is set in H W V Temperley (ed), _A History of the Peace Conference of Paris_ , Volume VI (Oxford University Press, Oxford: 1924; reprinted 1969). Essential modern accounts of the Peace Conference are Alan Sharp, _The Versailles Settlement: Peacemaking after the First World War, 1919–1923_ (Palgrave Macmillan, Basingstoke: Second Edition, 2008) and Margaret MacMillan, _Peacemakers: The Paris Peace Conference of 1919 and its attempt to End War_ (John Murray, London: 2003).
In 2008, Haus Publishing (with some volumes published by Harvard University Press in the United States) embarked on a 32-title series, 'Makers of the Modern World' covering the participants in the Peace Conferences following the First World War, including those of the Middle East, and and the consequences of the peace settlements.
The Middle East
The best general account of the Middle East in the period from the French Revolution to the First World War is Malcolm Yapp's excellent _The Making of the Modern Near East, 1792–1923_ (Longman, Harlow: 1987). Two useful books that cover the period from 1914 to 1922 in great detail are Howard Morley Sachar, _The Emergence of the Middle East, 1914–1924_ (Allen Lane, Penguin Press, London: 1970), and the more recent and bestselling David Fromkin, _A Peace to End All Peace: Creating the Modern Middle East, 1914–1922_ (Deutsch, London: 1989). Both view the Middle East very much from a Eurocentric point of view and are primarily based on the excellent collections of British documents produced under the _Documents on British Foreign Policy 1919–1939_ series. Fromkin's volume has the advantage of building on the vast documentation in the relevant companion volumes of Martin Gilbert's official biography of Winston Churchill.
A wealth of articles can be found in the following journals: _The Historical Journal_ , _International Journal of Middle East Studies_ , _Journal of Palestine Studies_ and _Middle Eastern Studies_. The middle two tend to reflect a line sympathetic to the Arab cause, while _Middle Eastern Studies_ was founded and edited for many years by Elie Kedourie and reflects his sceptical line.
The Hashemite Kingdom
Broad overviews of Middle Eastern history include the late Albert Hourani's justly acclaimed _A History of the Arab Peoples_ (The Belknap Press of Harvard University Press, Cambridge, MA: 1991) and Ira M Lapidus's massive study _A History of Islamic Societies_ (Cambridge University Press, Cambridge: 2002 edition). Both are focused more on developments within the region and its societies than the influence of external powers. Lapidus' work, as its title indicates, has a broader compass that ranges beyond the Middle East. Both are highly sophisticated works of history and broadly sympathetic to the region and its inhabitants. Peter Mansfield and Nicholas Pelham, _A History of the Middle East_ (Penguin Books, New York: 2004) is much more focused on the international history of the region and the impact of foreign powers.
The fall of Feisal's kingdom in Syria is the subject of Zeine N Zeine, _The Struggle for Arab Independence: Western Diplomacy & the Rise and Fall of Faisal's Kingdom in Syria_ (Khayats, Beirut: 1960); Malcolm Russell, _The First Modern Arab State: Syria Under Faysal, 1918–1920_ (Bibliotheca Islamica, Minneapolis: 1985); and James Gelvin, _Divided Loyalties: Nationalism and Mass Politics in Syria at the Close of Empire_ (University of California Press, Berkeley: 1998). The fate of the successor states, Syria, Iraq and Jordan, can be traced in Charles Tripp, _A History of Iraq_ (Cambridge University Press, Cambridge: Third Printing: 2010); Phoebe Marr, _The Modern History of Iraq_ (Westview Press, Boulder, CO: 2004 edition); Kamal S Salibi, _The Modern History of Jordan_ (I B Tauris, London: 1993); and Philip S Khoury, _Syria and the French Mandate: The Politics of Arab Nationalism, 1920–1945, Princeton Studies on the Near East_ (Princeton University Press, Princeton: 1987). The post-First World War history of the entire Middle East is skilfully drawn in Malcolm Yapp, _The Near East Since the First World War: A History to 1995_ (Longman, Harlow: 1996).
Arab Nationalism and Palestine
Arab nationalism is central to this story. For an Arab perspective on these events, George Antonius, _The Arab Awakening_ (Hamish Hamilton, London: 1938) remains indispensable. Antonius viewed Arab nationalism as an organic vibrant force even before the First World War. C Ernest Dawn, whose work beginning more than 40 years ago is perhaps best encapsulated in _From Ottomanism to Arabism: Essays on the Origins of Arab Nationalism_ (University of Illinois Press, Urbana: 1973) frames much of the current debate. There are important syntheses in the essays in Rashid Khalidi _et al_ (eds), _The Origins of Arab Nationalism_ (Columbia University Press, New York: 1991) and in A Dawisha, _Arab Nationalism in the Twentieth Century: From Triumph to Despair_ (Princeton University Press, Princeton: 2003). Eliezer Tauber, _The Emergence of the Arab Movements_ (Frank Cass, London: 1993) and _The Formation of Modern Syria and Iraq_ (Frank Cass, London: 1995) are recent detailed reconstructions of Arab national movements before, during and after the war based on huge research. A useful counterpoint is the critical essay on Arab nationalism by Efraim and Inari Karsh, 'Myth in the desert, or not the Great Arab Revolt' in the journal _Middle Eastern Studies_ (1997). There is useful information in Philip Mattar, _The Mufti of Jerusalem: Al-Hajj Amin al-Husayni and the Palestinian National Movement_ (Columbia University Press, New York: 1988).
British Relations and the Middle East
The late Elie Kedourie wrote two of the key texts on Britain's relations with the Hashemites in _England and the Middle East_ (Bowes & Bowes, London: 1956) and In the _Anglo-Arab Labyrinth: The McMahon-Husayn Correspondence and Its Interpretations, 1914–1939_ (Cambridge University Press, Cambridge: 1976). Kedourie was a tireless interpreter of the vast documentation on the First World War Middle East in the British National Archives. He tends to be a harsh critic of the Hashemites and those British politicians and administrators who accepted their version of British betrayal as articulated in George Antonius' _The Arab Awakening_. Isaiah Friedman's _The Question of Palestine, 1914–1918: British-Jewish-Arab Relations_ (Routledge and Kegan Paul, London: 1973) is another book sceptical of the Hashemite viewpoint. Both Kedourie and Friedman are challenged by Charles D Smith in his article 'The Invention of a Tradition: The Question of Arab Acceptance of the Zionist Right to Palestine during World War I' in the _Journal of Palestine Studies_ (Winter 1993). More recently Efraim and Inari Karsh have followed on from the Kedourie position and extended it into an even harsher critique of the Hashemites, Arab nationalism and Islamic assertiveness in a series of books and articles, most notably _Empires of the Sand: The Struggle for Mastery in the Middle East, 1789–1923_ (Harvard University Press, Cambridge, MA: 1999). The Karshs' work is characterised by wide-ranging research, judgemental conclusions and a very hostile tone towards the Hashemites.
British policy during the war and its aftermath is well covered in Jukka Nevakivi, _Britain, France and the Arab Middle East 1914–1920_ (Athlone Press, London: 1969) and Timothy J Paris, _Britain, the Hashemites, and Arab Rule, 1920–1925: The Sherifian Solution_ (Frank Cass, London: 2003), as well as Fromkin and Sachar. The best overview contextualising half a century of British Middle Eastern policy remains Elizabeth Monroe's acclaimed classic _Britain's Moment in the Middle East 1914–1956_ (Methuen, London: 1963). D K Fieldhouse, _Western Imperialism in the Middle East 1914–1958_ (Oxford University Press, Oxford: 2006), is an excellent modern assessment. French policy can be traced in Jan Karl Tanenbaum's lengthy essay 'France and the Arab Middle East, 1914–1920' in _Transactions of the American Philosophical Society_ (1978) and C M Andrew and A S Kanya-Forstner, _France Overseas: The Great War and the Climax of French Imperial Expansion_ (Thames and Hudson, London: 1981). German policy is described by Sean McMeekin in his recently published magisterial _The Berlin–Baghdad Express: the Ottoman Empire and Germany's Bid for World Power 1898–1918_ (Allen Lane, London: 2010).
Zionism and the history of Israel
The standard account of Zionism remains Walter Laqueur, _A History of Zionism_ (Schocken Books, New York: 1972; 1989 edition), and for the period under review it can be supplemented by David Vital, _Zionism: The Crucial Phase_ (Oxford University Press, Oxford: 1987). Nahum Sokolow's two-volume _History of Zionism 1600–1918_ (Longman, Green and Co., London: 1919) remains invaluable. Herzl's career is best studied in Alex Bein, _Theodore Herzl: A Biography, translated by Maurice Samuel_ (The Jewish Publication Society of America, Philadelphia: 1940), and his thinking in _The Jewish State: An Attempt at a Modern Solution of the Jewish Question_ , translated by Sylvie d'Avigdor (H Pordes, London: 1972). Leonard Stein's _The Balfour Declaration_ (Valentine, Mitchell, London: 1961) is a classic piece of historical writing, but since he did not then have access to the British records, it should be used together with Isaiah Friedman, _The Question of Palestine, 1914–1918: British-Jewish-Arab Relations_ (Routledge & Kegan Paul, London: 1973), who did. A recent study is Jonathan Schneer, _The Balfour Declaration: The Origins of the Arab-Israeli Conflict_ (Bloomsbury, London: 2010).
There are also worthwhile perspectives in the works of two British Zionist sympathisers: Herbert Sidebotham, _Great Britain and Palestine_ (Macmillan, London: 1937); and Trevor Wilson (ed), _The Political Diaries of C. P. Scott 1911–1928_ (Collins, London: 1970). There is a mine of information in _Palestine: A Study of Jewish, Arab, and British Policies_ , two volumes (Yale University Press, New Haven: 1947). No student of the period can afford to ignore the _Palestine Royal Commission Report_ (Cmd 5479, London: 1937), especially since Weizmann adopted its views on partition; these are analysed in T G Fraser, 'A Crisis of Leadership: Weizmann and the Zionist Reactions to the Peel Commission's Proposals, 1937–8', _Journal of Contemporary History_ , Volume 23, No. 4 (October 1988).
From the Ottoman Empire to modern Turkey
There are two recent short histories of modern Turkey: Erik Zurcher's _Turkey: A Modern History_ (revised edition, paperback, I B Tauris, London: 2004) and Sina Akşin's _Turkey: From Empire To Revolutionary Republic_ (Hurst, London: 2007). Andrew Mango, _Atatürk_ (John Murray, London: 1999) and its sequel _The Turks Today_ (John Murray, London: 2004) relate the birth and development of the Turkish Republic. For more detailed treatment consult Reşat Kasaba (ed), _The Cambridge History of Turkey, Volume.4: Turkey in the Modern World_ (CUP: 2008) and Caroline Finkel, _Osman's Dream: The Story of the Ottoman Empire 1300–1923_ (John Murray, London: 2005). Alan Palmer's _The Decline and Fall of the Ottoman Empire_ (John Murray, London: 1992) provides a readable non-academic treatment of the subject.
More specialised books on Turkey's participation in the First World War include Ulrich Trumpener's _Germany and the Ottoman Empire 1914–1918_ (Princeton University Press: 1968), which remains a classic. Consult also Edward Erickson, _Ordered to Die: A History of the Ottoman Army in the First World War_ (Greenwood Press, Westport, Conn.: 2001) and Hikmet Özdemir, _The Ottoman Army 1914–1918: Disease and Death on the Battlefield_ (University of Utah, Salt Lake City: 2008). There are several studies of the Gallipoli campaign, the best known being Alan Moorehead's _Gallipoli_ (latest reprint of paperback, Aurum Press, London: 2007). The British campaign in Mesopotamia is described in A J Barker's _The Neglected War_ (Faber and Faber, London: 1967). For the 1922 Chanak Crisis, consult David Walder, _The Chanak Affair_ (Hutchinson, London: 1969). The highly controversial subject of the Armenian deportations is ably covered in Guenter Lewy's _The Armenian Massacres in Ottoman Turkey: A Disputed Genocide_ (University of Utah, Salt Lake City: 2005). Michael Llewellyn Smith's _Ionian Vision: Greece and Asia Minor 1919–1922_ (Allen Lane, London: 1973) is impartial and readable.
Biographies and Memoirs
The Hashemites have been the subject of a number of studies. The dearth of primary source material means they tend to be based on British, and to a lesser extent, French documents. The only memoir is Abdullah's _Memoirs of King Abdullah of Transjordan_ (Cape, London: 1950). J Nevo assesses its value in his essay 'Abdullah's memoirs as historical source material' in Asher Susser and Aryeh Shmuelevitz (eds), _The Hashemites in the Modern Arab World: Essays in Honour of the Late Professor Uriel Dann_ (Frank Cass, London: 1995). Mary C Wilson, _King Abdullah, Britain, and the Making of Jordan_ , Cambridge Middle East Library (Cambridge University Press. Cambridge: 1987) is a study of his relations with Britain but contains a wealth of biographical material. Feisal, perhaps the most interesting Hashemite, is given voice in Beatrice Erskine, _King Faisal of Iraq: An Authorised and Authentic Study_ (Hutchinson, London: 1933), which was based partly on interviews with him before his premature death. A popular and highly readable biographical study of the family is James Morris, _The Hashemite Kings_ (Faber and Faber, London: 1959). Hussein has received coverage ranging from the hagiographic in Randall Baker, _King Husain and the Kingdom of Hejaz_ (Oleander Press, Cambridge: 1979) to the insightful and critical work of Joshua Teitelbaum in a number of books and articles, most notably _The Rise and Fall of the Hashimite Kingdom of Arabia_ (Hurst, London: 2001).
For Turkey, Andrew Mango's _Atatürk_ (John Murray, London: 1999), and its sequel _The Turks Today_ (John Murray, London: 2004) relate the birth and development the Turkish Republic and Mustafa Kemal's role in it. There are two English-language academic studies of İsmet İnönü: Faruk Loğoğlu, _İsmet İnönü and the Making of Modern Turkey_ (İnönü Vakfı, Ankara: 1997) and Metin Heper, _İsmet İnönü, Turkish Diplomat and Statesman_ (Brill, Leiden: 1998). Enver Pasha awaits his English-language biographer.
The student of Weizmann is fortunate in many respects. The essential starting point for any study of his life and career is his autobiography, _Trial and Error_ , which he published in 1949 (Hamish Hamilton, London: 1949). Book One, which covers the period down to the Balfour Declaration, was finished in 1941; Book Two, which takes his story down to November 1947, was completed that year; and in 1948 he wrote an Epilogue. The autobiography is full of fascinating insights, not least into his early life in Tsarist Russia and the formative years of the Zionist movement, but it sometimes strays over dates and the sequence of events. Shortly before her death in September 1966, Vera Weizmann recounted her memoirs to David Tutaev, and these were published the following year as _The Impossible takes Longer_ (Hamish Hamilton, London: 1967). It is full of sharp observations, as well as valuable extracts from her diary.
_The Letters and Papers of Chaim Weizmann_ are the rock on which any study of his career must be based. Of fundamental importance are: Leonard Stein (ed), Series A, Volume VII, August 1914–November 1917 (Oxford University Press, Israel Universities Press, London and New York: 1975); Dvorah Barzilay and Barnet Livinoff (eds), Series A, Volume VIII, November 1917–October 1918 (Transaction Books, Rutgers University, Israel Universities Press, Jerusalem: 1977); Jehuda Reinharz (ed), Series A, Volume IX, October 1918–July 1920 (Transaction Books, Rutgers University, Israel Universities Press, Jerusalem: 1977). Weizmann's appearance before the Paris Peace Conference may be studied in M Dockrill (ed), _British Documents on Foreign Affairs: Reports and Papers from the Foreign Office Confidential Print, Part II: From the First to the Second World War, Series I, The Paris Peace Conference of 1919_ , General Editors Kenneth Bourne and D Cameron Watt, _Volume 2: Supreme Council Minutes, January–March 1919_ , (University Publications of America, Frederick, Maryland: 1989).
Weizmann has been well served by his biographers. _Chaim Weizmann: A Tribute on his Seventieth Birthday_ , edited by Paul Goodman (Victor Gollancz, London: 1945), contains reminiscences, appropriately reverential, from a number of colleagues, and a particularly valuable section on his scientific work. An even more useful collaborative work is _Chaim Weizmann: A biography by several hands_ , edited by Meyer W Weisgal and Joel Carmichael (Weidenfeld and Nicolson, London: 1962). In 1976, Barnet Litvinoff published a well-written overview, _Weizmann: Last of the Patriarchs_ (Hodder and Stoughton, London: 1976). Norman Rose wrote a masterly account in _Chaim Weizmann: A Biography_ (Weidenfeld and Nicolson, London: 1987). It is replete with insights. Finally, there are the two magisterial volumes by Jehuda Reinharz: _Chaim Weizmann: The Making of a Zionist Leader_ (Oxford University Press, Oxford: 1985), covering his life down to 1914, which was followed by _Chaim Weizmann: The Making of a Statesman_ (Oxford University Press, Oxford: 1993), which continued the story down to 1922.
Four published lectures on Weizmann by his friends and contemporaries also give valuable insights. In 1955, the British international historian and veteran of the Paris Peace Conference Sir Charles Webster delivered 'The Chaim Weizmann Memorial Lecture' on _The Founder of the National Home_ , subsequently published by the Yad Chaim Weizmann. The next year, Weizmann's American colleague, Louis Lipsky, continued with 'The Chaim Weizmann Memorial Lecture' on _Herzl, Weizmann and the Jewish State_ (Yad Chaim Weizmann, n.d.: c. 1957). The 1958 Herbert Samuel Lecture at Hebrew University was given by the eminent scholar Isaiah Berlin, and published as _Chaim Weizmann_ (Herzl Institute, New York: 1958). Finally, in 1960 a lecture given at Rehovoth entitled 'Chaim Weizmann' by the British politician R H S Crossman appeared in the journal _Encounter_. All four repay study.
The British military administration of Palestine is covered, somewhat opaquely, in the memoirs of Ronald Storrs, _Orientations_ (Ivor Nicholson and Watson, London: 1939). _The Memoirs of Viscount Samuel_ (The Cresset Press, London: 1945) provide his important testimony. Balfour's role is traced in _Arthur James Balfour: First Earl of Balfour, by his niece Blanche E C Dugdale_ , two volumes (Hutchinson, London: 1939), especially useful since she became a close friend of Weizmann. For biographies of the major British participants in the Near Eastern peace settlement, consult Alan Sharp, _David Lloyd George_ (Haus Publishing, London: 2008), David Gilmour, _Curzon_ (John Murray, London: 1994) and Martin Gilbert, _Sir Horace Rumbold: Portrait of a Diplomat 1869–1941_ (Heinemann, London: 1973). Crown Copyright materials are published with the permission of the Controller of Her Majesty's Stationery Office.
First published in Great Britain in 2011 by
Gingko Library
70 Cadogan Place
London SW1X 9AH
www.gingkolibrary.com
Copyright their text © T G Fraser, Robert McNamara and Andrew Mango, 2011
The moral right of the authors has been asserted
A CIP catalogue record for this book is available from the British Library
ebook ISBN 978-1-909942-01-1
Maps by Martin Lubikowski, ML Design, London
All rights reserved.
| {
"redpajama_set_name": "RedPajamaBook"
} | 7,966 |
Mutemath est le premier album complet de Mutemath, sorti le . Il est publié une première fois par le label indépendant Teleprompt, puis réédité par Warner Records en 2006 avec des morceux supplémentaires. Il atteint la place du Top Heatseekers de Billboard.
Historique
Publié sous le label indépendant Teleprompt , l'album est initialement vendu exclusivement lors des concerts de leur tournée 2006 sous forme de CD. La date de sortie est le 19 janvier, première date de la tournée. Au début du mois de février 2006, l'album est ajouté à la boutique en ligne de Teleprompt Records, et est désormais vendu sous forme de digipack, à la fois en ligne et lors des concerts. Selon les responsables de Mutemath, l'album s'est vendu à près de au cours du premier mois de sa sortie, avec une vente de près de 100 exemplaires par jour via leur site Web. L'album est également sorti sous forme de disque vinyle à deux disques en mai 2006.
Le 26 septembre 2006, l'album est réédité sur le label Warner Records, avec des morceaux supplémentaires de . Un EP live en édition limitée est inclus dans les premiers exemplaires. L'album débute au Top Heatseekers de Billboard à la place. Il réapparait dans le même classement presque un an plus tard, à la place, le 4 août 2007. Le premier single radio , sorti le 10 avril 2007, entre à la place du classement Billboard US Modern Rock la même semaine. L'album s'est vendu à plus de depuis sa sortie originale.
Le deuxième single de Mutemath, , sort en radio le 15 janvier 2008.
Liste des titres
édition Teleprompt
édition Warner Records
Personnel
Darren King – batterie et samples
Greg Hill – guitare
Paul Meany – voix, claviers
Roy Mitchell-Cárdenas – guitare basse, contrebasse
Historique des sorties
Notes et références
Liens externes
Album musical sorti en 2006 | {
"redpajama_set_name": "RedPajamaWikipedia"
} | 8,147 |
\section{}
In Appendix, we present some details of the reconstruction process.
We first give an example of constructing the element patch in two
dimensional case. For element $K$, the construction of $S(K)$ with
$\# S(K) = 15$ is presented in Fig.~\ref{fig:buildpatch}.
\begin{figure}
\centering \captionsetup[subfigure]{labelformat=empty}
\begin{subfigure}{.35\textwidth}
\centering
\begin{tikzpicture}[scale=3.5]
\input{./figure/m0.tex}
\end{tikzpicture}
\caption{$S_0(K)=\{K\}$}
\end{subfigure}
\begin{subfigure}{.1\textwidth}
\centering
\begin{tikzpicture}[scale=3.5]
\draw[very thick, ->] (0.35, 0.5) -- (0.7, 0.5);
\end{tikzpicture}
\end{subfigure}
\begin{subfigure}{.35\textwidth}
\centering
\begin{tikzpicture}[scale=3.5]
\input{./figure/m1.tex}
\end{tikzpicture}
\caption{$S_1(K)$}
\end{subfigure}
\vspace{15pt}
\hspace{200pt}
\begin{subfigure}{.1\textwidth}
\centering
\begin{tikzpicture}[scale=3.5]
\draw[very thick, <-, rotate=90] (0.5, 0.5) -- (0.75, 0.5);
\end{tikzpicture}
\end{subfigure}
\vspace{20pt}
\begin{subfigure}{.35\textwidth}
\centering
\begin{tikzpicture}[scale=3.5]
\input{./figure/m3.tex}
\end{tikzpicture}
\caption{$S(K)$}
\end{subfigure}
\begin{subfigure}{.1\textwidth}
\centering
\begin{tikzpicture}[scale=3.5]
\draw[very thick, <-] (0.35, 0.5) -- (0.7, 0.5);
\end{tikzpicture}
\end{subfigure}
\begin{subfigure}{.35\textwidth}
\centering
\begin{tikzpicture}[scale=3.5]
\input{./figure/m2.tex}
\end{tikzpicture}
\caption{$S_2(K)$}
\end{subfigure}
\caption{Build patch for element $K$ with $\# S(K) = 15$}
\label{fig:buildpatch}
\end{figure}
Then we give more details about the space $\bmr{U}_h^m$. As we
mentioned before, the operator $\mc R^m$ embeds the space
$\bmr{C}^0(\Omega) \cap H(\curl^0; \Omega)$ to the piecewise
irrotational polynomial space of degree $m$ by solving the local
least squares problem. We define $\bmr{w}_K^i(\bm x) \in
\bmr{C}^0(\Omega)(1 \leq i \leq d)$ that
\begin{displaymath}
\bmr{w}_K^i(\bm x) = \begin{cases}
\bm e_i, \quad \bm x = \bm x_K, \\
\bm 0, \quad \bm x \in \widetilde{K}, \quad \widetilde{K} \neq
K,
\end{cases}
\quad \forall K \in \MTh,
\end{displaymath}
where $\bm e_i$ is a $d \times 1$ unit vector whose $i$-th entry is
$1$. Then $\bmr{U}_{h}^m = \text{span}\{\bmr{\lambda}_K^i\ |\
\bmr{\lambda}_K^i = \mc R^m \bmr{w}_K^i,\ 1 \leq i \leq d, \ K \in
\MTh\}$, and one can write the operator $\mc R^m$ in an explicit
way: for a function $\bmr{g} = (g^1, \cdots, g^d) \in
\bmr{C}^0(\Omega) \cap H(\curl^0; \Omega)$ we have
\begin{displaymath}
\mc R^m \bmr{g} = \sum_{K \in \MTh} \sum_{i=1}^d g^i(\bm x_{K})
\bmr{\lambda}_K^i(\bm x).
\end{displaymath}
Clearly, the number of DOFs of our method is always $d$ times the
number of elements in partition.
Further, we give some details about the computer implementation of
the reconstructed space. We take the case $d = 2$ to illustrate. We
first outline the bases of the space $\bmr{S}_m(D)$, it is easily
verified that for $d=2$,
\begin{displaymath}
\bmr{S}_1(D) = \left\{ \vecd{1}{0}, \vecd{0}{1}, \vecd{x}{0},
\vecd{0}{y}, \vecd{y}{x} \right\}.
\end{displaymath}
Similarly for $m=2, 3$, there is
\begin{displaymath}
\begin{aligned}
\bmr{S}_2(D) = \bmr{S}_1(D) \cup &\left\{ \vecd{x^2}{0},
\vecd{2xy}{x^2}, \vecd{y^2}{2xy}, \vecd{0}{y^2} \right\}, \\
\bmr{S}_3(D) = \bmr{S}_2(D) \cup &\left\{ \vecd{x^3}{0},
\vecd{3x^2}{y}, \vecd{2xy^2}{2x^2y}, \vecd{y^3}{3xy^2},
\vecd{0}{y^3} \right\}.
\end{aligned}
\end{displaymath}
Then we shall solve the least squares problem \eqref{eq:lsproblem}
on every element. We take $K_0$ and $m = 1$ for an instance (see
Fig.~\ref{fig:Kexample}), and we let $S(K_0) = \left\{ K_0, K_1,
K_2, K_3 \right\}$ where $K_i(i=1,2,3)$ are the adjacent
edge-neighbouring elements of $K_0$. We denote by $\bm{x}_i = (x_i,
y_i)$ the barycenter of the element $K_i$ and we obtain the
collocation points set $\mc I_{K_0} = \left\{ \bm{x}_0, \bm{x}_1,
\bm{x}_2, \bm{x}_3 \right\}$.
\begin{figure}[htp]
\centering
\begin{tikzpicture}[scale=1]
\coordinate (A) at (1, 0);
\coordinate (B) at (-0.5, -0.6);
\coordinate (C) at (-0.5, 0.8);
\coordinate (D) at (1.2, 1.5);
\coordinate (E) at (-2, 0);
\coordinate (F) at (0.8, -1.5);
\draw[fill, red] (A) -- (B) -- (C);
\draw[thick, black] (A) -- (C) -- (B) -- (A);
\draw[thick, black] (A) -- (D) -- (C);
\draw[thick, black] (C) -- (E) -- (B);
\draw[thick, black] (A) -- (F) -- (B);
\node at(0, 0) {$K_0$}; \node at(1.7/3, 2.3/3) {$K_1$};
\node at(1.3/3, -2.1/3) {$K_2$}; \node at(-1, 0.2/3) {$K_3$};
\end{tikzpicture}
\caption{$K$ and its neighbours}
\label{fig:Kexample}
\end{figure}
Then for the function $\bmr{g} = (g^1, g^2) \in \bmr{C}^0(\Omega)
\cap H(\curl^0; \Omega)$ the least squares problem on $K_0$ reads
\begin{displaymath}
\mathop{\arg\min}_{\bm a \in \mb R^5} \sum_{i = 0}^3 \left\| a_0
\vecd{1}{0} + a_1 \vecd{0}{1} + a_2 \vecd{x_i}{0} + a_3
\vecd{0}{y_i} + a_4\vecd{y_i}{x_i} - \vecd{g^1(x_i)}{g^2(y_i)}
\right\|^2.
\end{displaymath}
It is easy to obtain its unique solution
\begin{displaymath}
\bm a = (A^TA)^{-1} A^T\bm q,
\end{displaymath}
where
\begin{displaymath}
A = \begin{bmatrix}
1 & 0 & x_0 & 0 & y_0 \\
0 & 1 & 0 & y_0 & x_0 \\
1 & 0 & x_1 & 0 & y_1 \\
0 & 1 & 0 & y_1 & x_1 \\
1 & 0 & x_2 & 0 & y_2 \\
0 & 1 & 0 & y_2 & x_2 \\
1 & 0 & x_3 & 0 & y_3 \\
0 & 1 & 0 & y_3 & x_3 \\
\end{bmatrix}, \qquad
\bm{q} = \begin{bmatrix}
g^1(x_0) \\ g^2(y_0) \\ g^1(x_1) \\ g^2(y_1) \\
g^1(x_2) \\ g^2(y_2) \\ g^1(x_3) \\ g^2(y_3) \\
\end{bmatrix}.
\end{displaymath}
We notice that the matrix $(A^TA)^{-1}A^T$ is independent of the
function $\bmr g$ and includes all information of the function
$\bmr{\lambda}_{K_j}^i(j=0,1,2,3,\ i=1,2)$ on the element $K_0$.
Thus we could store the matrix $(A^TA)^{-1}A^T$ for every element to
represent our approximation space. The idea of the implementation
could be adapted to the high-order accuracy case and the high
dimensional problem without any difficulty.
\end{appendix}
\section{Conclusion}
We proposed a sequential least squares finite element method for the
Poisson equation. The novel piecewisely irrotational approximation
space is constructed by solving local least squares problem and we use
this space to decouple the least squares minimization problem. We
proved the convergences for pressure and flux in $L^2$ norm and energy
norm. By a series of numerical results, not only the error estimates
are verified, but also we exhibited the flexibility and the great
efficiency of our method.
\section*{Acknowledgements}
This research is supported by the National Natural Science Foundation
of China (Grant No. 91630310, 11421110001, and 11421101) and the
Science Challenge Project, No. TZ2016002.
\section{Sequential Least Squares Finite Element Approximation}
\label{sec:lsfem}
Let us define a new functional $\wt{J}_h(\cdot)$ by
\begin{equation}
\begin{aligned}
\wt{J}_h(\bmr{q}_h) \triangleq \sum_{K \in \MTh} \| \nabla \cdot
\bmr{q}_h + f\|_{L^2(K)}^2 + &\sum_{e \in \MEh^i}
\frac{1}{h} \| \jump{\bmr{q}_h \otimes \un} \|_{L^2(e)}^2 \\
+ &\sum_{e \in \MEh^b} \frac{1}{h} \|\bmr{q}_h \times \un -
\nabla g \times \un\|_{L^2(e)}^2. \\
\end{aligned}
\label{eq:funcp}
\end{equation}
The terms in $\wt{J}_h(\bmr{q}_h)$ include the part related to the
flux in \eqref{eq:infdgep} and the term on boundary. We minimize this
functional in $\bmr{U}_h^m$ to have an approximate flux. The
corresponding minimization problem reads: {\it find
$\bmr{p}_h \in \bmr{U}_h^m$ such that
\begin{equation}
\wt{J}_h(\bmr{p}_h) = \inf_{\bmr{q}_h \in \bmr{U}_h^m} \wt{J}_h(
\bmr{q}_h).
\label{eq:discretepinf}
\end{equation}}
The Euler-Lagrange equation of this minimization problem is as: {\it
find $\bmr{p}_h \in \bmr{U}_h^m$ such that
\begin{equation}
\wt{a}_h(\bmr{p}_h, \bmr{q}_h) = \wt{l}_h(\bmr{q}_h), \quad
\bmr{q}_h \in \bmr{U}_h^m,
\label{eq:variational}
\end{equation}
where the bilinear form $\wt{a}_h(\cdot, \cdot)$ is
\begin{displaymath}
\begin{aligned}
\wt{a}_h(\bmr{p}_h, \bmr{q}_h) = \sum_{K \in \MTh} \int_K \nabla
\cdot \bmr{p}_h \nabla \cdot \bmr{q}_h \d{x} &+ \sum_{e \in
\MEh^i} \int_e \frac{1}{h} \jump{\bmr{p}_h \otimes \un} \jump{\bmr{q}_h
\otimes \un} \d{s} \\
&+ \sum_{e \in \MEh^b} \int_e \frac{1}{h} (\bmr{p}_h \times \un) \cdot
(\bmr{q}_h \times \un) \d{s}, \\
\end{aligned}
\end{displaymath}
and the linear form $\wt{l}_h(\cdot)$ is
\begin{displaymath}
\wt{l}_h(\bmr{q}_h) = \sum_{K \in \MTh} \int_K f \nabla \cdot \bmr{q}_h
\d{x} + \sum_{e \in \MEh^b} \int_e \frac{1}{h} (\bmr{p}_h \times \un)
\cdot (\nabla g \times \un) \d{s}.
\end{displaymath}}
Let
\begin{equation}
\begin{aligned}
\enorm{\bmr{q}_h}_{\bmr{p}}^2 \triangleq \sum_{K \in \MTh} \|
\nabla \cdot \bmr{q}_h\|_{L^2(K)}^2 + \sum_{e \in \MEh^i}
\frac{1}{h} \| \jump{\bmr{q}_h \otimes \un} \|_{L^2(e)}^2 +
\sum_{e \in \MEh^b} \frac{1}{h} \|\bmr{q}_h \times
\un\|_{L^2(e)}^2\\
\end{aligned}
\label{eq:pnorm}
\end{equation}
for
$\forall \bmr{q}_h \in \bmr{U}_h^m + \bmr{H}^1(\Omega) \cap H(\curl^0;
\Omega)$. The following lemma shows that $\enorm{\cdot}_{\bmr{p}}$
actually defines a norm on the space
$\bmr{U}_h^m + \bmr{H}^1(\Omega) \cap H(\curl^0; \Omega)$, referred as
the {\it energy norm} later on.
\begin{lemma}
For any $\bmr{q}_h \in \bmr{U}_h^m + \bmr{H}^1(\Omega) \cap
H(\curl^0; \Omega)$, there exists a constant $C$ such that
\begin{equation}
\|\bmr{q}_h\|_{L^2(\Omega)} \leq C \enorm{\bmr{q}_h}_{\bmr{p}}.
\label{eq:pisnorm}
\end{equation}
\label{le:pisnorm}
\end{lemma}
\begin{proof}
The idea follows \cite[Lemma 1]{Bensow2005discontinuous} to apply
the orthogonal decomposition of $\bmr{L}^2(\Omega)$. We only proof
for the case $d = 2$ and it is almost trivial to extend the result
for three dimensional case. Since $\bmr{q}_h \in \bmr{L}^2(\Omega)$,
we let $\phi \in H^1(\Omega) \backslash \mb R$ be the only solution
of
\begin{displaymath}
(\nabla \times \phi, \nabla \times \chi) = (\bmr{q}_h, \nabla
\times \chi), \quad \forall \chi \in H^1(\Omega).
\end{displaymath}
This solution $\phi$ satisfies
\begin{displaymath}
-\Delta \phi = \nabla \times \bmr{q_h}, \quad \text{in}\
H^{-1}(\Omega).
\end{displaymath}
Applying the Green's formula, we have
\begin{displaymath}
0 = (\bmr{q}_h - \nabla \times \phi, \nabla \times \chi) = \left(
(\bmr{q}_h - \nabla \times\phi) \times \un, \chi
\right)_{L^2(\partial \Omega)}, \quad \forall \chi \in
H^1(\Omega).
\end{displaymath}
Thus there exists $v \in H^1_0(\Omega)$ such that $\nabla v =
\bmr{q}_h - \nabla \times \phi$ \cite{girault1986finite}. Besides we
have the stability estimates
\begin{equation}
\|\chi\|_{H^1(\Omega)} \leq C \|\bmr{q}_h\|_{\bmr{L}^2(\Omega)} ,
\quad
\|v\|_{H^1(\Omega)} \leq C \|\bmr{q}_h\|_{\bmr{L}^2(\Omega)}.
\label{eq:chiqstability}
\end{equation}
Further, we use the decomposition to obtain
\begin{displaymath}
\begin{aligned}
\|\bmr{q}_h\|_{\bmr{L}^2(\Omega)}^2 &= \left( \sum_{K \in \MTh}
\int_K \bmr{q}_h \cdot \nabla v \d{x} + \int_K \bmr{q}_h \cdot
\nabla \times \chi \d{x} \right) \\
&= \sum_{K \in \MTh} \left( \int_{\partial K} v \bmr{q}_h \cdot
\un \d{s} - \int_K v \nabla \cdot \bmr{q}_h \d{x} +
\int_{\partial K} \chi \bmr{q}_h \times \un \d{s} \right). \\
&= \sum_{e \in \MEh^i} \int_e \left( v \jump{\bmr{q}_h \cdot
\un} + \chi \jump{\bmr{q}_h \times \un} \right) \d{s} + \sum_{e
\in \MEh^b} \int_e \chi \bmr{q}_h \times \un \d{s} - \int_{K} v
\nabla \cdot \bmr{q}_h \d{x}\\
\end{aligned}
\end{displaymath}
And we have that
\begin{displaymath}
\sum_{e \in \MEh^i} \int_e \left( \|\jump{ \bmr{q}_h \cdot \un}
\|_{L^2(e)}^2 + \| \jump{ \bmr{q}_h \times \un} \|_{L^2(e)}^2
\right) \d{s} \leq C \sum_{e \in \MEh^i} \int_e \| \jump{
\bmr{q}_h \otimes \un}\|_{L^2(e)}^2 \d{s}.
\end{displaymath}
Using the Cauchy-Schwarz inequality, trace inequality
\eqref{eq:traceinequality} and the stability estimate
\eqref{eq:chiqstability} could yield the estimate
\eqref{eq:pisnorm}, which completes the proof.
\end{proof}
Since for
$\forall \bmr{q}_h \in \bmr{U}_h^m + \bmr{H}^1(\Omega) \cap H(\curl^0;
\Omega)$ we have
$\wt{a}_h(\bmr{q}_h, \bmr{q}_h) = \enorm{\bmr{q}_h}_{\bmr{p}}^2$, it
is implied that the problem \eqref{eq:variational} has a unique
solution. Moreover, we could establish the convergence result with
respect to the norm $\enorm{\cdot}_{\bmr{p}}$.
\begin{theorem}
Let the solution
$\bmr{p} \in \bmr{H}^{m+1}(\Omega) \cap H(\curl^0; \Omega)$ and let
$\bmr{p}_h \in \bmr{U}_h^m$ be the solution to
\eqref{eq:variational}, then we have
\begin{equation}
\enorm{\bmr{p} - \bmr{p}_h}_{\bmr{p}} \leq Ch^m
\|\bmr{p}\|_{\bmr{H}^{m+1}(\Omega)}.
\label{eq:pconvergence}
\end{equation}
\label{th:pconvergence}
\end{theorem}
\begin{proof}
Since $\bmr{p}_h$ minimizes the problem \eqref{eq:discretepinf} and
$\jump{\bmr{p} \otimes \un} = 0$, we have
\begin{displaymath}
\enorm{\bmr{p} - \bmr{p}_h}_{\bmr{p}}^2 = \wt{J}_h(\bmr{p}_h) \leq
\wt{J}_h(\mc R^m \bmr{p}) = \enorm{\bmr{p} - \mc R^m
\bmr{p}}_{\bmr{p}}^2.
\end{displaymath}
Therefore, we only need to bound
$\enorm{\bmr{p} - \mc R^m \bmr{p}}_{\bmr{p}}$.
By the approximation \eqref{eq:approximation} and trace inequality
\eqref{eq:traceinequality}, we obtain that for element $K$,
\begin{displaymath}
\|\nabla\cdot \bmr{p} - \nabla \cdot \mc R_m \bmr{p} \|_{L^2(K)}
\leq Ch_K^m \|\bmr{p}\|_{\bmr{H}^{m+1}(S(K))},
\end{displaymath}
and
\begin{displaymath}
\begin{aligned}
\|(\bmr{p} - \mc R_m \bmr{p}) \otimes \un \|_{L^2(\partial K)}^2
& \leq C \| \bmr{p} - \mc R_m \bmr{p} \|_{L^2(\partial K)}^2\\
& \leq C (h_K^{-1} \|\bmr{p} - \mc R_m \bmr{p} \|_{L^2(K)}^2 + h_K
\|\nabla( \bmr{p} - \mc R_m \bmr{p}) \|_{L^2(K)}^2 ) \\
& \leq Ch_K^{2m+1} \|\bmr{p}\|_{\bmr{H}^{m+1}(S(K))}. \\
\end{aligned}
\end{displaymath}
The inequality \eqref{eq:pconvergence} is concluded by summing over
all elements in the partition, which completes the proof.
\end{proof}
After getting the numerical flux $\bmr{p}_h$, the next step is to plug
it into the functional \eqref{eq:infdgep} to calculate the pressure
$u$. We define the functional ${J}^u_h(\cdot)$ as below:
\begin{equation}
{J}^u_h(v) \triangleq \sum_{K \in \MTh} \|\nabla v -
\bmr{p}_h\|_{L^2(K)}^2 + \sum_{e \in \MEh^i} \frac{1}{h} \| \jump{v}
\|_{L^2(e)}^2 + \sum_{e \in \MEh^b} \frac{1}{h} \| v -
g\|_{L^2(e)}^2.
\label{eq:infu}
\end{equation}
To get an approximation to $u$, one may solve the minimization problem
for the functional ${J}^u_h(\cdot)$ in a certain approximation space.
We note that it is very flexible to choose the approximation space for
$u$. For instance, one may use the discontinuous finite element space
$V_h^m$ or the patch reconstructed space proposed in
\cite{li2016discontinuous}. Here we solve the pressure $u$ with the
standard Lagrange finite element space, which is defined as
\begin{displaymath}
\wh{V}_h^m \triangleq \left\{ v_h \in C(\Omega) \ |\ v_h|_K \in
\mathbb P_m(K), \quad \forall K \in \MTh\right\}.
\end{displaymath}
Due to the continuity of the space $\wh{V}_h^m$, the functional
${J}^u_h(v)$ is simplified as
\begin{equation}
{J}^u_h(v) = \sum_{K \in \MTh} \|\nabla v -
\bmr{p}_h\|_{L^2(K)}^2 + \sum_{e \in \MEh^b} \frac{1}{h} \| v -
g\|_{L^2(e)}^2, \quad \forall v \in H^1(\Omega).
\label{eq:infucfem}
\end{equation}
The following minimization problem gives the numerical solution to the
pressure $u$ in $\wh{V}_h^m$:
\begin{displaymath}
\min_{v_h \in \wh{V}_h^m} {J}^u_h(v_h).
\end{displaymath}
The discrete variational problem equivalent to the minimization
problem reads: {\it find $u_h \in \wh{V}_h^m$ such that
\begin{equation}
{a}^u_h(u_h, v_h) = {l}^u_h(v_h), \quad \forall v_h \in
\wh{V}_h^m,
\label{eq:discreteuinf}
\end{equation}
where the bilinear form ${a}^u_h(\cdot, \cdot)$ is given by
\begin{displaymath}
{a}^u_h(u_h, v_h) = \sum_{K \in \MTh} \int_K \nabla u_h \cdot
\nabla v_h \d{x} + \sum_{e \in \MEh^b} \int_e \frac{1}{h} u_h v_h
\d{s},
\end{displaymath}
and the linear form ${l}^u_h(\cdot)$ is given by
\begin{displaymath}
{l}^u_h = \sum_{K \in \MTh} \int_K \nabla v_h \cdot \bmr{p}_h \d{x}
+ \sum_{e \in \MEh^b} \int_e \frac{1}{h}v_h g \d{s}.
\end{displaymath}}
Analogous to the procedure we solve the flux $\bmr p$, we define
$\enorm{\cdot}_u$ as
\begin{displaymath}
\enorm{v}_u^2 \triangleq \sum_{K \in \MTh} \| \nabla v\|_{L^2(K)}^2
+ \sum_{e \in \MEh^b} \frac{1}{h} \|v\|_{L^2(e)}^2, \quad \forall v
\in H^1(\Omega).
\end{displaymath}
The inequality $\|v\|_{L^2(\Omega)} \leq C \enorm{v}_u$ \cite[Lemma
2.1]{arnold1982interior} ensures $\enorm{\cdot}_u$ is actually a norm
on $H^1(\Omega)$, which actually guarantees the unisolvability of the
problem \eqref{eq:discreteuinf}. $\enorm{\cdot}_u$ is referred as the
{\it energy norm} on $\wh{V}_h^m$ since now on. Further, the error
estimate with respect to $\enorm{\cdot}_u$ is given in the theorem
below as:
\begin{theorem}
Let the solution $u \in H^{m+1}(\Omega)$ and let $u_h \in
\wh{V}_h^m$ be the solution to \eqref{eq:discreteuinf}, then we have
\begin{equation}
\enorm{u - u_h}_u \leq C\|\bmr{p} - \bmr{p}_h
\|_{\bmr{L}^2(\Omega)} + Ch^m \|u\|_{H^{m+1}(\Omega)},
\label{eq:uconvergence}
\end{equation}
where $\bmr{p}_h$ is the solution to \eqref{eq:discretepinf}.
\label{th:uconvergence}
\end{theorem}
\begin{proof}
Let $u_I \in \wh{V}_h^m$ be the interpolant of $u$ and we have that
\begin{displaymath}
\begin{aligned}
{J}^u_h(u_h) &\leq {J}^u_h(u_I) \\
\enorm{u - u_h}_u^2 &\leq C({J}^u_h(u_I) + \|\nabla
u - \bmr{p}_h\|^2_{\bmr{L}^2(\Omega)}) \\
&\leq C \left( \enorm{u - u_I}_u^2 + \|\bmr{p} - \bmr{p}_h
\|_{L^2(\Omega)}^2\right). \\
\end{aligned}
\end{displaymath}
The approximation property of the space $\wh{V}_h^m$ gives us
\cite{ciarlet2002finite}:
\begin{displaymath}
\enorm{u - u_I}_u \leq Ch^m\|u\|_{H^{m+1}(\Omega)},
\end{displaymath}
which yields the estimate \eqref{eq:uconvergence} and completes the
proof.
\end{proof}
Then we can have the error estimate under $L^2$-norm:
\begin{theorem}
Let the solution $u \in H^{m+1}(\Omega)$ and let $u_h
\in \wh{V}_h^m$ be the solution to \eqref{eq:discreteuinf}, then we
have
\begin{equation}
\|u - u_h\|_{L^2(\Omega)} \leq C_0 \| \bmr{p} -
\bmr{p}_h\|_{L^2(\Omega)} + C_1h^{m+1}\|u\|_{H^{m+1}(\Omega)},
\label{eq:ul2estiate}
\end{equation}
where $\bmr{p}_h$ is the solution to \eqref{eq:discretepinf}.
\label{th:ul2estiate}
\end{theorem}
\begin{proof}
Let $e_h = u - u_h$ and from the definition of ${a}^u_h(\cdot,
\cdot)$, one see that
\begin{displaymath}
{a}^u_h(e_h, v_h) = (\bmr{p} - \bmr{p}_h, v_h), \quad \forall v_h
\in \wh{V}_h^m.
\end{displaymath}
We first show that
$\|e_h\|_{H^{-1/2}(\partial \Omega)} \leq C_0h \enorm{e_h}_u + C_1h
\|\bmr{p} - \bmr{p}_h\|_{L^2(\Omega)}$, where
\begin{displaymath}
\|e_h\|_{H^{-1/2}(\partial \Omega)} = \sup_{\tau \in
H^{1/2}(\partial \Omega)} \frac{\left( e_h, \tau
\right)_{L^2(\partial \Omega)}}{\|\tau\|_{H^{1/2}(\partial
\Omega)}}.
\end{displaymath}
We let $\alpha \in H^1(\Omega)$ which solves $\Delta \alpha = 0$ in
$\Omega$, $\alpha = \tau$ on $\partial \Omega$, and we let $\alpha_I
\in \wh{V}_h^m$ be interpolant of $\alpha$. Then we have that
\begin{displaymath}
\begin{aligned}
(e_h, \tau)_{L^2(\partial \Omega)} &= h(h^{-1}(e_h,
\alpha)_{L^2(\partial \Omega)}) \\
&= h(h^{-1}(e_h, \alpha)_{L^2(\partial \Omega)} - {a}^u_h(e_h,
\alpha_I)) + h
(\bmr{p} - \bmr{p}_h, \alpha_I) \\
&= h(h^{-1}(e_h, \alpha - \alpha_I)_{L^2(\partial \Omega)} -
(\nabla e_h, \nabla \alpha_I)_{L^2(\Omega)}) + h (\bmr{p} -
\bmr{p}_h, \alpha_I) \\
&\leq C_0h \enorm{e_h}_u (\|h(\alpha - \alpha_I)\|_{L^2(\partial
\Omega)} + \|\nabla \alpha_I\|_{L^2(\Omega)}) + C_1h \|\bmr{p}
-
\bmr{p}_h\|_{L^2(\Omega)} \|\alpha_I\|_{L^2(\Omega)} \\
& \leq C_0h \enorm{u_h}_u \|\alpha\|_{H^1(\Omega)} + C_1h
\|\bmr{p} - \bmr{p}_h\|_{L^2(\Omega)} \|\alpha\|_{H^1(\Omega)}.
\\
\end{aligned}
\end{displaymath}
We complete the proof by the regularity estimate
$\|\alpha\|_{H^1(\Omega)} \leq C \|\tau\|_{H^{1/2}(\partial
\Omega)}$.
Given $\psi \in L^2(\Omega)$ and we let $w \in H^2(\Omega)$ which
solves $- \Delta w = \psi$ in $\Omega$, $w = 0$ on $\partial
\Omega$. We denote by $w_I \in \wh{V}_h^m$ the interpolant of $w$.
Then we could deduce that
\begin{displaymath}
\begin{aligned}
(e_h, \psi) &= (\nabla e_h, \nabla w) - \left(e_h,
\frac{\partial
w}{\partial \un}\right)_{L^2(\partial \Omega)} \\
&= {a}^u_h(e_h, w - w_I) + (\bmr{p} - \bmr{p}_h, w_I) -
\left(e_h,
\frac{\partial w}{\partial \un}\right)_{L^2(\partial \Omega)} \\
& \leq Ch \enorm{e_h} \|w\|_{H^2(\Omega)} + \|\bmr{p} -
\bmr{p}_h \|_{\bmr{L}^2(\Omega)} \|w\|_{H^2(\Omega)} +
\|e_h\|_{H^{-1/2}(\partial \Omega)} \left\|\frac{\partial
w}{\partial \un} \right\|_{H^{1/2}(\partial \Omega)}.
\end{aligned}
\end{displaymath}
Let $\psi = e_h$, and combining the bound of
$\|e_h\|_{H^{-1/2}(\Omega)}$, the regularity estimate
$\|w\|_{H^2(\Omega)} \leq C \|\psi\|_{L^2(\Omega)}$ and the
approximation property of $\enorm{e_h}_u$ could yield the estimate
\eqref{eq:ul2estiate}, which completes the proof.
\end{proof}
\begin{remark}
Until now the method we established is only for the problem with the
Dirichlet boundary condition. For the Neumann boundary condition
$\nabla u \cdot \un = g$ on $\partial \Omega$, the boundary term in
\eqref{eq:funcp} and \eqref{eq:infucfem} should be modified as
\begin{displaymath}
\sum_{e \in \MEh^b} \frac{1}{h} \|\bmr{q}_h \cdot \un -
g\|_{L^2(e)}^2 \qquad \text{and} \qquad \sum_{e \in \MEh^b} \frac{1}{h} \left\|
\frac{\partial v}{\partial \un} - g\right\|_{L^2(e)}^2,
\end{displaymath}
respectively. It is almost trivial to extend our method in this
section to the problem with the Neumann boundary condition.
\end{remark}
\section{Introduction}
The least squares finite element method (LSFEM) is a sophisticated
technique for solving the partial differential equation. For
second-order elliptic problems, we refer to \cite{Bochev2009least,
Jiang1993optimal, Bramble1997least, Pehlivanov1994least,
Aziz1985least}, for the Navier-Stokes problem, we refer to
\cite{Bochev1993accuracy, Bochev2012locally, Lung1994stokes}. For an
overview of the least squares finite element methods, we refer to
\cite{Bochev1998review} and the references therein. Different from the
Galerkin method, the lease squares method is based on the minimization
of the $L^2$-norm residual over a proper approximation space. An
immediate advantage is the symmetric positive definite resulting
linear system, which has made the method attractive in several
fields. Instantly, one may see the condition number of the resulting
linear system is squared due to the formation of the approximation. To
relieve the curse due to the condition number, one may write the
equation into low order formation. Taking the Poisson equation as an
example, we may introduce a flux variable to write it into the mixed
formation, resulting a system coupled by the flux and pressure. Though
the mixed form is helpful in reducing condition number, more degree of
freedoms(DOF) are introduced to achieve the same accuracy.
Discontinuous Galerkin(DG) methods have received massive attention in
the past two decades due to its great flexibility in mesh partition
and easy implementation of the approximation spaces especially for the
spaces of high order. We refer to the review paper
\cite{arnold2002unified} and the references therein. Using the
approximation space from the DG methods, discontinuous least squares
(DLS) finite element methods have been developed in
\cite{Ye2018discontinuous, Bensow2005discontinuous, Bensow2005div} for
solving the elliptic system. In \cite{Bochev2012locally,
Bochev2013nonconforming}, the authors extend the DLS finite element
methods to the Stokes problem in velocity-vorticity-pressure form. The
same as the least squares methods using continuous approximation
space, the technique to write the equation into low order system is
adopted in DLS methods either to reduce the condition number of
resulting linear systems. To achieve the high order accuracy,
discontinuous finite element space requires a huge number of degrees
of freedom which leads to a very large linear system
\cite{hughes2000comparison, zienkiewicz2003discontinuous} in
comparison to the methods using continuous approximation spaces. The
coupling of the variables in the mixed form and the increasing of the
number of DOFs make one hard to satisfy with its efficiency.
In this paper, a new least squares finite element method is proposed
to solve the Poisson equation. The novel point is that we split the
solver into two sequential steps. This is motivated from the idea in
\cite{Bensow2005div} to decouple the least-squares-type functional
into two subproblems. In the first step, we approximate the flux still
using a discontinuous approximation space. This space is the piecewise
irrotational polynomial space, which is a generalization of the
reconstructed space proposed in \cite{li2012efficient,
li2016discontinuous}. The new space is obtained by solving a local
least squares problem based on the irrotational polynomial bases and
only one unknown locates inside each element. With such a space, we
makes the idea in \cite{Bensow2005div} to decouple the flux and the
pressure implementable. For the flux, the optimal error estimate with
respect to the energy norm is derived. We can only prove the
suboptimal convergence rate in $L^2$ norm for the flux until now,
while in numerical experiments we obverse the optimal convergence
behavior for the space of odd order.
Once we get the numerical approximation to the flux, one then could
use the numerical flux to obtain the pressure in a very flexible
manner. As a demonstration, we adopt the standard $C^0$ finite element
space to solve the pressure. We give the error estimates of the
pressure in both energy norm and $L^2$ norm. By a series of numerical
examples, we at first verify the convergence order given in the error
estimate and illustrate the flexibility we inherit from the DG
method. Particularly, by the comparison \cite{hughes2000comparison} of
the number of DOFs used to achieve the same
numerical error, we show that our method has a great saving in DOFs
compared to the standard DLS finite element method. Consequently, by
the decoupling of the flux and the pressure and by the saving in the
number of DOFs, a much better efficiency could be attained by our
method.
The rest of this paper is organized as follows. In Section
\ref{sec:fems}, we review the standard DLS finite element method and
present the corresponding error estimates. In Section
\ref{sec:irrotationbasis}, we introduce a reconstruction operator to
define the piecewise irrotational approximation space and we give the
approximation property of the new space. In Section \ref{sec:lsfem},
the approximation to the flux and the pressure of the Poisson problem
is proposed, and we derive the error estimates for both flux and
pressure in energy norm and $L^2$ norm. In Section
\ref{sec:numericalresults}, we present the numerical examples on
meshes with different geometry to verify the convergence order in the
error estimates. Besides, we make a comparison of number of DOFs
respect to the numerical error between our method and the method in
Section \ref{sec:fems} to show the great efficiency of our method.
\section{Approximation Space with Irrotational Basis}
\label{sec:irrotationbasis}
In this section, we follow the idea in \cite{li2016discontinuous,
li2017discontinuous} to define an approximation space using a patch
reconstruction operator. Purposely, the reconstruction operator we
propose here will use the irrotational basis, thus the approximation space
obtained is piecewise rotation free. With this new approximation
space, we will decouple the minimization problem \eqref{eq:infdgep}
into two sub-problems, that we can numerically solve $\bmr{p}$ at
first and then solve $u$. Let us introduce an irrotational space
$\bmr{S}_m$ which plays a key role in the construction of the
operator,
\begin{displaymath}
\bmr{S}_m(D) = \left\{ \bmr{v} \in [\mathbb P_m(D)]^d\ |\
\nabla \times \bmr{v} = 0\right\}.
\end{displaymath}
For the irrotational space, we have that:
\begin{lemma}
For $\forall \bmr{q} \in \bmr{H}^{m+1}(K) \cap H(\curl^0, K)$,
there exists a constant $C$ such that there is a polynomial
$\widetilde{\bmr{q}}_h \in \bmr{S}_m(K)$ such that
\begin{equation}
\| \bmr{q} - \widetilde{\bmr{q}}_h\|_{L^2(K)} + h_K \| \nabla
\left( \bmr{q} - \widetilde{\bmr{q}}_h \right) \|_{L^2(K)} \leq C
h_K^{m+1} \|\bmr{q}\|_{ \bmr{H}^{m+1}(K)}.
\label{eq:appirr}
\end{equation}
\label{le:appirr}
\end{lemma}
\begin{proof}
Since $H(\curl^0, K) = \nabla H^1(K)$ \cite{girault1986finite},
there exists a $v \in H^{m+2}(K)$ such that $\bmr{q} = \nabla
v$. Let $\widetilde{v} \in \mb P_{m+2}(K)$ be the standard nodal
interpolation polynomial of $v$, and let
$\widetilde{\bmr{q}}_h = \nabla \widetilde{v}_h$. The inequality
\eqref{eq:appirr} directly follows from the approximation properties
of $\widetilde{v}_h$.
\end{proof}
With the partition $\MTh$, we define a reconstruction operator from
$\bmr{C}^0(\Omega)$ to the piecewise irrotational polynomial
space. For any element $K \in \MTh$, we prescribe a point
$\bm x_K \in K$, referred as the {\it sampling node} later on, which
is preferred to be the barycenter of $K$. Then, for each element $K$
we construct an element patch $S(K)$ which is an agglomeration of
elements that contain $K$ itself and some elements around $K$. There
are a variety of approaches to build the element patch and in this
paper we agglomerate elements to form the element patch
recursively. For element $K$, we first let
$S_0(K) = \left\{ K \right\}$ and we define $S_t(K)$ as
\begin{displaymath}
S_t(K) = S_{t-1}(K) \cup \left\{ K'\ |\ \exists \widetilde{K} \in
S_{t-1}(K)\ \text{s.t.}\ K' \cap \widetilde{K} = e \in \MEh\right\},
\quad t = 1, 2, \cdots
\end{displaymath}
In the implementation of our code, at the depth $t$ we enlarge $S_t(K)$
element by element and once $S_t(K)$ has collected sufficiently large
number of elements we stop the recursive procedure and let $S(K) =
S_t(K)$, otherwise we let $t = t + 1$ and continue the recursion. The
cardinality of $S(K)$ is denoted by $\# S(K)$.
Further, for element $K$ we denote by $\mc I_K$ the set of sampling
nodes located inside the element patch $S(K)$,
\begin{displaymath}
\mc I_K \triangleq \left\{ \bm x_{\widetilde{K}}\ |\ \forall
\widetilde{K} \in S(K) \right\}.
\end{displaymath}
For any function $\bmr{f} \in \bmr{C}^0(\Omega) \cap H(\curl^0;
\Omega)$ and an element $K \in \MTh$, we seek a polynomial $\mc{R}^m_K
\bmr{f}$ of degree $m$ defined on $S(K)$ by solving the following
least squares problem:
\begin{equation}
\mc{R}^m \bmr{f} = \mathop{\arg \min}_{\bmr{v} \in \bmr{S}_m(S(K))}
\sum_{\bm x_{\widetilde{K}} \in \mc I_K } |\bmr{v}(\bm
x_{\widetilde{K}}) - \bmr{f}(\bm x_{\widetilde{K}})|^2.
\label{eq:lsproblem}
\end{equation}
We note that the existence of the solution to \eqref{eq:lsproblem} is
obvious but the uniqueness of the solution depends on the position of
the sampling nodes in $\mc I_K$, here we follow
\cite{li2016discontinuous} to state the following assumption:
\begin{assumption}
For all element $K \in \MTh$ and $\bmr{v} \in \bmr{S}_m(S(K))$,
\begin{displaymath}
\bmr{v}|_{\mc I_K} = \bmr{0} \quad \text{implies} \quad
\bmr{v}|_{S(K)} \equiv \bmr{0}.
\end{displaymath}
\end{assumption}
This assumption demands the number $\# S(K)$ shall be greater than
$\text{dim}(\bmr{S}_m) / d$ and excludes the situation that all the
points in $\mc I_K$ lie on an algebraic curve of degree $m$.
Hereafter, we always require the assumption holds.
Due to the linear dependence of the solution \eqref{eq:lsproblem}, a
global reconstruction operator $\mc{R}^m$ for $\bmr{f}$ can be defined
by restricting the polynomial $\mc{R}^m_K \bmr{f}$ on $K$:
\begin{displaymath}
(\mc{R}^m \bmr{f})|_K = (\mc{R}^m_K \bmr{f})|_K, \quad \forall K \in \MTh.
\end{displaymath}
It is clear that the operator $\mc{R}^m$ embeds the space
$\bmr{C}^0(\Omega) \cap H(\curl^0; \Omega)$ to a piecewise
irrotational polynomial space of degree $m$, and we denote by
$\bmr{U}_h^m$ the image of the operator $\mc{R}^m$. In Appendix, we
give more details about our reconstructed space and the computer
implementation.
We next focus on the approximation property of the operator $\mc{R}^m$.
For element $K$, we define a constant
\begin{displaymath}
\Lambda(m, S(K)) = \max_{v \in \mb P_m(S(K))} \frac{\max_{\bm x \in
S(K)} |v(\bm x)|}{\max_{\bm x \in \mc I_K} | v(\bm x)|}.
\end{displaymath}
We note that under some mild and practical conditions about $S(K)$,
the $\Lambda(m, S(K))$ has a uniform upper bound $\Lambda_m$, which
plays an important role in the approximation property analysis. We
refer to \cite{li2012efficient, li2016discontinuous} for the
conditions and more details about the constant $\Lambda(m, S(K))$ and
the uniform upper bound. Besides, under such conditions the Lemma
\ref{le:appirr} could be generalized as
\begin{lemma}
For any function $\bmr{q} \in \bmr{H}^{m+1}(S(K)) \cap H(\curl^0,
S(K))$, there exists a constant $C$ such that there is a polynomial
$\widetilde{\bmr{q}}_h \in \bmr{S}_m(S(K))$ such that
\begin{equation}
\| \bmr{q} - \widetilde{\bmr{q}}_h\|_{L^2(S(K))} + h_K \| \nabla
\left( \bmr{q} - \widetilde{\bmr{q}}_h \right) \|_{L^2(S(K))} \leq
C h_K^{m+1} \|\bmr{q}\|_{ \bmr{H}^{m+1}(S(K))}.
\label{eq:appirrpatch}
\end{equation}
\label{le:appirrpatch}
\end{lemma}
\begin{proof}
It directly follows from \cite[Assumption A and Property M3]{li2016discontinuous}.
\end{proof}
With $\Lambda_m$, let us state the approximation property of the
operator $\mc{R}^m_K$.
\begin{theorem}
Let $\bmr{f} \in \bmr{H}^{m+1}(\Omega) \cap H(\curl^0; \Omega)$ and
$K \in \MTh$, there exists a constant $C$ such that
\begin{equation}
\begin{aligned}
\|\bmr{f} - \mc{R}^m_K \bmr{f} \|_{\bmr{H}^q(K)} &\leq C
\Lambda_m h_K^{m+1-q} \|\bmr{f}\|_{\bmr{H}^{m+1}(S(K))}, \quad q
= 0, 1, \\
\| \nabla^q(\bmr{f} - \mc{R}^m_K \bmr{f}) \|_{L^2(\partial K)} &
\leq C \Lambda_m h_K^{m+1 - q -1/2} \| \bmr{f} \|_{\bmr{H}^{m+1}
(S(K))}, \quad q = 0, 1.\\
\end{aligned}
\label{eq:approximation}
\end{equation}
\label{th:approximation}
\end{theorem}
\begin{proof}
The estimates directly follows the proof of \cite[Lemma
2.4]{li2016discontinuous} and the Lemma \ref{le:appirrpatch}.
\end{proof}
\section{Discontinuous Least Squares Finite Element Method}
\label{sec:fems}
Let $\Omega$ be a bounded polygonal domain in $\mathbb{R}^d(d=2, 3)$.
Let $\MTh$ be a partition of $\Omega$ into polygonal (polyhedral)
elements. We denote by $\MEh^i$ the set of interior element faces of
$\MTh$ and by $\MEh^b$ the set of the element faces on the boundary
$\partial \Omega$, thus the set of all element faces $\MEh = \MEh^b
\cup \MEh^i$. The diameter of an element $K$ is denoted by $h_K =
\text{diam}(K)$, $\forall K \in \MTh$ and the size of the face $e$ is
$h_e = |e|$, $\forall e \in \MEh$. We denote $h = h_{\max} = \max_{K
\in \MTh} h_K$. It is assumed that the elements in $\MTh$ are
shape-regular according to the conditions specified in
\cite{antonietti:2013}, which read: {\it there are
\begin{itemize}
\item two positive numbers $N$ and $\sigma$ which are independent of
$h$;
\item a compatible sub-decomposition $\widetilde{\mc T}_h$
consisting of shape-regular triangles;
\end{itemize}
such that
\begin{itemize}
\item any element $K \in \MTh$ admits a decomposition $\widetilde{\mc
T}_{h|K}$ which is composed of less than $N$ shape-regular
triangles;
\item the triangle $\widetilde{K} \in \widetilde{\mc T}_h$ is
shape-regular in the sense of that the ratio between
$h_{\widetilde{K}}$ and $\rho_{\widetilde{K}}$ is bounded by
$\sigma$: $h_{\widetilde{K}} / \rho_{\widetilde{K}} \leq \sigma $
where $\rho_{\widetilde{K}}$ is the radius of the largest ball
inscribed in $\widetilde{K}$.
\end{itemize}}
The regularity conditions could lead to some useful consequences
which are easily verified:
\newcounter{regularity}
\setcounter{regularity}{1}
\begin{enumerate}
\item[M\arabic{regularity}] There exists a positive constant
$\sigma_s$ such that $\sigma_v h_K \leq h_e$ for any element $K$
and every edge $e$ of $K$;
\addtocounter{regularity}{1}
\item[M\arabic{regularity}][{\it trace inequality}] There exists a
positive constant $C$ such that
\begin{equation}
\|v\|_{L^2(\partial K)}^2 \leq C \left( h_K^{-1} \| v\|_{L^2(
K)}^2 + h_K \| \nabla v\|_{L^2(K)}^2 \right), \quad \forall v
\in H^1(K).
\label{eq:traceinequality}
\end{equation}
\addtocounter{regularity}{1}
\item[M\arabic{regularity}][{\it inverse inequality}] There exists a
positive constant $C$ such that
\begin{equation}
\| \nabla v\|_{L^2(K)} \leq Ch_K^{-1} \|v\|_{L^2(K)}, \quad
\forall v \in \mb P_m(K),
\label{eq:inverse}
\end{equation}
where $\mb P_m(\cdot)$ is the polynomial space of degree $\leq m$.
\end{enumerate}
Next, we introduce the standard trace operators in the discontinuous
Galerkin (DG) framework \cite{arnold2002unified}. Let $v$ be a scalar-
or vector-valued function and $e \in \MEh^i$ shared by two adjacent
elements $K^+$ and $K^-$ with the unit outward normal $\un^+$ and
$\un^-$ corresponding to $\partial K^+$ and $\partial K^-$,
respectively. We define the average operator $\aver{\cdot}$ and the
jump operator $\jump{\cdot}$ as
\begin{displaymath}
\aver{v} = \frac{1}{2}\left( v|_{K^+} + v|_{K^-} \right), \quad
\forall e \in \MEh^i,
\end{displaymath}
and
\begin{displaymath}
\jump{v} = v|_{K^+}\un^+ + v|_{K^-}\un^-, \quad \jump{v \otimes \un}
= v|_{K^+}\otimes \un^+ + v|_{K^-} \otimes \un^-, \quad \forall e
\in \MEh^i.
\end{displaymath}
In the case $e \in \MEh^b$, $\aver{\cdot}$ and $\jump{\cdot}$ are
modified as
\begin{displaymath}
\aver{v} = v, \quad \jump{v} = v\un, \quad \jump{v \otimes \un} = v
\otimes \un, \quad \forall e \in \MEh^b,
\end{displaymath}
where $\un$ denotes the unit outward normal to $e$.
Throughout the paper, let us note that $C$ and $C$ with a subscript
are generic constants which may be different from line to line but are
independent of the mesh size, and we follow the standard definitions
for the spaces: $L^2(D)$, $H^t(D)$, $C^t(D)$, $\bmr{L}^2(D) :=
[L^2(D)]^d$, $\bmr{H}^t(D) = [H^t(D)]^d$, $\bmr{C}^t(D) = [C^t(D)]^d(t
\geq 0)$ and we define
\begin{displaymath}
H(\text{curl}^0; D) \triangleq \left\{ \bm v \in \bmr{L}^2(D)\ |\
\nabla \times \bm v = 0 \right\}.
\end{displaymath}
The problem considered in this article is the Poisson's equation: {\it
seek $u$ such that}
\begin{equation}
\begin{aligned}
- \Delta u &= f, \quad \text{in}\ \Omega, \\
u &= g, \quad \text{on}\ \partial \Omega. \\
\end{aligned}
\label{eq:elliptic}
\end{equation}
The first step of usual least squares finite element methods
\cite{Ye2018discontinuous, Bensow2005discontinuous} is to write the
problem \eqref{eq:elliptic} into an equivalent mixed form: {\it seek
$\bmr p$ and $u$ such that
\begin{equation}
\begin{aligned}
\bmr p - \nabla u &= \bm 0, \quad \text{in}\ \Omega, \\
-\nabla \cdot \bmr p &= f, \quad \text{in}\ \Omega, \\
u &= g, \quad \text{on}\ \partial \Omega.
\end{aligned}
\label{eq:ellipticmixed}
\end{equation}}
In the mixed form, we refer $u$ as the pressure and $\bmr p$ as the
flux later on based on the terminology of the background of this
equation in fluid dynamics. Here we introduce two discontinuous
approximation spaces: $V_h^m$ for the pressure $u$ and $\bmr{W}_h^m$
for the flux $\bmr q$, which are defined as below:
\begin{displaymath}
\begin{aligned}
V_h^m &= \left\{ v_h \in L^2(\Omega)\ |\ v_h|_K \in \mb P_m(K), \
\forall K \in \MTh\right\}, \\
\bmr{W}_h^m &= \left\{ \bmr{q}_h \in \bmr{L}^2(\Omega) \ |\
\bmr{q}_h |_K \in \left[ \mb P_m(K) \right]^d, \ \forall K \in
\MTh \right\}, \\
\end{aligned}
\end{displaymath}
where $m$ is a positive integer. We equip these two approximation
spaces with the following norms, $\|\cdot\|_{u}$ for $V_h^m$ and
$\|\cdot\|_{\bmr{p}}$ for $\bmr{W}_h^m$, respectively, as
\begin{displaymath}
\begin{aligned}
\|v_h\|_{u}^2 \triangleq & \sum_{K \in \MTh} \|\nabla
v_h\|_{L^2(K)}^2 + \sum_{e \in \MEh} h^{-1} \|
\jump{v_h}\|_{L^2(e)}^2, \quad \forall v_h \in V_h^m,\\
\|\bmr{q}_h\|_{\bmr{p}}^2 \triangleq &\sum_{K \in \MTh} \left( \|
\nabla \cdot \bmr{q}_h\|_{L^2(K)}^2 + \|\bmr{q}_h\|_{L^2(K)}^2
\right) + \sum_{e \in \MEh^i} h^{-1} \| \jump{\bmr{q_h}}
\|_{L^2(e)}^2, \quad \forall \bmr{q}_h \in \bmr{W}_h^m. \\
\end{aligned}
\end{displaymath}
The standard least squares finite element method based on mixed form
\eqref{eq:ellipticmixed} reads \cite{Ye2018discontinuous}: {\it find
$(u_h, \bmr{p}_h) \in V_h^m \times \bmr{W}_h^m$ such that
\begin{equation}
J_h(u_h, \bmr{p}_h) = \inf_{ (v_h, \bmr{q}_h) \in V_h^m \times
\bmr{W}_h^m} J_h(v_h, \bmr{q}_h),
\label{eq:infdg}
\end{equation}
where $J_h(\cdot, \cdot)$ is the least squares functional which is
defined as
\begin{equation}
\begin{aligned}
J_h(v_h, \bmr{q}_h)& \triangleq \sum_{K \in \MTh} \left(
\| \nabla \cdot \bmr{q}_h + f\|_{L^2(K)}^2 + \| \nabla v_h -
\bmr{q}_h \|_{L^2(K)}^2\right) \\
& + \sum_{e \in\MEh^i} \frac{1}{h} \| \jump{v_h}\|_{L^2(e)}^2
+ \sum_{e \in \MEh^i} \frac{1}{h} \| \jump{\bmr{q_h} \otimes
\un} \|_{L^2(e)}^2 + \sum_{e \in \MEh^b} \frac{1}{h} \| v_h - g
\|_{L^2(e)}^2. \\
\end{aligned}
\label{eq:infdgep}
\end{equation}}
To solve the minimization problem \eqref{eq:infdg}, one has its
corresponding variational equation which takes the form: {\it find $( u_h,
\bmr{p}_h) \in V_h^m \times \bmr{W}_h^m$ such that
\begin{equation}
a_h(u_h, \bmr{p}_h; v_h, \bmr{q}_h) = l_h(v_h, \bmr{q}_h), \quad
\forall (v_h, \bmr{q}_h) \in V_h^m \times \bmr{W}_h^m,
\label{eq:dgweakform}
\end{equation}
where the bilinear form $a_h(\cdot; \cdot)$ and the linear form
$l_h(\cdot)$ are defined by
\begin{displaymath}
\begin{aligned}
a_h(u_h, &\bmr{p}_h; v_h, \bmr{q}_h) = \sum_{K \in \MTh} \left(
\int_K \nabla \cdot \bmr{p}_h \nabla \cdot \bmr{q}_h \d{x} +
\int_K (\nabla u_h - \bmr{p}_h)(\nabla v_h - \bmr{q}_h) \d{x}
\right) \\
&+ \sum_{e \in\MEh^i} \int_e \frac{1}{h} \jump{u} \jump{v} \d{s}
+ \sum_{e \in \MEh^i} \int_e \frac{1}{h} \jump{\bmr{p}_h \otimes
\un} \jump{ \bmr{q}_h \otimes \un} \d{s} + \sum_{e \in \MEh^b}
\int_e \frac{1}{h} u_h v_h \d{s}, \\
\end{aligned}
\end{displaymath}
and
\begin{displaymath}
l_h(v_h, \bmr{q}_h) = \sum_{K \in \MTh} \int_K f \nabla \cdot
\bmr{q}_h \d{x} + \sum_{e \in \MEh^b} \frac{1}{h} \int_e g v_h
\d{s}.
\end{displaymath}}
The coercivity of the bilinear form $a_h(\cdot; \cdot)$ are given in
\cite[Lemma 3.1]{Ye2018discontinuous} as
\begin{lemma}
For any $(v_h, \bmr{q}_h) \in V_h^m \times \bmr{W}_h^m$, there
exists a constant $C$ such that
\begin{equation}
a_h(v_h, \bmr{q}_h; v_h, \bmr{q}_h) \geq C\left( \|v_h\|_{u}^2 +
\|\bmr{q}_h\|_{\bmr{p}}^2 \right).
\label{eq:dgcoercivity}
\end{equation}
\label{le:dgcoercivity}
\end{lemma}
The uniqueness of the solution to \eqref{eq:dgweakform} instantly
follows from Lemma \ref{le:dgcoercivity} and the trivial boundedness
of $a_h(\cdot; \cdot)$. Further, it is direct to derive the error
estimate with respect to the norms $\| \cdot\|_{u}$ and
$\| \cdot \|_{\bmr{p}}$ by the approximation properties of spaces
$V_h^m$ and $\bmr{W}_h^m$ \cite[Theorem 4.1]{Ye2018discontinuous}.
\begin{theorem}
Let $u_h \times \bmr{q}_h \in V_h^m \times \bmr{W}_h^m$ be the
solution to \eqref{eq:dgcoercivity}, and assume the exact solution
$u \in H^{m+1}(\Omega)$ and $\bmr{q} \in \bmr{H}^{m+1}(\Omega)$,
then there exists a constant $C$ such that
\begin{equation}
\|u - u_h\|_{u} + \|\bmr{q} - \bmr{q}_h\|_{\bmr{p}} \leq Ch^{m} \left(
\|u\|_{H^{m+1}(\Omega)} + \|\bmr{q} \|_{\bmr{H}^{m+1}(\Omega)}
\right).
\label{eq:dgestimate}
\end{equation}
\label{th:dgestimate}
\end{theorem}
\section{Numerical Results}
\label{sec:numericalresults}
In this section, we conduct some numerical experiments to show the
accuracy and efficiency of the proposed method in
Section~\ref{sec:lsfem}. For simplicity, we select the cardinality $\#
S(K)$ uniformly and we list a group of reference values of $\# S(K)$
for different $m$ in Tab.~\ref{tab:numSK}.
\begin{table}
\centering
\renewcommand\arraystretch{1.3}
\begin{tabular}{p{2.0cm}| p{2.0cm}|p{1.5cm}|p{1.5cm}|p{1.5cm} }
\hline\hline
\multirow{2}{*}{$d = 2$} & $m$ & 1 & 2 & 3 \\
\cline{2-5}
& $\# S(K)$ & 6 & 10 & 16 \\
\hline
\multirow{2}{*}{$d = 3$} & $m$ & 1 & 2 & 3 \\
\cline{2-5}
& $\# S(K)$ & 8 & 15 & 25 \\
\hline \hline
\end{tabular}
\caption{$\# S(K)$ for $1 \leq m \leq 3$.}
\label{tab:numSK}
\end{table}
\subsection{Convergence order study}
We first examine the numerical convergence to verify the theoretical
prediction and exhibit the flexibility of our method.
\paragraph{\bf Example 1} We first consider a two-dimensional Poisson
problem with Dirichlet boundary condition on the domain $\Omega = [0,
1] \times [0, 1]$. The exact solution $u(x, y)$ is taken as
\begin{displaymath}
u(x, y) = \sin(2\pi x) \sin(4\pi y),
\end{displaymath}
and the source term $f$ and the boundary data $g$ are chosen
accordingly.
We solve this problem on a series of triangular meshes (see
Fig.~\ref{fig:triangulation}) with mesh size $h = 1/10$, $1/20$,
$c\dots$, $1/80$ and we first use the space pairs $\bmr{U}_h^m \times
\wh{V}_h^m(1 \leq m \leq 3)$ to solve the flux and pressure. In this
setting, from \eqref{eq:ul2estiate} we could see that the optimal
convergence order of $u_h$ depends on the convergence rate of
$\|\bmr{p} - \bmr{p}_h\|_{\bmr{L}^2(\Omega)}$. Although, we can not
develop a theoretical verification for the optimal convergence of
$\bmr{p}_h$ under $L^2$ norm, the computed convergence rates of
$\|\bmr{p} - \bmr{p}_h\|_{\bmr{L}^2(\Omega)}$ seem optimal for odd
$m$. The $L^2$ norm and the energy norm of the errors in the
approximation to the exact solution are gathered in
Tab.~\ref{tab:ex1errorm1}. We could observe that for odd $m$, the
errors $\|u -u_h\|_{L^2(\Omega)}$, $\enorm{ u - u_h}_u$, $\|\bmr{p} -
\bmr{p}_h\|_{\bmr{L}^2(\Omega)}$ and $\enorm{\bmr{p} -
\bmr{p}_h}_{\bmr{p}}$ converge to zero optimally as the mesh is
refined. For even $m$, the orders of convergence under $L^2$-norm are
suboptimal. Moreover, from the estimate \eqref{eq:ul2estiate} one
could observe that if we decrease the space approximating pressure by
one order, we could obtain the optimality for $u$ approximations. The
errors with the space pairs $\bmr{U}_h^m \times \wh{V}_h^{m-1}$ are
collected in Tab.~\ref{tab:ex1errorm2}, which clearly shows the
optimal convergence of $u_h$ for both measurements. Besides, we note
that all the convergence rates are consistence with the theoretical
predictions.
\begin{figure}[!htp]
\centering
\includegraphics[width=0.4\textwidth]{./figure/tri1-crop.pdf}
\hspace{25pt}
\includegraphics[width=0.4008\textwidth]{./figure/tri2-crop.pdf}
\caption{The triangular meshes with mesh size $h = 1/10$ (left) and
$h = 1/20$ for Example 1.}
\label{fig:triangulation}
\end{figure}
\begin{table}
\centering
\renewcommand\arraystretch{1.2}
\begin{tabular}{p{0.3cm}| p{0.2cm} p{1.8cm} p{0.8cm} p{1.8cm}
p{0.8cm} p{1.8cm} p{0.8cm} p{1.8cm} p{0.8cm}}
\hline\hline
$m$ & & $\|e_u\|_{L^2(\Omega)} $ & order & $\enorm{e_u}_u$ & order
& $\| e_{\bmr{p}} \|_{\bmr{L}^2(\Omega)} $ & order &
$\enorm{e_{\bmr{p}}}_{\bmr{p}}$ & order \\
\hline
\multirow{5}{*}{$1$}
& 1 & 1.0602e-01 & - & 2.5550e-00 & -
& 1.1553e-00 & - & 2.9109e+01 & - \\
& 2 & 3.0872e-02 & 1.80 & 1.2677e-00 & 1.01
& 3.3347e-01 & 1.80 & 1.5319e+01 & 0.93 \\
& 3 & 8.3590e-03 & 1.90 & 6.3053e-01 & 1.01
& 8.7712e-02 & 1.90 & 7.9176e+00 & 0.95 \\
& 4 & 2.1548e-03 & 1.96 & 3.1463e-01 & 1.00
& 2.2647e-02 & 1.96 & 4.0133e+00 & 0.98 \\
& 5 & 5.4473e-04 & 1.98 & 1.5723e-02 & 1.00
& 5.7033e-03 & 1.98 & 2.0137e+00 & 1.00 \\
\hline
\multirow{5}{*}{$2$}
& 1 & 5.5862e-02 & - & 9.3425e-01 & -
& 9.1461e-01 & - & 8.0168e+00 & - \\
& 2 & 1.8898e-02 & 1.57 & 2.8628e-01 & 1.71
& 2.7402e-01 & 1.73 & 1.7807e+00 & 2.17 \\
& 3 & 4.9746e-03 & 1.93 & 7.3469e-02 & 1.93
& 7.1190e-02 & 1.95 & 4.1888e-01 & 2.08 \\
& 4 & 1.2538e-03 & 1.99 & 1.8776e-02 & 1.98
& 1.8016e-02 & 1.98 & 1.0111e-01 & 2.03 \\
& 5 & 3.1393e-04 & 2.00 & 4.7137e-03 & 1.99
& 4.5126e-03 & 2.00 & 2.4633e-02 & 2.02 \\
\hline
\multirow{5}{*}{$3$}
& 1 & 5.2485e-03 & - & 1.6872e-01 & -
& 1.2492e-01 & - & 3.7196e+00 & - \\
& 2 & 3.9516e-04 & 3.73 & 1.9952e-02 & 3.07
& 9.2700e-03 & 3.75 & 4.6565e-01 & 2.95 \\
& 3 & 2.1869e-05 & 4.17 & 2.0437e-03 & 3.28
& 5.9833e-04 & 3.95 & 6.0447e-02 & 2.97 \\
& 4 & 1.1300e-06 & 4.27 & 2.2652e-04 & 3.17
& 3.8808e-05 & 3.95 & 7.7175e-03 & 2.97 \\
& 5 & 6.0716e-08 & 4.07 & 2.7352e-05 & 3.05
& 2.4584e-06 & 3.98 & 9.7343e-04 & 2.99 \\
\hline\hline
\end{tabular}
\caption{Example 1. The errors $e_u = u - u_h, e_{\bmr{p}} = \bmr{p}
- \bmr{p}_h$, and the orders of convergence with the spaces
$\bmr{U}_h^m \times \wh{V}_h^m(1 \leq m \leq 3)$.}
\label{tab:ex1errorm1}
\end{table}
\begin{table}
\centering
\renewcommand\arraystretch{1.2}
\begin{tabular}{p{0.3cm}| p{0.2cm} p{1.8cm} p{0.8cm} p{1.8cm}
p{0.8cm} p{1.8cm} p{0.8cm} p{1.8cm} p{0.8cm}}
\hline\hline
$m$ & & $\|e_u\|_{L^2(\Omega)} $ & order & $\enorm{e_u}_u$ & order
& $\| e_{\bmr{p}} \|_{\bmr{L}^2(\Omega)} $ & order &
$\enorm{e_{\bmr{p}}}_{\bmr{p}}$ & order \\
\hline
\multirow{5}{*}{$2$}
& 1 & 6.8296e-02 & - & 2.4561e-00 & -
& 9.1461e-01 & - & 8.0168e+00 & - \\
& 2 & 1.7533e-02 & 1.96 & 1.2484e-00 & 0.97
& 2.7402e-01 & 1.73 & 1.7807e+00 & 2.17 \\
& 3 & 4.4126e-03 & 1.99 & 6.2683e-01 & 0.99
& 7.1190e-02 & 1.95 & 4.1888e-01 & 2.08 \\
& 4 & 1.1050e-03 & 2.00 & 3.3137e-01 & 1.00
& 1.8016e-02 & 1.98 & 1.0111e-01 & 2.03 \\
& 5 & 2.7636e-04 & 2.00 & 1.5691e-01 & 1.00
& 4.5126e-03 & 2.00 & 2.4633e-02 & 2.02 \\
\hline
\multirow{5}{*}{$3$}
& 1 & 4.9662e-03 & - & 3.8263e-01 & -
& 1.2492e-01 & - & 3.7196e+00 & - \\
& 2 & 6.3248e-04 & 2.97 & 9.7317e-02 & 1.97
& 9.2700e-03 & 3.75 & 4.6565e-01 & 2.95 \\
& 3 & 7.9437e-05 & 2.99 & 2.4434e-02 & 1.99
& 5.9833e-04 & 3.95 & 6.0447e-02 & 2.97 \\
& 4 & 9.9415e-06 & 3.00 & 6.1151e-03 & 2.00
& 3.8808e-05 & 3.95 & 7.7175e-03 & 2.97 \\
& 5 & 1.2430e-06 & 3.00 & 1.5291e-03 & 2.00
& 2.4584e-06 & 3.98 & 9.7343e-04 & 2.99 \\
\hline\hline
\end{tabular}
\caption{Example 1. The errors $e_u = u - u_h, e_{\bmr{p}} = \bmr{p}
- \bmr{p}_h$, and the orders of convergence with the spaces
$\bmr{U}_h^{m} \times \wh{V}_h^{m-1}(2 \leq m \leq 3)$.}
\label{tab:ex1errorm2}
\end{table}
\paragraph{\bf Example 2} In this example, we consider the sample
problem as in Example 1. But we use a sequence of polygonal meshes
consisting of elements with various geometries (see Fig.
\ref{fig:voroni}), which are generated by {\tt PolyMesher}
\cite{talischi2012polymesher}. We only solve the flux, and we present
the corresponding errors in the energy norm and $L^2$ norm and their
respective computed rates in Tab. ~\ref{tab:ex2error1}. Again we
observe the optimal convergence for both norms when $m$ is odd. For
even $m$, $\|\bmr{p} - \bmr{p}_h \|_{\bmr{L}^2(\Omega)}$ tends to zero
in a suboptimal way. To apply the method on meshes with different
geometry, it is an advantage inherited from the DG method. On such
meshes, the convergence order is agreed with our error estimates again.
\begin{figure}[!htp]
\centering
\includegraphics[width=0.4\textwidth]{./figure/M1-crop.pdf}
\hspace{25pt}
\includegraphics[width=0.4\textwidth]{./figure/M2-crop.pdf}
\caption{The polygonal meshes with 250 elements (left) / 1000
elements (right).}
\label{fig:voroni}
\end{figure}
\begin{table}
\centering
\begin{tabular}{p{0.3cm}| p{1.5cm} p{2.5cm} p{2cm} p{2.5cm} p{2cm}}
\hline\hline
$m$ & DOFs & $\|e_{\bmr{p}} \|_{\bmr{L}^2(\Omega)}$ & order & $\|
e_{\bmr{p}}\|_{\bmr{p}}$ & order \\
\hline
\multirow{4}{*}{$1$}
& 500 & 1.0485e-00 & - & 2.6456e+01 & - \\
& 2000 & 2.7316e-01 & 1.94 & 1.3244e+01 & 0.99 \\
& 8000 & 6.5948e-02 & 2.05 & 6.5998e-00 & 1.00 \\
& 32000 & 1.6203e-02 & 2.03 & 3.2658e-00 & 1.01 \\
\hline
\multirow{4}{*}{$2$}
& 500 & 4.4773e-01 & - & 6.1493e-00 & - \\
& 2000 & 1.2630e-01 & 1.83 & 1.3713e-00 & 2.16 \\
& 8000 & 3.0209e-02 & 2.06 & 3.3353e-01 & 2.03 \\
& 32000 & 7.4860e-03 & 2.01 & 8.2873e-02 & 2.01 \\
\hline
\multirow{5}{*}{$3$}
& 500 & 1.6412e-01 & - & 4.5508e-00 & - \\
& 2000 & 1.0449e-02 & 3.97 & 6.2226e-01 & 2.88 \\
& 8000 & 6.3315e-04 & 4.05 & 8.1210e-02 & 2.95 \\
& 32000 & 3.8188e-05 & 4.03 & 1.0205e-02 & 2.99 \\
\hline\hline
\end{tabular}
\caption{Example 2. The errors $e_{\bmr{p}} = \bmr{p} - \bmr{p}_h$,
and the orders of convergence with the spaces $\bmr{U}_h^m(1 \leq m
\leq
3)$.}
\label{tab:ex2error1}
\end{table}
\paragraph{\bf Example 3} In this example, we consider the mild wave
front problem, which is the Poisson equation on the unit square with
Dirichlet boundary conditions. The data functions $f$ and $g$ are
selected such that the exact solution is
\begin{displaymath} u(x, y) =
\arctan(\alpha(r - r_0)), \quad (x, y) \in [0, 1]^2,
\end{displaymath}
where $r = \sqrt{(x - x_0)^2 + (y - y_0)^2}$. The
mild wave front uses $(x_0, y_0) = (-0.05, -0.05)$, $r_0 = 0.7$,
$\alpha = 10$ and it is a problem of near singularities. For this
problem, the high-order accuracy is preferred \cite{Mitchell2015high}.
We use a sequence of quasi-uniform triangular meshes (see Fig.
\ref{fig:ex3triangulation}) and we solve the problem with spaces
$\bmr{U}_h^m \times \wh{V}_h^m(1 \leq m \leq 3)$. We list the errors
in approximation to $\bmr{p}$ and $u$ in Tab. ~\ref{tab:ex3errorm1}.
It is clear that the proposed method yields the same convergence rates
as the Example 1, which validates our theoretical estimates.
\begin{figure}[!htp]
\centering
\includegraphics[width=0.4\textwidth]{./figure/d0tri0.pdf}
\hspace{25pt}
\includegraphics[width=0.4\textwidth]{./figure/d0tri1.pdf}
\caption{The triangular meshes with 246 elements (left) and
984 elements (right) for Example 3.}
\label{fig:ex3triangulation}
\end{figure}
\begin{table}
\centering
\renewcommand\arraystretch{1.2}
\begin{tabular}{p{0.3cm}| p{0.2cm} p{1.8cm} p{0.8cm} p{1.8cm}
p{0.8cm} p{1.8cm} p{0.8cm} p{1.8cm} p{0.8cm}}
\hline\hline
$m$ & & $\|e_u\|_{L^2(\Omega)} $ & order & $\enorm{e_u}_u$ & order
& $\| e_{\bmr{p}} \|_{\bmr{L}^2(\Omega)} $ & order &
$\enorm{e_{\bmr{p}}}_{\bmr{p}}$ & order \\
\hline
\multirow{5}{*}{$1$}
& 1 & 4.3807e-02 & - & 4.9822e-01 & -
& 1.1553e-00 & - & 1.0256e+01 & - \\
& 2 & 1.6473e-02 & 1.41 & 4.0917e-01 & 1.03
& 3.3347e-01 & 1.80 & 5.3347e+00 & 0.95 \\
& 3 & 3.5661e-03 & 2.21 & 1.9515e-01 & 1.07
& 8.7712e-02 & 1.90 & 2.6486e+00 & 1.01 \\
& 4 & 8.6682e-04 & 2.03 & 9.5962e-02 & 1.02
& 2.2647e-02 & 1.96 & 1.3231e+00 & 1.00 \\
& 5 & 2.1263e-04 & 2.03 & 4.7761e-02 & 1.00
& 5.7033e-03 & 1.98 & 6.6057e-01 & 1.00 \\
\hline
\multirow{5}{*}{$2$}
& 1 & 1.5200e-02 & - & 2.9032e-01 & -
& 2.4411e-01 & - & 5.6918e+00 & - \\
& 2 & 5.3703e-03 & 1.51 & 9.0132e-02 & 1.68
& 8.9263e-02 & 1.45 & 1.3870e+00 & 2.03 \\
& 3 & 1.4510e-03 & 1.89 & 2.5011e-02 & 1.85
& 2.5413e-02 & 1.82 & 3.1295e-01 & 2.10 \\
& 4 & 3.6778e-04 & 1.98 & 6.5013e-02 & 2.00
& 6.7113e-03 & 1.92 & 7.1999e-02 & 2.11 \\
& 5 & 9.1211e-05 & 2.01 & 1.6380e-03 & 1.98
& 1.6989e-03 & 1.99 & 1.7550e-02 & 2.03 \\
\hline
\multirow{5}{*}{$3$}
& 1 & 1.0333e-02 & - & 8.0091e-02 & -
& 2.0391e-01 & - & 5.8500e+00 & - \\
& 2 & 1.1023e-03 & 3.23 & 1.2076e-02 & 2.72
& 1.7701e-02 & 3.52 & 9.7265e-01 & 2.59 \\
& 3 & 6.7612e-05 & 4.03 & 1.2368e-03 & 3.28
& 1.1398e-03 & 3.96 & 1.3999e-01 & 2.80 \\
& 4 & 4.2528e-06 & 4.00 & 1.2956e-04 & 3.26
& 7.4761e-05 & 3.93 & 1.8073e-02 & 2.96 \\
& 5 & 2.2322e-07 & 4.12 & 1.4319e-05 & 3.17
& 4.7259e-06 & 3.98 & 2.2425e-03 & 3.01 \\
\hline\hline
\end{tabular}
\caption{Example 3. The errors $e_u = u - u_h, e_{\bmr{p}} = \bmr{p}
- \bmr{p}_h$, and the orders of convergence with the spaces
$\bmr{U}_h^m \times \wh{V}_h^m(1 \leq m \leq 3)$.}
\label{tab:ex3errorm1}
\end{table}
\paragraph{\bf Example 4} In this example, we exhibit the performance
of the proposed method with the problem with a corner singularity. We
consider the L-shaped domain $\Omega = [-1, 1]^2 \backslash [0, 1)
\times (-1, 0]$ and we use a series of triangular meshes, see Fig.
\ref{fig:Lshapetriangulation}. Following
\cite{Mitchell2013collection}, we let the exact solution be
\begin{displaymath}
u(r, \theta) = r^{5/3} \sin(5\theta/3)
\end{displaymath}
in polar coordinate and impose the Dirichlet boundary condition. The
data $f$ and the function $g$ are chosen accordingly. We notice that
$u(r, \theta)$ only belongs to $H^{2 + s}$ with $s < 2/3$. In Tab.
\ref{tab:ex4error}, we list the errors measured in the energy norm and
$L^2$ norm for both flux and pressure. Here we observe that the error
$\enorm{\bmr{p} - \bmr{p}_h}_{\bmr{p}}$ decreases at the rate
$O(h^{2/3})$ which matches with the fact that $\bmr{p}$ only belongs
to $H^{5/3 - \varepsilon}(\Omega)$. The computed orders of $\|\bmr{p} -
\bmr{p}_h\|_{L^2(\Omega)}$, $\enorm{u - u_h}_u$ and $\|u -
u_h\|_{L^2(\Omega)}$ are about $1$. A possible explanation of the
rates may be traced back to the lack of $H^3$-regularity of the exact
solution on the whole domain.
\begin{figure}[!htp]
\centering
\includegraphics[width=0.4\textwidth]{./figure/L1-crop.pdf}
\hspace{25pt}
\includegraphics[width=0.4\textwidth]{./figure/L2-crop.pdf}
\caption{The triangular meshes with 250 elements (left) and
1000 elements for Example 3.}
\label{fig:Lshapetriangulation}
\end{figure}
\begin{table}
\centering
\renewcommand\arraystretch{1.2}
\begin{tabular}{p{0.3cm}| p{0.2cm} p{1.8cm} p{0.8cm} p{1.8cm}
p{0.8cm} p{1.8cm} p{0.8cm} p{1.8cm} p{0.8cm}}
\hline\hline
$m$ & & $\|e_u\|_{L^2(\Omega)} $ & order & $\enorm{e_u}_u$ & order
& $\| e_{\bmr{p}} \|_{\bmr{L}^2(\Omega)} $ & order &
$\enorm{e_{\bmr{p}}}_{\bmr{p}}$ & order \\
\hline
\multirow{5}{*}{$1$}
& 1 & 4.5059e-03 & - & 1.5490e-01 & -
& 3.9382e-02 & - & 4.2524e-02 & - \\
& 2 & 1.3528e-03 & 1.73 & 7.7746e-02 & 0.99
& 1.8681e-02 & 1.07 & 2.5539e-02 & 0.73 \\
& 3 & 4.0795e-04 & 1.73 & 3.8900e-02 & 1.00
& 9.3165e-03 & 1.00 & 1.5859e-02 & 0.68 \\
& 4 & 1.3376e-04 & 1.61 & 1.9563e-02 & 1.00
& 4.5537e-03 & 1.03 & 9.9689e-03 & 0.67 \\
& 5 & 5.2105e-05 & 1.36 & 9.7263e-03 & 1.00
& 2.2927e-03 & 1.00 & 6.2815e-03 & 0.67 \\
\hline
\multirow{5}{*}{$2$}
& 1 & 2.2627e-03 & - & 9.3186e-03 & -
& 3.4672e-02 & - & 5.1619e-02 & - \\
& 2 & 6.8183e-04 & 1.73 & 2.6548e-03 & 1.81
& 1.6061e-02 & 1.11 & 2.9373e-02 & 0.81 \\
& 3 & 2.3956e-04 & 1.51 & 9.2329e-04 & 1.52
& 8.0869e-03 & 0.99 & 1.8481e-02 & 0.67 \\
& 4 & 1.0011e-04 & 1.99 & 3.7505e-04 & 1.29
& 4.0509e-03 & 1.26 & 1.1383e-02 & 0.68 \\
& 5 & 4.5381e-05 & 1.13 & 1.7137e-04 & 1.12
& 2.0293e-03 & 1.00 & 7.0855e-03 & 0.68 \\
\hline
\multirow{5}{*}{$3$}
& 1 & 2.5557e-03 & - & 1.1823e-02 & -
& 4.1292e-02 & - & 5.7175e-02 & - \\
& 2 & 8.6799e-04 & 1.55 & 4.1778e-03 & 1.50
& 1.9767e-02 & 1.06 & 3.0635e-02 & 0.90 \\
& 3 & 3.3653e-04 & 1.36 & 1.4712e-03 & 1.50
& 9.6459e-03 & 1.03 & 1.0801e-02 & 0.76 \\
& 4 & 1.5550e-04 & 1.13 & 5.9787e-04 & 1.29
& 4.9361e-05 & 0.98 & 1.1136e-02 & 0.68 \\
& 5 & 7.5031e-05 & 1.06 & 2.8188e-04 & 1.08
& 2.5011e-05 & 0.99 & 6.9361e-03 & 0.68 \\
\hline\hline
\end{tabular}
\caption{Example 4. The errors $e_u = u - u_h, e_{\bmr{p}} = \bmr{p}
- \bmr{p}_h$, and the orders of convergence with the spaces
$\bmr{U}_h^{m} \times \wh{V}_h^m(1 \leq m \leq 3)$.}
\label{tab:ex4error}
\end{table}
\paragraph{\bf Example 5} We consider a three-dimensional Poisson
problem on a unit cube $\Omega = [0, 1]^3$. The domain is partitioned
into a series of tetrahedral meshes with mesh size $h = 1/5, 1/10,
1/20, 1/40$ by {\tt Gmsh} \cite{geuzaine2009gmsh}. The exact solution
is taken as
\begin{displaymath}
u(x, y, z) = \sin(2\pi x) \sin(2\pi y) \sin(2 \pi z),
\end{displaymath}
and the Dirichlet function $g$ and the source term $f$ are taken
suitably. We use the spaces $\bmr{U}_h^m \times \wh{V}_h^m(1 \leq m
\leq 3)$ to approximate $\bmr{p}$ and $u$, respectively. The numerical
results are presented in Tab.~\ref{tab:ex5errorm}. We still observe
the optimal convergence rate for $\bmr{p}_h$ under $\bmr{L}^2$ norm
when $m$ is odd, and all computed convergence orders agree with the
theoretical analysis.
\begin{table}
\centering
\renewcommand\arraystretch{1.2}
\begin{tabular}{p{0.3cm}| p{0.2cm} p{1.8cm} p{0.8cm} p{1.8cm}
p{0.8cm} p{1.8cm} p{0.8cm} p{1.8cm} p{0.8cm}}
\hline\hline
$m$ & & $\|e_u\|_{L^2(\Omega)} $ & order & $\enorm{e_u}_u$ & order
& $\| e_{\bmr{p}} \|_{\bmr{L}^2(\Omega)} $ & order &
$\enorm{e_{\bmr{p}}}_{\bmr{p}}$ & order \\
\hline
\multirow{5}{*}{$1$}
& 1 & 2.0159e-01 & - & 2.6227e-00 & -
& 1.4772e-00 & - & 2.0737e+01 & - \\
& 2 & 6.7739e-02 & 1.76 & 1.4117e-00 & 0.89
& 4.3453e-01 & 1.80 & 1.0927e+01 & 0.93 \\
& 3 & 1.8200e-02 & 1.90 & 7.3125e-01 & 0.95
& 1.1641e-02 & 1.90 & 5.4683e+00 & 0.99 \\
& 4 & 4.6456e-03 & 1.96 & 3.6691e-01 & 1.00
& 2.9923e-02 & 1.96 & 2.7331e+00 & 1.00 \\
\hline
\multirow{5}{*}{$2$}
& 1 & 2.8293e-02 & - & 7.6111e-01 & -
& 3.6002e-01 & - & 7.0288e+00 & - \\
& 2 & 9.1341e-02 & 1.63 & 2.2963e-01 & 1.73
& 1.0421e-01 & 1.79 & 1.7895e+00 & 1.97 \\
& 3 & 2.5926e-03 & 1.82 & 6.1281e-02 & 1.91
& 2.8129e-02 & 1.89 & 4.6372e-01 & 1.95 \\
& 4 & 6.8012e-04 & 1.93 & 1.5021e-02 & 2.01
& 7.2823e-03 & 1.95 & 1.1599e-01 & 2.00 \\
\hline
\multirow{5}{*}{$3$}
& 1 & 7.2877e-03 & - & 1.8326e-01 & -
& 1.7658e-01 & - & 3.0434e+00 & - \\
& 2 & 7.3997e-04 & 3.30 & 2.1873e-02 & 3.06
& 1.3510e-02 & 3.71 & 3.9250e-01 & 2.96 \\
& 3 & 5.6061e-05 & 3.73 & 2.7168e-03 & 3.28
& 9.2336e-04 & 3.87 & 5.1203e-02 & 3.01 \\
& 4 & 3.6203e-06 & 3.96 & 3.3962e-04 & 3.17
& 5.9170e-05 & 3.96 & 6.4123e-03 & 3.00 \\
\hline\hline
\end{tabular}
\caption{Example 5. The errors $e_u = u - u_h, e_{\bmr{p}} = \bmr{p}
- \bmr{p}_h$, and the orders of convergence with the spaces
$\bmr{U}_h^m \times \wh{V}_h^m(1 \leq m \leq 3)$.}
\label{tab:ex5errorm}
\end{table}
\subsection{Efficiency comparison}
The number of the degrees of freedom of a discretized system is a
suitable indicator for the efficiency, as illustrated by Hughes et al
in \cite{hughes2000comparison}. In our method, the accuracy of
$\bmr{p}_h$ determines the convergence behavior of the pressure. Thus,
to show the efficiency of the proposed method, we make a comparison
between the standard least squares discontinuous finite element method
presented in Section~\ref{sec:fems} and the proposed method by
comparing the error of the numerical flux $\bmr{p}_h$.
For both methods, we select the finite element spaces of equal order
for solving the Poisson problem. Here we solve the problems that are
taken from the Example 1 and Example 5 for two and three dimensional
case, respectively. We implement the two methods on successively
refined meshes. In Fig.~\ref{fig:compared2}, we plot the errors of
numerical flux in the DLS energy norm $\| \cdot \|_{\bmr{p}}$ against
the number of degrees of freedom with $1 \leq m \leq 3$ in two and
three dimension. All convergence orders are in perfect agreement
with the theoretical results.
There are two points notable for us. To achieve the same accuracy, the
proposed method uses much less DOFs than the DLS finite element
method. The saving of number of DOFs is more remarkable for higher
order approximation. For $d=2$, the number of DOFs used in our method
is about $36\%$ of that in DLS method for linear approximation to
achieve the same accuracy. Meanwhile, the number of DOFs used in our
method is about $31\%$ and $27\%$ of the number of DOFs used in DLS
method for $m=2$ and $3$, respectively (see
Fig.~\ref{fig:compared2}). In Fig.~\ref{fig:compared2}, one may see
that the saving of number DOFs for 3D problems is even more
significant than 2D problems. For $d=3$, the percentages of number of
DOFs reduce to about $30\%$, $12\%$, and $5\%$ of that in DLS method
for $m=1$, $2$, and $3$, respectively.
Let us note at last that the numerical flux $\bmr{p}_h$ obtained by
our method is locally irrotational, which is a natural property as the
gradient of a function.
\begin{figure}[!htp]
\centering
\includegraphics[width=0.45\textwidth]{./figure/compared2.pdf}
\hspace{25pt}
\includegraphics[width=0.45\textwidth]{./figure/compared3.pdf}
\caption{Comparison of the error $\|\bmr{p} - \bmr{p}_h\|_{\bmr{p}}$
in number of DOFs by two methods with $m =1, 2, 3$ in two
dimension (left) and three dimension (right).}
\label{fig:compared2}
\end{figure}
| {
"redpajama_set_name": "RedPajamaArXiv"
} | 1,318 |
Q: Flask sqlalchemy InterfaceError I'm not sure whats going wrong here...I get this error:
InterfaceError: (InterfaceError) Error binding parameter 0 - probably unsupported type. u'SELECT contact.id AS contact_id, contact.surname AS contact_surname, contact.firstname AS contact_firstname, contact.email AS contact_email, contact.mobile AS contact_mobile, contact.work_location AS contact_work_location \nFROM contact \nWHERE contact.id = ?' ([1],)
My method:
@app.route('/contacts/<int:contact_id>', methods=['GET'])
def contact_detail(contact_id):
if request.method == 'GET':
db.session.query(Contact).filter_by(id=[contact_id]).all()
return render_template('modcontact.html', title = 'Contact Detail')
My models:
class Contact(db.Model):
id = db.Column(db.Integer, primary_key = True)
surname = db.Column(db.String(100))
firstname = db.Column(db.String(100))
email = db.Column(db.String(100))
mobile = db.Column(db.String(20))
work_location = db.Column(db.String(100))
#user_id = db.Column(db.Integer, db.ForeignKey('user.id'))
def __repr__(self):
return '<Contact %r>' % (self.surname)
template:
{% extends "base.html" %}
{% block content %}
<h1>List of contacts</h1>
<ul class=contacts>
{% for contacts in contacts %}
<li><h3>
<a href="{{ url_for('contact_detail',contact_id=contacts.id)}}">
{{ contacts.surname }}, {{ contacts.firstname }}
</a>
</h3></li>
{% else %}
<li><em>No contacts available</em></li>
{% endfor %}
</ul>
<a href="/addcontact/">Add a new contact</a>
{% endblock %}
A: You pass a list in your query filter. So the parameter in the query is a list therefore the 'Error binding parameter 0'.
Try this instead: db.session.query(Contact).filter_by(id=contact_id).all()
| {
"redpajama_set_name": "RedPajamaStackExchange"
} | 2,319 |
Středozemní moře je rozsáhlé vnitřní moře Atlantského oceánu, které se rozkládá mezi Evropou, Asií a Afrikou. S oceánem je propojeno 13 km širokým Gibraltarským průlivem. Přes průlivy Dardanely a Bospor (a Marmarské moře) na něj navazuje Černé moře. Uměle je propojeno také s Rudým mořem (a potažmo Indickým oceánem) prostřednictvím Suezského průplavu.
Ačkoliv z definice je Středozemní moře součástí Atlantiku, často je bráno jako samostatná část světového oceánu, neboť hydrologicky i geologicky je na Atlantském oceánu prakticky nezávislé a nadto má samo řadu vlastních okrajových moří.
Severní (evropské) pobřeží je členité s množstvím ostrovů a velkými poloostrovy Pyrenejským, Apeninským, Balkánským a Malou Asií. Jižní (africké) pobřeží je členité poměrně málo. Oblast okolo Středozemního moře se označuje jako Středozemí nebo Středomoří. Středozemí je kolébkou řady vyspělých starověkých kultur, např. Egypta, Řecka nebo Říma. V moderní době se jedná především o jednu ze světově nejvyhledávanějších turistických destinací.
Pojem středozemní moře má v oceánografii také obecný význam značící část světového oceánu, která je převážně obklopena pevninou a má jen zanedbatelnou výměnu vody s okolním oceánem. Konkrétní Středozemní moře se v tomto kontextu specifikuje jako "evropské", "africké" nebo "euroafrické středozemní moře".
Názvy
Středozemní moře má řadu označení v jazycích národů obývajících jeho pobřeží, převážně ale téhož významu. Označení pro moře je ("Vnitřní moře") nebo , , , , , , , , černohorsky a , , (Mesógeio Thálassa, Mesojio Thalasa), , (al-bahhr al-abyadd al-mutawasitt), (ha-yam ha-tíqón) a .
V minulosti bylo nazýváno též Bílé moře, což je význam jeho tureckého pojmenování (z pohledu Turků jde o protiváhu Černému moři). Římané ho nazývali Mare nostrum, tedy "Naše moře".
Geografické charakteristiky
rozloha 2,6 mil. km²
maximální hloubka 5 267 m
objem 3,7 mil. km³
teplota vody v zimě 11 °C na západě až 16 °C na východě, v létě 20 až 28 °C
salinita vody od západu k východu stoupá a pohybuje se mezi 3,60 až 3,95 % (36 – 39,5 promile)
příliv nízký, většinou do 0,5 m
Okrajová moře a zálivy
Středozemní moře má na severní straně svá vlastní okrajová moře (s Atlantským oceánem jsou spojena pouze jeho prostřednictvím), která mohou a nemusejí být považována za jeho součást. Rozdíl mezi mořem a zálivem tkví v některých případech jen v názvu. Černé moře se obvykle za součást Středozemního moře nepovažuje. Seznam okrajových moří a zálivů následuje:
Gibraltarská zátoka
Alboránské moře
Alicantský záliv
Baleárské moře
Valencijský záliv
Lví záliv
Ligurské moře
Janovský záliv
Golfe de Saint-Florent
Golfe de Porto
Golfe de Sagone
Golfe d'Ajaccio
Golfe de Valinco
Golfo dell'Asinara
Cagliarský záliv
Tyrhénské moře
Golfo di Gaeta
Salernský záliv
Golfo di Policastro
Golfo di Sant'Eufemia
Golfo di Milazzo
Golfo di Patti
Golfo di Termini
Golfo di Castellammare
Golfo di Gela
Jaderské moře
Golfo di Manfredonia
Benátský záliv
Terstský záliv
Kvarnerský záliv
Riječki zaljev
Jónské moře
Golfo di Noto
Golfo di Catania
Golfo di Squillace
Tarentský záliv
Pellg i Drinit
Giji i Rodonit
Giji i Lalzës
Dračský záliv
Giji i Karavastas
Gjol i Nartës
Giji i Vlorës
Amvrakíkos Kólpos
Patraïkós Kólpos
Korintský záliv
Kólpos Argostóliou
Kólpos Laganá
Kyparissiakós Kólpos
Messiniakós Kólpos
Lakonikós Kólpos
Krétské moře
Argolikós Kólpos
Saronikós Kólpos
Egejské moře
Kólpos Petalió
Pagasitikós Kólpos
Thermský záliv
Soluňský záliv
Kólpos Kassándras
Kólpos Agíou Órous
Kólpos Ieríssou
Kólpos Orfánou
Kólpos Kaválas
Saros Körfezi
Thrácké moře
Marmarské moře
Černé moře
Azovské moře
Edremit Körfezi
Çandarlı Körfezi
İzmir Körfezi
Kuşadası Körfezi
Güllük Körfezi
Gökova Körfezi
Fethiye Körfezi
Finike Körfezi
Antalya Körfezi
Ovacık Körfezi
Taşucu Körfezi
Mersin Körfezi
İskenderun Körfezi
Kólpos Mórfou
Kólpos Chrysochoús
Kólpos Episkopís
Kólpos Akrotíri
Kólpos Lárnakos
Kólpos Ammóchostou
Buḥayrat Manzilah
Buḥayrat al-Burullus
Khalīj Abū Qīr
Libyjské moře
Velká Syrta
Malá Syrta
Bardawil
Tuniský záliv
Ostrovy a poloostrovy
Ve Středozemním moři se nacházejí četné ostrovy a souostroví. Cestou od západu na východ jsou to zejména Baleáry, Korsika, Sardinie, Sicílie, Malta, Džerba, Kréta a Kypr. V okrajových mořích se dále nacházejí Toskánské ostrovy, Liparské ostrovy, Kvarnerské ostrovy, Dalmatské ostrovy, Jónské ostrovy či Egejské ostrovy. Nejvíce středomořských ostrovů patří Řecku, na celkovou rozlohu ostrovů vede Itálie. Ostrovy nebo jejich skupiny vymezují některá středomořská okrajová moře (Ligurské, Tyrhénské, Egejské, Krétské, Thrácké).
Zejména na členitém severním pobřeží se nachází i mnoho poloostrovů. Největší jsou Apeninský a Balkánský poloostrov (z nějž vybíhá Peloponéský a řada dalších) a Malá Asie. Velký strategický význam má výběžek Gibraltar. Na jižním pobřeží jsou významné poloostrovy Bon a Kyrenaika.
Přítoky
Zdaleka největší řekou ústící do Středozemního moře je africký veletok Nil.
Další významné přítoky jsou z Evropy: Júcar, Ebro, Rhôna, Tibera, Pád, Adiže, Piava, Soča, Neretva, Drin, Aliákmon, Vardar, Struma, Marica.
Z asijské strany jsou největšími přítoky Gediz, Velký Menderes, Seyhan, Ceyhan, Orontes.
Státy na pobřeží
Díky své rozloze a členitosti omývá Středozemní moře břehy mnoha států (přes 20); pro většinu z nich tvoří jediný přístup k moři. To jsou: Albánie, Alžírsko, Bosna a Hercegovina, Černá Hora, Chorvatsko, Itálie, Libanon, Libye, Monako, Řecko, Slovinsko, Sýrie, Tunisko, Turecko, případně Palestina (skrze Pásmo Gazy). Rovněž 2 z Britských zámořských teritorií, Gibraltar a vojenská základna Akrotiri a Dekelia na Kypru, jsou omývany pouze Středozemním mořem. Dva ostrovní státy leží celé přímo v tomto moři: Kypr, Malta.
Pět států na pobřeží má přístup do oceánu i jinou cestou: Egypt, Francie, Izrael, Maroko a Španělsko.
Středozemní moře je také jedinou námořní cestou do světového oceánu pro tyto státy u Černého moře: Bulharsko, Gruzie, Rumunsko, Ukrajina.
Města a přístavy
Největšími městy na pobřeží jsou (tučně hlavní města): Alexandrie, Alžír, Antalya, Athény, Barcelona, Bejrút, Benghází, Janov, Málaga, Marseille, Neapol, Oran, Palermo, Smyrna, Soluň, Tel Aviv, Tripolis, Tunis, Valencie. Blízko pobřeží se nachází také Řím. Pokud bychom za součást Středozemního moře považovali i Marmarské moře, byl by největším městem na pobřeží Istanbul.
Nejrušnějšími středomořskými přístavy co do kontejnerové dopravy jsou Pireus, Valencie, Algeciras a Port Said.
Mezi nejvýznamnější přístavy dále patří (z dosud neuvedených) Alicante, Bar, Bari, Bastia, Benátky, Cagliari, Civitavecchia, Drač, Gioia Tauro, Gozo, Haifa, Iraklion, Koper, La Spezia, Limassol, Mersin, Messina, Nice, Palma de Mallorca, Patra, Pula, Reggio Calabria, Rijeka, Rhodos, Salamis, Savona, Sfax, Split, Taranto, Terst, Valletta, Zadar.
Reference
Externí odkazy
článek "Šok: Na dně Středozemního moře byla poušť!"
článek "Středozemní moře vzniklo díky ohromné potopě"
"Články o Chorvatsku"
Moře Evropy
Moře Atlantského oceánu
Vodstvo Afriky
Moře Asie
Geografie střední Evropy
Geografie jižní Evropy
Geografie západní Evropy
Středomoří | {
"redpajama_set_name": "RedPajamaWikipedia"
} | 2,025 |
\section{Introduction}
\label{sec:intro}
The standard model (SM) has been extremely successful at describing particle physics phenomena. Nevertheless, it suffers from shortcomings such as the hierarchy problem~\cite{'tHooft:1979bh,Witten:1981nf,Dine:1981za,Dimopoulos:1981au,Dimopoulos:1981zb,Kaul:1981hi}, the need for fine-tuned cancellations of large quantum corrections to keep the Higgs boson mass near the electroweak scale.
Supersymmetry (SUSY), based on a symmetry between bosons and fermions, is an attractive extension of the SM. A key feature of SUSY is the existence of a superpartner for every SM particle with the same quantum numbers, except for spin, which differs by one half unit. In R-parity conserving SUSY models~\cite{Wess:1974tw,Farrar:1978xj}, supersymmetric particles are created in pairs, and the lightest supersymmetric particle (LSP) is stable~\cite{djoua,carena} and considered to be a candidate for dark matter~\cite{darkmatter}.
Supersymmetry can potentially provide a ``natural'', \ie not fine-tuned, solution to the hierarchy problem through the cancellation of quadratic divergences in particle and sparticle loop corrections to the Higgs boson mass.
In natural SUSY models light top and bottom squarks with masses close to the electroweak scale are preferred.
This paper presents three complementary searches for direct production of a pair of top ($\ensuremath{\PSQt_{1}}\xspace\ensuremath{\PASQt_{1}}\xspace$) or bottom squarks ($\ensuremath{\PSQb_{1}}\xspace\ensuremath{\PASQb_{1}}\xspace$), where the subscript here denotes the less massive partner of the corresponding SM fermion's chirality states. The first search targets top squark pair production in the all-jet final state, while the second focuses on the single-lepton final state.
These two analyses were explicitly designed for complementarity, allowing for a combination of the results to enhance the sensitivity. The third search targets bottom squark pair production in the all-jet final state.
The searches are performed using the data collected in proton-proton collisions at a centre-of-mass energy of 13\TeV with the CMS detector at the CERN LHC in 2015, corresponding to an integrated luminosity of 2.3\fbinv .
The results of similar searches were previously reported by the ATLAS and CMS collaborations using proton-proton collisions at 7 and 8\TeV~\cite{ATLAS1,ATLAS2,ATLAS5,ATLAS5a,ATLAS6,ATLAS7,ATLAS8,atlas-stop0l-2014,atlas-stop1l-2015,CMS-STOP-lepton,CMS-alphaT,RAZOR_8TeV,stop8TeV,stop0l_8TeV} and by the CDF and D0 collaborations in $\Pp\bar{\Pp}$ collisions at 1.96\TeV at the Fermilab Tevatron~\cite{Abazov:2003wt,Abazov:2012cz,Abazov:2007ak,Aaltonen:2010uf,Acosta:2003ys}.
With the increase in LHC collision energy from 8 to 13\TeV, the cross section to produce signal events is enhanced by a factor of 8--12 for a top or bottom squark mass in the range 700--1000\GeV~\cite{Borschensky:2014cia,SUSYXCLHC}. Therefore, new territory can be explored even with the relatively small amount of data collected in 2015. The CMS and ATLAS collaborations have already provided first exclusion results for these models in the all-jet and single-lepton final states~\cite{CMS-PAS-SUS-15-003,CMS-PAS-SUS-15-004,CMS-PAS-SUS-15-005,atlas-stop1l-2016}. Unlike the more generic searches for new phenomena presented by the CMS collaboration in Refs.~\cite{CMS-PAS-SUS-15-003,CMS-PAS-SUS-15-004,CMS-PAS-SUS-15-005}, the searches described in this paper directly target top and bottom squark production through the design of search regions that exploit the specific characteristics of these signal models, for instance through the use of a top quark tagging algorithm in the top squark search in the all-jet final state to identify boosted hadronically decaying top quarks originating from top squark decays.
The decay modes of top squarks depend on the sparticle mass spectrum. Figure~\ref{fig:diagram} illustrates the top and bottom squark decay modes explored in this paper. The simplest top squark decay modes are $\ensuremath{\PSQt_{1}}\xspace \to \PQt^{(*)} \PSGczDo$ and $\ensuremath{\PSQt_{1}}\xspace \to \PQb \PSGcpmDo \to \PQb \ensuremath{\PW}\xspace^{\pm(*)} \PSGczDo$, with $\PSGcpmDo$ representing the lightest chargino, and with intermediate particles that can be virtual marked by asterisks. In these decay modes, the neutralino and charginos are mixtures of the superpartners of
electroweak gauge and Higgs bosons, and $\PSGczDo$ is considered to be an LSP that escapes detection, leading to a potentially large transverse momentum imbalance in the detector.
The two analyses of top squark pair production in the all-jet and single-lepton final states probe both of these $\ensuremath{\PSQt_{1}}\xspace$ decay modes.
In the $\ensuremath{\PSQt_{1}}\xspace \to \PQt^{(*)} \PSGczDo$ decay mode, the top quark is produced off-shell when $\Delta m \equiv m_{\ensuremath{\PSQt_{1}}\xspace}-m_{\PSGczDo} < m_{\PQt}$, while in the $\ensuremath{\PSQt_{1}}\xspace \to \PQb \PSGcpmDo$ decay mode, the experimental signature is affected by the mass of the chargino.
We consider a model in which both top squarks decay via the $\ensuremath{\PSQt_{1}}\xspace \to \PQt^{(*)} \PSGczDo$ decay mode. A second model in which the branching fraction for each of the two top squark decay modes is 50\% is also considered, under the assumption of a compressed mass spectrum in which the mass of $\PSGcpmDo$ is only 5\GeV greater than that of $\PSGczDo$, with the \ensuremath{\PW}\xspace~bosons resulting from chargino decays consequently being produced heavily off-shell.
If $\Delta m <m_{\ensuremath{\PW}\xspace}$, $\ensuremath{\PSQt_{1}}\xspace$ can decay through a four-body decay involving an SM fermion pair \ensuremath{\cmsSymbolFace{f}\overline{\cmsSymbolFace{f}}}\xspace as $\ensuremath{\PSQt_{1}}\xspace\to\PQb\ensuremath{\cmsSymbolFace{f}\overline{\cmsSymbolFace{f}}}\xspace\PSGczDo$, or through a flavour changing neutral current decay $\ensuremath{\PSQt_{1}}\xspace\to\cPqc\PSGczDo$. The analysis of bottom squark pair production considers the decay mode $\ensuremath{\PSQb_{1}}\xspace\to\PQb\PSGczDo$ within the allowed phase space, and also probes top squark pair production in the $\ensuremath{\PSQt_{1}}\xspace\to\cPqc\PSGczDo$ decay scenario.
\begin{figure*}[!htpb]
\centering
\includegraphics[width=\textwidth]{Figure_001.pdf}\caption{
\label{fig:diagram}
Feynman diagrams for pair production of top and bottom squarks via the decay modes considered in this paper. The model with 50\% branching fractions for $\ensuremath{\PSQt_{1}}\xspace \to \PQt^{(*)} \PSGczDo$ and $\ensuremath{\PSQt_{1}}\xspace \to \PQb \PSGcpmDo \to \PQb \ensuremath{\PW}\xspace^{\pm*} \PSGczDo$ decays leads to the final states in diagrams (a)--(c).}
\end{figure*}
This paper is organized as follows. Section~\ref{sec:detector} contains a brief description of the CMS detector, while Section~\ref{sec:obj} discusses the event reconstruction and simulation. Sections~\ref{sec:stop0l},~\ref{sec:1lstop}, and~\ref{sec:sbottom} present details for the all-jet top squark search, the single-lepton top squark search, and the all-jet bottom squark search, respectively.
Section~\ref{sec:systematics} describes the systematic uncertainties affecting the results of the three analyses. The interpretation of the results in the form of exclusion limits on models of top or bottom squark pair production is discussed in Section~\ref{sec:interpretation}, followed by a summary in Section~\ref{sec:summary}.
\section{The CMS detector}
\label{sec:detector}
The central feature of the CMS apparatus is a superconducting solenoid of 6\unit{m} internal diameter,
providing a magnetic field of 3.8\unit{T}. Within the solenoid volume are an all-silicon pixel and strip tracker, a
lead tungstate crystal electromagnetic calorimeter (ECAL), and a brass and scintillator hadron calorimeter (HCAL), each composed of
a barrel and two endcap sections.
Forward calorimeters extend the pseudorapidity ($\eta$) coverage provided by the barrel and endcap detectors.
Muons are measured in gas-ionization detectors embedded in the steel flux-return yoke outside
the solenoid. The first level of the CMS trigger system, composed of custom hardware processors, uses information from the
calorimeters and muon detectors to select the most interesting events in a fixed time interval of less than 4\mus. The high-level
trigger processor farm further decreases the event rate from around 100\unit{kHz} to around 1\unit{kHz}, before data storage.
A more detailed description of the CMS detector, together with a definition of the coordinate system used and the relevant
kinematic variables, can be found in Ref.~\cite{JINST}.
\section{Reconstruction algorithms and simulation}
\label{sec:obj}
Event reconstruction uses the particle-flow (PF) algorithm \cite{CMS:2009nxa,CMS:2010eua}, combining information from the tracker, calorimeter, and muon systems to identify charged hadrons, neutral hadrons, photons, electrons, and muons in an event. The missing transverse momentum, \ptvecmiss, is computed as the negative vector sum of the transverse momenta (\ptvec) of all PF candidates reconstructed in an event, and its magnitude \MET is an important discriminator between signal and SM background. Events selected for the searches are required to pass filters designed to remove detector- and beam-related noise and must have at least one reconstructed vertex. Usually more than
one such vertex is reconstructed, due to pileup, i.e. multiple pp collisions within the same or neighbouring bunch crossings. The reconstructed vertex with the largest $\sum{\pt^2}$ of associated tracks is designated as the primary vertex.
Charged particles originating from the primary vertex, photons, and neutral hadrons are clustered into jets using the anti-\kt algorithm~\cite{Cacciari:2008gp} implemented in FastJet~\cite{Cacciari:2011ma} with a distance parameter of 0.4. The jet energy is corrected to account for the contribution of additional pileup interactions in an event and to compensate for variations in detector response~\cite{Cacciari:2011ma,pileup}. Jets considered in the searches are required to have their axes within the tracker volume, within the range $\abs{\eta} < 2.4$.
Jets originating from \PQb~quarks are identified with the combined secondary vertex (CSV) algorithm~\cite{Chatrchyan:2012jua,CMS-PAS-BTV-15-001} using two different working points, referred to as ``loose" and ``medium". The \PQb~tagging efficiency for jets originating from \PQb~quarks is about 80\% and 60\% for the loose and medium working point, respectively, while the misidentification rates for jets from charm quarks, and from light quarks or gluons are about 45\% and 12\%, and 10\% and 2\%, respectively.
The ``CMS top (quark) tagging'' (CTT) algorithm~\cite{CMS:2014fya,CMS:2016tvk,Kaplan:2008ie} is used to identify highly energetic top quarks decaying to jets with the help of observables related to jet substructure~\cite{Dasgupta:2013ihk,Cacciari:2005hq} and mass.
For a relativistic top quark with a Lorentz boost $\gamma = E/m$, the \ensuremath{\PW}\xspace~boson and \PQb~quark produced in the top quark decay are expected to be separated by a distance $R \equiv \sqrt{\smash[b]{(\Delta\eta)^2 + (\Delta\phi)^2} }\approx 2/\gamma$ (where $\phi$ is the azimuthal angle in radians).
In cases where the \ensuremath{\PW}\xspace~boson subsequently decays hadronically, the three resulting jets from the \ensuremath{\PW}\xspace~boson decay and the hadronization of the \PQb~quark are likely to be merged into a single jet by a clustering algorithm with a distance parameter larger than $2/\gamma$.
To identify hadronically decaying top quarks with $\pt > 400$\GeV, we therefore use jets reconstructed using the anti-\kt algorithm with a distance parameter of 0.8 to try to cluster the top quark decay products into a single jet.
The next step of top quark reconstruction is an attempt to decompose the candidate jet into at least three subjets with the help of the Cambridge-Aachen jet clustering algorithm~\cite{Dokshitzer:1997in,CACluster2}, the invariant mass of which is required to be consistent with the top quark mass (140--250\GeV). The final requirement of top quark identification is that the minimum invariant mass of any pair of the three subjets with the highest \pt must exceed 50\GeV.
The efficiency of the CTT algorithm to identify jets originating from top quark decays is measured to be about 30--40\% while the misidentification rate is found to be about 4--6\%, depending on the \pt of the top quark candidates. No disambiguation is performed between top quark candidates and jets reconstructed with a distance parameter of 0.4.
Electron candidates are reconstructed by first matching clusters of energy deposited in the ECAL to reconstructed tracks. Selection criteria based on the distribution of the shower shape, track--cluster matching, and consistency between the cluster energy and track momentum are then used in the identification of electron candidates~\cite{Khachatryan:2015hwa}. Muon candidates are reconstructed by requiring consistent hit patterns in the tracker and muon systems~\cite{Chatrchyan:2012xi}. Electron and muon candidates are required to be consistent with originating from the primary vertex by imposing restrictions on the size of their impact parameters in the transverse plane and longitudinal direction with respect to the beam axis. The relative isolation variable $I_\text{rel}$ for these candidates is defined as the scalar sum of the transverse momenta of all PF candidates, excluding the lepton, within a \pt-dependent cone size of radius $R$ around the candidate's trajectory, divided by the lepton \pt. The size $R$ depends on lepton \pt as follows:
\begin{equation}
R =
\begin{cases}
0.2, & \pt \leq 50\GeV, \\
10\GeV/\pt, & 50 < \pt < 200\GeV, \\
0.05, & \pt \geq 200\GeV.
\end{cases}
\end{equation}
The shrinking cone radius for higher-\pt leptons allows us to maintain high efficiency for the collimated decay products of boosted heavy objects. The isolation sum is corrected for contributions originating from pileup interactions through an area-based estimate~\cite{pileup} of the pileup energy deposited in the cone.
Hadronically decaying $\Pgt$ lepton ($\tauh$) candidates are reconstructed using the CMS hadron-plus-strips (HPS) algorithm~\cite{Khachatryan:2015dfa}. The constituents of the reconstructed jets are used to identify individual $\Pgt$ lepton decay modes with one charged hadron and up to two neutral pions, or three charged hadrons. The presence of
extra particles within the jet, not compatible with the reconstructed decay mode, is
used as a criterion to discriminate $\tauh$ decays from other jets.
Photon candidates are reconstructed from energy deposited in the ECAL, and selected using the distribution of the shower shape variable, the photon isolation, and the amount of leakage of the photon shower into the HCAL~\cite{Khachatryan:2015iwa}.
Monte Carlo (MC) simulations of events are used to study the properties of SM backgrounds and signal models. The \MADGRAPH5\_a\MCATNLO 2.2.2 generator~\cite{Alwall:2014hca} is used in leading-order (LO) mode to simulate events originating from \ttbar, \ensuremath{\PW+}jets\xspace, \ensuremath{\Z+}jets\xspace, \ensuremath{\gamma+}jets\xspace, and quantum chromodynamics multijet processes~('QCD'), as well as signal events, based on LO NNPDF3.0~\cite{Ball:2014uwa} parton distribution functions (PDFs). Single top quark events produced in the \PQt\ensuremath{\PW}\xspace~channel and \ttbar samples used in the single-lepton analysis are generated at next-to-leading order (NLO) with \textsc{Powheg} v2~\cite{Nason:2004rx,Frixione:2007vw,Alioli:2010xd,Re:2010bp}, while rare SM processes such as \ensuremath{\ttbar\cPZ}\xspace~and \ensuremath{\ttbar\PW}\xspace~are generated at NLO using the \MADGRAPH5\_a\MCATNLO 2.2.2 program, using NLO NNPDF3.0 PDFs. Parton showering and hadronization is generated using \textsc{Pythia}8.205~\cite{Sjostrand:2014zea}. The response of the CMS detector for the SM backgrounds is simulated via the \GEANTfour~\cite{geant4} package. The CMS fast simulation package \cite{fastsim} is used to simulate all signal samples, and is verified to provide results that are consistent with those obtained from the full \GEANTfour-based simulation. Event reconstruction is performed in the same manner as for collision data. A nominal distribution of pileup interactions is used when producing the simulated samples. The samples are then reweighted to match the pileup profile observed in the collected data. The signal production cross sections are calculated using NLO with next-to-leading logarithm (NLL) soft-gluon resummation calculations~\cite{Borschensky:2014cia}. The most precise cross section calculations are used to normalize the SM simulated samples, corresponding most often to next-to-next-to-leading order (NNLO) accuracy.
\section{Search for top squarks in the fully-hadronic final state}
\label{sec:stop0l}
The top squark search in the all-jet final state is characterized by the categorization of events into exclusive search regions based on selection criteria applied to kinematic variables related to jets and \MET, and the use of the CTT algorithm to identify boosted top quark candidates. The main backgrounds in the search regions are estimated from dedicated data control samples.
\subsection{Analysis strategy}
\label{sec:stop0l_strategy}
The events in this analysis are recorded using a trigger that requires the presence of two or more energetic jets within the tracker acceptance and large \MET. To be efficient, events selected offline are therefore required to have at least two jets with $\pt > 75$\GeV, $\abs{\eta} < 2.4$, and $\MET > 250$\GeV.
In order to reduce SM backgrounds with intrinsic \MET such as leptonic $\ttbar$ and \ensuremath{\PW+}jets\xspace events, we reject events with isolated electrons or muons that have $\pt > 5$\GeV, $\abs{\eta} < 2.4$, and $I_\text{rel}$ less than 0.1 or 0.2, respectively. The contribution from events in which a \ensuremath{\PW}\xspace~boson decays to a $\Pgt$ lepton is reduced by rejecting events containing isolated charged-hadron PF candidates with $\pt>10$\GeV and $\abs{\eta} < 2.5$ that are consistent with $\tauh$ decays. The isolation requirement applied is based on a discriminant obtained from a multivariate boosted decision tree (BDT) trained to distinguish the characteristics of charged hadrons originating from $\tauh$ decays. The transverse mass \ensuremath{M_{\mathrm{T}}}\xspace of the system comprising the charged-hadron PF candidate and \ptvecmiss is required to be less than 100\GeV assuring consistency with $\tauh$ originating from a \ensuremath{\PW}\xspace~boson decay, to minimize loss of signal at high jet multiplicity. The transverse mass for a particle q (in this case, the $\tauh$ candidate) is defined as:
\begin{equation}
M_\mathrm{T}({q}, \ptvecmiss) \equiv \sqrt{2 q_{\mathrm{T}} \MET (1 - \cos \Delta\phi)},\label{eq:MT}
\end{equation}
with $q_{\mathrm{T}}$ denoting the particle transverse momentum, and $\Delta\phi$ the azimuthal separation between the particle and \ptvecmiss.
Events selected for the search sample must also have at least five jets with $\pt>20$\GeV, at least two of which must be \PQb-tagged satisfying the loose working point of the CSV algorithm, with one or more of them required to additionally satisfy the medium working point. In addition, the absolute value of the azimuthal angle between \ptvecmiss and the closest of the four highest-\pt (leading) jets, $\ensuremath{\Delta\phi_{1234}}\xspace$, must be at least 0.5.
An imbalance in event \pt is produced in QCD events through a mismeasurement of jet $\pt$, and is often aligned with one of the leading jets in the event. The requirement on $\ensuremath{\Delta\phi_{1234}}\xspace$ therefore greatly reduces the contribution of the QCD background. The set of selection criteria defined above will be referred to as the ``baseline selection'' for this search.
After imposing the baseline selection, we subdivide the event sample into categories based on kinematic observables related to jets and \MET to improve the power of the analysis to discriminate between signal and the remaining SM background.
The dominant sources of SM background are \ttbar, \ensuremath{\PW+}jets\xspace, and \ensuremath{\Z+}jets\xspace events. The contribution from \ttbar and \ensuremath{\PW+}jets\xspace processes arises from events with \ensuremath{\PW}\xspace~bosons decaying leptonically, in which the charged lepton either falls outside of the kinematic acceptance, or, in most cases, evades identification, and may be reconstructed as a jet. Large \MET can be generated by the associated neutrino, allowing such events to satisfy the baseline selection criteria. This background is collectively referred to as the ``lost-lepton background''. Contributions arising from \ensuremath{\ttbar\PW}\xspace~and single top quark processes also enter this category, but with lesser importance. The contributions from \ensuremath{\Z+}jets\xspace and \ensuremath{\ttbar\cPZ}\xspace~events arise when the \cPZ~boson decays to neutrinos, producing thereby a significant amount of \MET. The QCD background is reduced to a subdominant level by the requirements of the baseline selection.
In \ttbar events with a lost lepton, the transverse mass of the \PQb~quark \ptvecmiss system arising from the same top quark decay as the lost lepton has a kinematic endpoint at the mass of the top quark. The observable~$\ensuremath{M_{\mathrm{T}}(\PQb_{1,2},\ptvecmiss)}\xspace$ is defined as
\begin{equation}
\ensuremath{M_{\mathrm{T}}(\PQb_{1,2},\ptvecmiss)}\xspace \equiv \min[ M_\mathrm{T}(\PQb_{1}, \ptvecmiss), M_\mathrm{T}(\PQb_{2}, \ptvecmiss) ],
\end{equation}
where $\PQb_1, \PQb_2$ are the two selected \PQb-tagged jets with highest values in the CSV discriminant. Imposing a minimum requirement of 175\GeV on $\ensuremath{M_{\mathrm{T}}(\PQb_{1,2},\ptvecmiss)}\xspace$ reduces a significant portion of the \ttbar background, but also results in a loss in signal efficiency for models with small $\Delta m$, as seen in Fig.~\ref{fig:catvars}, in which signal models with different top squark and neutralino mass hypotheses are shown, with the first number indicating the assumed top squark mass in units of \GeV and the second the neutralino mass. To benefit from the separation power provided by this variable, we define two search categories, one with $\ensuremath{M_{\mathrm{T}}(\PQb_{1,2},\ptvecmiss)}\xspace\geq175$\GeV, taking advantage of the corresponding reduction in \ttbar background for signal models with large $\Delta m$, and another with $\ensuremath{M_{\mathrm{T}}(\PQb_{1,2},\ptvecmiss)}\xspace<175$\GeV to retain the statistical power of events populating the low-$\ensuremath{M_{\mathrm{T}}(\PQb_{1,2},\ptvecmiss)}\xspace$ region for models with small $\Delta m$.
Signal events with all-jet top quark decays should have at least six jets in the final state, although in the case of signals with compressed mass spectra these jets can be too soft in \pt to satisfy the jet selection threshold. Additional jets may be produced through initial-state radiation (ISR). The jet multiplicity is lower for the semileptonic \ttbar background, as well as for the other backgrounds remaining after the baseline selection. A requirement of higher reconstructed jet multiplicity therefore improves the discrimination of signal events from the SM background. We consider two regions in jet multiplicity for the analysis, a high-$\ensuremath{N_{\mathrm{j}}}\xspace$~region ($\geq 7$ jets) that benefits from this improved discrimination, and a medium-$\ensuremath{N_{\mathrm{j}}}\xspace$~region (5--6 jets) to preserve signal events with fewer reconstructed jets. The high-$\ensuremath{N_{\mathrm{j}}}\xspace$~region in conjunction with the low threshold on the $\pt$~of selected jets improves sensitivity for signal models with soft decay products in the final state.
In the high-$\ensuremath{M_{\mathrm{T}}(\PQb_{1,2},\ptvecmiss)}\xspace$ category, requiring the presence of at least one top quark reconstructed by the CTT algorithm ($\ensuremath{N_{\PQt}}\xspace \geq 1$) ensures a high-purity selection of signal events with highly boosted top quarks, at the sacrifice of some loss in signal efficiency. To benefit from this high-purity region, without giving up signal events that would enter the $\ensuremath{N_{\PQt}}\xspace = 0$ region, we use both regions to extract the final signal. Figure~\ref{fig:catvars} shows the $\ensuremath{N_{\PQt}}\xspace$ distribution for events in the high-$\ensuremath{M_{\mathrm{T}}(\PQb_{1,2},\ptvecmiss)}\xspace$ category. Subdividing each $\ensuremath{N_{\PQt}}\xspace$ region by the number of \PQb-tagged jets ($\ensuremath{N_{\PQb}}\xspace$) that satisfy the medium working point of the CSV algorithm provides even greater discrimination of signal from background.
Since there are relatively few events in the $\ensuremath{N_{\PQt}}\xspace \geq 1$ category, the subcategorization in $\ensuremath{N_{\mathrm{j}}}\xspace$~is not performed for these events because it provides no additional gain after the $\ensuremath{N_{\PQb}}\xspace$~subdivision.
\begin{figure}[!htbp]
\centering
\includegraphics[width=0.48\textwidth]{Figure_002-a.pdf}
\includegraphics[width=0.48\textwidth]{Figure_002-b.pdf}
\caption{\label{fig:catvars} The $\ensuremath{M_{\mathrm{T}}(\PQb_{1,2},\ptvecmiss)}\xspace$ distribution after the baseline selection of the top squark search in the all-jet final state (\cmsLeft), and the number of reconstructed top quarks for events in the high-$\ensuremath{M_{\mathrm{T}}(\PQb_{1,2},\ptvecmiss)}\xspace$ category (\cmsRight). Signal models with different top squark and neutralino mass hypotheses are shown, with the first number indicating the assumed top squark mass in units of\GeV and the second the neutralino mass. The expected signal yields are scaled up by a factor of 10 to facilitate comparison of the distributions with expectations from SM backgrounds. In this and subsequent figures, the last bin shown includes the overflow events.}
\end{figure}
The event categorization according to $\ensuremath{M_{\mathrm{T}}(\PQb_{1,2},\ptvecmiss)}\xspace$, $\ensuremath{N_{\mathrm{j}}}\xspace$, $\ensuremath{N_{\PQb}}\xspace$, and $\ensuremath{N_{\PQt}}\xspace$ is summarized in Table~\ref{tab:evtcategories}. In each of these categories, we use \MET as the final discriminant to characterize and distinguish potential signal from the SM background by defining five \MET regions.
The analysis is therefore carried out in a total of 50 disjoint search regions (SRs).
\begin{table}[htb]
\centering
\topcaption{\label{tab:evtcategories} Categorization in $\ensuremath{M_{\mathrm{T}}(\PQb_{1,2},\ptvecmiss)}\xspace$, $\ensuremath{N_{\mathrm{j}}}\xspace$, $\ensuremath{N_{\PQb}}\xspace$, and $\ensuremath{N_{\PQt}}\xspace$ used to define the SRs for the top squark search in the all-jet final state. Events in each category are further separated into the following \MET regions: 250--300, 300--400, 400--500, 500--600, and $>$600\GeV, resulting in 50 disjoint SRs.}
{\begin{tabular}{c|cc|c}
\hline
\multicolumn{2}{c}{$\ensuremath{M_{\mathrm{T}}(\PQb_{1,2},\ptvecmiss)}\xspace<175$\GeV} & \multicolumn{2}{c}{$\ensuremath{M_{\mathrm{T}}(\PQb_{1,2},\ptvecmiss)}\xspace\geq175$\GeV}\\
\hline
$\ensuremath{N_{\PQb}}\xspace = 1$ & $\ensuremath{N_{\PQb}}\xspace \geq 2$ & $\ensuremath{N_{\PQb}}\xspace = 1$ & $\ensuremath{N_{\PQb}}\xspace \geq 2$ \\
\hline
\multirow{3}{*}{$5 \leq \ensuremath{N_{\mathrm{j}}}\xspace \leq 6$} & \multirow{3}{*}{$5 \leq \ensuremath{N_{\mathrm{j}}}\xspace \leq 6$} & \multicolumn{2}{c}{$\ensuremath{N_{\PQt}}\xspace = 0$} \\
\cline{3-4}
& & $5 \leq \ensuremath{N_{\mathrm{j}}}\xspace \leq 6$ & $5 \leq \ensuremath{N_{\mathrm{j}}}\xspace \leq 6$ \\
& & $\ensuremath{N_{\mathrm{j}}}\xspace \geq 7$ & $\ensuremath{N_{\mathrm{j}}}\xspace \geq 7$ \\
\cline{3-4}
\multirow{2}{*}{$\ensuremath{N_{\mathrm{j}}}\xspace \geq 7$} & \multirow{2}{*}{$\ensuremath{N_{\mathrm{j}}}\xspace \geq 7$} & \multicolumn{2}{c}{$\ensuremath{N_{\PQt}}\xspace \geq 1$}\\
\cline{3-4}
& & $\ensuremath{N_{\mathrm{j}}}\xspace \geq 5$ & $\ensuremath{N_{\mathrm{j}}}\xspace \geq 5$ \\
\hline
\end{tabular}
}
\end{table}
\subsection{Background estimation}
\label{sec:stop0l_bkgest}
\subsubsection{Estimation of the lost-lepton background}
\label{sec:stop0l_llbkg}
The lost-lepton background is estimated from a single-lepton control sample, selected using the same trigger as the search sample, and consisting of events that have at least one lepton~($\ell$) obtained by inverting the electron and muon rejection criteria. Studies in simulation indicate that the event kinematics for different lepton flavours are similar enough to estimate them collectively from the same control sample. Potential signal contamination is suppressed by requiring $\ensuremath{M_{\mathrm{T}}(\ell,\ptvecmiss)}\xspace<100$\GeV. If there is more than one lepton satisfying the selection criteria, the lepton used to determine $\ensuremath{M_{\mathrm{T}}(\ell,\ptvecmiss)}\xspace$ is chosen randomly. The events selected in the lepton control sample are further subdivided into control regions (CRs) using the same selection criteria as in the search sample, according to $\ensuremath{M_{\mathrm{T}}(\PQb_{1,2},\ptvecmiss)}\xspace$, $\ensuremath{N_{\mathrm{j}}}\xspace$, $\ensuremath{N_{\PQt}}\xspace$, and $\MET$. However with the requirement $\ensuremath{N_{\PQb}}\xspace\geq1$ the distribution in \MET originating from lost-lepton processes is independent of $\ensuremath{N_{\PQb}}\xspace$, and therefore the CRs are not subdivided according to the number of \PQb-tagged jets. These CRs generally have a factor of 2--4 more events than the corresponding SRs.
The estimation of the lost-lepton background in each SR is based on the event count in data in the corresponding single-lepton CR ($N^{\text{data}}_{1\ell}$). We translate this event count to the SR by means of a lost-lepton transfer factor $\ensuremath{T_{\text{LL}}}\xspace$ obtained from simulation. The lost-lepton background prediction can therefore be extracted as
\begin{equation}
N^\text{pred}_{\text{LL}} = N^{\text{data}}_{1\ell}~\ensuremath{T_{\text{LL}}}\xspace,\quad \ensuremath{T_{\text{LL}}}\xspace = \frac{N^{\text{sim}}_{0\ell}}{N^{\text{sim}}_{1\ell}},
\end{equation}
where $N^{\text{sim}}_{0\ell}$ and $N^{\text{sim}}_{1\ell}$ are the simulated lost-lepton background yields in the corresponding zero- and single-lepton regions, respectively, taking into account contributions from \ttbar and \ensuremath{\PW+}jets\xspace events, with smaller contributions from single top quark and \ensuremath{\ttbar\PW}\xspace~processes. The contamination from other SM processes in the single-lepton CRs is found to be negligible in studies of simulated events. Monte Carlo simulated samples are used to estimate the small component of the lost-lepton background that originates from leptons falling outside the kinematic acceptance, since this component is not accounted for in the CRs.
To improve the statistical power of the estimation, CRs with $\ensuremath{N_{\PQt}}\xspace\geq1$ are summed over \MET bins as well as over $\ensuremath{N_{\PQb}}\xspace$. We rely on the simulation through $N^\text{sim}_{0\ell}$ to provide the \MET-dependence and to predict the yield in each of the SRs with $\ensuremath{N_{\PQt}}\xspace\geq1$. We check this procedure by computing the data-to-simulation ratios $N^\text{data}_{1\ell}/N^\text{sim}_{1\ell}$ in the higher-statistics region of $\ensuremath{M_{\mathrm{T}}(\PQb_{1,2},\ptvecmiss)}\xspace\geq175$\GeV with $\ensuremath{N_{\PQt}}\xspace = 0$, and find no evidence of a dependence on \MET. We assign the relative statistical uncertainties of these ratios as systematic uncertainties in the SRs.
The dominant uncertainty in the lost-lepton prediction is due to the limited number of events in the CRs, and can be as large as $100\%$. The statistical uncertainties in the simulated samples also affect the uncertainty in the prediction via the transfer factors. The effect in the uncertainty ranges between $3\%$ and $50\%$. A source of bias in the prediction can arise from a possible difference between data and simulation in the background composition, which is assessed by independently changing the cross sections of the \ensuremath{\PW+}jets\xspace and $\ttbar$ processes by ${\pm}20\%$ based on CMS differential cross section measurements~\cite{Khachatryan:2014uva,CMS-PAS-TOP-16-008}. The effect of these changes is as large as $11\%$ for the transfer factors. The uncertainties in the measurements of correction factors in lepton efficiency that are applied to the simulation to reduce discrepancies with the data lead to a systematic uncertainty of up to $7\%$ in $\ensuremath{T_{\text{LL}}}\xspace$. All other sources of systematic uncertainty, to be discussed in Section~\ref{sec:systematics}, have a negligible effect on the prediction.
\subsubsection{Estimation of the \texorpdfstring{$\ensuremath{\cPZ\to\cPgn\cPagn}\xspace$}{Znunu} background}
\label{sec:stop0l_znunu}
Two methods are traditionally used to estimate the \ensuremath{\cPZ\to\cPgn\cPagn}\xspace~background in searches involving all-jet final states with large \MET. The first method relies on a sample dominated by \ensuremath{\cPZ\to\ell\ell}+jets events, which has the advantage of accessing very similar kinematics to the \ensuremath{\cPZ\to\cPgn\cPagn}\xspace~process, after correcting for the difference in acceptance between charged-lepton pairs and pairs of neutrinos, but is statistically limited in regions defined with stringent requirements on jets and \MET. The second method utilizes \ensuremath{\gamma+}jets\xspace events that have a significantly larger production cross section than the \ensuremath{\cPZ\to\ell\ell}+jets process, but similar leading-order Feynman diagrams. The two main differences between the processes that must be taken into account, namely, different quark-boson couplings and the massive nature of the \cPZ~boson, become less important at large \cPZ~boson \pt, which is the kinematic region we are probing in this search.
We have therefore adopted a hybrid method to estimate the \ensuremath{\cPZ\to\cPgn\cPagn}\xspace~background by combining information from \ensuremath{\Z+}jets\xspace, with \ensuremath{\cPZ\to\ell\ell}, and \ensuremath{\gamma+}jets\xspace events. \ensuremath{\cPZ\to\ell\ell}~events are used to obtain the normalization for the $\ensuremath{\cPZ\to\cPgn\cPagn}\xspace$ background in different ranges of $\ensuremath{N_{\PQb}}\xspace$ to account for potential effects related to heavy-flavour production, while the much higher yields from the \ensuremath{\gamma+}jets\xspace sample are exploited to extract corrections to distributions of variables used to characterize the SRs. The \ensuremath{\cPZ\to\ell\ell}~events are obtained from dielectron and dimuon triggers, with the leading lepton required to have $\pt>20$\GeV, and the trailing lepton $\pt>15$ and $>10$\GeV for electrons and muons, respectively. Both leptons must also have $\abs{\eta} < 2.4$. The \ensuremath{\gamma+}jets\xspace sample is collected through a single-photon trigger, and consists of events containing photons with $\pt>180$\GeV and $\abs{\eta} < 2.5$. The transverse momentum of the dilepton or photon system is added vectorially to \ptvecmiss in each event of the corresponding data samples to emulate the kinematics of the \ensuremath{\cPZ\to\cPgn\cPagn}\xspace~process. The modified \MET, denoted by \ensuremath{E^{\text{miss},\ell\ell}_{\mathrm{T}}}\xspace and \ensuremath{E^{\text{miss},\gamma}_{\mathrm{T}}}\xspace for the \ensuremath{\cPZ\to\ell\ell}~and \ensuremath{\gamma+}jets\xspace processes, respectively, is used to calculate related kinematic variables.
The prediction for the \ensuremath{\cPZ\to\cPgn\cPagn}\xspace~background is given by:
\begin{equation}
N^{\text{pred}}_{\ensuremath{\cPZ\to\cPgn\cPagn}\xspace} = N^{\text{sim}}_{\ensuremath{\cPZ\to\cPgn\cPagn}\xspace} R_{\cPZ} S_{\gamma},
\end{equation}
where $N^{\text{sim}}_{\ensuremath{\cPZ\to\cPgn\cPagn}\xspace}$ is the expected number of \ensuremath{\cPZ\to\cPgn\cPagn}\xspace~events obtained from simulation, $R_{\cPZ}$ is the flavour-dependent \ensuremath{\Z+}jets\xspace normalization factor measured with the \ensuremath{\cPZ\to\ell\ell}~~sample, and $S_{\gamma}$ is the correction factor for distributions in \MET and jet kinematic variables extracted from the \ensuremath{\gamma+}jets\xspace sample.
The underlying assumption of this hybrid estimation method is that the differences in the \MET (or \ensuremath{E^{\text{miss},\gamma}_{\mathrm{T}}}\xspace) distributions between data and simulation are similar for $\ensuremath{\cPZ\to\cPgn\cPagn}\xspace$ and photon events. We checked this assumption by comparing the ratios of data to simulation observed in the \ensuremath{E^{\text{miss},\ell\ell}_{\mathrm{T}}}\xspace and \ensuremath{E^{\text{miss},\gamma}_{\mathrm{T}}}\xspace distributions for \ensuremath{\cPZ\to\ell\ell}+jets and \ensuremath{\gamma+}jets\xspace samples, respectively, and found them to agree.
The factor $R_{\cPZ}$ is calculated by comparing the observed and expected \ensuremath{\cPZ\to\ell\ell}~yields for a relaxed version of the baseline selection. In particular, we remove the requirements on $\ensuremath{\Delta\phi_{1234}}\xspace$ after confirming that this does not bias the result, and relax the requirements on \ensuremath{E^{\text{miss},\ell\ell}_{\mathrm{T}}}\xspace from a threshold of 250\GeV to a threshold of 100\GeV. To increase the purity of the \ensuremath{\cPZ\to\ell\ell}~events, we require the dilepton invariant mass to lie within the \cPZ~boson mass window of $80<M_{\ell\ell}<100$\GeV. The normalization of the nonnegligible \ttbar~contamination is estimated in the region outside the \cPZ~boson mass window ($20<M_{\ell\ell}<80$ or $M_{\ell\ell}>100$\GeV) and taken into account. Small contributions from $\PQt\cPZ$ and \ensuremath{\ttbar\cPZ}\xspace~production, estimated from simulation, are included in the \ensuremath{\cPZ\to\ell\ell}~sample when measuring $R_{\cPZ}$. Contributions from $\PQt\ensuremath{\PW}\xspace$ and \ensuremath{\ttbar\PW}\xspace~are included in the simulation sample used to obtain the normalization factor for the \ttbar contamination. As discussed previously, we calculate $R_{\cPZ}$ separately for different $\ensuremath{N_{\PQb}}\xspace$ requirements. The values obtained are $0.94\pm0.13$ and $0.84\pm0.19$ for $\ensuremath{N_{\PQb}}\xspace = 1$ and ${\geq}2$, respectively. The uncertainty in $R_{\cPZ}$ originates from the limited event counts in data and simulation, and from the extrapolation in \MET.
The quantity $S_{\gamma}$ is the correction factor related to the modelling of the distributions in the kinematic variables of \ensuremath{\cPZ\to\cPgn\cPagn}\xspace~events. It is calculated via a comparison of the \ensuremath{E^{\text{miss},\gamma}_{\mathrm{T}}}\xspace distributions of \ensuremath{\gamma+}jets\xspace events in simulation and data. The simulation is normalized to the number of events in data after applying the baseline selection. To suppress potential contamination from signal and avoid overlap with the search sample, we only consider events with $\MET<200\GeV$. The $S_{\gamma}$ factor is estimated separately for each SR to account for any potential mismodelling of the observables $M_{\mathrm{T}}(\PQb_{1,2},\ensuremath{E^{\text{miss},\gamma}_{\mathrm{T}}}\xspace)$, $\ensuremath{N_{\mathrm{j}}}\xspace$, $\ensuremath{E^{\text{miss},\gamma}_{\mathrm{T}}}\xspace$, and $\ensuremath{N_{\PQt}}\xspace$ in simulation. Since no statistically significant dependence of \ensuremath{E^{\text{miss},\gamma}_{\mathrm{T}}}\xspace on $\ensuremath{N_{\PQb}}\xspace$ is observed, we improve the statistical power of the correction by combining the $\ensuremath{N_{\PQb}}\xspace=1$ and $\ensuremath{N_{\PQb}}\xspace \geq 2$ subsets of the \ensuremath{\gamma+}jets\xspace sample to extract the $S_{\gamma}$ corrections. The correction factors range between 0.3 and 2, with uncertainties of up to 100\% due to the limited number of events in the data sample.
The \ensuremath{\gamma+}jets\xspace control data have contributions from three main components: prompt photons produced directly or via fragmentation, and other objects misidentified as photons. The prompt photon purity measured in Ref.~\cite{CMS-PAS-SUS-15-003} shows good agreement between data and simulation. In addition, the impact of varying the fraction of misidentified photons, or those produced via fragmentation, by $50\%$ in simulated events results in a bias of less than $5\%$ in the \MET distribution from the predicted \ensuremath{\cPZ\to\cPgn\cPagn}\xspace~background. We therefore rely on simulation to estimate the relative contributions of the three different components.
The statistical uncertainty in the \ensuremath{\gamma+}jets\xspace control data and the uncertainty in $R_{\cPZ}$ are the main sources of uncertainty in the \ensuremath{\cPZ\to\cPgn\cPagn}\xspace~prediction. The statistical uncertainties in the simulated samples, ranging up to $50\%$ in both the SRs and in the \ensuremath{\gamma+}jets\xspace CRs, also makes sizeable contributions.
\subsubsection{Estimation of the QCD background}
\label{sec:stop0l_qcd}
The QCD background is estimated using a data CR selected with the same trigger as the SR and enriched in QCD events by imposing a threshold on the azimuthal separation between \ptvecmiss and the closest of the three leading jets, namely $\ensuremath{\Delta\phi_{123}}\xspace < 0.1$. After correcting for the contribution from other SM processes (\ie \ttbar and \ensuremath{\PW+}jets\xspace), estimated by applying the normalization factor obtained in the corresponding single-lepton control sample to simulation, we translate the observation in this CR to a prediction in the SR by means of transfer factors obtained from simulation. Each transfer factor is defined as the ratio of the expected QCD events satisfying $\ensuremath{\Delta\phi_{1234}}\xspace > 0.5$ to the expected QCD events with $\ensuremath{\Delta\phi_{123}}\xspace < 0.1$. The estimation is carried out in each search category. Since the distributions in key observables show little dependence on $\ensuremath{N_{\PQb}}\xspace$, the QCD CR is summed over $\ensuremath{N_{\PQb}}\xspace$ to improve the statistical precision of the estimation.
The main source of QCD events populating the SR is from severe mismeasurement of the \pt~of one or more jets in the event. Correct modelling of jet mismeasurement in simulation is therefore an important part of the QCD prediction. The level of mismeasurement of a simulated event is parameterized by the jet response of the most mismeasured jet, which is the jet with the greatest absolute difference between the reconstructed and generated $\pt$. The jet response, $\ensuremath{r_{\text{jet}}}\xspace$, is defined as the ratio of the reconstructed $\pt$ of a jet to its generated \pt, computed without including the loss of visible momentum due to neutrinos. We use the observable $\ensuremath{r^{\mathrm{pseudo}}_{\text{jet}}}\xspace$, defined as the ratio of the $\pt$ of a jet to the magnitude of the vector sum of its transverse momentum and $\ptvecmiss$, as an approximate measure of the true jet response in data, and extract mismeasurement correction factors for the simulation by comparing $\ensuremath{r^{\mathrm{pseudo}}_{\text{jet}}}\xspace$ of the jet closest in $\phi$ to $\ptvecmiss$ between data and simulation. The correction factors extracted from simulation are parameterized by $\ensuremath{r_{\text{jet}}}\xspace$ and the flavour of the most mismeasured jet. The correction factors range between 0.44 and 1.13, and are applied in the simulation on an event-by-event basis.
The largest sources of uncertainty in the QCD prediction originate from the limited event counts in data and simulated samples surviving the selection, giving rise to uncertainties of up to 100\% in the estimated QCD background contribution in some SRs. The uncertainty due to jet response corrections is up to 15\%, while the uncertainty due to contributions from non-QCD processes in the data CR ranges from 7\% to 35\%.
\subsubsection{Estimation of the \texorpdfstring{$\ensuremath{\ttbar\cPZ}\xspace$}{ttbar Z} background}
\label{sec:stop0l_ttz}
Contributions from the $\ensuremath{\ttbar\cPZ}\xspace$ process are generally small since this is a relatively rare process. However, it has a final state very similar to signal when the \cPZ~boson decays to neutrinos and both top quarks decay only into jets, which can constitute up to 25\% of the total SM background in some SRs with large $\MET$ and $\ensuremath{N_{\PQt}}\xspace \geq 1$. The $\ensuremath{\ttbar\cPZ}\xspace$ prediction is obtained from simulation. We assign a 30$\%$ uncertainty to the \ensuremath{\ttbar\cPZ}\xspace~cross section, based on the $8\TeV$ CMS measurement~\cite{Khachatryan:2015sha}. Additional theoretical and experimental uncertainties in the prediction are evaluated as will be discussed in Section~\ref{sec:systematics}, and range up to 25\% and 20\%, respectively, depending on the SR. We also take into consideration the statistical uncertainty in the simulation, which ranges from 5\% to 100\% for regions with small $\ensuremath{\ttbar\cPZ}\xspace$ contributions.
\subsection{Results}
\label{sec:stop0l_results}
Figure~\ref{fig:sryields} shows the yields in each of the SR bins, as well as the predicted SM backgrounds based on the background estimation methods discussed in Section~\ref{sec:stop0l_bkgest}. The results are also summarized in Table~\ref{tab:all-bin-yields}. Expected yields are also shown for two benchmark models for the pure $\ensuremath{\PSQt_{1}}\xspace \to \PQt^{(*)} \PSGczDo$ decay and one for the mixed ($\ensuremath{\PSQt_{1}}\xspace\to \PQt \PSGczDo$ or $\ensuremath{\PSQt_{1}}\xspace\to \PQb \PSGcpmDo$) decay. No statistically significant deviation from the SM prediction is observed in the data.
\begin{figure*}[hp]
\centering
\includegraphics[width=0.49\textwidth]{Figure_003-a.pdf}
\includegraphics[width=0.49\textwidth]{Figure_003-b.pdf}
\includegraphics[width=0.49\textwidth]{Figure_003-c.pdf}
\includegraphics[width=0.49\textwidth]{Figure_003-d.pdf}
\includegraphics[width=0.49\textwidth]{Figure_003-e.pdf}
\topcaption{Observed and estimated SM background and signal yields in the SRs of the top squark search in the all-jet final state: $\ensuremath{M_{\mathrm{T}}(\PQb_{1,2},\ptvecmiss)}\xspace<175$\GeV, $5 \leq \ensuremath{N_{\mathrm{j}}}\xspace \leq 6$ (upper left), $\ensuremath{M_{\mathrm{T}}(\PQb_{1,2},\ptvecmiss)}\xspace<175$\GeV, $\ensuremath{N_{\mathrm{j}}}\xspace \geq 7$ (upper right), $\ensuremath{M_{\mathrm{T}}(\PQb_{1,2},\ptvecmiss)}\xspace\geq175$\GeV, $\ensuremath{N_{\PQt}}\xspace = 0, 5 \leq \ensuremath{N_{\mathrm{j}}}\xspace \leq 6$ (middle left), $\ensuremath{M_{\mathrm{T}}(\PQb_{1,2},\ptvecmiss)}\xspace\geq175$\GeV, $\ensuremath{N_{\PQt}}\xspace = 0, \ensuremath{N_{\mathrm{j}}}\xspace \geq 7$ (middle right), $\ensuremath{M_{\mathrm{T}}(\PQb_{1,2},\ptvecmiss)}\xspace\geq175$\GeV, $\ensuremath{N_{\PQt}}\xspace \geq 1, \ensuremath{N_{\mathrm{j}}}\xspace \geq 5$ (bottom row). The first 5 bins in each plot correspond to $\MET$ ranges of 250--300, 300--400, 400--500, 500--600, $>600$\GeV for $\ensuremath{N_{\PQb}}\xspace = 1$, and the second 5 bins correspond to the same \MET binning for $\ensuremath{N_{\PQb}}\xspace \geq 2$. The SM background predictions shown do not include the effects of the maximum likelihood fit to the data. The ratio of the data to the SM prediction extracted from CRs is shown in the lower panel of each plot. The shaded black band represents the statistical and systematic uncertainty in the background prediction.
}
\label{fig:sryields}
\end{figure*}
\begin{table*}[htbp]
\centering
\topcaption{\label{tab:all-bin-yields} Observed and predicted background yields in the different search regions for the top squark search in the all-jet final state. The total uncertainty is given for each background prediction. }
\cmsTable{
\begin{tabular}{ c cccc c c }
\hline
\MET [\GeVns{}] & Lost-lepton & \ensuremath{\cPZ\to\cPgn\cPagn}\xspace & QCD & \ensuremath{\ttbar\cPZ}\xspace & Total SM & Data \\
\hline
\multicolumn{7}{c}{$\ensuremath{M_{\mathrm{T}}(\PQb_{1,2},\ptvecmiss)}\xspace < 175$\GeV, $5\leq\ensuremath{N_{\mathrm{j}}}\xspace\leq6$, $\ensuremath{N_{\PQb}}\xspace = 1$} \\
\hline
250-300 & 60 $\pm$ 6 & 14 $\pm$ 3 & 4.1 $\pm$ 1.7 & 0.59 $\pm$ 0.21 & 79 $\pm$ 7 & 68 \\
300-400 & 23 $\pm$ 3 & 7.4 $\pm$ 1.9 & 1.5 $\pm$ 0.8 & 0.39 $\pm$ 0.14 & 32 $\pm$ 4 & 23 \\
400-500 & 2.5 $\pm$ 1.0 & 1.6 $\pm$ 0.8 & 0.21 $\pm$ 0.15 & 0.08 $\pm$ 0.04 & 4.3 $\pm$ 1.3 & 5 \\
500-600 & 1.9 $\pm$ 1.0 & 0.25 $^{+0.27}_{-0.25}$ & 0.14 $^{+0.15}_{-0.14}$ & 0.04 $\pm$ 0.02 & 2.3 $\pm$ 1.0 & 1 \\
$>$600 & 0.28 $^{+0.31}_{-0.28}$ & 0.13 $^{+0.15}_{-0.13}$ & 0.01 $\pm$ 0.01 & $<$0.01 & 0.42 $\pm$ 0.34 & 0 \\
\hline
\multicolumn{7}{c}{$\ensuremath{M_{\mathrm{T}}(\PQb_{1,2},\ptvecmiss)}\xspace < 175$\GeV, $5\leq\ensuremath{N_{\mathrm{j}}}\xspace\leq6$, $\ensuremath{N_{\PQb}}\xspace \geq 2$} \\
\hline
250-300 & 61 $\pm$ 6 & 4.7 $\pm$ 1.4 & 1.1 $\pm$ 0.5 & 0.63 $\pm$ 0.22 & 68 $\pm$ 6 & 61 \\
300-400 & 24 $\pm$ 3 & 3.0 $\pm$ 1.0 & 0.44 $\pm$ 0.23 & 0.50 $\pm$ 0.18 & 28 $\pm$ 4 & 29 \\
400-500 & 2.8 $\pm$ 1.2 & 0.61 $\pm$ 0.33 & 0.16 $\pm$ 0.13 & 0.12 $\pm$ 0.06 & 3.7 $\pm$ 1.2 & 7 \\
500-600 & 1.7 $\pm$ 0.9 & 0.13 $^{+0.15}_{-0.13}$ & 0.05 $^{+0.06}_{-0.05}$ & $<$0.01 & 1.9 $\pm$ 0.9 & 2 \\
$>$600 & 0.38 $^{+0.41}_{-0.38}$ & 0.04 $^{+0.06}_{-0.04}$ & $<$0.01 & 0.01 $\pm$ 0.01 & 0.43 $\pm$ 0.41 & 0 \\
\hline
\multicolumn{7}{c}{$\ensuremath{M_{\mathrm{T}}(\PQb_{1,2},\ptvecmiss)}\xspace < 175$\GeV, $\ensuremath{N_{\mathrm{j}}}\xspace\geq7$, $\ensuremath{N_{\PQb}}\xspace = 1$} \\
\hline
250-300 & 30 $\pm$ 4 & 3.0 $\pm$ 1.0 & 1.8 $\pm$ 0.6 & 0.79 $\pm$ 0.28 & 36 $\pm$ 4 & 34 \\
300-400 & 17 $\pm$ 3 & 4.6 $\pm$ 1.6 & 1.1 $\pm$ 0.5 & 0.58 $\pm$ 0.21 & 24 $\pm$ 3 & 26 \\
400-500 & 2.9 $\pm$ 0.9 & 0.82 $\pm$ 0.64 & 0.40 $\pm$ 0.27 & 0.12 $\pm$ 0.07 & 4.2 $\pm$ 1.1 & 4 \\
500-600 & 1.3 $\pm$ 0.7 & 0.09 $^{+0.11}_{-0.09}$ & 0.05 $\pm$ 0.05 & 0.09 $\pm$ 0.05 & 1.5 $\pm$ 0.7 & 3 \\
$>$600 & $<$0.56 & 0.39 $^{+0.46}_{-0.39}$ & 0.02 $\pm$ 0.02 & 0.05 $\pm$ 0.03 & 0.46 $^{+0.72}_{-0.46}$ & 2 \\
\hline
\multicolumn{7}{c}{$\ensuremath{M_{\mathrm{T}}(\PQb_{1,2},\ptvecmiss)}\xspace < 175$\GeV, $\ensuremath{N_{\mathrm{j}}}\xspace\geq7$, $\ensuremath{N_{\PQb}}\xspace \geq 2$} \\
\hline
250-300 & 36 $\pm$ 4 & 0.96 $\pm$ 0.38 & 1.1 $\pm$ 0.5 & 0.83 $\pm$ 0.30 & 38 $\pm$ 4 & 33 \\
300-400 & 20 $\pm$ 3 & 2.1 $\pm$ 0.9 & 0.34 $\pm$ 0.19 & 0.58 $\pm$ 0.22 & 23 $\pm$ 3 & 18 \\
400-500 & 4.5 $\pm$ 1.4 & 0.15 $\pm$ 0.13 & 0.07 $\pm$ 0.05 & 0.15 $\pm$ 0.07 & 4.9 $\pm$ 1.4 & 1 \\
500-600 & 1.5 $\pm$ 0.8 & 0.09 $^{+0.11}_{-0.09}$ & 0.01 $\pm$ 0.01 & 0.03 $\pm$ 0.03 & 1.6 $\pm$ 0.8 & 0 \\
$>$600 & $<$0.59 & 0.10 $^{+0.12}_{-0.10}$ & 0.01 $\pm$ 0.01 & 0.03 $\pm$ 0.02 & 0.13 $^{+0.60}_{-0.13}$ & 0 \\
\hline
\multicolumn{7}{c}{$\ensuremath{M_{\mathrm{T}}(\PQb_{1,2},\ptvecmiss)}\xspace \geq 175$\GeV, $5\leq\ensuremath{N_{\mathrm{j}}}\xspace\leq6$, $N_\mathrm{t} = 0$, $\ensuremath{N_{\PQb}}\xspace = 1$} \\
\hline
250-300 & 20 $\pm$ 3 & 12 $\pm$ 3 & 0.66 $\pm$ 0.37 & 0.50 $\pm$ 0.19 & 33 $\pm$ 5 & 30 \\
300-400 & 9.6 $\pm$ 2.3 & 17 $\pm$ 4 & 0.63 $\pm$ 0.32 & 0.82 $\pm$ 0.27 & 28 $\pm$ 4 & 27 \\
400-500 & 4.4 $\pm$ 1.9 & 8.6 $\pm$ 2.6 & 0.52 $\pm$ 0.35 & 0.28 $\pm$ 0.12 & 14 $\pm$ 3 & 13 \\
500-600 & 0.82 $\pm$ 0.63 & 3.8 $\pm$ 1.8 & 0.40 $\pm$ 0.35 & 0.09 $\pm$ 0.06 & 5.1 $\pm$ 1.9 & 3 \\
$>$600 & $<$0.4 & 1.2 $\pm$ 0.7 & 0.05 $\pm$ 0.05 & 0.08 $\pm$ 0.04 & 1.3 $\pm$ 0.8 & 1 \\
\hline
\multicolumn{7}{c}{$\ensuremath{M_{\mathrm{T}}(\PQb_{1,2},\ptvecmiss)}\xspace \geq 175$\GeV, $5\leq\ensuremath{N_{\mathrm{j}}}\xspace\leq6$, $N_\mathrm{t} = 0$, $\ensuremath{N_{\PQb}}\xspace \geq 2$} \\
\hline
250-300 & 11 $\pm$ 2 & 4.5 $\pm$ 1.4 & 0.45 $\pm$ 0.27 & 0.70 $\pm$ 0.24 & 17 $\pm$ 3 & 25 \\
300-400 & 4.9 $\pm$ 1.2 & 6.3 $\pm$ 1.8 & 0.37 $\pm$ 0.23 & 0.60 $\pm$ 0.22 & 12 $\pm$ 2 & 18 \\
400-500 & 1.6 $\pm$ 0.7 & 3.1 $\pm$ 1.1 & 0.18 $\pm$ 0.17 & 0.31 $\pm$ 0.12 & 5.3 $\pm$ 1.4 & 6 \\
500-600 & 0.29 $\pm$ 0.24 & 1.4 $\pm$ 0.8 & 0.01 $\pm$ 0.01 & 0.13 $\pm$ 0.06 & 1.9 $\pm$ 0.8 & 0 \\
$>$600 & $<$0.49 & 0.32 $\pm$ 0.20 & 0.01 $^{+0.02}_{-0.01}$ & 0.02 $\pm$ 0.02 & 0.36 $^{+0.53}_{-0.36}$ & 1 \\
\hline
\multicolumn{7}{c}{$\ensuremath{M_{\mathrm{T}}(\PQb_{1,2},\ptvecmiss)}\xspace \geq 175$\GeV, $\ensuremath{N_{\mathrm{j}}}\xspace\geq7$ $N_\mathrm{t} = 0$, $\ensuremath{N_{\PQb}}\xspace = 1$} \\
\hline
250-300 & 8.8 $\pm$ 1.9 & 2.5 $\pm$ 1.0 & 1.2 $\pm$ 0.6 & 0.29 $\pm$ 0.18 & 13 $\pm$ 2 & 10 \\
300-400 & 7.1 $\pm$ 1.8 & 3.9 $\pm$ 1.5 & 0.76 $\pm$ 0.46 & 0.42 $\pm$ 0.18 & 12 $\pm$ 2 & 20 \\
400-500 & 2.0 $\pm$ 0.8 & 1.3 $\pm$ 0.7 & 0.08 $\pm$ 0.07 & 0.16 $\pm$ 0.09 & 3.6 $\pm$ 1.1 & 5 \\
500-600 & 0.38 $^{+0.40}_{-0.38}$ & 0.40 $^{+0.43}_{-0.40}$ & 0.02 $\pm$ 0.02 & $<$0.01 & 0.80 $\pm$ 0.59 & 1 \\
$>$600 & 0.28 $^{+0.33}_{-0.28}$ & 2.2 $\pm$ 1.2 & 0.02 $^{+0.03}_{-0.02}$ & $<$0.01 & 2.5 $\pm$ 1.2 & 1 \\
\hline
\multicolumn{7}{c}{$\ensuremath{M_{\mathrm{T}}(\PQb_{1,2},\ptvecmiss)}\xspace \geq 175$\GeV, $\ensuremath{N_{\mathrm{j}}}\xspace\geq7$ $N_\mathrm{t} = 0$, $\ensuremath{N_{\PQb}}\xspace \geq 2$} \\
\hline
250-300 & 5.9 $\pm$ 1.3 & 1.2 $\pm$ 0.5 & 0.46 $\pm$ 0.24 & 0.57 $\pm$ 0.21 & 8.1 $\pm$ 1.5 & 13 \\
300-400 & 3.8 $\pm$ 1.0 & 1.6 $\pm$ 0.7 & 0.08 $\pm$ 0.06 & 0.70 $\pm$ 0.26 & 6.2 $\pm$ 1.2 & 6 \\
400-500 & 1.5 $\pm$ 0.6 & 0.48 $\pm$ 0.27 & 0.01 $\pm$ 0.01 & 0.28 $\pm$ 0.12 & 2.2 $\pm$ 0.7 & 2 \\
500-600 & 0.22 $^{+0.25}_{-0.22}$ & 0.11 $^{+0.12}_{-0.11}$ & 0.01 $\pm$ 0.01 & 0.18 $\pm$ 0.08 & 0.51 $\pm$ 0.29 & 0 \\
$>$600 & 0.06 $^{+0.07}_{-0.06}$ & 0.73 $\pm$ 0.44 & 0.02 $^{+0.03}_{-0.02}$ & 0.02 $^{+0.03}_{-0.02}$ & 0.84 $\pm$ 0.45 & 1 \\
\hline
\multicolumn{7}{c}{$\ensuremath{M_{\mathrm{T}}(\PQb_{1,2},\ptvecmiss)}\xspace \geq 175$\GeV, $\ensuremath{N_{\mathrm{j}}}\xspace\geq5$, $N_\mathrm{t} \geq 1$, $\ensuremath{N_{\PQb}}\xspace = 1$} \\
\hline
250-300 & 1.2 $\pm$ 0.5 & 0.30 $\pm$ 0.25 & 0.26 $\pm$ 0.21 & 0.02 $^{+0.03}_{-0.02}$ & 1.8 $\pm$ 0.6 & 0 \\
300-400 & 1.5 $\pm$ 0.7 & 0.34 $\pm$ 0.26 & 0.02 $\pm$ 0.01 & 0.14 $\pm$ 0.06 & 2.0 $\pm$ 0.8 & 0 \\
400-500 & 0.73 $\pm$ 0.40 & 0.20 $^{+0.22}_{-0.20}$ & 0.13 $^{+0.17}_{-0.13}$ & 0.04 $^{+0.05}_{-0.04}$ & 1.1 $\pm$ 0.5 & 1 \\
500-600 & 0.25 $\pm$ 0.22 & 0.54 $\pm$ 0.34 & 0.12 $^{+0.16}_{-0.12}$ & 0.10 $\pm$ 0.06 & 1.0 $\pm$ 0.4 & 4 \\
$>$600 & 0.15 $^{+0.33}_{-0.15}$ & 0.59 $\pm$ 0.49 & 0.07 $\pm$ 0.07 & 0.11 $\pm$ 0.05 & 0.92 $\pm$ 0.60 & 1 \\
\hline
\multicolumn{7}{c}{$\ensuremath{M_{\mathrm{T}}(\PQb_{1,2},\ptvecmiss)}\xspace \geq 175$\GeV, $\ensuremath{N_{\mathrm{j}}}\xspace\geq5$, $N_\mathrm{t} \geq 1$, $\ensuremath{N_{\PQb}}\xspace \geq 2$} \\
\hline
250-300 & 0.66 $\pm$ 0.26 & 0.11 $\pm$ 0.09 & 0.06 $\pm$ 0.05 & 0.09 $\pm$ 0.05 & 0.92 $\pm$ 0.29 & 3 \\
300-400 & 0.92 $\pm$ 0.39 & 0.12 $\pm$ 0.10 & 0.03 $\pm$ 0.03 & 0.14 $\pm$ 0.08 & 1.2 $\pm$ 0.4 & 3 \\
400-500 & 0.31 $\pm$ 0.17 & 0.03 $^{+0.04}_{-0.03}$ & $<$0.01 & 0.09 $\pm$ 0.06 & 0.43 $\pm$ 0.18 & 0 \\
500-600 & 0.30 $\pm$ 0.30 & 0.30 $\pm$ 0.21 & $<$0.01 & 0.09 $\pm$ 0.04 & 0.70 $\pm$ 0.37 & 0 \\
$>$600 & 0.13 $^{+0.29}_{-0.13}$ & 0.37 $\pm$ 0.32 & $<$0.01 & 0.12 $\pm$ 0.05 & 0.62 $\pm$ 0.43 & 1 \\
\hline
\end{tabular}
}
\end{table*}
\section{Search for top squarks in the single-lepton final state}
\label{sec:1lstop}
We also perform a search for top squarks in events with exactly one isolated electron or muon and considerable \MET. The main SM backgrounds originating from \ttbar and \ensuremath{\PW+}jets\xspace~processes are suppressed using dedicated kinematic variables. The dominant remaining backgrounds arise from lost-lepton processes and the surviving \ensuremath{\PW+}jets\xspace~background, both of which are estimated from control samples in data.
\subsection{Analysis strategy}
\label{sec1l:evtsel}
The search sample is selected using triggers that require either large \MET or the presence of an isolated electron or muon. The combined trigger efficiency for a selection of \MET$>250$\GeV and at least one lepton, as measured in a data sample with large $H_{\rm T}$, is
found to be $99\%$ with an asymmetric uncertainty of $^{+1}_{-3}\%$.
Selected events are required to have at least two jets with $\pt>30$\GeV, at least one of which must be \PQb-tagged using the medium working point. We require exactly one well-identified and isolated electron or muon with $\pt > 20$\GeV, $\abs{\eta} < 1.442$ or $< 2.4$, respectively, and $I_\text{rel} < 0.1$. Electrons in the forward region of the detector are not considered in this search due to a significant rate for a jet to be misidentified as an electron. To reduce the dilepton background originating from \ttbar and $\mathrm{tW}$ production, events are rejected if they contain a second electron or muon with $\pt > 5$\GeV and $I_\text{rel}<$ 0.2. A significant fraction of the remaining SM background originates from events with $\tauh$ decays. This contribution is reduced by rejecting events that have an isolated $\tauh$ candidate reconstructed using the HPS algorithm with $\pt > 20$\GeV and $\abs{\eta} < 2.4$. A further veto is placed on events containing isolated charged-hadron PF candidates with $\pt>10$\GeV and $\abs{\eta} < 2.5$. Candidates are categorized as being isolated if their isolation sum, \ie the scalar sum of the \pt of charged PF candidates within a fixed cone of $R = 0.3$ around the candidate, is less than 6\GeV and smaller than $10\%$ of the candidate \pt.
Single-lepton backgrounds originating from semileptonic \ttbar, \ensuremath{\PW+}jets\xspace, and single top quark processes are suppressed through the \ensuremath{M_{\mathrm{T}}}\xspace of the lepton-neutrino system.
Background processes containing a single lepton from \ensuremath{\PW}\xspace~boson decay have a kinematic endpoint for \ensuremath{M_{\mathrm{T}}}\xspace at the \ensuremath{\PW}\xspace~boson mass, modulo detector resolution and off-shell \ensuremath{\PW}\xspace~boson mass effects.
In this analysis we require $\ensuremath{M_{\mathrm{T}}}\xspace > 150$\GeV, which significantly reduces single-lepton backgrounds.
To further reduce the \ttbar background, we require the absolute value of the azimuthal angle between \ptvecmiss and the closest of the two highest-\pt jets, $\Delta\phi_{12}$, to be larger than 0.8, since the events that satisfy the \MET and \ensuremath{M_{\mathrm{T}}}\xspace requirements tend to have higher-\pt top quarks, and therefore smaller values of $\Delta\phi_{12}$ than signal events.
The remaining background after the preselection is dominated by dilepton events from \ttbar and $\PQt\ensuremath{\PW}\xspace$ production, where one of the leptons is not reconstructed or identified, and the
presence of the additional neutrino from the second leptonically decaying \ensuremath{\PW}\xspace~boson makes it possible to satisfy the \ensuremath{M_{\mathrm{T}}}\xspace requirement.
\label{sec1l:srdef}
Kinematic properties of signal events such as \MET, \ensuremath{M_{\mathrm{T}}}\xspace, and jet multiplicity depend on the decay modes of top squarks, as well as on the
mass splittings ($\Delta m$) between the top squark, neutralino, and chargino (if present). As a basis for the search strategy in the topologies shown in Figs.~\ref{fig:diagram}(a) and~\ref{fig:diagram}(b), we require the presence of at least four jets.
Events are then categorized based on the value of the \ensuremath{M_{\mathrm{T2}}^{\PW}}\xspace variable~\cite{Bai:2012gs}, which is calculated for each event under the assumption that it originates from the dilepton \ttbar process with a lost lepton:
\begin{multline}\label{eq:mt2w}
\ensuremath{M_{\mathrm{T2}}^{\PW}}\xspace \equiv \mathrm{Min}\{m_\mathrm{y},\text{ consistent with: } \\
[p_\mathrm{1}^{2}=0,~(p_\mathrm{1}+p_{\ell})^2=p_\mathrm{2}^{2} = M_\mathrm{W}^{2},~\ptvec^{1} + \ptvec^{2}=\VEtmiss, \\
(p_\mathrm{1}+p_{\ell}+p_\mathrm{b_{1}})^{2}=(p_\mathrm{2}+p_\mathrm{b_{2}})^{2}=m_\mathrm{y}^{2} ]\},
\end{multline}
where $m_\mathrm{y}$ is the fitted parent particle mass, and $p_\mathrm{1},~p_{\ell},$ $p_\mathrm{2}$, $p_\mathrm{b_{1}},$ and $p_\mathrm{b_{2}}$ are the four momenta of the neutrino corresponding to the visible \ensuremath{\PW}\xspace~boson decay, the lepton from the same decay, the \ensuremath{\PW}\xspace~boson whose decay gives rise to the undetected lepton, and the two \PQb~jet candidates, respectively. To select the \PQb~jet candidates, we examine all possible pairings with the three jets that have the highest CSV discriminator values. The pairing that gives the lowest value of \ensuremath{M_{\mathrm{T2}}^{\PW}}\xspace defines the final estimate. The reconstruction of an event using the \ensuremath{M_{\mathrm{T2}}^{\PW}}\xspace variable helps discriminate signal from the dominant dilepton \ttbar background.
For large mass differences between the top squark and the neutralino, the $\ensuremath{M_{\mathrm{T2}}^{\PW}}\xspace>200$\GeV requirement significantly reduces the background while maintaining reasonable
signal efficiency. In contrast, for small-$\Delta m$ models, such a requirement results in a significant loss in signal efficiency.
To preserve sensitivity to both high- and low-$\Delta m$ scenarios, we subdivide the search sample into two event categories with $\ensuremath{M_{\mathrm{T2}}^{\PW}}\xspace>200$\GeV and $\leq200$\GeV.
The \ensuremath{M_{\mathrm{T2}}^{\PW}}\xspace distribution for events with at least four jets is shown in Fig.~\ref{fig:mt2w_tmod}~(\cmsLeft).
In signals with a large difference in mass between the top squark and the neutralino, a significant fraction of events can contain two quarks that merge into a single
jet as a result of the large boost of the top quark or \ensuremath{\PW}\xspace~boson that decay into jets. These events would fail the four-jet requirement. To recover acceptance for such topologies,
we define an additional SR in events with three jets. Since this region targets large $\Delta m$ signal scenarios, only events with
$\ensuremath{M_{\mathrm{T2}}^{\PW}}\xspace>200\GeV$ are considered.
To increase the sensitivity of this analysis to a mixed decay scenario (Fig.~\ref{fig:diagram}c) when the chargino and neutralino are nearly degenerate in mass,
SRs with exactly two jets are added. In events with low jet multiplicity the modified topness
variable ($t_\text{mod}$)~\cite{Graesser:2012qy} provides improved dilepton \ttbar\ rejection:
\ifthenelse{\boolean{cms@external}}{
\begin{equation} \label{eq:modtopness}
\begin{aligned}
t_\text{mod} = \ln(\min S),\quad\text{with}\\
S(\vec{p}_{\PW}, p_{z},\nu) =& \frac{(m_{\PW}^2-(p_\nu+p_{\ell})^2)^2}{a_{\PW}^4} \\
&+
\frac{(m_{\PQt}^2 - (p_{\PQb}+p_{\PW})^2)^2}{a_{\PQt}^4}.
\end{aligned}
\end{equation}
}{
\begin{equation} \label{eq:modtopness}
t_\text{mod} = \ln(\min S),
\text{ with }
S(\vec{p}_{\PW}, p_{z},\nu) = \frac{(m_{\PW}^2-(p_\nu+p_{\ell})^2)^2}{a_{\PW}^4} +
\frac{(m_{\PQt}^2 - (p_{\PQb}+p_{\PW})^2)^2}{a_{\PQt}^4}.
\end{equation}
}
This equation uses the mass constraints for the particles and also the assumption that $\ptvecmiss=\vec{p}_\mathrm{T,W}+\vec{p}_{\mathrm{T},\nu}$. The first term constrains the \ensuremath{\PW}\xspace~boson whose lepton decay product is the detected lepton, while the second term constrains the top quark for which the lepton from the \ensuremath{\PW}\xspace~boson decay is lost in the reconstruction.
Once again, we consider all possible pairings of \PQb~jet candidates with up to three jets with highest CSV discriminator values.
The calculation of modified topness uses the resolution parameters $a_\mathrm{W} = 5$\GeV and $a_\mathrm{t} = 15$\GeV, which determine the relative weighting of the mass shell conditions.
We select events with $t_\text{mod}>6.4$. The definition of topness used in this analysis is modified from the one originally proposed
in Ref.~\cite{Graesser:2012qy}: namely, the terms corresponding to the detected leptonic top quark decay and the centre-of-mass energy are dropped since in events with low jet multiplicity the second \PQb~jet is often not identified.
In these cases, the discriminating power of the topness variable is reduced when a light-flavour jet is used instead in the calculation.
The modified topness is more robust against such effects and provides better signal sensitivity in these SRs than the $\ensuremath{M_{\mathrm{T2}}^{\PW}}\xspace$ variable.
The distribution of modified topness for events with at least two jets is shown in Fig.~\ref{fig:mt2w_tmod}~(\cmsRight).
\begin{figure}[htb]
\centering
\includegraphics[width=0.48\textwidth]{Figure_004-a.pdf}
\includegraphics[width=0.48\textwidth]{Figure_004-b.pdf}
\caption{\label{fig:mt2w_tmod}
{The \ensuremath{M_{\mathrm{T2}}^{\PW}}\xspace (\cmsLeft) and $t_\text{mod}$ (\cmsRight) distributions for signal and backgrounds after the preselection are shown. The \ensuremath{M_{\mathrm{T2}}^{\PW}}\xspace variable is shown for events with four or more jets,
while $t_\text{mod}$ is shown for events with at least two jets. Signal models with different top squark and neutralino mass hypotheses are shown for comparison.}}
\end{figure}
Finally, events in each of the categories described above are further classified into different SRs
based on the value of \MET. This results in a total of nine exclusive SRs as summarized in Table~\ref{tab1l:SR}.
\begin{table*}
\centering
\topcaption{\label{tab1l:SR} Summary of the SR definitions for the single-lepton search.}
\begin{tabular}{lrrr|rrr}
\hline
Targeted models & $\ensuremath{N_{\mathrm{j}}}\xspace$ & $M_\mathrm{T2}^{\PW}$ [\GeVns{}] & $t_\text{mod}$ & \multicolumn{3}{c}{$E_\mathrm{T}^\text{miss}$ [\GeVns{}]} \\
\hline
Low-${\Delta}m$ & $\geq4$ & $\leq 200$ & & $250$--$325$ & $>325$ & \\
High-${\Delta}m$ & $\geq4$ & $> 200$ & & $250$--$350$ & $350$--$450$ & $>450$ \\
\hline
Boosted high-${\Delta}m$ & $=$3 & $>$200 & & 250--350 & $>$350 & \\
\hline
Degenerate $\PSGcpmDo$ and $\PSGczDo$ & $=$2 & & $>$6.4 & 250--350 & $>$350 & \\
\hline
\end{tabular}
\end{table*}
\subsection{Background estimation}
\label{Sec1l:BkgEst}
Three categories of backgrounds originating from SM processes remain after the preselection described in Section~\ref{sec1l:evtsel}.
The dominant contribution arises from backgrounds with a lost lepton, primarily from the dilepton \ttbar process.
A second class of background events originates from SM processes with a single leptonically decaying \ensuremath{\PW}\xspace~boson. Preselection
requirements of $\MET>250\GeV$ and $\ensuremath{M_{\mathrm{T}}}\xspace>150\GeV$ strongly suppress this background. The suppression is much stronger
for events with a \ensuremath{\PW}\xspace~boson originating from the decay of a top quark than for direct \ensuremath{\PW}\xspace~boson production, as the mass of the
top quark imposes a constraint on $M_{\ensuremath{\PW}\xspace}$. As a result, large values of \ensuremath{M_{\mathrm{T}}}\xspace in semileptonic \ttbar events are
dominated by \MET resolution effects, while for events in which the \ensuremath{\PW}\xspace~boson is produced directly (\ensuremath{\PW+}jets\xspace) they are mainly a function of the width of the \ensuremath{\PW}\xspace~boson.
The third class of background events includes rare SM processes such as \ensuremath{\PW}\xspace\Z~and $\ensuremath{\ttbar\cPZ}\xspace$ (where the
\Z~boson decays to neutrinos), with smaller contributions from $\ensuremath{\ttbar\PW}\xspace$, $\ttbar\gamma$, and processes with two or three
electroweak vector bosons. The QCD background is negligible in this
search due to requirements on the presence of a high-\pt isolated lepton, large \MET, and large \ensuremath{M_{\mathrm{T}}}\xspace.
\subsubsection{Lost-lepton background}\label{sec1l:dilepton}
The lost-lepton background is estimated from data in dilepton CRs, where we require the presence of a second lepton passing the rejection requirements but with $\pt>10\GeV$, an isolated track, or a $\tauh$ candidate. This is done again by extrapolating the data in the dilepton CRs to the SRs using transfer factors obtained from simulation. We use the same preselection requirements on $\MET$ and $\ensuremath{M_{\mathrm{T}}}\xspace$ as in the search regions.
We remove the subdivision in \MET and the separation of the three and at least four jet regions to increase the statistical power of the CRs, and arrive at three CRs: exactly two jets and $t_\text{mod}>6.4$, at least three jets and $\ensuremath{M_{\mathrm{T2}}^{\PW}}\xspace\leq200$\GeV, and at least three jets and $\ensuremath{M_{\mathrm{T2}}^{\PW}}\xspace>200$\GeV. These control regions have a purity in dilepton events of $>$ 97\%. Additional transfer factors are therefore needed to account for the extrapolation in jet multiplicity and \MET requirements; these are derived from simulation. The background estimate can be written as follows:
\ifthenelse{\boolean{cms@external}}{
\begin{equation}\label{eq:diLep_SR_est_full}
\begin{aligned}
N^\text{pred}_\mathrm{LL} &= N^\text{data}_{2\ell}~T_\text{LL}~T_{\MET,\ensuremath{N_{\mathrm{j}}}\xspace}, \\
T_\text{LL} &= \frac{N^\text{sim}_{1\ell}}{N^\text{sim}_{2\ell}}, \quad T_{\MET,\ensuremath{N_{\mathrm{j}}}\xspace} = \frac{N^\text{sim}_{1\ell}(\MET,\ensuremath{N_{\mathrm{j}}}\xspace)}{N^\text{sim}_{1\ell}},
\end{aligned}
\end{equation}
}{
\begin{equation}\label{eq:diLep_SR_est_full}
N^\text{pred}_\mathrm{LL} = N^\text{data}_{2\ell}~T_\text{LL}~T_{\MET,\ensuremath{N_{\mathrm{j}}}\xspace}, \quad
T_\text{LL} = \frac{N^\text{sim}_{1\ell}}{N^\text{sim}_{2\ell}}, \quad T_{\MET,\ensuremath{N_{\mathrm{j}}}\xspace} = \frac{N^\text{sim}_{1\ell}(\MET,\ensuremath{N_{\mathrm{j}}}\xspace)}{N^\text{sim}_{1\ell}},
\end{equation}
}
where $N^\text{data}_{2\ell}$ is the number of events observed in data in the dilepton CR. The largest systematic uncertainty in the background estimate is due to the statistical uncertainties of the event yields in data CRs and the estimates from simulated samples (10--30\%). The signal contamination in this CR is around 10\% for the bulk of the studied parameter space and is taken into account in the final interpretation.
The transfer factor $T_\text{LL}$ is obtained from simulation, and estimates the probability that a lepton is not identified in the detector, accounting for the kinematic acceptance and the efficiency of the lepton selection criteria.
The second transfer factor, $T_{\MET,\ensuremath{N_{\mathrm{j}}}\xspace}$, extrapolates the inclusive estimate to individual SR bins. This transfer factor, also obtained from simulation, is validated by checking the modelling of the jet multiplicity and of the \MET spectrum in dedicated data CRs, which will be described in the following paragraphs.
The dilepton \ttbar background contributes to the SRs with three or more jets only if jets from ISR or final-state radiation (FSR) are also present, or when a $\tau_h$ decay is misidentified as an additional jet. The modelling of jet multiplicity is checked in a high-purity dedicated dilepton data control sample with one electron and one muon, at least two \PQb-tagged jets, and $\MET > 250$\GeV.
The differences between data and simulation are used to estimate scale factors relative to the baseline selection of events with at least two jets. The scale factors are $1.10\pm0.06$ for three-jet events and $0.94\pm0.06$ for events with at least four jets. Within statistical uncertainties, these factors display no \MET dependence. The scale factors are applied to the dilepton \ttbar simulation when extrapolating the inclusive background prediction into the specified jet multiplicity bins. The statistical uncertainties in these scale factors are also propagated to the predictions in the SRs. The uncertainty in the modelling of the jet multiplicity ranges up to 3\%.
The extrapolation in \MET is carried out through simulation, and it must be verified that its resolution is accurately modelled.
Changing the resolution can lead to a different \MET spectrum. In this analysis we are interested in the effect of the \MET resolution in events containing intrinsic \MET because of the presence of neutrinos in the events.
This effect is estimated by comparing a \ensuremath{\gamma+}jets\xspace sample in data with simulation.
The events are selected using a single-photon trigger with $\pt> 165$\GeV and $\abs{\eta} < 2.4$. Photons are required to pass stringent identification criteria.
We use the photons to mimic the neutrinos in the event, with the photon momentum serving as an estimate of the sum of the neutrino momenta.
The photon \pt spectrum in data and in simulation is reweighted to match that of the neutrinos in the background-simulation sample.
For dilepton \ttbar events, this corresponds to the $\nu\nu$-$\pt$ spectrum. To model the \MET resolution, the transverse momentum of the photon system is added vectorially to the \ptvecmiss and the resulting \MET spectrum is compared between data and simulation. We use this modified \MET definition to calculate our discriminants. For this CR, we then apply selection criteria close to the SR criteria, except that selections related to the lepton are dropped, the presence of a well-identified photon is required, and the requirement of a \PQb-tagged jet is reversed so as to suppress effects related to semileptonic heavy-flavourdecays. Corrections for the observed differences, which can go up to 15\%, are applied to events in the simulated samples and the uncertainties propagated to the final background estimate, resulting in an uncertainty of 1--4\% in the lost-lepton background prediction.
\subsubsection{One-lepton background}\label{sec1l:onelepton}
In SRs with a high \ensuremath{M_{\mathrm{T2}}^{\PW}}\xspace or modified topness requirement, the \ensuremath{\PW+}jets\xspace background is estimated using a data control sample containing no \PQb-tagged jets. For SRs with a low-\ensuremath{M_{\mathrm{T2}}^{\PW}}\xspace requirement, this background constitutes less than 10\% of the total SM background. In these SRs we do not employ an estimate based on data, but instead use the \ensuremath{\PW+}jets\xspace~background estimate directly from simulation. The semileptonic \ttbar background is also estimated from simulation.
The CRs used to extract the \ensuremath{\PW+}jets\xspace background in the SRs with a high \ensuremath{M_{\mathrm{T2}}^{\PW}}\xspace or modified topness requirement are again not subdivided in \MET to have a sufficient number of events to carry out the prediction. We therefore use three CRs for this background estimate: exactly two jets with $t_{\text{mod}} >$ 6.4, exactly three jets with \ensuremath{M_{\mathrm{T2}}^{\PW}}\xspace $>$ 200\GeV, and at least four jets with $\ensuremath{M_{\mathrm{T2}}^{\PW}}\xspace > 200$\GeV.
We extrapolate the yields from the CRs to the SRs by applying transfer factors from simulation for the extrapolation in \MET and number of \PQb-tagged jets:
\begin{equation}
N^\text{pred}_{\ensuremath{\PW+}jets\xspace} = (N^\text{data}_{\ensuremath{N_{\PQb}}\xspace = 0} - N^\text{non-\ensuremath{\PW+}jets\xspace}_{\ensuremath{N_{\PQb}}\xspace = 0})~T_{\MET}~T_{\ensuremath{N_{\PQb}}\xspace},
\end{equation}
with $N^\text{data}_{\ensuremath{N_{\PQb}}\xspace = 0} - N^{\text{non-\ensuremath{\PW+}jets\xspace}}_{\ensuremath{N_{\PQb}}\xspace = 0}$ representing the event yield in the CR after subtracting the estimated contribution from other SM background processes. The non-1$\ell$ contribution in the CRs, $N^{\text{non-\ensuremath{\PW+}jets\xspace}}_{\ensuremath{N_{\PQb}}\xspace = 0}$, is estimated from simulation and amounts to roughly 25--35\%. A 50\% uncertainty is assigned to the subtraction. The largest source of uncertainty is again the limited size of the data and simulation samples. The statistical uncertainty of these samples results in an uncertainty of 20--40\% in the \ensuremath{\PW+}jets\xspace background estimate.
The transfer factor $T_{\MET}$ extrapolates the yields from the inclusive CR with $\MET>50$\GeV to the exclusive \MET regions. The main uncertainties in this extrapolation factor can be attributed to the modelling of the neutrino \pt spectrum, the \ensuremath{\PW}\xspace~boson width, and the \MET resolution. The neutrino \pt spectrum is checked in a data sample enriched in \ensuremath{\PW+}jets\xspace, with no \PQb-tagged jets and $60<\ensuremath{M_{\mathrm{T}}}\xspace<120$\GeV. No large mismodelling of \MET is observed. Therefore, we do not apply any corrections to the neutrino \pt spectrum but only propagate the statistical limitation of this study as the uncertainty (6--22\%) in the modelling of the neutrino \pt spectrum. The uncertainty in the \ensuremath{\PW}\xspace~boson width (3\%~\cite{PDG}) is estimated by scaling the four-vectors of the \ensuremath{\PW}\xspace~boson decay products appropriately. The \MET resolution effects on this background are studied using the same method as described in Section~\ref{sec1l:dilepton}, giving rise to a 1--3\% uncertainty.
The other transfer factor, $T_{\ensuremath{N_{\PQb}}\xspace}$, performs the extrapolation in the number of \PQb-tagged jets for each \MET bin. Scale factors are applied to the simulation to match the \PQb~tagging efficiency in data. The largest uncertainty in this transfer factor is the fraction of the heavy-flavour component in the \ensuremath{\PW+}jets\xspace sample; we assign a 50\% uncertainty to this component. We performed a dedicated cross-check in a CR with one or two jets and at least 50\GeV of \MET. Data and simulation were found to be in agreement in the \PQb~jet multiplicity within uncertainties.
After taking into consideration the additional sources of systematic uncertainty described in Section~\ref{sec:systematics}, the total uncertainty in the \ensuremath{\PW+}jets\xspace estimate varies from 50\% to 70\%.
The semileptonic \ttbar background is never larger than 10\% of the total background estimate. We rely on simulation to estimate it. The main source of uncertainty in this estimate is the modelling of the \MET resolution because poor resolution can enhance the contributions at large \ensuremath{M_{\mathrm{T}}}\xspace. The studies of \MET resolution presented in Section~\ref{sec1l:dilepton} indicate that it could be mismodelled by about 10\% in simulation. Changes in the simulated \MET resolution by a corresponding amount provide an uncertainty of 100\% in the semileptonic \ttbar estimate.
\subsubsection{Rare standard model backgrounds}
The ``rare'' background category includes $\ttbar$ production in association with a vector boson (\ensuremath{\PW}\xspace, \Z, or $\gamma$), diboson, and triboson events.
Within this category, \ensuremath{\PW}\xspace\Z~events dominate the SRs with two jets, and $\ensuremath{\ttbar\cPZ}\xspace$ events with the \Z~boson decaying into a pair of neutrinos ($\ensuremath{\cPZ\to\cPgn\cPagn}\xspace$) dominate regions of higher jet multiplicity.
The expected contributions from these backgrounds are small, and the simulation is expected to model the kinematics of these processes well in the regions of phase space relevant to the SRs. The rare backgrounds are therefore estimated using simulation. We assess the theoretical and experimental uncertainties affecting the estimates as described in Section~\ref{sec:systematics}, resulting in a total uncertainty of 15--26\%, depending on the SR.
\subsection{Results}
The background expectations and the corresponding yields for each SR are summarized in Table~\ref{tab1l:results} and in Fig.~\ref{fig1l:results}. Overall, the observed and predicted yields agree within two standard deviations in all SRs.
For signals of top squark pair production for different mass hypotheses, the maximum observed significance obtained by combining the results in different SRs is 1.2 standard deviations for a top squark mass of $\approx$400\GeV and a massless LSP hypothesis. We therefore find no evidence for top squark pair production.
\begin{table*}[htb]
\centering
\topcaption{\label{tab1l:results} Background estimates from data and simulation, and observed data yields for the single-lepton top squark analysis using 2.3\fbinv of data collected during 2015 pp collisions. The uncertainties are the quadratic sums of statistical and systematic uncertainties.}
\begin{tabular}{rr@{\,$\pm$\,}lr@{\,$\pm$\,}lr@{\,$\pm$\,}lr@{\,$\pm$\,}lr@{\,$\pm$\,}lr}
\hline
\multirow{2}{*}{\MET [\GeVns{}]} & \multicolumn{2}{c}{\multirow{2}{*}{Lost-lepton}} & \multicolumn{2}{c}{$1\ell$ (not} & \multicolumn{2}{c}{\multirow{2}{*}{$\ttbar\to\
1\ell$}} & \multicolumn{2}{c}{\multirow{2}{*}{$\cPZ\to\cPgn\cPagn$}} & \multicolumn{2}{c}{Total} & \multirow{2}{*}{Data} \\
& \multicolumn{2}{c}{~} & \multicolumn{2}{c}{from top)} & \multicolumn{2}{c}{~} & \multicolumn{2}{c}{~} & \multicolumn{2}{c}{background} & \\
\hline
& \multicolumn{11}{l}{Degenerate $\PSGcpmDo$ and $\PSGczDo$: $2$ jets, $t_\text{mod}>6.4$} \\
\hline
$250$--$350$ & 4.4&1.4 & 2.61&0.99 & 0.09&0.09 & 0.60&0.12 & 7.7&1.7 & 8 \\
$>$350 & 0.62&0.23 & 0.98&0.47 & \multicolumn{2}{c}{$<$0.03} & 0.36&0.13 & 1.96&0.54 & 5 \\
\hline
& \multicolumn{11}{l}{Boosted high $\Delta m$: $3$ jets, $\ensuremath{M_{\mathrm{T2}}^{\PW}}\xspace>200\GeV$} \\
\hline
$250$--$350$ & 2.83&0.73 & 0.92&0.52 & 0.12&0.12 & 0.64&0.13 & 4.51&0.91 & 8 \\
$>$350 & 0.74&0.21 & 0.88&0.50 & 0.05&0.05 & 0.41&0.09 & 2.08&0.55 & 2 \\
\hline
& \multicolumn{11}{l}{Low $\Delta m$: $\geq4$ jets, $\ensuremath{M_{\mathrm{T2}}^{\PW}}\xspace\leq200\GeV$} \\
\hline
$250$--$325$ & 23.0&3.2 & 0.61&0.61 & 0.88&0.88 & 0.74&0.17 & 25.2&3.4 & 14 \\
$>$325 & 7.9&1.5 & 0.45&0.45 & 0.40&0.40 & 0.30&0.11 & 9.0&1.6 & 8 \\
\hline
& \multicolumn{11}{l}{High $\Delta m$: $\geq4$ jets, $\ensuremath{M_{\mathrm{T2}}^{\PW}}\xspace>200\GeV$} \\
\hline
$250$--$350$ & 3.29&0.91 & 0.92&0.46 & 0.78&0.78 & 0.76&0.19 & 5.8&1.3 & 13 \\
$350$--$450$ & 0.94&0.27 & 0.54&0.34 & 0.18&0.18 & 0.46&0.14 & 2.13&0.48 & 4 \\
$>$450 & 0.57&0.21 & 0.55&0.36 & 0.07&0.07 & 0.52&0.17 & 1.71&0.45 & 0 \\
\hline
\end{tabular}
\end{table*}
\begin{figure}[htb]
\centering
\includegraphics[width=\cmsFigWidth]{Figure_005.pdf}
\caption{\label{fig1l:results} Background estimates from data and simulation, together with the observed yields in the SRs of the single-lepton analysis, described in Table~\ref{tab1l:SR}. The uncertainties, which are the quadratic sums of statistical and systematic uncertainties, are indicated by the cross-hatched areas. The SM background predictions shown do not include the effects of the maximum likelihood fit to the data. Three signal hypotheses are overlaid. The hypothesis $\ensuremath{\PSQt_{1}}\xspace\to\PQt\PSGczDo/\ensuremath{\PSQt_{1}}\xspace\to\PQb\PSGcpmDo$ has branching fractions $\mathcal{B}(\ensuremath{\PSQt_{1}}\xspace\to\PQt\PSGczDo)=\mathcal{B}(\ensuremath{\PSQt_{1}}\xspace\to\PQb\PSGcpmDo)=0.5$.}
\end{figure}
\section{Search for pair production of bottom squarks or of top squarks decaying to charm quarks}
\label{sec:sbottom}
This search is motivated by the production
of pairs of bottom or top squarks, in which each $\ensuremath{\PSQb_{1}}\xspace$ or $\ensuremath{\PSQt_{1}}\xspace$ decays, respectively, into a bottom or a charm quark
and a neutralino.
In the latter search, the difference between the $\ensuremath{\PSQt_{1}}\xspace$ and $\PSGczDo$ masses is assumed to be less than 80\GeV, and the only top squark decay mode considered is through a flavour changing neutral current to $\cPqc\PSGczDo$. Small
mass splittings $\Delta m = m_{\ensuremath{\PSQt_{1}}\xspace}-m_{\PSGczDo}$ or $\Delta m = m_{\ensuremath{\PSQb_{1}}\xspace}-m_{\PSGczDo}$ between the top or bottom squark and the
neutralino leave little visible energy in the detector, making signal events difficult to distinguish from
SM background. However, events with an energetic ISR jet recoiling against the \ptvecmiss originating from the neutralino can provide a distinct topology for signals with compressed mass spectra, \ie with small $\Delta m$. We thus perform a search for
events with an ISR jet and significant \MET.
\subsection{Analysis strategy}
\label{sec:sbottomsel}
Events in the search sample are recorded using the same trigger as that for the top squark search in the all-jet final state, requiring the presence of large \MET and at least two energetic jets within the tracker acceptance. After applying an offline selection requiring $\MET>250$\GeV and at least two
jets with $\pt>60$\GeV, we find the trigger efficiency to be greater than 97\%.
We veto events that have at least four jets with \pt above 50\GeV.
The veto and its threshold are motivated by the harder \pt spectrum of the fourth jet in semileptonic \ttbar events compared to the signal, in which extra jets originate from ISR or FSR.
To reduce the SM background from processes with a leptonically decaying \ensuremath{\PW}\xspace~boson, we reject events containing isolated electrons or muons with $I_\text{rel}<0.1$ and $\abs{\eta} < 2.5$, or $I_\text{rel}<0.2$ and $\abs{\eta} < 2.4$, respectively, and with $\pt > 10$\GeV. The contribution containing $\tauh$ decays is reduced by placing a veto on events containing charged-hadron PF candidates with $\pt>10$\GeV, $\abs{\eta} < 2.5$, and an isolation sum smaller than $10\%$ of the candidate \pt.
The dominant SM background sources are \ensuremath{\Z+}jets\xspace production with \ensuremath{\cPZ\to\cPgn\cPagn}\xspace, and the lost-lepton background originating from \ensuremath{\PW+}jets\xspace, \ttbar, and single top quark processes with leptonic \ensuremath{\PW}\xspace~boson decays.
A smaller background contribution comes from QCD events in which large \MET originates from jet mismeasurements and the direction of \ptvecmiss is often aligned with one of the jets. To suppress this background we require that the absolute difference in azimuthal angle between the \ptvecmiss and the closest of the three leading jets ($\ensuremath{\Delta\phi_{123}}\xspace$) is greater than 0.4. Two sets of SRs are defined to optimize the sensitivity for signal models with either compressed or noncompressed mass spectra.
In addition to the criteria discussed above, for regions targeting noncompressed scenarios we require that the \pt of the leading jet be above 100\GeV
and that the event contain at least one additional jet with \pt above 75\GeV. We also require that the two highest-\pt jets be identified as \PQb~jets. These requirements suppress events originating from \ensuremath{\PW}\xspace~and \Z~boson production, for which the leading jets have a softer \pt spectrum since they are produced by ISR or FSR.
To maintain a stable \PQb~tagging efficiency as a function of jet \pt, both the loose and medium working points of the \PQb~tagging algorithm are used to identify \PQb~jets. The \PQb~tagging efficiency of the medium working point depends strongly on the jet \pt and degrades by about 20--30\% for jets with \pt above 500\GeV, while the efficiency of the loose working point is more stable with increasing jet \pt. Specifically, we use the loose working point to identify \PQb-tagged jets when the leading jet has \pt above 500\GeV, and the medium working point otherwise. Since such high-\pt jets are less likely to occur in SM processes, the higher misidentification rate of the loose working point results in only a small increase in the SM background.
{\sloppypar
The distribution of $\ensuremath{M_{\mathrm{T}}(\mathrm{j}_{1,2},\ptvecmiss)}\xspace \equiv \min[\ensuremath{M_{\mathrm{T}}}\xspace(\text{j}_{1}, \ptvecmiss), \ensuremath{M_{\mathrm{T}}}\xspace(\text{j}_{2}, \ptvecmiss)]$, where $\text{j}_{1}, \text{j}_{2}$ are the two highest-\pt jets, is expected to have a kinematic endpoint
at the mass of the top quark when \ptvecmiss and the closest jet originate from the semileptonic decay of a top quark. In the noncompressed search sample we require \ensuremath{M_{\mathrm{T}}(\mathrm{j}_{1,2},\ptvecmiss)}\xspace to be greater than 250\GeV.
Events in this sample are then categorized by \ensuremath{H_{\mathrm{T,12}}}, defined for the purposes of this analysis as the scalar sum of the \pt of the two leading jets, and the \ensuremath{m_{\mathrm{CT}}}\xspace kinematic variable. The boost-corrected cotransverse mass~\cite{MCT,MCT1}, \ensuremath{m_{\mathrm{CT}}}\xspace, is defined by:
\par}
\begin{equation}
\ensuremath{m_{\mathrm{CT}}}\xspace^2(\mathrm{j_1, j_2})= 2\pt(\mathrm{j_1})\pt(\mathrm{j_2}) [1+\cos\Delta\phi(\mathrm{j_1,j_2})].
\end{equation}
For scenarios in which two particles are pair-produced and have the same decay chain, the \ensuremath{m_{\mathrm{CT}}}\xspace distribution has an endpoint determined by the masses of the parent and decay-product particles. For $\ensuremath{\PSQb_{1}}\xspace \to \PQb\PSGczDo$ this endpoint is at $(m(\ensuremath{\PSQb_{1}}\xspace)^{2}-m(\PSGczDo)^2)/m(\ensuremath{\PSQb_{1}}\xspace)$.
For signals with compressed mass spectra,
high-\pt ISR is required to be able to reconstruct the quarks as jets and obtain a large value of \MET. Compressed SRs require therefore a leading jet with $\pt>250$\GeV that is back-to-back relative to the \ptvecmiss ($\ensuremath{\Delta\phi(\mathrm{j}_{1},\ptvecmiss)}\xspace>2.3$). Since such ISR jets are not expected to originate from \PQb~quarks, we require that the leading jet fail the loose \PQb-tagging requirement.
We relax the thresholds on the second jet \pt and on the \ensuremath{M_{\mathrm{T}}(\mathrm{j}_{1,2},\ptvecmiss)}\xspace to 60 and 200\GeV, respectively, and categorize events in the search sample according to the number of \PQb-tagged jets. The \ensuremath{m_{\mathrm{CT}}}\xspace observable loses its discriminating power for these compressed signal models due to the small mass splitting
between the parent particle and $\PSGczDo$.
The \MET is therefore used as the main discriminant, with different \MET thresholds applied to define the final SRs.
The baseline selections for both noncompressed and compressed regions are summarized in Table~\ref{tab:selection}, while the definitions of the two sets of SRs are described in Table~\ref{tab:noncompandcomp}.
\begin{table*}[!ht]
\centering
\topcaption{A summary of the baseline selections used for the noncompressed and compressed $\ensuremath{\PSQb_{1}}\xspace$ and $\ensuremath{\PSQt_{1}}\xspace \to \cPqc \PSGczDo$ compressed SRs.}
\begin{tabular}{lll}
\hline
Selection& Noncompressed & Compressed \\ \hline
$\ensuremath{N_{\mathrm{j}}}\xspace$ & 2$\leq\ensuremath{N_{\mathrm{j}}}\xspace\leq$3 & 2$\leq\ensuremath{N_{\mathrm{j}}}\xspace\leq$3 \\
First jet \pt &$> 100$\GeV &$> 250$\GeV \\
Second jet \pt &$> 75$\GeV &$> 60$\GeV \\
Veto fourth jet & \pt $>$ 50\GeV & \pt $>$ 50\GeV \\
Lepton and isolated track veto &\pt$>$ 10\GeV& \pt$>$ 10\GeV \\
\PQb~tagging & First and second jets are \PQb-tagged & Leading jet is not \PQb-tagged \\
\MET & $>$250\GeV& $>$250\GeV \\
$\ensuremath{\Delta\phi_{123}}\xspace$ & $>$0.4 & $>$0.4 \\
\ensuremath{\Delta\phi(\mathrm{j}_{1},\ptvecmiss)}\xspace& \NA & $>$2.3\\
\ensuremath{M_{\mathrm{T}}(\mathrm{j}_{1,2},\ptvecmiss)}\xspace&$>$ 250\GeV& $>$200\GeV \\
\ensuremath{H_{\mathrm{T,12}}}&$>$ 200\GeV& \NA \\
\ensuremath{m_{\mathrm{CT}}}\xspace&$>$250\GeV& \NA \\
\hline
\end{tabular}
\label{tab:selection}
\end{table*}
\begin{table*}[!htb]
\centering
\topcaption{\label{tab:noncompandcomp} The categorization in \ensuremath{H_{\mathrm{T,12}}}\ and \ensuremath{m_{\mathrm{CT}}}\xspace for the SRs targeting noncompressed signal scenarios, and in $\ensuremath{N_{\PQb}}\xspace$ and \MET for those targeting compressed signal scenarios.}
{\begin{tabular}{cc c c c c c c}
\multicolumn{1}{c}{} & \multicolumn{7}{c}{Noncompressed SRs}
\\
\hline
\ensuremath{H_{\mathrm{T,12}}} [\GeVns{}] & \multicolumn{7}{c}{\ensuremath{m_{\mathrm{CT}}}\xspace [\GeVns{}]} \\
\hline
250--500 & & 250--350 & & 350--500 & & $>$500 & \\
$>$500 & & 250--350 & & 350--500 & & $>$500 & \\
\hline
\\[-0.5ex]
\multicolumn{1}{c}{} & \multicolumn{7}{c}{Compressed SRs}
\\
\hline
$\ensuremath{N_{\PQb}}\xspace$ & \multicolumn{7}{c}{\MET [\GeVns{}]} \\
\hline
0 & 250--350 & 350--450 & 450--550 & 550--700 & 700--850 & 850--1000 & $>$1000 \\
1 &
250--350 & 350--450 & 450--550 & 550--700 & $>$700 & & \\
2 & $>$250 & & & & & & \\
\hline
\end{tabular}
}
\end{table*}
\subsection{Background estimation}
\label{sec:sbottombackgrounds}
The SM background contributions originating from \ensuremath{\cPZ\to\cPgn\cPagn}\xspace, lost-lepton, and QCD processes are estimated from dedicated data CRs as discussed below. Smaller contributions from other SM processes, such as diboson (VV) processes, are estimated from simulation, and an uncertainty of 50\% is assigned to these contributions.
\subsubsection{Estimation of the \texorpdfstring{\ensuremath{\cPZ\to\cPgn\cPagn}\xspace}{Z nu nu}~background}
\label{sec:zinv_dy}
The \ensuremath{\cPZ\to\cPgn\cPagn}\xspace\ background is estimated from a high-purity data sample of \ensuremath{\cPZ\to\mu^{+}\mu^{-}}\xspace~events in which we remove the muons and recalculate the relevant kinematic variables to emulate \ensuremath{\cPZ\to\cPgn\cPagn}\xspace\ events. The trigger used to collect this CR requires the presence of a high-\pt muon with $\abs{\eta} < 2.1$. In keeping with the trigger constraints, the sample is selected by requiring the presence of two isolated muons in the event with $\pt> 50\,(10)$\GeV and
$\abs{\eta}<2.1$\,(2.4) for the leading (trailing) muon. The invariant mass of the dimuon pair is required to be within 15\GeV of the \Z~boson mass~\cite{PDG}. Each muon is required to be separated from jets in the event by $\Delta R > 0.3$.
Apart from the lepton selection, we apply the same object and event selection criteria as described in
Section~\ref{sec:sbottomsel} to this sample, with the exception that \PQb~jets are selected using the loose working point of the \PQb~tagging algorithm to improve the statistical power of the data CR. Events in the selected sample are subdivided into CRs corresponding to the noncompressed and compressed SRs.
The observed events in these data CRs, $N^\text{data}_{\mu\mu}$, are translated into an estimation of the \ensuremath{\cPZ\to\cPgn\cPagn}\xspace\ contribution in the SRs with the help of simulation, as follows:
\begin{equation}
N^\text{pred}_{\ensuremath{\cPZ\to\cPgn\cPagn}\xspace} = \frac{N^\text{data}_{\mu\mu}-N^{\text{non-\Z}}_{\mu\mu}}{A~\epsilon}~~R_{\rm Z}^{\mu\mu\to\nu\nu}~~\kappa,
\label{equ:Zvv}
\end{equation}
where $N^{\text{non-}\Z}_{\mu\mu}$, representing the small contamination in the CRs due to \ttbar, \ensuremath{\PW+}jets\xspace, single top quark, and diboson processes, is estimated from simulation.
The corrected dimuon event yield is scaled by the kinematic and detector acceptance of muons from \Z~bosons, $A$, and the muon reconstruction, identification, and isolation efficiency $\epsilon$. The acceptance and efficiency are determined from simulation. Efficiency scale factors are applied to correct for differences between data and simulation. These scale factors are determined with a ``tag-and-probe" method in \ensuremath{\cPZ\to\mu^{+}\mu^{-}}\xspace\ events~\cite{Chatrchyan:2012xi}.
The product of the muon acceptance and efficiency, $A\epsilon$, varies from 0.6 in the low-\ensuremath{m_{\mathrm{CT}}}\xspace and low-\MET regions to 0.9 in the high-\ensuremath{m_{\mathrm{CT}}}\xspace and high-\MET regions.
The correction factor $R_{\rm Z}^{\mu\mu\to\nu\nu} = 5.942\pm0.019$~\cite{PDG} represents the ratio of the \Z~boson branching fractions to neutrinos and leptons.
The remaining term, $\kappa$, accounts for differences in the \PQb~tagging efficiency and misidentification rate between the CRs and SRs, resulting from the use of different \PQb~tagging working points.
These $\kappa$ factors are determined from \ensuremath{\cPZ\to\ell\ell}~simulation and corrected for known differences in the performance of the \PQb~tagging algorithm between data and simulation
as measured in samples of multijet and \ttbar events~\cite{CMS-PAS-BTV-15-001}.
The value of the \PQb~tagging $\kappa$ factor ranges from 0.10 to 0.15 for the noncompressed SRs, and from 0.20 to 0.25 for the $\ensuremath{N_{\PQb}}\xspace = 1$ compressed SRs, while it is about 0.15 for the $\ensuremath{N_{\PQb}}\xspace = 2$ compressed SR.
The largest uncertainty in the \ensuremath{\cPZ\to\cPgn\cPagn}\xspace\ background estimate arises from the limited event yields in the dimuon CR, corresponding to a 10--100\% uncertainty in the \ensuremath{\cPZ\to\cPgn\cPagn}\xspace\ prediction.
We correct for the estimated contributions to the CR from SM processes other than \ensuremath{\cPZ\to\mu^{+}\mu^{-}}\xspace\ using simulation samples with an assigned uncertainty of 50\% in their normalization. This leads to an uncertainty of 2--20\% in the background estimate.
Other experimental and theoretical sources of uncertainty, to be discussed in Section~\ref{sec:systematics}, result in an additional 2--8\% uncertainty in $A\epsilon$, and a 2\% uncertainty is assigned in
all SRs to account for the uncertainty in the \Z~boson branching fractions.
The uncertainty in the \PQb~tagging $\kappa$ factors is assessed by varying the data-to-simulation \PQb~tagging correction factors according to their measured uncertainties.
Additionally, the dependence of $\kappa$ on the heavy-flavour content in \Z~boson events is evaluated by varying the $\cPZ+$\bbbar and $\cPZ+$\ccbar
fractions in simulation by 20\% based on the uncertainty in the CMS $\cPZ+$\bbbar measurement~\cite{Zbb}, resulting in an additional uncertainty of 10--20\% in the \ensuremath{\cPZ\to\cPgn\cPagn}\xspace\ estimate.
\subsubsection{Estimation of the lost-lepton background}
\label{sec:lostlep}
The lost-lepton background in each SR is estimated from a single-lepton CR in data selected by inverting the electron and muon vetoes in events collected with the same trigger as used to record the signal sample.
We relax the \PQb~tagging requirement in the CRs using the loose working point in the noncompressed selection,
while keeping the same requirement as in the SRs for the compressed regions. In all other respects, the CRs are defined through the same selection criteria as the corresponding SRs, including requirements on the \ensuremath{H_{\mathrm{T,12}}}, \ensuremath{m_{\mathrm{CT}}}\xspace, $\ensuremath{N_{\PQb}}\xspace$, and \MET, to remove any dependence of the prediction on the modelling of these kinematic variables in simulation. The possible contamination from signal in the single-lepton CR is negligible, less than 1\%, so no extra requirement on \ensuremath{M_{\mathrm{T}}(\ell,\ptvecmiss)}\xspace is made.
The lost-lepton component of the SM background in each SR, $N^\text{pred}_{\rm LL}$,
is estimated once again from the corresponding data via a transfer factor, $T_\mathrm{LL}$, determined from simulation:
\begin{equation}
\label{equ:lostlep}
N^\text{pred}_{\rm LL} = N^\text{data}_{1\ell} T_\mathrm{LL},\quad T_\mathrm{LL} = \frac{N^\text{sim}_{0\ell}}{N^\text{sim}_{1\ell}},
\end{equation}
where $ N^\text{data}_{1\ell}$ is the observed event yield in the single-lepton CR. The transfer factor $T_\mathrm{LL}$ accounts for effects related to lepton acceptance and efficiency.
The largest uncertainty in the lost-lepton estimate is, as in the previous analyses, due to the statistical uncertainty in the event yields, ranging from 3 to 50\%, depending on the SR.
Contributions to the CRs from \ensuremath{\cPZ\to\ell\ell}~and diboson processes are subtracted using estimates from simulation, and a 50\% uncertainty is applied to this subtraction, which leads to an uncertainty of 3--10\% in the lost-lepton prediction. The limited event counts in the simulation sample result in a 2--12\% uncertainty, while uncertainties related to discrepancies between the lepton selection efficiency in data and simulation give rise to a 3--4\% uncertainty in the final estimate. An additional uncertainty of 7\% in the $\tau_{\rm h}$ component accounts for differences in isolation efficiency between muons and single-prong $\tau_{\rm h}$ decays, as determined from studies with simulated samples of \ensuremath{\PW+}jets\xspace and \ttbar events.
A systematic uncertainty of 5--10\% is found for the uncertainties in the \PQb~tagging scale factors that are applied to the simulation for the differences in b tagging performance between data and simulation and the different b tagging working points.
Finally, we estimate a systematic uncertainty in the transfer factor to account for differences in the \ttbar and \ensuremath{\PW+}jets\xspace admixture in the search and control regions. This results in a 20--30\% uncertainty in the final prediction.
\subsubsection{Estimation of the QCD background}
\label{sec:qcd}
The $\ensuremath{\Delta\phi_{123}}\xspace > 0.4$ requirement reduces the QCD contribution to a small fraction of the total background in all SRs for both compressed and noncompressed models. We estimate this contribution for each SR by applying a transfer factor to the number of events observed in a CR enriched in QCD events. The CRs are obtained by inverting the $\ensuremath{\Delta\phi_{123}}\xspace$ requirement. The transfer factor, \ensuremath{T_{\mathrm{QCD}}}\xspace, is measured in a sideband region in data with \MET$\in[200,250]$\GeV and the same requirements on the other variables as in the SRs. This factor is the ratio between the number of QCD events in the $\ensuremath{\Delta\phi_{123}}\xspace > 0.4$ and $\ensuremath{\Delta\phi_{123}}\xspace < 0.4$ subsets of this sideband region. The estimated contribution of other SM processes (\ttbar, \ensuremath{\PW+}jets\xspace, single top quark, and diboson production) based on simulated samples is subtracted from the event yields in the CR and each subset of the sideband.
The transfer factor for the noncompressed regions does not vary significantly as a function of \ensuremath{H_{\mathrm{T,12}}}\ and \ensuremath{m_{\mathrm{CT}}}\xspace. Therefore, we extract the value of \ensuremath{T_{\mathrm{QCD}}}\xspace used for the noncompressed SRs from a sideband selected with an inclusive requirement on \ensuremath{H_{\mathrm{T,12}}}\ and \ensuremath{m_{\mathrm{CT}}}\xspace to reduce the statistical uncertainty in the transfer factor. The transfer factors for the compressed SRs are obtained from sidebands that are subdivided according to the number of \PQb-tagged jets into $\ensuremath{N_{\PQb}}\xspace = 0$ and $\ensuremath{N_{\PQb}}\xspace \geq 1$ regions, with the latter used to extract the QCD predictions for the $\ensuremath{N_{\PQb}}\xspace = 1$ and $\ensuremath{N_{\PQb}}\xspace \geq 2$ SRs.
The statistical uncertainties due to the limited number of events in the data CRs and the non-QCD simulated samples are propagated to the final QCD estimate, ranging from 10 to 100\%. The main uncertainty in \ensuremath{T_{\mathrm{QCD}}}\xspace also originates from the statistical uncertainty of the observed and simulated event yields in the sideband region. We assign additional uncertainties for differences in \PQb~tagging efficiency between data and simulation and for the subtraction of the non-QCD background contribution in the sideband. The total systematic uncertainty in the QCD prediction varies between 27\% and 76\% in the compressed SRs, but can be as large as 550\% in the noncompressed SRs due to the small event samples in the corresponding sideband in data.
\subsection{Results}
\label{sec:result}
The expected SM background yields and the number of events observed in data are
summarized in Table~\ref{tab:pred} and shown in Fig.~\ref{fig:allPred}. The observed yields agree well with the predicted SM background.
\begin{table*}[!ht]
\centering
\topcaption{Observed number of events and background prediction in the different SRs for the $\ensuremath{\PSQb_{1}}\xspace$ and $\ensuremath{\PSQt_{1}}\xspace \to \cPqc \PSGczDo$ searches. The total uncertainty in the background predictions is also shown.
}
\begin{tabular}{ c cccc c c}
\hline
& \ensuremath{\cPZ\to\cPgn\cPagn}\xspace & Lost-lepton & QCD & Rare SM & Total SM & Data \\
\hline
\ensuremath{m_{\mathrm{CT}}}\xspace [\GeVns{}] & \multicolumn{6}{c}{$200$\GeV$< \ensuremath{H_{\mathrm{T,12}}} \leq 500$\GeV} \\
\hline
250--350 & 12.5$\pm$6.3 & 5.3$\pm$2.0 & 0.6$^{+3.3}_{-0.6}$ & 1.09$\pm$0.54 & 19.4$^{+7.4}_{-6.6}$ & 12 \\
$>$350 & 0.9$^{+1.1}_{-0.9}$ & 1.28$\pm$0.46 & $<$0.34 & 0.18$\pm$0.09 & 2.4$^{+1.3}_{-1.1}$ & 3 \\
\hline
\ensuremath{m_{\mathrm{CT}}}\xspace [\GeVns{}] &\multicolumn{6}{c}{$\ensuremath{H_{\mathrm{T,12}}} >500$\GeV } \\
\hline
250--350 &$<$1.5 &1.34$\pm$0.78 & $<$0.34 &$<$0.12 & 1.34$\pm$0.78 & 1 \\
350--500 & 0.84$\pm$0.94 & 0.67$\pm$0.35 & $<$0.34 &$<$0.12 & 1.51$\pm$0.98 &1 \\
$>$500 & 2.0$\pm$1.6 & 0.34$\pm$0.20 & 0.2$^{+1.6}_{-0.2}$ & $<$0.12 & 2.3$^{+2.2}_{-1.6}$ & 0\\
\hline
\MET [\GeVns{}] &\multicolumn{6}{c}{$\ensuremath{N_{\PQb}}\xspace = 0$} \\
\hline
250--350 & 680$\pm$78 & 530$\pm$120 & 86$\pm$25 & 14.2 $\pm$7.1 & 1310$\pm$150 & 1250 \\
350--450 & 454$\pm$63 & 270$\pm$64 & 24.9$\pm$8.8 & 11.0$\pm$5.5 & 760$\pm$89 & 802 \\
450--550 & 226$\pm$42 & 82$\pm$52 & 0.8$^{+2.7}_{-0.8}$ & 4.8$\pm$2.4 & 314 $\pm$67 & 305 \\
550--700 & 94$\pm$27 & 27 $\pm$21 &$<$0.95 & 1.75$\pm$0.87 & 122 $\pm$34 & 137 \\
700--850 & 26$\pm$14 & 7.0$\pm$6.1& 1.6$\pm$1.4 & 0.43$\pm$0.21& 35$\pm$15 & 37 \\
850--1000& 7.2$^{+7.6}_{-7.2}$ &1.6$^{+1.8}_{-1.6}$ &$<$0.95 & 0.13$\pm$0.06 & 7.3$^{+7.9}_{-7.3}$ & 13 \\
$>$1000 & $<$2.0 & 0.48$^{+0.51}_{-0.48}$ & 0.12$^{+0.53}_{-0.12}$ &0.11$\pm$0.05 & 0.71$^{+0.71}_{-0.52}$ & 1\\
\hline
\MET [\GeVns{}] & \multicolumn{6}{c}{$\ensuremath{N_{\PQb}}\xspace = 1$} \\
\hline
250--350 & 29.2$\pm$5.0 & 43$\pm$11 & 5.1$\pm$4.2 & 1.32$\pm$0.65 & 79$\pm$13 & 93 \\
350--450 & 27.7$\pm$4.7 & 17.1$\pm$4.9 & $<$0.47& 0.99$\pm$0.49& 45.8$\pm$6.8 & 47 \\
450--550 & 10.8$\pm$2.0 & 4.9$\pm$2.0 & $<$0.47& 0.41$\pm$0.20 & 16.2$\pm$2.8 & 18 \\
550--700 & 6.0$\pm$1.3 & 1.82$\pm$0.96 & $<$0.47& 0.23$\pm$0.11& 8.1$\pm$1.6 & 8\\
$ > 700 $ & 3.07$\pm$0.64 & 0.59$\pm$0.47 & $<$0.47& $<$0.12 &3.66$\pm$0.80 & 2 \\
\hline
\MET [\GeVns{}] & \multicolumn{6}{c}{$\ensuremath{N_{\PQb}}\xspace = 2$} \\
\hline
$>$250 & 1.6$\pm$1.6 & 4.7$\pm$2.5 & 0.32$^{+0.40}_{-0.32}$ & 0.19$\pm$0.09 & 6.5$\pm$2.9 & 11 \\
\hline
\end{tabular}
\label{tab:pred}
\end{table*}
\begin{figure}[!ht]
\centering
\includegraphics[width=0.9\columnwidth]{Figure_006-a.pdf}
\includegraphics[width=0.9\columnwidth]{Figure_006-b.pdf}
\caption{Observed events and estimated SM background and signal yields for the compressed (top) and noncompressed (bottom) SRs for the bottom squark search in the all-jet final state. The observed data yield is shown as black points and the total background predictions are shown in solid area. The SM background predictions shown do not include the effects of the maximum likelihood fit to the data. The bottom panel shows the ratio of data to the total background prediction in each search bin. Only statistical uncertainties are propagated to the ratio. }
\label{fig:allPred}
\end{figure}
\section{Systematic uncertainties}
\label{sec:systematics}
Several categories of systematic uncertainties apply to all three analyses. These include uncertainties arising from the limited event counts in control samples, uncertainties related to the use of simulation in SM background predictions, and a 2.7\% uncertainty in integrated luminosity~\cite{CMS-PAS-LUM-15-001} that applies to the estimated signal yields and contributions from rare background processes that are taken directly from simulation, without the use of data control samples.
The limited number of simulated events surviving the stringent requirements on jets and \MET in all three searches can lead to a significant statistical uncertainty in background predictions. In the case of background predictions that rely on simulation for accurate modelling of the relevant event kinematics, we assess theoretical uncertainties, primarily those associated with missing higher-order corrections, in the simulated samples by varying the renormalization and factorization scales up and down by a factor of two~\cite{Catani2003zt,Cacciari2003fi} and by variations of PDFs. The PDF uncertainties are defined by the standard deviation obtained from 100 variations of the NNPDF3.0~\cite{Ball:2014uwa} PDFs. The uncertainties are then propagated to the final background estimates.
When the simulation of the detector response does not adequately describe the data, correction factors are applied to account for the observed discrepancies. Differences in the efficiencies for selecting isolated leptons between simulation and data are measured in \ensuremath{\cPZ\to\ell\ell}~events in the case of electrons and muons and in a \ttbar-enriched sample for hadronically decaying $\tau$ leptons. The observed deviations are accounted for in the form of corrections to the simulation, and the corresponding uncertainties are propagated to the predicted SM yields in the SRs. Correction factors and uncertainties based on measurements of \PQb~tagging performance in data and simulation~\cite{CMS-PAS-BTV-15-001} are also applied. They are parameterized by jet kinematics and flavour. We also assess an uncertainty related to the modelling of additional interactions in the simulation. For the rare SM backgrounds with top quarks, predominantly from \ttbar production in association with a \Z boson, where the \Z boson decays to a pair of neutrinos, an extra uncertainty is estimated to account for the possible mismodelling of the top quark \pt spectrum.
The efficiency and misidentification rates for the top quark tagging algorithm are compared between data and simulation in CRs as a function of the key kinematic variables. The correction factors are found not to be strongly dependent on the different kinematic variables. The efficiency estimated in simulation agrees with the measured efficiency while the misidentification rate has to be corrected by 30\%. Both correction factors have a 10\% uncertainty, estimated from the variations of the efficiency measurement.
All these uncertainties are propagated to the different signal and background estimates to which they apply. The background predictions from control samples in data are affected through the transfer factors that are calculated from simulation corrected to reproduce data. In general these uncertainties are subdominant and the uncertainty in the final background estimate is dominated by the statistical uncertainty of the data control sample.
For the signal samples differences between the fast simulation and the full \GEANTfour-based model are also taken into account. Lepton selection efficiencies and \PQb~tagging performance are found to be different in the fast simulation. We derive appropriate corrections for the fast simulation and propagate the corresponding uncertainties to the predicted signal yields. We also assess an additional uncertainty for the difference in \MET resolution between the fast simulation and the full \GEANTfour-based model. This difference in \MET resolution has the largest impact on signal models with small intrinsic \MET, as is the case for compressed mass spectra. The modelling of the ISR plays an important role in cases where the top squark and $\PSGczDo$ masses are very similar. The uncertainty is determined by comparing the simulated and observed \pt spectra of the system recoiling against the ISR jets in \ttbar events, using the method described in Ref.~\cite{CMS-STOP-lepton}. The effect is generally found to be small, although in scenarios with a compressed mass spectrum the effect can be as large as 30\%.
The uncertainties in the signal modelling are determined in each analysis for every SR. The dominant uncertainties in the predicted signal yield arise from the size of the simulated samples in some of the SRs (1--100\%), jet energy scale corrections (1--50\%), $\PQb$ tagging efficiency corrections used to scale simulation to data (1--35\%), and ISR (1--30\%). The largest uncertainties are in SRs that have small signal acceptance to a specific model.
The statistical uncertainties of the signal samples are uncorrelated, whereas all other signal systematic uncertainties are considered to be fully correlated among the different SRs and analyses. Since the three analyses predict the backgrounds with different CRs, the treatment of systematic uncertainties is mostly uncorrelated among analyses, except for the estimates based on simulation. Here only the statistical component of the uncertainty is treated as uncorrelated. Systematic uncertainties due to jet energy scale corrections, $\PQb$ tagging efficiency and selection efficiencies are treated as correlated among the different background estimates.
\section{Interpretation}
\label{sec:interpretation}
The data in all three searches are consistent with the background expected from SM processes. The results are interpreted as limits on supersymmetric particle masses in the context of simplified models~\cite{Simp,Simp1,Simp2,Simp3}
of top or bottom squark pair production.
Different decay modes are considered for top squark pair production. For mass splittings $\Delta m$ larger than the \ensuremath{\PW}\xspace~boson mass, we consider two decay modes for the top squark: to a top quark and a neutralino, or to a bottom quark and a chargino, where the chargino decays to an LSP. Scenarios with $\ensuremath{\PSQt_{1}}\xspace\to \PQt^{(*)}\PSGczDo$ branching fractions of 50 or 100\% are considered.
The results of the top squark searches in the all-jet and single-lepton final states are combined for these interpretations. For $\Delta m$ smaller than the \ensuremath{\PW}\xspace~boson mass, only the decay of top squarks to a charm quark and an LSP is considered in this paper. For the pair production of bottom squarks, all bottom squarks are assumed to decay to a bottom quark and an LSP.
The signal yield is corrected for signal contamination of data CRs for each mass hypothesis and each analysis. Typical values are around 5--10\%, except for compressed mass spectra, where it can vary between 10 and 50\%. The signal contamination is most significant for the top squark production models with a 100\% $\ensuremath{\PSQt_{1}}\xspace\to \PQt^{(*)}\PSGczDo$ branching fraction, a light LSP, and $\Delta m$ close to the top quark mass. The 95\% confidence level (CL) upper limits on SUSY production cross sections are calculated using a modified frequentist approach with the CL$_\mathrm{S}$ criterion~\cite{Junk:1999kv,Read:2002hq} and asymptotic results for the test statistic~\cite{LHC-HCG,Cowan:2010js}.
The SRs and CRs for top squark searches in the all-jet and single-lepton final states are mutually exclusive. We combine the results of the two searches, treating the systematic uncertainties assigned to the predicted signal and background yields as correlated or uncorrelated depending on the source, as detailed in Section~\ref{sec:systematics}.
Figure~\ref{fig:limits:T2tt} shows 95\% CL exclusion limits for $\Pp\Pp\to\ensuremath{\PSQt_{1}}\xspace\ensuremath{\PASQt_{1}}\xspace\to \PQt^{(*)}\PSGczDo\cPaqt^{(*)}\PSGczDo$, assuming the top quarks in the decay to be unpolarized, together with the upper limit at 95\% CL on the excluded signal cross section. All top squarks are assumed to decay to a top quark and an LSP. For $\Delta m<m_{\PQt}$ the signal samples assume a three-body decay without an off-shell top quark as intermediate particle. The expected exclusion is given by the dashed red line, with the one standard deviation (s.d.) experimental uncertainty. The observed exclusion curve is shown as a solid black line together with the 1 s.d. uncertainty in the theoretical cross section. We do not interpret in the region near $\Delta m \approx m_{\PQt}$ when \PSGczDo is very light because of the difficulty in modelling rapidly varying kinematics in this region. In this region an indirect search for top squark pair production can be performed by looking for a small excess in the measured \ttbar cross section compared to the SM expectation~\cite{TOP-13-004,atlas-stop1l-2015}. We exclude top squark masses from 280\GeV to 830\GeV for a massless LSP and LSP masses up to 260\GeV for 675\GeV top squarks. At 8 TeV top squark masses were excluded up to 780\GeV for a massless LSP~\cite{stop0l_8TeV}. For models with heavy top squarks and light LSPs, the sensitivity is driven by the top squark analysis in the all-jet final state of Section~\ref{sec:stop0l}, which is more sensitive than the single-lepton analysis (Section~\ref{sec:1lstop}) because of the larger acceptance for signal. The combination extends the expected reach in top squark mass by about 45\GeV. When the LSP is heavier, the cleaner search in the single-lepton final state becomes more important. Both analyses have similar sensitivity in this area of parameter space, and combining them extends the reach in LSP mass by about 30\GeV.
\begin{figure}[htb]
\centering
\includegraphics[width=\cmsFigWidth]{Figure_007.pdf}
\caption{\label{fig:limits:T2tt}Exclusion limits at 95\% CL for direct top squark pair production for the decay mode $\ensuremath{\PSQt_{1}}\xspace\to\PQt^{(*)}\PSGczDo$.
The interpretation is performed in the two-dimensional space of $m_{\ensuremath{\PSQt_{1}}\xspace}$ vs. $m_{\PSGczDo}$. The color indicates the 95\% CL upper
limit on the product of cross section and branching fraction at each point in the $m_{\ensuremath{\PSQt_{1}}\xspace}$-$m_{\PSGczDo}$ plane.
The regions enclosed by the thick black curves represent the observed exclusion at 95\% CL, while the dashed red lines indicate the expected limits at 95\% CL and their $\pm$1 s.d. experimental uncertainties. The thin black lines show the impact of the $\pm$1 s.d. theoretical uncertainties in the signal cross section. The magenta short-dashed curve and the blue dotted curve show the expected limits for the analysis in the all-jet (Section~\ref{sec:stop0l}) and single-lepton (Section~\ref{sec:1lstop}) final states, respectively. The limits in the region near $\Delta m\approx m_{\PQt}$ and low $\PSGczDo$ mass are not shown due to the difficulty in modelling rapidly varying kinematics in this region.}
\end{figure}
Figure~\ref{fig:limits:T2tb} shows the 95\% CL exclusion limits for $\ensuremath{\PSQt_{1}}\xspace\ensuremath{\PASQt_{1}}\xspace$ production, assuming equal probabilities for the decay modes $\ensuremath{\PSQt_{1}}\xspace\to \PQt^{(*)}\PSGczDo$ and $\ensuremath{\PSQt_{1}}\xspace\to \PQb\PSGcpmDo$. The chargino in the latter mode decays to a \ensuremath{\PW}\xspace~boson and an LSP. In this model, the chargino is considered to be nearly mass-degenerate with the LSP ($m_{\PSGcpmDo} = m_{\PSGczDo} + 5$\GeV). The \ensuremath{\PW}\xspace~boson decay products originating from the chargino decay are very soft because of the small mass splitting, and might not be detectable. For intermediate LSP masses, top squark masses are probed up to 725\GeV.
The LSP masses up to 210\GeV are probed for a top squark mass of around 500\GeV. Here, the single-lepton analysis does not contribute much to the combination because of the larger acceptance in the all-jet final state, except at low LSP masses. In most of the mass parameter space the combination reaches $\approx$ 15\GeV higher than the analysis in the all-jet final state.
\begin{figure}[htb]
\centering
\includegraphics[width=\cmsFigWidth]{Figure_008.pdf}
\caption{\label{fig:limits:T2tb}Exclusion limits at 95\% CL for direct top squark pair production assuming equal branching fractions for the decays $\ensuremath{\PSQt_{1}}\xspace\to\PQt^{(*)}\PSGczDo$ and $\ensuremath{\PSQt_{1}}\xspace\to \PQb\PSGcpmDo$.
The interpretation is performed in the two-dimensional space of $m_{\ensuremath{\PSQt_{1}}\xspace}$ vs. $m_{\PSGczDo}$. The chargino is considered to be nearly mass-degenerate with the LSP ($m_{\PSGcpmDo} = m_{\PSGczDo} + 5$\GeV). The caption of Fig.~\ref{fig:limits:T2tt} explains the use of lines and colors in detail.}
\end{figure}
The compressed SRs from the bottom squark analysis in the all-jet final state (Section~\ref{sec:sbottom}) are used to set upper limits on the top squark cross sections when the mass splitting between the top squark and the LSP is smaller than the mass of the \ensuremath{\PW}\xspace~boson. Figure~\ref{fig:limits:T2cc} shows the expected and observed 95\% CL upper limits on the top squark cross sections in the $m_{\ensuremath{\PSQt_{1}}\xspace}$-$m_{\PSGczDo}$ plane assuming the top squark always decays to a charm quark and an LSP. Top squarks with masses below 240\GeV are probed in this model, when the mass splitting between the top squark and the LSP is close to 10\GeV. At 8\TeV top squark masses up to 270\GeV were probed for the same $\Delta$m~\cite{atlas-stop1l-2015}.
\begin{figure}[htb]
\centering
\includegraphics[width=\cmsFigWidth]{Figure_009.pdf}
\caption{\label{fig:limits:T2cc}Exclusion limits at 95\% CL for direct top squark pair production with decay $\ensuremath{\PSQt_{1}}\xspace\to \cPqc\PSGczDo$ using the compressed SRs of the bottom squark analysis (Section~\ref{sec:sbottom}).
The interpretation is done in the two-dimensional space of $m_{\ensuremath{\PSQt_{1}}\xspace}$ vs. $m_{\PSGczDo}$. The caption of Fig.~\ref{fig:limits:T2tt} explains the use of lines and colors in detail.}
\end{figure}
Figure \ref{fig:limits:T2bb} shows the expected and observed 95\% CL upper limits on the bottom squark cross sections in the $m_{\ensuremath{\PSQb_{1}}\xspace}$-$m_{\PSGczDo}$ plane using both the compressed and noncompressed SRs of the bottom squark analysis. We probe bottom squark masses up to 890\GeV for small LSP masses. With 8 TeV data bottom squark masses below 650\GeV were excluded.~\cite{atlas-stop1l-2015,stop8TeV}.
\begin{figure}[htb]
\centering
\includegraphics[width=\cmsFigWidth]{Figure_010.pdf}
\caption{\label{fig:limits:T2bb}Exclusion limits at 95\% CL for direct bottom squark pair production with decay $\ensuremath{\PSQb_{1}}\xspace\to \PQb\PSGczDo$.
The interpretation is performed in the two-dimensional space of $m_{\ensuremath{\PSQb_{1}}\xspace}$ vs. $m_{\PSGczDo}$ using the results of the bottom squark analysis (Section~\ref{sec:sbottom}). The caption of Fig.~\ref{fig:limits:T2tt} explains the use of lines
and colors in detail.}
\end{figure}
\section{Summary}
\label{sec:summary}
Results are presented from three complementary searches for top or bottom squark-antisquark pairs in data collected with the CMS detector in proton-proton collisions at a centre-of-mass energy of 13\TeV, corresponding to an integrated luminosity of 2.3\fbinv . The search for top squarks is carried out in the all-jet and single-lepton final states, which are combined for the final result. A second search in all-jet events is designed for bottom squark pairs and for top squarks decaying to charm quarks through a flavour changing neutral current process. No statistically significant excess of events is observed above the expected standard model background, and exclusion limits are set at 95\% confidence level in the context of simplified models of direct top and bottom squark pair production. Limits for top squark masses of 830\GeV are established for a massless lightest supersymmetric particle (LSP), and for LSP masses up to 260\GeV for a 675\GeV top squark mass, when all top squarks are assumed to decay to a top quark and an LSP. When the top squarks can also decay to a bottom quark and a chargino, this reach is reduced. Assuming a mass splitting between the top squark and the LSP close to 10\GeV, and top squarks that decay to a charm quark and an LSP, top squark mass limits up to 240\GeV are established. Finally, bottom squark mass limits up to 890\GeV are established for small LSP masses. The results extend the reach with respect to previous limits obtained from LHC Run 1 data in most of the parameter space.
\begin{acknowledgments}
\hyphenation{Bundes-ministerium Forschungs-gemeinschaft Forschungs-zentren Rachada-pisek} We congratulate our colleagues in the CERN accelerator departments for the excellent performance of the LHC and thank the technical and administrative staffs at CERN and at other CMS institutes for their contributions to the success of the CMS effort. In addition, we gratefully acknowledge the computing centres and personnel of the Worldwide LHC Computing Grid for delivering so effectively the computing infrastructure essential to our analyses. Finally, we acknowledge the enduring support for the construction and operation of the LHC and the CMS detector provided by the following funding agencies: the Austrian Federal Ministry of Science, Research and Economy and the Austrian Science Fund; the Belgian Fonds de la Recherche Scientifique, and Fonds voor Wetenschappelijk Onderzoek; the Brazilian Funding Agencies (CNPq, CAPES, FAPERJ, and FAPESP); the Bulgarian Ministry of Education and Science; CERN; the Chinese Academy of Sciences, Ministry of Science and Technology, and National Natural Science Foundation of China; the Colombian Funding Agency (COLCIENCIAS); the Croatian Ministry of Science, Education and Sport, and the Croatian Science Foundation; the Research Promotion Foundation, Cyprus; the Secretariat for Higher Education, Science, Technology and Innovation, Ecuador; the Ministry of Education and Research, Estonian Research Council via IUT23-4 and IUT23-6 and European Regional Development Fund, Estonia; the Academy of Finland, Finnish Ministry of Education and Culture, and Helsinki Institute of Physics; the Institut National de Physique Nucl\'eaire et de Physique des Particules~/~CNRS, and Commissariat \`a l'\'Energie Atomique et aux \'Energies Alternatives~/~CEA, France; the Bundesministerium f\"ur Bildung und Forschung, Deutsche Forschungsgemeinschaft, and Helmholtz-Gemeinschaft Deutscher Forschungszentren, Germany; the General Secretariat for Research and Technology, Greece; the National Scientific Research Foundation, and National Innovation Office, Hungary; the Department of Atomic Energy and the Department of Science and Technology, India; the Institute for Studies in Theoretical Physics and Mathematics, Iran; the Science Foundation, Ireland; the Istituto Nazionale di Fisica Nucleare, Italy; the Ministry of Science, ICT and Future Planning, and National Research Foundation (NRF), Republic of Korea; the Lithuanian Academy of Sciences; the Ministry of Education, and University of Malaya (Malaysia); the Mexican Funding Agencies (BUAP, CINVESTAV, CONACYT, LNS, SEP, and UASLP-FAI); the Ministry of Business, Innovation and Employment, New Zealand; the Pakistan Atomic Energy Commission; the Ministry of Science and Higher Education and the National Science Centre, Poland; the Funda\c{c}\~ao para a Ci\^encia e a Tecnologia, Portugal; JINR, Dubna; the Ministry of Education and Science of the Russian Federation, the Federal Agency of Atomic Energy of the Russian Federation, Russian Academy of Sciences, the Russian Foundation for Basic Research and the Russian Competitiveness Program of NRNU MEPhI (M.H.U.); the Ministry of Education, Science and Technological Development of Serbia; the Secretar\'{\i}a de Estado de Investigaci\'on, Desarrollo e Innovaci\'on and Programa Consolider-Ingenio 2010, Spain; the Swiss Funding Agencies (ETH Board, ETH Zurich, PSI, SNF, UniZH, Canton Zurich, and SER); the Ministry of Science and Technology, Taipei; the Thailand Center of Excellence in Physics, the Institute for the Promotion of Teaching Science and Technology of Thailand, Special Task Force for Activating Research and the National Science and Technology Development Agency of Thailand; the Scientific and Technical Research Council of Turkey, and Turkish Atomic Energy Authority; the National Academy of Sciences of Ukraine, and State Fund for Fundamental Researches, Ukraine; the Science and Technology Facilities Council, UK; the US Department of Energy, and the US National Science Foundation.
Individuals have received support from the Marie-Curie programme and the European Research Council and EPLANET (European Union); the Leventis Foundation; the A. P. Sloan Foundation; the Alexander von Humboldt Foundation; the Belgian Federal Science Policy Office; the Fonds pour la Formation \`a la Recherche dans l'Industrie et dans l'Agriculture (FRIA-Belgium); the Agentschap voor Innovatie door Wetenschap en Technologie (IWT-Belgium); the Ministry of Education, Youth and Sports (MEYS) of the Czech Republic; the Council of Science and Industrial Research, India; the HOMING PLUS programme of the Foundation for Polish Science, cofinanced from European Union, Regional Development Fund, the Mobility Plus programme of the Ministry of Science and Higher Education, the National Science Center (Poland), contracts Harmonia 2014/14/M/ST2/00428, Opus 2014/13/B/ST2/02543, 2014/15/B/ST2/03998, and 2015/19/B/ST2/02861, Sonata-bis 2012/07/E/ST2/01406; the Thalis and Aristeia programmes cofinanced by EU-ESF and the Greek NSRF; the National Priorities Research Program by Qatar National Research Fund; the Programa Clar\'in-COFUND del Principado de Asturias; the Rachadapisek Sompot Fund for Postdoctoral Fellowship, Chulalongkorn University and the Chulalongkorn Academic into Its 2nd Century Project Advancement Project (Thailand); and the Welch Foundation, contract C-1845.
\end{acknowledgments}
| {
"redpajama_set_name": "RedPajamaArXiv"
} | 6,264 |
package jp.fieldnotes.hatunatu.dao.dataset.types;
import jp.fieldnotes.hatunatu.api.ValueType;
import jp.fieldnotes.hatunatu.dao.dataset.ColumnType;
import jp.fieldnotes.hatunatu.dao.types.ValueTypes;
import java.math.BigDecimal;
import java.sql.Timestamp;
import java.sql.Types;
import java.util.Calendar;
import java.util.Map;
import java.util.concurrent.ConcurrentHashMap;
/**
* カラムの型を管理するクラスです。
*/
public class ColumnTypes {
/**
* 文字列用の {@link ColumnType}です。
*
* @see StringType
*/
public static final ColumnType STRING = new StringType();
/**
* トリムをしない文字列用の {@link ColumnType}です。
*
* @see StringType
*/
public static final ColumnType NOT_TRIM_STRING = new StringType(false);
/**
* 数値用の {@link ColumnType}です。
*
* @see BigDecimalType
*/
public static final ColumnType BIGDECIMAL = new BigDecimalType();
/**
* 日付用の {@link ColumnType}です。
*
* @see TimestampType
*/
public static final ColumnType TIMESTAMP = new TimestampType();
/**
* バイナリ用の {@link ColumnType}です。
*
* @see BinaryType
*/
public static final ColumnType BINARY = new BinaryType();
/**
* オブジェクト用の {@link ColumnType}です。
*
* @see ObjectType
*/
public static final ColumnType OBJECT = new ObjectType();
/**
* 論理値用の {@link ColumnType}です。
*
* @see BooleanType
*/
public static final ColumnType BOOLEAN = new BooleanType();
private static Map typesByClass = new ConcurrentHashMap(20);
private static Map typesBySqlType = new ConcurrentHashMap(20);
static {
registerColumnType(String.class, STRING);
registerColumnType(short.class, BIGDECIMAL);
registerColumnType(Short.class, BIGDECIMAL);
registerColumnType(int.class, BIGDECIMAL);
registerColumnType(Integer.class, BIGDECIMAL);
registerColumnType(long.class, BIGDECIMAL);
registerColumnType(Long.class, BIGDECIMAL);
registerColumnType(float.class, BIGDECIMAL);
registerColumnType(Float.class, BIGDECIMAL);
registerColumnType(double.class, BIGDECIMAL);
registerColumnType(Double.class, BIGDECIMAL);
registerColumnType(boolean.class, BOOLEAN);
registerColumnType(Boolean.class, BOOLEAN);
registerColumnType(BigDecimal.class, BIGDECIMAL);
registerColumnType(Timestamp.class, TIMESTAMP);
registerColumnType(java.sql.Date.class, TIMESTAMP);
registerColumnType(java.util.Date.class, TIMESTAMP);
registerColumnType(Calendar.class, TIMESTAMP);
registerColumnType(new byte[0].getClass(), BINARY);
registerColumnType(Types.TINYINT, BIGDECIMAL);
registerColumnType(Types.SMALLINT, BIGDECIMAL);
registerColumnType(Types.INTEGER, BIGDECIMAL);
registerColumnType(Types.BIGINT, BIGDECIMAL);
registerColumnType(Types.REAL, BIGDECIMAL);
registerColumnType(Types.FLOAT, BIGDECIMAL);
registerColumnType(Types.DOUBLE, BIGDECIMAL);
registerColumnType(Types.DECIMAL, BIGDECIMAL);
registerColumnType(Types.NUMERIC, BIGDECIMAL);
registerColumnType(Types.BOOLEAN, BOOLEAN);
registerColumnType(Types.DATE, TIMESTAMP);
registerColumnType(Types.TIME, TIMESTAMP);
registerColumnType(Types.TIMESTAMP, TIMESTAMP);
registerColumnType(Types.BINARY, BINARY);
registerColumnType(Types.VARBINARY, BINARY);
registerColumnType(Types.LONGVARBINARY, BINARY);
registerColumnType(Types.CHAR, STRING);
registerColumnType(Types.LONGVARCHAR, STRING);
registerColumnType(Types.VARCHAR, STRING);
}
/**
* インスタンスを構築します。
*/
protected ColumnTypes() {
}
/**
* S2JDBC用の型を返します。
*
* @param type 型
* @return JDBC用の型
* @see ValueTypes
*/
public static ValueType getValueType(int type) {
switch (type) {
case Types.TINYINT:
case Types.SMALLINT:
case Types.INTEGER:
case Types.BIGINT:
case Types.REAL:
case Types.FLOAT:
case Types.DOUBLE:
case Types.DECIMAL:
case Types.NUMERIC:
return ValueTypes.BIGDECIMAL;
case Types.BOOLEAN:
return ValueTypes.BOOLEAN;
case Types.DATE:
case Types.TIME:
case Types.TIMESTAMP:
return ValueTypes.TIMESTAMP;
case Types.BINARY:
case Types.VARBINARY:
case Types.LONGVARBINARY:
return ValueTypes.BINARY;
case Types.CHAR:
case Types.LONGVARCHAR:
case Types.VARCHAR:
return ValueTypes.STRING;
default:
return ValueTypes.OBJECT;
}
}
/**
* カラムの型を返します。
*
* @param type 型
* @return カラムの型
*/
public static ColumnType getColumnType(int type) {
ColumnType columnType = (ColumnType) typesBySqlType.get(new Integer(
type));
if (columnType != null) {
return columnType;
}
return OBJECT;
}
/**
* カラムの型を返します。
*
* @param value 値
* @return カラムの型
*/
public static ColumnType getColumnType(Object value) {
if (value == null) {
return OBJECT;
}
return getColumnType(value.getClass());
}
/**
* カラムの型を返します。
*
* @param clazz クラス
* @return カラムの型
*/
public static ColumnType getColumnType(Class clazz) {
ColumnType columnType = (ColumnType) typesByClass.get(clazz);
if (columnType != null) {
return columnType;
}
return OBJECT;
}
/**
* カラムの型を登録します。
*
* @param sqlType SQL型
* @param columnType カラムの型
* @return 指定されたSQL型に関連した以前のカラムの型。カラムの型にマッピングなかった場合には<code>null</code>
*/
public static ColumnType registerColumnType(int sqlType,
ColumnType columnType) {
return (ColumnType) typesBySqlType
.put(new Integer(sqlType), columnType);
}
/**
* カラムの型を登録します。
*
* @param clazz クラス
* @param columnType カラムの型
* @return 指定されたクラスに関連した以前のカラムの型。カラムの型にマッピングなかった場合には<code>null</code>
*/
public static ColumnType registerColumnType(Class clazz,
ColumnType columnType) {
return (ColumnType) typesByClass.put(clazz, columnType);
}
}
| {
"redpajama_set_name": "RedPajamaGithub"
} | 4,534 |
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Helena Parmask
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THE 2018 INC. 5000 LIST
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Scoro is the most comprehensive business management solution for creative and professional services. It helps to streamline work and eliminate routine tasks to ensure a business runs as smoothly and efficiently as possible – from sales right through to billing. There's a team of 60 highly motivated people working in our offices across Europe and US, dedicated to helping companies bring structure to their work.
Helena is part of the Marketing Team at Scoro since 2017. She is well-versed in the world of advertising, digital projects management, and time management, having worked in both in-house and agency environments. When Helena is not at work you will often find her travelling, hiking, jogging, and walking her spaniel Ruben.
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"redpajama_set_name": "RedPajamaCommonCrawl"
} | 4,802 |
Dads Play Big Role in Parenting
Back in the '60s when girls' sport were taboo, my dad taught me how to throw a perfect spiral, pitch a baseball and shoot a basket. Each time he tossed the ball to my brother, he also threw once to me. He made sure to hit each of us an equal number of pop ups to field. He showed me how to hold a baseball glove, pump up a basketball and take a fish off the hook.
Papa Mac passes on tradition
Like the Pied Piper, as soon as kids saw my dad arrive home from his teaching job, they lined up for a turn at bat. Soon he was pitching whiffle balls to the entire neighborhood. Instead of grass in our backyard, we had permanent dirt-patch bases, a diamond in the rough, the Field of Dreams for an entire generation.
Even though I never saw any other fathers in the yard shooting hoops with their daughters, I never thought it odd. Chasing grounders, running passing patterns and learning the baseline drive with my dad seemed as natural as breathing. After all, he was a coach and I was an athlete. So what if it took the rest of the society a few decades to catch up.
Today with the acceptance of girls' sports and working moms the norm, dads' coaching daughters is no longer an anomaly. The Women's Rights Movement also liberated men to assume a greater hands-on role in fatherhood.
Today's dads are free to coach Little League AND girls' soccer, to build camp fires, make tree forts, piece together Legos, to change diapers, give baths, bandage cuts. They can also bake birthday cakes, read Good Night Moon, cook bœuf bourguignon and grill burgers.
French dad at 1st Final Four
Throughout our children's youth, my husband worked the score table, drove the van for our daughter and son's teams and prepared gourmet meals for all of us. Gérald never batted an eye about running a printing business during the day, and then wearing the apron at night. Though it may have been a typical behavior for a Frenchman, he paid the bills, balanced the budget and brought home the bacon, proud to be a family man.
Just as I witnessed my dad in multiple roles – caring teacher, inspiring coach, loyal husband -my children saw their father as tough and tender, demanding and nuturing, competitive and compassionate.
Kids raised in families with ball-playing moms and story-reading dads make for a balanced, healthy, wholesome childhood. Whether organizing car pools, building sand castles or playing catch, adults investing time in youth yields the greatest dividends. Worth all the gold in the world !
Bold, Buff and Beautiful – Rugby Girls Rock
No one who knows me believes that my first love was not basketball, but football, American football (not what the rest of the world calls football, and we call soccer). I longed to play the game reserved for boys only.
The greatest thrill of my athletic career was not breaking scoring records or winning basketball championships, but playing right offensive end in our powder puff football game the night before homecoming 1974.
In a tied ball game, with 58 seconds left on the clock, my BF Peggy "Super Crunch" Dietz and her defensive line stopped the ball at our 2-yard line. Another good buddy, QB Chrissie "Iron Arm" hit me with a perfect spiral on the sideline. I ran 98 yards to victory, spiked the ball in the end zone and danced under the stars.
For one night I felt invincible in the glory of Friday Night Lights.
So naturally, thirty-five years later, no one cheered louder than me when my niece Hannah, started playing rugby. Rugby? Yup, you betcha. Cute blondes in the Land of 10,000 Lakes, getting down and dirty, hitting hard, laughing loud, locking arms, and building bonds.
Hannah joined the team her junior year, learned the rules on the fly and found out, oh yeah, girls hit hard, too. Long-legged Hannah became the girl they throw in the air as the Robbinsdale Armstrong defending state champions returned for a repeat.
jumping for the ball
As a grassroots club team, not yet recognized as a high school sport, the no-glory girls fought for recognition, raised their own money for red and blue uniforms, and traveled in family vans to compete in tournaments.
Rugby is the ultimate team sport. Last year's team graduated 13 of 15 starters. "Your bench has to be as good as what you have on the field," Coach Hanson said. And they were. Last week, Armstrong girls rugby entered the tournament undefeated and claimed the crown.
Tim Nolan's Robbinsdale girls'rugby club, started in 2004, was ahead of the game and like Sterling High School girls' basketball in the 70's, developed into a state powerhouse. In 1977, my sister, Karen, played for Sterling in first state girls high school championship. Now Mom and daughter can boast of being state champs in the infancy of their respective sports.
But what really tickled me pink was the fan club. Proud rugby dads with painted faces and red-tinted hair, cheered on daughters who loved to tackle.
Hannah bejeweled in a purple gown, gossamer slippers and hair coiffed in a French braid, was a Prom night princess one weekend and hit the dirt wearing a mouth guard and headgear the next.
It's a win-win situation. Bold, buff and beautiful! Today girls can paint nails, lead cheers and body slam. Too cool!
First Doctor in the Family
I slouched through school feeling ashamed with three strikes against me: tall, smart and athletic. Not cool. In the 70', girls pursuing advanced careers in sports or academics were scorned minorities. Fast-forward four decades. Our Franco-American daughter, Nathalie stood proud, set shot blocking records in college and aced medical boards, playing the game her way.
Ironically, I, who grew up with hospital phobia and feared white coats, gave birth to a doctor. Yet in retrospect, I saw the makings of a medicine woman early on. As a precocious child, Nat spoke two languages, read books at the dinner table and excelled in her studies. As a youngster, she had an innate ability to sense others' pain. She held her great grandpa's hand when his footsteps faltered from Parkinson disease and leaned her head into Great Grandma's shoulder to make her feel special. She distracted her little brother when he threw tantrums and settled squabbles between cousins.
Fascinated with body parts and blood cells, she insisted we read « The Way Your Body Works » over and over again in childhood. While I cringed at the word science and the sight of blood, she loved chemistry and biology, mixing chemicals and dissecting animals.
She paved her own path sans doctors in the family on either side. Born of blue collar and modest teachers' families, she jumped social classes to become a doctor of medicine, following her dream 4,000 miles away from home.
I marveled at her persistence; the greater obstacle, the harder she grit her teeth. The night her college team got knocked out of the conference championship, she mourned the end of her basketball career. Yet hours later, she cracked open books and crammed for the biochem exam scheduled for 8 am the next day. She survived four years of boot camp for doctor wannabees in the grueling med school program enduring thirty-hour shifts and studying every free second. Med school is intense from the get go. …First day meet body buddies, second day meet body – as in cadaver.
Nat's medical school graduation
The afternoon of Nat's graduation from the University of Minnesota Medical School, her dad and I stayed up late in Switzerland to watch live on webcam. When they announced, « Doctor Nathalie Lechault » and she stepped forward to be hooded, my throat tightened. I blinked back bittersweet tears filled with awe.
In 2011, nearly half of the 238 students in Nathalie's graduating class were female. From the Susan B. Anthonys and suffragettes of the late 1800s, to the Rosa Parks of the civil rights, to the Gloria Steinems of the liberation movement – hats off to all the women, who dared to think outside the box, who dreamed big, who helped give birth to our alpha daughters of the 21st century.
Senseless Racism, a songwriter's opinion
The inspiration of children from around the world challenges each of us to work together to create a better world.
Etre né quelque part, a song by French singer, poet and guitarist, Maxime Leforestier, loosely translated in English shows the nonsense of racism.
On choisit pas ses parents, We don't choose our parents
on choisit pas sa famille We don't choose our family
On choisit pas non plus We don't choose
les trottoirs de Manille the sidewalks of Manila,
De Paris ou d'Alger or Paris, or Algiers either,
Pour apprendre à marcher To learn to walk
Etre né quelque part The place where one is born
Pour celui qui est né For whoever is born
C'est toujours un hazard is always random chance
Nom'inqwando yes qxag iqwahasa
Y a des oiseaux de basse cour et There are domesticated birds and
des oiseaux de passage migratory birds
Ils savent où sont leur nids, they always find their nests
quand ils rentrent de voyage whether they return from travel
Ou qu'ils restent chez eux Or they stay home
Ils savent où sont leurs œufs they know where their eggs lay
C'est partir quand on veut, Means leaving when we choose
Revenir quand on part Coming back after leaving
Est-ce que les gens naissent Are people born equal
Egaux en droits
A l'endroit Wherever they were born
Où ils naissent
Est-ce que les gens naissent Are people born
Pareils ou pas The same or not
Je suis né quelque part I was born somewhere
Laissez moi ce repère Leave me that reference point
Ou je perds la mémoire Or I will lose my identity
Nom'inqwando yes qxag iqwaha.sa
Education, Racism, Football, and Mama
If you want to capture boys' attention, talk football (at least in Europe). Paul Canoville, who helped break the color barrier in British soccer spoke at the International School of Geneva about racism in sport to tie in with United Nations Day of Tolerance Nov. 17, 2010 and March 21st International Day for the Elimination of Racial Discrimination.
« Mama said, 'get an education ! » Canoville said in a high pitched voice with a Caribbean accident, wiggling his hips imitating his mama.
Chelsea's player Paul Canoville
« Don't worry Mama, football gonna take care of me. » said the first black man to play for Chelsea in 1981, who still remembers that pain of racial abuse when even his own fans called him animal names.
« My Mama, from a poor Caribbean family, came to England alone and dreamed of becoming a nurse, but never had the chance to become educated. She worked hard all her life. She didn't care about football ; she wanted me to go to school.»
When Canoville's career ended to a knee injury at age 25, no one took care of him, especially not football. After a downward spiral of drug addiction, street life and jail time, he turned his life around. His autobiography, Black and Blue received the best British sport book award in 2009.
After Canoville's visit to our campus, three of my freshman students, a a tall dark-haired Italian basketball player, a blond blue-eyed Austrian footballer, and a young Swiss tennis man wrote him this letter.
Dear Mr. Canoville
Thank you for coming to tell us a story that has the power to make people change their way of thinking about racism. In school we always learn about the history of racism, what it is about, what it provokes, but we have never had a witness talk to us about his experiences. It is a privilege that students will cherish. Most kids are sports fans, and many would love to play professional football later in life. The opportunity to hear a famous footballer sharing important views so freely is fantastic. It has even more of an impact when you are funny. When you tell your life altering stories and describe the appalling behavior you confronted, you showcased your great sense of humor and positive way of seeing things. A person will always face challenging times, but if you fight for what you believe in, no matter how unfair things seem to be, you can do just about anything. You taught us this. We would love for you to come back and pass your experiences and knowledge on to other generations of students.
Canoville's final words to our students were "Always have a back up plan. Get an education. And listen to mama. Mama knows best!"
Here's to all the mamas around the world, making sacrifices everyday, giving children a better chance through the opportunity of education.
Anne Frank, Miep Gies, Erin Gruwell –Solitary Voices Speak Out To Make a Difference
We hear the stories of great male leaders discovering new lands, leading nations to battle, defending human rights, but what about everyday valiant acts by ordinary women. "Courage doesn't always roar. "
"You are not defined by this moment in time
You are not defined by what has happened to you
It is the way that your choose to respond
That matters what you do
And what you decide to do
Courage is not the absence of fear
But a powerful choice we make…"
From Courage Doesn't Always Roar By Paula Fox
During WWII, a soft-spoken, young secretary helped hide her boss's Jewish family in an attic in Amsterdam. When the Gestapo discovered the Frank family, Miep Gies risked her life again, by hiding Anne's diary (written between June 12, 1942 – August 1, 1944) from authorities. In 1947, Otto Frank, the only family member who survived the concentration camp, published Anne Frank Diary of A Young Girl, which sold 31 million copies, was translated into 67 languages, and has been studied worldwide including my English class at the International School of Geneva.
Miep Gies Feb. 15, 1909 – Jan. 11, 2010
In my class, I continued my lesson about Dr. Boswell's pre Civil War quilt codes guiding slaves to freedom on the Underground Railroad with another exercise to show the bravery and ingenuity of everyday people.
Franco-Suisse Hotel Arbez
A half hour from our campus, the Franco- Swiss Hotel Arbez at La Cure sits on the borderline dividing the two countries. During WWII, the owners hid British and American soldiers and Jewish civilians from the Nazis. The bottom of the staircase lies in German Occupied France; the top of the stairs "the Hideaway," a second floor room, is on Swiss territory. Refugees disappeared into the mountains on the neutral Swiss side.
After showing examples messages stitched in quilts, I asked my students to sketch symbols that could help map the route for imaginary refugees escaping from our school to the French border at La Cure.
Over a half-century later, another daring woman, Erin Gruwell, inspired 150 disillusioned tough kids from broken homes and street gangs, to use writing to bring about change. The Freedom Writer's Diary, published in 1999, was the true story her freshman English class at Wilson High School in Long Beach, California. In 2007 the movie Freedom Writers was released, and the Freedom Writer's Foundation website was established. http://www.freedomwritersfoundation.org/site/
After reading Anne Frank, Miss Gruwell's class then raised funds to fly Miep Gies over from the Netherlands to speak at their school. After Miep speech,
Marcus, a husky, former gang member, once living in the street, raised his hand and stated, "You are my hero!"
"Oh no, young man, I am not a hero," she said. "You are the heroes in your own life story – I just did the right thing at the right time."
Single voices. Small steps. Soft whispers. Subtle strength. Simple women of courage stand out.
« Previous 1 … 15 16 17 18 19 20 21 22 Next » | {
"redpajama_set_name": "RedPajamaCommonCrawl"
} | 3,948 |
package javarepl.console;
import javarepl.completion.CompletionResult;
import javarepl.rendering.ExpressionTemplate;
public interface Console {
ConsoleResult execute(String expression);
CompletionResult completion(String expression);
ExpressionTemplate template(String expression);
ConsoleStatus status();
ConsoleHistory history();
void start();
void shutdown();
}
| {
"redpajama_set_name": "RedPajamaGithub"
} | 4,716 |
{"url":"https:\/\/www.popflock.com\/learn?s=Modern_Arabic_mathematical_notation","text":"Modern Arabic Mathematical Notation\nGet Modern Arabic Mathematical Notation essential facts below. View Videos or join the Modern Arabic Mathematical Notation discussion. Add Modern Arabic Mathematical Notation to your PopFlock.com topic list for future reference or share this resource on social media.\nModern Arabic Mathematical Notation\n\nModern Arabic mathematical notation is a mathematical notation based on the Arabic script, used especially at pre-university levels of education. Its form is mostly derived from Western notation, but has some notable features that set it apart from its Western counterpart. The most remarkable of those features is the fact that it is written from right to left following the normal direction of the Arabic script. Other differences include the replacement of the Latin alphabet letters for symbols with Arabic letters and the use of Arabic names for functions and relations.\n\n## Features\n\n\u2022 It is written from right to left following the normal direction of the Arabic script. Other differences include the replacement of the Latin alphabet letters for symbols with Arabic letters and the use of Arabic names for functions and relations.\n\u2022 The notation exhibits one of the very few remaining vestiges of non-dotted Arabic scripts, as dots over and under letters (i'jam) are usually omitted.\n\u2022 Letter cursivity (connectedness) of Arabic is also taken advantage of, in a few cases, to define variables using more than one letter. The most widespread example of this kind of usage is the canonical symbol for the radius of a circle (Arabic pronunciation:\u00a0[n?q]), which is written using the two letters n?n and q?f. When variable names are juxtaposed (as when expressing multiplication) they are written non-cursively.\n\n## Variations\n\nNotation differs slightly from region to another. In tertiary education, most regions use the Western notation. The notation mainly differs in numeral system used, and in mathematical symbol used.\n\n### Numeral systems\n\nThere are three numeral systems used in right to left mathematical notation.\n\n European(descended from Western Arabic) 0 1 2 3 4 5 6 7 8 9 Arabic-Indic (Eastern Arabic) ?\u200e ?\u200e ?\u200e ?\u200e ?\u200e ?\u200e ?\u200e ?\u200e ?\u200e ?\u200e Perso-Arabic variant ? ? ? ? ? ? ? ? ? ? Urdu variant\n\nWritten numerals are arranged with their lowest-value digit to the right, with higher value positions added to the left. That is identical to the arrangement used by Western texts using Hindu-Arabic numerals even though Arabic script is read from right to left. The symbols \"?\" and \"?\" may be used as the decimal mark and the thousands separator respectively when writing with Eastern Arabic numerals, e.g. ?3.14159265358, ?1,000,000,000. Negative signs are written to the left of magnitudes, e.g. ?--3. In-line fractions are written with the numerator and denominator on the left and right of the fraction slash respectively, e.g. ?\/?2\/7.\n\n### Mirrored Latin symbols\n\nSometimes, symbols used in Arabic mathematical notation differ according to the region:\n\nLatin Arabic Persian x4 \u200e [a] \u200e [b]\n\u2022 ^a ?n?n-h-?alif is derived from the first three letters of Arabic nih?ya \"limit\".\n\u2022 ^b ?add is Persian for \"limit\".\n\nSometimes, mirrored Latin symbols are used in Arabic mathematical notation (especially in western Arabic regions):\n\nLatin Arabic ?\u202d?\u202c?\u200e[c] 3\u202d?\u202c?\u200e\n\nma?m means \"sum\" in Arabic.\n\nHowever, in Iran, usually Latin symbols are used.\n\n## Examples\n\n### Mathematical letters\n\nLatin Arabic Notes\n${\\displaystyle a}$ ? From the Arabic letter ??alif; a and ??alif are the first letters of the Latin alphabet and the Arabic alphabet's ?abjad? sequence respectively\n${\\displaystyle b}$ ? A dotless ?b; b and ?b are the second letters of the Latin alphabet and the ?abjad? sequence respectively\n${\\displaystyle c}$ From the initial form of ?, or that of a dotless ?j?m; c and ?j?m are the third letters of the Latin alphabet and the ?abjad? sequence respectively\n${\\displaystyle d}$ ? From the Arabic letter ?d?l; d and ?d?l are the fourth letters of the Latin alphabet and the ?abjad? sequence respectively\n${\\displaystyle x}$ ? From the Arabic letter ?s?n. It is contested that the usage of Latin x in maths is derived from the first letter ?n (without its dots) of the Arabic word ?ay?(un) [?aj?(un)], meaning thing.[1] (X was used in old Spanish for the sound \/?\/). However, according to others there is no historical evidence for this.[2][3]\n${\\displaystyle y}$ ? From the Arabic letter ?d\n${\\displaystyle z}$ ? From the Arabic letter ??ayn\n\n### Mathematical constants and units\n\nDescription Latin Arabic Notes\nEuler's number ${\\displaystyle e}$ ? Initial form of the Arabic letter ?h. Both Latin letter e and Arabic letter ?h are descendants of Phoenician letter h?.\nimaginary unit ${\\displaystyle i}$ ? From ?t, which is in turn derived from the first letter of the second word of ? wa?da?un taliyya \"imaginary unit\"\npi ${\\displaystyle \\pi }$ ? From ?; also ${\\displaystyle \\pi }$ in some regions\nradius ${\\displaystyle r}$ From ?n?n followed by a dotless ?q?f, which is in turn derived from nu?fu l-qu?r \"radius\"\nkilogram kg From k?f-j?m-m?m. In some regions alternative symbols like ( k?f-?ayn) or ( k?f-l?m-?ayn) are used. All three abbreviations are derived from k?lr?m \"kilogram\" and its variant spellings.\ngram g From j?m-m?m, which is in turn derived from ?jr?m, a variant spelling of ??r?m \"gram\"\nmeter m ? From ?m?m, which is in turn derived from mitr \"meter\"\ncentimeter cm From s?n-m?m, which is in turn derived from ?\u200e \"centimeter\"\nmillimeter mm From m?m-m?m, which is in turn derived from mill?mitr \"millimeter\"\nkilometer km From k?f-m?m; also ( k?f-l?m-m?m) in some regions; both are derived from ?k?l?mitr \"kilometer\".\nsecond s ? From ?, which is in turn derived from niya \"second\"\nminute min ? From ?d?l?, which is in turn derived from daq?qa \"minute\"; also ( ?, i.e. dotless ?q?f) in some regions\nhour h ? From ?s?n?, which is in turn derived from ?sa \"hour\"\nkilometer per hour km\/h \/? From the symbols for kilometer and hour\ndegree Celsius \u00b0C \u00b0? From ?s?n, which is in turn derived from the second word of ? ?darajat s?lss \"degree Celsius\"; also ( \u00b0?) from ?m?m?, which is in turn derived from the first letter of the third word of ? \u200e \"degree centigrade\"\ndegree Fahrenheit \u00b0F \u00b0? From ?f, which is in turn derived from the second word of ? darajat fahranh?yt \"degree Fahrenheit\"\nmillimeters of mercury mmHg \u200c? From \u200c?m?m-m?m zayn, which is in turn derived from the initial letters of the words ?\u200e \"millimeters of mercury\"\n\u00c5ngstr\u00f6m \u00c5 From ?alif with hamzah and ring above, which is in turn derived from the first letter of \"\u00c5ngstr\u00f6m\", variously spelled \u200e or\n\n### Sets and number systems\n\nDescription Latin Arabic Notes\nNatural numbers ${\\displaystyle \\mathbb {N} }$ ? From ?, which is in turn derived from the first letter of the second word of ?adadun ?abiyyun \"natural number\"\nIntegers ${\\displaystyle \\mathbb {Z} }$ ? From ?d, which is in turn derived from the first letter of the second word of ??adadun ?aun \"integer\"\nRational numbers ${\\displaystyle \\mathbb {Q} }$ ? From ?n?n, which is in turn derived from the first letter of ?nisba \"ratio\"\nReal numbers ${\\displaystyle \\mathbb {R} }$ ? From ?, which is in turn derived from the first letter of the second word of ?adadun ?aq?qiyyun \"real number\"\nImaginary numbers ${\\displaystyle \\mathbb {I} }$ ? From ?t, which is in turn derived from the first letter of the second word of ?adadun taliyyun \"imaginary number\"\nComplex numbers ${\\displaystyle \\mathbb {C} }$ ? From ?m?m, which is in turn derived from the first letter of the second word of ??adadun markabun \"complex number\"\nEmpty set ${\\displaystyle \\varnothing }$ ${\\displaystyle \\varnothing }$ ?\nIs an element of ${\\displaystyle \\in }$ ${\\displaystyle \\ni }$ ? A mirrored ?\nSubset ${\\displaystyle \\subset }$ ${\\displaystyle \\supset }$ ? A mirrored ?\nSuperset ${\\displaystyle \\supset }$ ${\\displaystyle \\subset }$ ? A mirrored ?\nUniversal set ${\\displaystyle \\mathbf {S} }$ ? From ?n, which is in turn derived from the first letter of the second word of majmatun mila \"universal set\"\n\n### Arithmetic and algebra\n\nDescription Latin Arabic Notes\nPercent % ? e.g. 100% \"?\u200e\"\nPermille ? ? ? is an Arabic equivalent of the per ten thousand sign ?.\nIs proportional to ${\\displaystyle \\propto }$ ? A mirrored ?\nn th root ${\\displaystyle {\\sqrt[{n}]{\\,\\,\\,}}}$ ?\u202d?\u202c ?\u200e is a dotless ?n?n while ? is a mirrored radical sign ?\nLogarithm ${\\displaystyle \\log }$ From l?m-w?w, which is in turn derived from lr?tm \"logarithm\"\nLogarithm to base b ${\\displaystyle \\log _{b}}$ ?\nNatural logarithm ${\\displaystyle \\ln }$ ? From the symbols of logarithm and Euler's number\nSummation ${\\displaystyle \\sum }$ m?m-medial form of j?m is derived from the first two letters of majm \"sum\"; also (?, a mirrored summation sign ?) in some regions\nProduct ${\\displaystyle \\prod }$ From j?m-l. The Arabic word for \"product\" is ? jadun. Also ${\\displaystyle \\prod }$ in some regions.\nFactorial ${\\displaystyle n!}$ ? Also ( ?!) in some regions\nPermutations ${\\displaystyle ^{n}\\mathbf {P} _{r}}$ ??? Also ( ?( ?)) is used in some regions as ${\\displaystyle \\mathbf {P} (n,r)}$\nCombinations ${\\displaystyle ^{n}\\mathbf {C} _{k}}$ ??? Also ( ?( ?)) is used in some regions as ${\\displaystyle \\mathbf {C} (n,k)}$ and (?\n?\n) as the binomial coefficient ${\\displaystyle n \\choose k}$\n\n### Trigonometric and hyperbolic functions\n\n#### Trigonometric functions\n\nDescription Latin Arabic Notes\nSine ${\\displaystyle \\sin }$ from (i.e. dotless ?j?m)-?alif; also ( j?m-b) is used in some regions (e.g. Syria); Arabic for \"sine\" is jayb\nCosine ${\\displaystyle \\cos }$ from (i.e. dotless ?j?m)-t-?alif; also ( t-j?m-b) is used in some regions (e.g. Syria); Arabic for \"cosine\" is ?\nTangent ${\\displaystyle \\tan }$ from (i.e. dotless ?)-?alif; also ( -l?m) is used in some regions (e.g. Syria); Arabic for \"tangent\" is ?ill\nCotangent ${\\displaystyle \\cot }$ from (i.e. dotless ?)-t-?alif; also ( t--l?m) is used in some regions (e.g. Syria); Arabic for \"cotangent\" is ?\nSecant ${\\displaystyle \\sec }$ from \u200e dotless ?q?f-?alif; Arabic for \"secant\" is ?\nCosecant ${\\displaystyle \\csc }$ from \u200e dotless ?q?f-t-?alif; Arabic for \"cosecant\" is ? ?\n\n#### Hyperbolic functions\n\nThe letter ( ? zayn, from the first letter of the second word of ? \u200e \"hyperbolic function\") is added to the end of trigonometric functions to express hyperbolic functions. This is similar to the way ${\\displaystyle \\operatorname {h} }$ is added to the end of trigonometric functions in Latin-based notation.\n\n Description Latin Arabic Hyperbolic sine Hyperbolic cosine Hyperbolic tangent Hyperbolic cotangent Hyperbolic secant Hyperbolic cosecant ${\\displaystyle \\sinh }$ ${\\displaystyle \\cosh }$ ${\\displaystyle \\tanh }$ ${\\displaystyle \\coth }$ ${\\displaystyle \\operatorname {sech} }$ ${\\displaystyle \\operatorname {csch} }$ \u200e ?\u200e \u200e ?\u200e \u200e ?\u200e\n\n#### Inverse trigonometric functions\n\nFor inverse trigonometric functions, the superscript -? in Arabic notation is similar in usage to the superscript ${\\displaystyle -1}$ in Latin-based notation.\n\n Description Latin Arabic Inverse sine Inverse cosine Inverse tangent Inverse cotangent Inverse secant Inverse cosecant ${\\displaystyle \\sin ^{-1}}$ ${\\displaystyle \\cos ^{-1}}$ ${\\displaystyle \\tan ^{-1}}$ ${\\displaystyle \\cot ^{-1}}$ ${\\displaystyle \\sec ^{-1}}$ ${\\displaystyle \\csc ^{-1}}$ -?\u200e -?\u200e -?\u200e -?\u200e -?\u200e -?\u200e\n\n#### Inverse hyperbolic functions\n\n Description Latin Arabic Inverse hyperbolic sine Inverse hyperbolic cosine Inverse hyperbolic tangent Inverse hyperbolic cotangent Inverse hyperbolic secant Inverse hyperbolic cosecant ${\\displaystyle \\sinh ^{-1}}$ ${\\displaystyle \\cosh ^{-1}}$ ${\\displaystyle \\tanh ^{-1}}$ ${\\displaystyle \\coth ^{-1}}$ ${\\displaystyle \\operatorname {sech} ^{-1}}$ ${\\displaystyle \\operatorname {csch} ^{-1}}$ -?\u200e ?-?\u200e -?\u200e ?-?\u200e -?\u200e ?-?\u200e\n\n### Calculus\n\nDescription Latin Arabic Notes\nLimit ${\\displaystyle \\lim }$ ? ?n?n-h-?alif is derived from the first three letters of Arabic nih?ya \"limit\"\nfunction ${\\displaystyle \\mathbf {f} (x)}$ ?(?) ?d?l is derived from the first letter of ?\u200e \"function\". Also called ?\u200e, \u200e for short, in some regions.\nderivatives ${\\displaystyle \\mathbf {f'} (x),{\\dfrac {dy}{dx}},{\\dfrac {d^{2}y}{dx^{2}}},{\\dfrac {\\partial {y}}{\\partial {x}}}}$ ?(?)? ?\u200c?\/ ?\u200c? ? ???\/ ?\u200c?? ? ??\/?? is a mirrored prime ? while ? is an Arabic comma. The ? signs should be mirrored: ?.\nIntegrals ${\\displaystyle \\int {},\\iint {},\\iiint {},\\oint {}}$ ? ?? ?? ?? Mirrored ?, ?, ? and ?\n\n### Complex analysis\n\nLatin Arabic\n${\\displaystyle z=x+iy=r(\\cos {\\varphi }+i\\sin {\\varphi })=re^{i\\varphi }=r\\angle {\\varphi }}$\n? = ? + ? ? = ?( ? + ? ?) = ? ??\u200c? = ???","date":"2021-06-17 17:58:14","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 72, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 0, \"mathjax_display_tex\": 0, \"mathjax_asciimath\": 1, \"img_math\": 0, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.8780988454818726, \"perplexity\": 5041.562471193458}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2021-25\/segments\/1623487630518.38\/warc\/CC-MAIN-20210617162149-20210617192149-00172.warc.gz\"}"} | null | null |
Q: Изучение AWT Есть ли смысл (практический, в первую очередь) в изучении AWT? Иначе: насколько востребованы в настоящее время знание его и навыки работы?
A: AWT не кроссплатформенна, да и не универсальна. Юзайте Swing. Для изучения идеальна книга Г.Шилдт "Swing".
Успехов :)
A: Естественно смысл есть т.к. swing пошла после awt, но глубоко вникать нет необходимости.
Вообщем ИМХО для самообразования и лучшего понимания нужно пробежаться, зацикливаться на ней 100% не стоит
A: AWT напрямую вызвает более низкоуровневую нативную подпрограмму, которая и создает компоненты. Другими словами, GUI программа, написанная с использованием AWT, выглядит как родное приложение Microsoft Windows, будучи запущенной на Windows, и в то же время как родное приложение Apple Macintosh, будучи запущенным на Mac, и т. д.. Однако, некоторым разработчикам не нравится эта модель, потому что они предпочитают, чтобы их приложения выглядели одинаково на всех платформах.
Swing обеспечивает возможность использования либо системного «look and feel», который использует родной «look and feel» платформы, либо кросс-платформенный внешний вид («Java Look and Feel»), который выглядят одинаково на всех платформах. Тем не менее, Swing использует AWT для взаимодействия с родной оконной системой.
Рекомендую прочитать первую главу этой книги и вы всё поймёте, займёт мин 30 -1ч, написано довольно интересно! ;) | {
"redpajama_set_name": "RedPajamaStackExchange"
} | 2,119 |
{"url":"https:\/\/socratic.org\/questions\/what-does-the-coefficients-a-b-c-and-d-to-the-graph-y-d-pm-a-cos-b-x-pm-c","text":"# What does the coefficients A, B, C, and D to the graph y=D \\pm A \\cos(B(x \\pm C))?\n\nDec 6, 2014\n\nThe general form of the cosine function can be written as\n\n$y = A \\cdot \\cos \\left(B x \\pm C\\right) \\pm D$, where\n\n$| A |$ - amplitude;\n$B$ - cycles from $0$ to $2 \\pi$ -> $p e r i o d = \\frac{2 \\pi}{B}$;\n$C$ - horizontal shift (known as phase shift when $B$ = 1);\n$D$ - vertical shift (displacement);\n\n$A$ affects the graph's amplitude, or half the distance betwen the maximum and minimum values of the function. this means that increasing $A$ will vertically stretch the graph, while decreasing $A$ will vertically shrink the graph.\n\n$B$ affects the function's period. SInce the cosine's period is $\\frac{2 \\pi}{B}$, a value of $0 < B < 1$ will cause the period to be greater than $2 \\pi$, which will stretch the graph horizontally.\n\nIf $B$ is greater than $1$. the period will be less than $2 \\pi$, so the graph will shrink horizontally. A good example of these is\n\nhttp:\/\/www.regentsprep.org\/regents\/math\/algtrig\/att7\/sinusoidal.htm\n\nVertical and horizontal shifts, $D$ and $C$, are pretty straightforward, these values only affecting the graph's vertical and horizontal positions, not its shape.\n\nHere's a good example of vertical and horizontal shifts:\n\nhttp:\/\/www.sparknotes.com\/math\/trigonometry\/graphs\/section3.rhtml","date":"2019-10-18 21:05:10","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 21, \"mathjax_inline_tex\": 1, \"mathjax_display_tex\": 0, \"mathjax_asciimath\": 1, \"img_math\": 0, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.7907270789146423, \"perplexity\": 598.8024750722501}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2019-43\/segments\/1570986684854.67\/warc\/CC-MAIN-20191018204336-20191018231836-00080.warc.gz\"}"} | null | null |
{"url":"https:\/\/www.mattwetmore.me\/posts\/parsing-combinators-with-parser-combinators","text":"Matt Wetmore\n\n# Parsing the untyped $\\lambda$-calculus with Parsec\n\nThe book Types and Programming Languages (briefly, TAPL) is a popular introduction to type systems and programming language theory. Starting with the untyped $\\lambda$-calculus, TAPL walks the reader through the construction of a simple expression-based language, focusing on type-checking and evaluation. One of the first exercises is an evaluator for the untyped $\\lambda$-calculus, in OCaml.\n\nI\u2019ve been working through the book in Haskell, which involves a pretty straightforward transcription from OCaml to Haskell. While the book gives an implementation of the evaluator, it doesn\u2019t include any discussion of parsing $\\lambda$-expressions such as $\\lambda x.\\lambda y.x\\;y$. Instead, to play around with the evaluator you must pass it an encoding of the term. That\u2019s a real hassle, so let\u2019s build a parser for such expressions.\n\nThe heavy lifting for this parser comes courtesy of the Haskell library Parsec. Parsec provides a monadic parsing system, which along with do notation provides a nice DSL for parsing. First, let\u2019s import what we need:\n\nimport Text.Parsec\nimport Text.Parsec.Combinator (between, sepBy1, chainr1)\nimport Data.List (elemIndex)\n\n\nIn TAPL, the format for encoding $\\lambda$-terms is prescribed. The usual grammar for $\\lambda$-terms is\n\n$M,N ::= x \\,|\\, \\lambda x.M \\,|\\, M\\;N$\n\nwhich is to say, a $\\lambda$-term is either a variable $x$, a $\\lambda$-abstraction $\\lambda x.M$, or an application of two terms $M\\;N$. In Haskell, the associated data type is given by:\n\ndata Term =\nTmVar Info Int Int\n| TmAbs Info String Term\n| TmApp Info Term Term\nderiving (Show)\n\ndata Info = Info { row :: Int, col :: Int } deriving (Show)\n\n\nInfo is used to hold row and column information about the terms as they are parsed, in case such information is necessary for error messages later.\n\nThe data constructors TmAbs and TmApp take predictable arguments - for an abstraction we track the name of the variable as a string, and an application stores the two terms involved. But why are there numbers stored in each TmVar?\n\nThe first number is the De Bruijn index[1], which cleverly encodes the variables in a nameless representation by storing \u201chow far\u201d the variable is from its binding $\\lambda$. The number represents how many other $\\lambda$-abstractions (which can be simply called \u201cbinders\u201d) there are in the scope of the variable. So, for example, the identity term $\\lambda x.x$ can be written as $\\lambda.0$ and our friend $\\lambda x.\\lambda y.x\\;y$ from before becomes $\\lambda.\\lambda.1\\;0$. This nameless representation does away with any issues caused by name collisions; more information about its advantages can be found in the link above.\n\nIn order to calculate a variable\u2019s de Bruijn index, we will need to keep track of a list of bound variables. Hence we will use the following type alias:\n\ntype BoundContext = [String]\n\n\nThe second number in the TmVar data constructor stores how many bound variables are in the variable\u2019s scope, and is used as a sanity check in TAPL\u2019s evaluator.\n\n## Munging info\n\nBefore we start writing the parser, we\u2019ll need a convenience function which will produce the Info we need during parsing. Parsec tracks its position within the source as it parses with the SourcePos type. We will use this to grab the row and column position:\n\ninfoFrom :: SourcePos -> Info\ninfoFrom pos = Info (sourceLine pos) (sourceColumn pos)\n\n\nIn order to use this function, we of course need a SourcePos to call it on. To get one of these, we first need to know how building parsers in Parsec works.\n\n## Parser combinators\n\nParsec parsers are built up by composing a variety of parser combinators. A combinator is technically a function with no free variables, i.e. one depending only on its arguments; some common examples are the indentity $I \\equiv \\lambda x.x$, or the constant function $K \\equiv \\lambda x.\\lambda y. x$. In the world of functional programming, however, our mental model of a combinator is not necessarily this definition \u2013 instead, we think of combinators as simple, self-contained building blocks with which we can construct more complicated functions. For example, the \u201cSKI combinator calculus\u201d is a system which only allows us to work with the combinators $K$ and $I$ above, as well as the substitution combinator $S \\equiv \\lambda x.\\lambda y.\\lambda z.(x\\;z)\\;(y\\;z)$. We can apply them to each other; for example, $I S = S$. From these simple combinators we can build much more complex ones; an interesting example is $S I I$, which takes some input and applies it to itself. In fact, any expression in the untyped $\\lambda$-calculus can be written as a combination of the $S$,$K$, and $I$ combinators!\n\nThis same spirit of complexity via composition drives Parsec. The library provides some simple parsers, like letter, which matches a single letter, or char c, which matches whatever character c is. Parsers have the type Parsec s u a, which we can break down like so:\n\n\u2022 s is the type of the input, such as String\n\u2022 u is the type of the \u201cuser state\u201d, i.e. whatever data you want to carry around as you parse\n\u2022 a is the type of the parser\u2019s output\n\nIn our case, we will be parsing Strings into Terms, and we will need to carry around a context storing which $\\lambda$-abstractions we\u2019ve seen in order to convert to de Bruijn notation, which will be a list of Strings as we mentioned earlier. So our final parser will have type Parsec String BoundContext Term. That\u2019s a bit of a mouthful, so lets use a type alias:\n\ntype LCParser = Parsec String BoundContext Term\n\n\nThese basic parsers can be combined into more complex beasts with a number of provided functions. One of the usual suspects is the infix function <|> (which you may recognize from the Alternative typeclass) . If p and q are two parsers, then p <|> q is a parser which tries parsing with p, and if that fails, parsing with q. So letter <|> char '\\'' matches either a letter, or a \u201cprime\u201d '.\n\nIn fact, this is part of the first building block we will need. We will allow variables which are strings consisting of letters or primes, such as \u201cx\u201d, \u201cy\u201d, \u201cx\u2019\u201d, or \u201clol\u201d. The parser for this is\n\nparseVarName :: Parsec String u String\nparseVarName = many1 $letter <|> char '\\'' The stranger here is many1, which is a rather predictable function. Given a parser p, many1 p will match 1 or more of the things p parses. In our case, this means 1 or more letters or primes - i.e. a string like described above. Note that the type of the state is left as a variable. In order to use a parser, we need to run it. Let\u2019s give ourselves a helper function for running the parsers we make as we go: parseWith :: Parsec String [u] a -> String -> Either ParseError a parseWith p = runParser p [] \"untyped lambda-calculus\" As the type signature suggests, parseWith takes a parser and a string and either gives you an parsing error, or whatever the output of the parser is. The empty list we hand it will be used later as the initial state for our parser (an empty context). The string \u201cuntyped lambda-calculus\u201d is used as the source name when Parsec prints errors. Here are a few examples of using the variable name parser. Notice what it accepts and rejects[2]: parseWith letter \"loasdfl\" parseWith parseVarName \"4x'\" parseWith parseVarName \"x'\" parseWith parseVarName \"y 5\" Right 'l' Left \"untyped lambda-calculus\" (line 1, column 1): unexpected \"4\" expecting letter or \"'\" Right \"x'\" Right \"y\" Notice that when the parser hits an invalid character right off the bat, it fails, because we wanted 1 or more characters. But if it has some valid characters and hits an invalid one, it stops parsing and returns the good stuff. Then it can continue trying another parser on the invalid part in more complex parsers. ## Monadic parsing The type Parsec s u, with the a dropped, has kind * -> *, i.e. it is a type constructor, like Maybe or Either a. Fixing a type for the input and the user state, Parsec s u is a monad. Recall that to make a monad out of a type constructor m, one must provide implementations of functions return :: a -> m a and (>>=) :: m a -> (a -> m b) -> m b. For Parsec parsers, these functions work like so: ### return return x creates a parser which reads no input, and outputs x. For example: parseWith (return \"output1\") \"\" parseWith (return \"output2\") \"This is not read.\" Right \"output1\" Right \"output2\" ### Bind, i.e. (>>=) p >>= f runs p, then passes the output of parsing with p to f. Recall the type signature for (>>=): in this case, Parsec s u a -> (a -> Parsec s u b) -> Parsec s u b. So passing the output of parsing with p to f gives us a parser, and we run it on the remaining input. Here is a particularly contrived example: announceLetter c = return$ \"The first letter is \" ++ [c]\nparseWith (letter >>= announceLetter) \"abc\"\n\nRight \"The first letter is a\"\n\n\nIt\u2019s worth looking at what (>>) does as well, even though it can be derived from (>>=). p >> q is a parser which runs p on the input, discards the result, then runs q on the remaining input. So, for example:\n\nparseWith (letter >> digit) \"r5\"\nparseWith (parseVarName >> many1 digit) \"lol46\"\n\nRight '5'\nRight \"46\"\n\n\nThis is useful when we want to parse pieces of the input which we do not need to store; for example, if we are parsing IP addresses, there is no need to store the dots.\n\nA big advantage of this monad instance is that we can use do notation. For example, here is how we might parse an IP address:\n\ndata IP = IP Int Int Int Int deriving (Show)\n\nnumber :: Parsec String u Int\nnumber = many1 digit >>= (return . read)\n\ndot = char '.'\n\nparseIP = do\np1 <- number\ndot\np2 <- number\ndot\np3 <- number\ndot\np4 <- number\nreturn $IP p1 p2 p3 p4 parseWith parseIP \"192.168.0.1\" parseWith parseIP \"192.168.0\" Right (IP 192 168 0 1) Left \"untyped lambda-calculus\" (line 1, column 10): unexpected end of input expecting digit or \".\" ## Parsing terms Let\u2019s begin building the parsers for the different types of terms. The abstraction parser is the most involved, and lays the groundwork for the stateful part of the parsing, so we will start with that. parseAbs :: LCParser -> LCParser parseAbs termParser = do char '\\\\' v <- parseVarName modifyState (v :) char '.' term <- termParser modifyState tail pos <- getPosition return$ TmAbs (infoFrom pos) v term\n\n\nFirst, we match a backslash, which begins the $\\lambda$-abstraction (the backslash syntax is inspired by Haskell). Next, we parse the subsequent variable name and store it. As we mentioned before, the state we carry around is a list of bound variables, so after we see the variable we push it onto the front of the list using modifyState, which applies the given function to the state. Next we pass by the dot after the variable, and parse the term in the body of the $\\lambda$-abstraction. Note that we haven\u2019t defined a parser for general terms yet; we can define it once we\u2019ve laid out how to parse each type of term[3].\n\nAfter parsing the body term, we pop abstraction\u2019s variable off of the context list, since we are leaving the scope of the abstraction. Having completed the parsing, we grab the SourcePos using getPosition and return a TmAbs filled in with all the necessary data we\u2019ve parsed.\n\nNow let\u2019s move on to parsing variables. When we parse a variable, we need to return a TmVar with the correct de Bruijn index. This index is the position of the variable in the context list, which is the state we store while parsing. If the variable name isn\u2019t found in the list, then it hasn\u2019t been bound anywhere and is free. This provides a small challenge though - what number should we use for the index of a free variable? In TAPL, the author defines a function for printing elements of Term as normal lambda expressions, but this function has no support for free variables (printing an error in their presence) so we will also elide the challenge of indexing and naming free variables by only parsing terms with no free variables (i.e., combinators). Hence the alternate title for the post: \u201cParsing combinators with parser combinators\u201d.\n\nBelow, we see an implementation for the variable parser:\n\nparseVar :: LCParser\nparseVar = do\nv <- parseVarName\nlist <- getState\nfindVar v list\n\nfindVar :: String -> BoundContext -> LCParser\nfindVar v list = case elemIndex v list of\nNothing -> fail $\"The variable \" ++ v ++ \" has not been bound\" Just n -> do pos <- getPosition return$ TmVar (infoFrom pos) n (length list)\n\n\nIt works as we\u2019ve discussed: first, we parse a variable name, then grab the BoundContext list from the parser state. The findVar function takes the variable name and list of bound variables, and returns a TmVar with the appropriate index when it can, failing otherwise.\n\nFinally, we need a parser which can handle applications. Now, ideally, once we had our application parser parseApp, we would be able to say something like:\n\nparseTerm = parseApp <|> parseAbs <|> parseVar\n\n\nHowever, this would lead to an infinite loop: the parseApp function would make a call to parseTerm for each space-separated term there is in the application. Moreover, parseApp must show up before parseAbs in the definition of parseTerm, because otherwise in a case like \u201c$\\lambda x.x \\; \\lambda y.y$\u201d the abstraction parser would consume the first abstraction, which is awfully short-sighted because then the parser doesn\u2019t see the entire terms as an application. But this means that when parseApp makes its call to parseTerm, it will just repeatedly call parseApp over and over again as that is the first parser it tries when running parseTerm.\n\nWe can fix this by parsing application terms and non-application terms separately. When we want to parse an application, we run the non-application parser on a space-separated series of terms. Since application in the $\\lambda$-calculus is left-associative, we can parse a string like \u201cM N O\u201d, where M, N, and O are terms, as \u201c(M N) O\u201d. Parsec includes a function which can help us in this situation:\n\nchainl1 :: Parsec s u a -> Parsec s u (a -> a -> a) -> Parsec s u a\n\n\nEssentially, chainl1 p q is a parser which matches 1 or more of whatever p parses, then performs a left fold with the function returned by the q parser. You can see it used in practice in the final part of our parser:\n\nparens :: Parsec String u a -> Parsec String u a\nparens = between (char '(') (char ')')\n\nparseNonApp :: LCParser\nparseNonApp = parens parseTerm -- (M)\n<|> parseAbs parseTerm -- $\\lambda$x.M\n<|> parseVar -- x\n\nparseTerm :: LCParser\nparseTerm = chainl1 parseNonApp $do space pos <- getPosition return$ TmApp (infoFrom pos)\n\n\nNotice that we\u2019ve also added a parser for terms within parentheses. We conclude by creating a parse function:\n\nparse :: String -> Either ParseError Term\nparse = parseWith parseTerm\n\n\nWe can test it out:\n\nparse \"\\\\x.\\\\y.x y\"\n\nRight\n(TmAbs (Info {row = 1, col = 10}) \"x\"\n(TmAbs (Info {row = 1, col = 10}) \"y\"\n(TmApp (Info {row = 1, col = 9})\n(TmVar (Info {row = 1, col = 8}) 1 2)\n(TmVar (Info {row = 1, col = 10}) 0 2)\n)\n)\n)\n\n\nHere is the function from TAPL for printing these terms in a nicer way:\n\ndata Binding = NameBind deriving (Show)\n\ntype Context = [(String, Binding)]\n\nctxLength :: Context -> Int\nctxLength = length\n\nindexToName :: Context -> Int -> String\nindexToName ctx n = fst $ctx !! n pickFreshName :: Context -> String -> (Context, String) pickFreshName ctx x | x elem (map fst ctx) = pickFreshName ctx$ x ++ \"'\"\n| otherwise = ((x, NameBind) : ctx , x)\n\nprintTm :: Context -> Term -> String\nprintTm ctx t = case t of\nTmAbs _ x t1 -> let\n(ctx', x') = pickFreshName ctx x\nin \"(\\\\\" ++ x' ++ \".\" ++ (printTm ctx' t1) ++ \")\"\nTmApp _ t1 t2 ->\n\"(\" ++ (printTm ctx t1) ++ \" \" ++ printTm ctx t2 ++ \")\"\nTmVar _ x n ->\nif ctxLength ctx == n then\nindexToName ctx x\nelse\n\n\nWe can hook this up to our parser to see that it works:\n\nprintTerm s = case parse s of\nLeft err -> print err\nRight t -> print \\$ printTm [] t\n\nprintTerm \"\\\\x.\\\\y.x y\"\nprintTerm \"\\\\f.(\\\\x.f (x x)) (\\\\x.f (x x))\" -- Y combinator\n\n\"(\\\\x.(\\\\y.(x y)))\"\n\n\"(\\\\f.((\\\\x.(f (x x))) (\\\\x.(f (x x)))))\"\n\n\n## Coda\n\nOnce you get the hang of it, Parsec makes writing parsers pretty fun. The parser combinator approach seems near-fetishized in the Haskell community; one oft-cited reason for their greatness is the fact that parser combinators allow us to write parsers in the host language (Haskell in this case) without needing to write a specification in some other language (the Yacc\/Bison approach[4]). Having little experience with parsers myself, I can\u2019t attest to this particular strength, but the fact that I could knock out a small parser in one sitting having never worked with Parsec before is a testament to its ease of use.\n\nIf you would like to see the parser implementation together in one place, instead of spread throughout this post, you can find it here. The parser and evaluator can be found together in this folder.\n\n1. Caveat: The Wikipedia article starts numbering at 1, but TAPL (and this post, as a result) start numbering at 0. So $\\lambda x.x$ is $\\lambda.1$ in the Wikipedia article, but $\\lambda.0$ for our purposes. Thanks platz for pointing this out. \u21a9\ufe0e\n\n2. The result of a call to parseWith is Either ParseError a. A successful parsing attempt will return Right x, where x is whatever was parsed. If there is a parsing error, we get a Left err instead, where err is a ParseError. An explanation of what Left and Right are can be found here. \u21a9\ufe0e\n\n3. We take the term parser in as an argument to parseAbs so that we can develop the parser step-by-step without IHaskell complaining that the term parser is undefined. The abstraction parser depends on the term parser and vice versa. If this was just in one file, then we could refer to the term parser directly. \u21a9\ufe0e\n\n4. Yacc is a parser generator, which means you write the grammar for the language you want to parse, and Yacc will spit out a parser for such a language in C or Java. Bison is the GNU version of Yacc, with a punning name in the GNU tradition. \u21a9\ufe0e","date":"2020-08-09 17:51:12","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 38, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 1, \"mathjax_display_tex\": 0, \"mathjax_asciimath\": 1, \"img_math\": 0, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.6579768061637878, \"perplexity\": 2518.528966412148}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2020-34\/segments\/1596439738562.5\/warc\/CC-MAIN-20200809162458-20200809192458-00360.warc.gz\"}"} | null | null |
Dick's Picks Volume 24 je koncertní dvojalbum americké rockové skupiny Grateful Dead, nahrané 23. března 1974 a vydané v roce 2002. Jedná se o čtyřiadvacátou část série Dick's Picks.
Seznam skladeb
Sestava
Jerry Garcia – sólová kytara, zpěv
Bob Weir – rytmická kytara, zpěv
Phil Lesh – basová kytara, zpěv
Donna Jean Godchaux – zpěv
Keith Godchaux – klávesy
Bill Kreutzmann – bicí
24
Koncertní alba z roku 2002
Dvojalba | {
"redpajama_set_name": "RedPajamaWikipedia"
} | 4,707 |
{"url":"https:\/\/www.cuemath.com\/geometry\/apothem\/","text":"# Apothem\n\nApothem\n\nTim and Sam were finding the area of various regular polygons. Tim divided\u00a0the polygons into triangles and was trying to calculate the area of the polygons, which took him too long. On the other hand, Sam found the area of the polygons easily, as he knew the length of the apothem. So let's learn about apothem today!\n\nBefore we get started, check out this interesting simulation to identify the apothem for various polygons. This apothem calculator will help you understand the lesson better.\n\n## Lesson Plan\n\n 1 What Is Meant by Apothem? 2 Important Notes on\u00a0Apothem 3 Solved Examples on\u00a0Apothem 4 Challenging Questions on\u00a0Apothem 5 Interactive Questions on\u00a0Apothem\n\n## What Is Meant by Apothem?\n\nApothem is a line drawn from the center of any polygon to the midpoint of one of the sides.\n\n## Formulas Used to Calculate the Apothem Length\n\nThe\u00a0apothem formula, when the side length is given is:\n\n $$a$$ = \\begin{align}\\frac{S}{2\\,\\, \\text{tan}\\left ( \\frac{180}{n} \\right )}\\end{align}\n\nWhere,\n\n$$a$$ = apothem length\n\n$$s$$ = side length\n\n$$n$$ = number of sides of a polygon.\n\nThe\u00a0apothem formula\u00a0, when the radius is given is:\n\n $$a$$ = $$r.cos\\frac{180}{n}$$\nWhere\n\n$$r$$\u00a0=\u00a0radius.\n\n$$n$$ =\u00a0number of sides\n\n$$Cos$$\u00a0=\u00a0cosine function which is calculated in degrees.\n\nWe can use the apothem area formula\u00a0of a polygon to calculate the length of the apothem.\n\n $$A$$ = $$\\dfrac{1}{2}aP$$\n\nWhere,\n\n$$A$$ = area of the polygon\n\n$$a$$ = apothem.\n\n$$P$$ = perimeter\n\n## How to Calculate Area of a Polygon Using Apothem?\n\nTo calculate the area of a polygon with the help of apothem, we use the formula:\n\n$$A$$ = $$\\dfrac{1}{2}aP$$\n\nWhere,\n\n$$a$$ = apothem.\n\n$$P$$ = perimeter.\n\nExample: Find the area of a regular hexagon, if the side length is $$5$$ inches, and the apothem is $$3$$ inches.\n\n$$A$$ = $$\\dfrac{1}{2}aP$$\n\nAs we know perimeter:\n\n\\begin{align}P &= [\\text{side length}]\\times [\\text{no. of sides}]\\\\&= 5\\times6 = 30\\end{align}\n\nAfter the perimeter is calculated, we use it in the formula of Area = $$A$$ = $$\\dfrac{1}{2}aP$$\n\n\\begin{align}A &= \\dfrac{1}{2}aP \\\\ & = \\dfrac{1}{2} \\left ( 3\\right )\\left (30 \\right )\\\\& = 45 \\text{ inches}^2\\end{align}\n\nImportant Notes\n1. The apothem is always perpendicular to the side on which it\u00a0ends.\n2. A regular polygon has all its sides and angles equal.\n\n## Solved Examples\n\n Example 1\n\nHelp Bryan find the length of the apothem of a regular pentagon of side = $$10$$ inches and area $$150\\sqrt{3}\\,\\,\\text {inches}^{2}$$.\n\nSolution\n\nGiven,\n\n$$L$$ = $$10$$ inches.\n\n$$A$$ = $$150\\sqrt{3}\\,\\,\\text {inches}^{2}$$\n\nSo, the perimeter will be $$P$$ = $$10\\times 5$$ = $$50$$ inches.\n\n\\begin{align}A&=\\dfrac{1}{2}aP\\\\ 150\\sqrt{3}&= \\dfrac{1}{2}a\\times 50\\\\ 25a&=150\\sqrt{3}\\\\ a&=\\dfrac{150\\sqrt{3}}{25}\\\\ a&=6\\sqrt{3}\\text{ inches}\\end{align}\n\nTherefore, Apothem = $$6\\sqrt{3}$$ inches.\n\n $$\\therefore$$ $$a$$ = $$6\\sqrt{3}$$ inches\n Example 2\n\nCan you help Dylan calculate the area\u00a0of a\u00a0regular hexagon of side 8\u00a0inches and apothem $$4\\sqrt{3}$$, using the area of polygon formula?\n\nSolution\n\nGiven,\n\nside length = 8\u00a0inches.\n\nperimeter $$P$$ = $$L\\times n$$\n\n= $$8\\times 6$$\n\n= $$48$$ inches\n\nArea of polygon = \\begin{align}A& = \\dfrac{1}{2}aP\\\\&= \\dfrac{1}{2}\\times4\\sqrt{3}\\times 48\\\\&= 96\\sqrt{3} \\text{ inches}^2\\end{align}\n\n $$\\therefore$$ The area of the polygon is $$96\\sqrt{3} \\text{ inches}^2$$\n Example 3\n\nEmily's teacher asked her\u00a0to calculate the area\u00a0of a regular hexagon, whose apothem is 7 inches and perimeter 48 inches.\n\nSolution\n\nGiven,\n\n$$a$$ = 7 inches.\n\n$$P$$ = 48 inches.\n\nThus, the Area of hexagon will be:\n\n\\begin{align}&\\frac{1}{2}aP\\\\ &=\\frac{1}{2}\\times 7\\times 48\\\\ &=\\frac{1}{2}\\times 336\\\\ &=\\frac{336}{2}\\\\ &=168 \\text{ inches}^2\\end{align}\n\n $$\\therefore$$ $$A$$ = $$168 \\text{ inches}^2$$\n Example 4\n\nCan you help Jose calculate the length of the apothem\u00a0of a square, which has a side length of 3 inches?\n\nSolution\n\nThe formula for calculating apothem, when side length is given is:\n\n$$a$$ = \\begin{align}\\frac{S}{2 \\,\\,\\text{tan}\\left ( \\frac{180}{n} \\right )}\\end{align}\n\n\\begin {align}a &=\\dfrac{S}{2\\,\\,\\text{tan}\\left ( \\dfrac{180}{n} \\right)}\\\\ &=\\dfrac{3}{2\\,\\,\\text{tan}\\left ( \\dfrac{180}{4} \\right)}\\\\ &=\\dfrac{3}{2\\,\\,\\text{tan} 45}\\\\ &=\\dfrac{3}{2\\times 1}\\\\ &=\\dfrac{3}{2}\\\\ &=1.5\\text{ inches}\\end{align}\n\n $$\\therefore$$ The length of apothem is $$1.5\\text{ inches}$$\n\nChallenging Question\n1. Devin wanted to calculate the area of a regular octagon of side 12\u00a0inches and apothem 14.5\u00a0inches. Help him find the answer.\n\n## Interactive Questions\n\nHere are a few activities for you to practice.\n\n## Let's Summarize\n\nWe hope you enjoyed learning about apothem\u00a0with the simulations and practice questions. Now you will be able to easily solve problems related to the apothem.\n\nAt\u00a0Cuemath, our team of math experts is dedicated to making learning fun for our favorite readers, the students!\n\nThrough an interactive and engaging learning-teaching-learning approach, the teachers explore all angles of a topic.\n\nBe it worksheets, online classes, doubt sessions, or any other form of relation, it\u2019s the logical thinking and smart learning approach that we at Cuemath believe in.\n\n## 1. Is the apothem the same as the radius?\n\nApothem is also a radius, but when we talk\u00a0about radius, we usually refer to a circle or a sphere.\n\nHowever,\u00a0when we talk about apothem, it can be any other polygon as well, such as the square, triangle, or hexagon.\n\n## 2. Is the Apothem Equal to the Side Length?\n\nNo, an apothem's length is not always equal to its side length. However, if we know the side length of a polygon, the apothem can be calculated.\n\n## 3. What is the Apothem of a Square?\n\nThe apothem of a square is equal to half of its side length.\n\nMore Important Topics\nNumbers\nAlgebra\nGeometry\nMeasurement\nMoney\nData\nTrigonometry\nCalculus","date":"2021-06-25 00:51:30","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 1, \"mathjax_display_tex\": 1, \"mathjax_asciimath\": 0, \"img_math\": 0, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 0, \"align\": 11, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.890903651714325, \"perplexity\": 1875.122153982086}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2021-25\/segments\/1623488560777.97\/warc\/CC-MAIN-20210624233218-20210625023218-00008.warc.gz\"}"} | null | null |
\section{Introduction}
Nonlinear spectroscopy has become an invaluable tool across many
fields of research
\cite{Shen1984Principles,Mukamel1999Principles}. In particular,
two-photon absorption (TPA) spectroscopy [for the scheme, see
Fig.~1] has allowed us to obtain information about a sample that
would not be accessible otherwise. Interestingly, the use of
entangled light in two-photon spectroscopy has received a great
deal of attention very recently
\cite{dayan2004two,kojima2004,Lee2006Entangled,Roslyak2009,guzman2010,oka2010,oka2011,oka2011-2,salazar2012,Schlawin2012,Raymer2013,kalashnikov2014,dorfman2016,kalashnikov2016,schlawin2017,villabona2017,varnavski2017,schlawin2017_njp}
because of the unique phenomena that arise in the interaction of
entangled photon pairs with matter. Examples of these effects are
the linear scaling of the TPA rates on the photon flux
\cite{Javanainen1990}, two-photon-induced transparency
\cite{Fei1997Entanglement}, the ability to select different states
in complex biological aggregates \cite{Schlawin2013Suppression},
and the control of entanglement in matter
\cite{Shapiro2011,Shapiro_book}. Indeed, the prediction and
observation of these fascinating effects can be understood as a
direct consequence of the dependence of the TPA signal on the
properties of quantum light that interacts with the sample
\cite{Perina1991Quantum}.
Among different techniques proposed over the years,
entangled-photon virtual-state spectroscopy (VSS)
\cite{Saleh1998Entangled,Perina1998Multiphoton,Leon2013Role} has
proved to be a unique tool for extracting information about the
virtual states --- energy non-conserving atomic transitions
\cite{Shore1979,SakuraiBook} --- that contribute to the two-photon
excitation of an absorbing medium. In this technique,
virtual-state transitions, a signature of the medium, are
experimentally revealed by introducing a time-delay between
frequency-correlated photons, and averaging over experimental
realizations differing in temporal correlations between them
\cite{Saleh1998Entangled}.
One important aspect of VSS is that the overall TPA rate, $R$, can be expressed as \cite{Fei1997Entanglement}
\begin{equation}
R = \sigma_{\rm E}\phi + \delta_{\rm r}\phi^{2},
\end{equation}
where $\sigma_{\rm E}$ is the entangled-light absorption cross
section, $\delta_{\rm r}$ is the random (classical) TPA cross section,
and $\phi$ is the flux density of photon pairs. Notice that Eq.
(1) states that entangled-photon effects will dominate the TPA
signal only when the photon-flux density is sufficiently small.
This conclusion has two opposite points of view when discussing
the experimental implementation of VSS. On one hand, the low
efficiency of spontaneous down-conversion in nonlinear crystals
guarantees the low photon-flux condition but, on the other, a low
photon-flux might result in an extremely weak TPA signal that
might require long measuring times, thus making the implementation
of virtual-state spectroscopy an unrealistic endeavor.
With the advent of ultrahigh flux sources of entangled photons
\cite{Brambilla2004,Jedrkiewicz2004,Bondani2007,Blanchet2008,dayan2005,shimizu2009},
one naturally wonders whether VSS can benefit from them,
especially because it has been shown that strong frequency
correlations between entangled beams persist at high photon-flux
conditions
\cite{Schlawin2013Photon,PerinaJr2015a,PerinaJr2016,PerinaJr2016a}.
Consequently, in this paper, we provide a thorough analysis of VSS
when implemented with intense entangled fields (further twin
beams). This allows us to determine the entangled-photon flux
threshold at which spectroscopic information about an absorbing
medium can be retrieved. Surprisingly, we find that virtual-state
spectroscopy may be implemented with twin beams carrying up to
$10^4$ photon pairs. This means that the strength of typical TPA
signals could be enhanced by up to four orders of magnitude, thus
paving the way towards the first experimental realization of
virtual-state spectroscopy.
The paper is structured as follows. In Sec. II we describe the
generation of twin beams, produced in a nonlinear crystal pumped
by an intense laser pulse. In Sec. III, we derive the explicit
form of the TPA signal for temporally-delayed intense twin beams.
In Sec. IV, we provide an example of the VSS implementation with
intense twin beams by extracting the energy level structure of a
model system, whose two-photon excitation takes place via three
intermediate states with randomly chosen energies. Finally, in
Sec. V we present our conclusions.
\begin{figure}
\centering
\includegraphics[width=8.5cm]{Fig1.eps}
\caption{Schematic representation of the two-photon absorption process caused by two mutually-delayed
beams that form a common twin beam. A nonlinear $\chi^{(2)}$ crystal is pumped by an intense laser pulse, thus producing two intense entangled beams.
These beams interact with an absorbing medium and the two-photon absorption signal is measured as a function of an externally-introduced delay $\tau$
between them; $\tau_{\mathrm p}$ stands for the pump-pulse duration and
$N_{\mathrm s,i}$ is the number of photons present in the signal and
idler beams, respectively.}
\end{figure}
\section{Generation of intense twin beams}
To describe the generation of twin beams, we follow the procedure
used by previous authors in Refs.
\cite{Wasilewski2006Pulsed,McKinstrie2009, McKinstrie2013,
christ2011,christ2013,Schlawin2013Photon,PerinaJr2015a}. The first
step is to solve the Schr\"{o}dinger equation in the first-order
perturbation approximation to obtain the two-photon spectral
amplitude. In the second step the Schmidt decomposition of the
two-photon spectral amplitude (TSA) of the generated photons is
calculated. This provides the Schmidt modes of the correlated
photon fields. The twin-beam description is then found by solving
the Heisenberg equations for the creation and annihilation
operators of the corresponding Schmidt spectral modes.
Let us start with the description of Spontaneous Parametric
Down-conversion (SPDC) in the Schr\"{o}dinger picture, based on the
momentum operator
\begin{eqnarray}
\hat{G}(z) &=& 4\epsilon_{\mathrm 0}A\int_{-\infty}^{\infty}dt\chi^{(2)}
\mathcal{E}_{\mathrm p}^{(+)}(z,t)\hat{E}_{\mathrm
s}^{(-)}(z,t)\hat{E}_{\mathrm
i}^{(-)}(z,t) \nonumber \\
& & +{\rm h.c.}
\label{Eq:1}
\end{eqnarray}
where $\epsilon_\mathrm{0}$ is the vacuum permittivity, $A$ is the traverse
area of interaction, $\chi^{(2)}$ is the second-order non-linear
susceptibility and h.c. stands for the Hermitian-conjugated term.
The pump field is modeled as a classical non-depleted field with
the form
\begin{equation}
\mathcal{E}_\mathrm{p}^{(+)}(z,t)=\frac{1}{\sqrt{2\pi}}\int_{-\infty}^\infty
d\omega_\mathrm{p} \; e_\mathrm{p}\left(\omega_\mathrm{p}\right)
\exp[-i(\omega_\mathrm{p} t-k_\mathrm{zp}z)]. \label{Eq:2}
\end{equation}
Notice that the spatial dependence is encapsulated in the
longitudinal wave vector $k_\mathrm{zp}$. Transversally, we consider the
pump homogeneous in the whole area $A$. The pump spectrum is given
by
\begin{equation}
e_\mathrm{p}\left(\omega_\mathrm{p}\right)=\xi_\mathrm{p}\sqrt{\frac{\tau_\mathrm{p}}{\sqrt{2\pi}}}
\exp\left[-\frac{\tau^2_\mathrm{p}}{4}\left(\omega_\mathrm{p}-\omega^0_\mathrm{p}\right)^2\right].
\label{Eq:3}
\end{equation}
Here, the pump pulse duration is denoted by $\tau_{\mathrm p}$ and the pump
amplitude is described by
$\xi_\mathrm{p}=\sqrt{P_\mathrm{p}/\epsilon_{0}cfn_\mathrm{p}}$,
which depends on the pump power $P_\mathrm{p}$ and the repetition frequency
$f$; $n_\mathrm{p}$ is the index of refraction of the crystal at the pump
wavelength, and $c$ is the speed of light. Finally, the generated
signal and idler photons are treated in a quantum manner and they
are described by the positive-frequency electric-field operator
amplitude
\begin{eqnarray}
\hat{E}^{(+)}_{\mathrm
j}(z,t)&=&\frac{i}{\sqrt{2\pi}}\int_{-\infty}^{\infty}d\omega_\mathrm{j}
\sqrt{\frac{\hbar\omega_\mathrm{j}}{2\epsilon_\mathrm{0}Acn_{\mathrm
j}}}\hat{a}\left(\omega_\mathrm{j}\right)
\nonumber \\
& & \mbox{} \times \exp[-i(\omega_\mathrm{j}t-k_\mathrm{j}z)],
\label{Eq:4}
\end{eqnarray}
with $\mathrm{j=s,i}$; $\hbar$ is the reduced Planck constant and
$\hat{a}_\mathrm{j}(\omega_\mathrm{j})$ is the bosonic annihilation operator of
the $\mathrm{j}$th photon with frequency $\omega_{j}$.
The first-order perturbation solution of the Schr\"{o}dinger
equation results in the following entangled two-photon state
\begin{eqnarray}
|\Phi\rangle&=&-\frac{i}{\hbar}\int_{0}^{L}dz\hat{G}\left(z\right)|{\rm
vac}\rangle=
\int_{-\infty}^{\infty}d\omega_\mathrm{s}\int_{-\infty}^{\infty}d\omega_\mathrm{i}\nonumber\\
&
&\Phi\left(\omega_\mathrm{s},\omega_\mathrm{i}\right)\hat{a}^{\dagger}_{\mathrm{s}}
\left(\omega_\mathrm{s}\right)\hat{a}^{\dagger}_{\mathrm
i}\left(\omega_\mathrm{i}\right)|{\rm vac}\rangle,
\label{Eq:5}
\end{eqnarray}
where $L$ stands for the length of the non-linear crystal and $
|{\rm vac}\rangle $ denotes the vacuum state of the signal and
idler fields in front of the crystal. The TSA
$\Phi\left(\omega_{\mathrm s},\omega_{\mathrm i}\right)$ is given
by
\begin{eqnarray}
\Phi\left(\omega_{\mathrm
s},\omega_\mathrm{i}\right)&=&\frac{i\chi^{(2)}\xi_{\mathrm p}L}{\sqrt{2\pi
n_{\mathrm p}n_{\mathrm s}n_{\mathrm
i}}}\sqrt{\frac{\tau_\mathrm{p}}{\sqrt{2\pi}}}\mathrm{sinc}\left[\Delta
k_{\mathrm{z}}\left(\omega_{\mathrm s},\omega_{\mathrm
i}\right)\frac{L}{2}\right]
\nonumber \\
& & \hspace{-15mm} \mbox{} \times \exp\left[-\frac{\tau^2_\mathrm
{p}}{4}\left(\omega_{\mathrm s}+\omega_{\mathrm
i}-\omega^{0}_{\mathrm p}\right)^2-i\Delta k_{\mathrm{z}}\left(\omega_{\mathrm
s},\omega_{\mathrm
i}\right)\frac{L}{2}\right]
\label{Eq:6}
\end{eqnarray}
with $\Delta k_{\mathrm{z}}\left(\omega_{\mathrm
s},\omega_{\mathrm i}\right)=k_{\mathrm zp}\left(\omega_{\mathrm
s}+\omega_{\mathrm i}\right)-k_{\mathrm
zs}\left(\omega_\mathrm{s}\right)-k_{\mathrm
zi}\left(\omega_{\mathrm i}\right)$.
We now proceed with the second step of the calculation, where the
Schmidt decomposition is applied to find pairs of spectral modes
\cite{Law2000Continous,Law2004Analysis} of the normalized TSA,
that is,
\begin{equation}
\tilde{\Phi}\left(\omega_{\mathrm s},\omega_{\mathrm
i}\right)=\sum_{g=1}^{\infty}\lambda_{g}
f^{*}_{\mathrm{s},g}\left(\omega_{\mathrm
s}\right)f^{*}_{\mathrm{i},g}\left(\omega_{\mathrm i}\right),
\label{Eq:8}
\end{equation}
with $\Phi=\mathcal{N}L\tilde{\Phi}$ and $\mathcal{N}^2 L^2=\int
d\omega_{\mathrm s}\int d\omega_{\mathrm
i}|\Phi\left(\omega_{\mathrm s},\omega_{\mathrm i}\right)|^2$,
where $\mathcal{N}$ is a numerically-calculated normalization
constant. Notice that in Eq.~(\ref{Eq:8}),
$\left\{\lambda_g\right\}_{g=1}^{\infty}$ describes the set of
eigenvalues with corresponding eigenfunctions
$\left\{f_{\mathrm{s},g}(\omega_{\mathrm
s})\right\}_{g=1}^{\infty}$ and
$\left\{f_{\mathrm{i},g}(\omega_{\mathrm
i})\right\}_{g=1}^{\infty}$.
Thus, by making use of this formalism, we can rewrite the state in
Eq.~(\ref{Eq:5}) as
\begin{eqnarray}
|\Phi\rangle&=&\mathcal{N}L\sum_{g=1}^{\infty}\lambda_{g}\int
d\omega_{\mathrm s}\int d\omega_{\mathrm i}
f^{*}_{\mathrm{s},g}\left(\omega_{\mathrm
s}\right)f^{*}_{\mathrm{i},g}\left(\omega_{\mathrm
i}\right)\hat{a}^{\dagger}_{\mathrm{s}}\hat{a}^{\dagger}_{\mathrm{i}}|{\rm
vac}\rangle \nonumber\\
&=&\mathcal{N}\sum_{g=1}^{\infty}\lambda_g\hat{a}^{\dagger}_{\mathrm{s},g}\hat{a}^{\dagger}_{\mathrm{i},g}|{\rm
vac}\rangle. \label{Eq:9}
\end{eqnarray}
Note that the signal- (idler-) field creation operators
$\hat{a}^{\dagger}_{\mathrm{s},g}$ ($\hat{a}^{\dagger}_{\mathrm{i},g}$) of
independent Schmidt modes may be related to the spectral ones by
writing
\begin{equation}
\hat{a}_{\mathrm
s}\left(\omega_{\mathrm{s}}\right)=\sum_{g=1}^{\infty}f_{\mathrm{s},g}^{*}\left(\omega_{\mathrm{s}}\right)\hat{a}_{\mathrm{s},g},
\label{Eq:10}
\end{equation}
and similarly for the idler field.
Using the newly introduced operators of the Schmidt modes, the
operator $\hat{G}\left(z\right)$ can be rewritten as
\begin{equation}
\hat{G}\left(z\right)=i\hbar\mathcal{N}\sum_{g=1}^{\infty}{\lambda_g}\hat{a}^{\dagger}_{\mathrm{s},g}\hat{a}^{\dagger}_{\mathrm{i},g}
+ {\rm h.c.}
\label{Eq:11}
\end{equation}
Finally, by using this simplified form of the momentum operator,
we can find the evolution of the operators that describe the
produced twin beam, i.e. $\hat{a}^{\dagger}_{\mathrm{s},g}$ and
$\hat{a}^{\dagger}_{\mathrm{i},g}$. To do this, we use the Heisenberg
equations with the momentum operator $ \hat{G} $ given in
Eq.~(\ref{Eq:11}), that is,
\begin{eqnarray}
\frac{\partial \hat{a}_{\mathrm{s},g}}{\partial
z}&=&\frac{i}{\hbar}\left[\hat{G},\hat{a}_{\mathrm{s},g}\right]=\lambda_g\mathcal{N}\hat{a}^{\dagger}_{\mathrm{i},g},\nonumber\\
\frac{\partial \hat{a}_{\mathrm{i},g}}{\partial
z}&=&\frac{i}{\hbar}\left[\hat{G},\hat{a}_{\mathrm{i},g}\right]=\lambda_g\mathcal{N}\hat{a}^{\dagger}_{\mathrm{s},g}.
\end{eqnarray}
Their solution takes the form
\begin{eqnarray}
\hat{a}_{\mathrm{s},g}\left(L\right)&=&
u_g\hat{a}_{\mathrm{s},g}\left(0\right)+v_g\hat{a}^{\dagger}_{\mathrm{i},g}\left(0\right),\nonumber\\
\hat{a}_{\mathrm{i},g}\left(L\right)&=&
u_g\hat{a}_{\mathrm{i},g}\left(0\right)+v_g\hat{a}^{\dagger}_{\mathrm{s},g}\left(0\right),
\label{Eq:13}
\end{eqnarray}
where $u_g=\cosh(\mathcal{N}\lambda_g)$ and
$v_g=\sinh(\mathcal{N}\lambda_g)$. Notice from Eq.~(\ref{Eq:13})
that one can easily determine the number of signal (idler)
photons, contained in all modes, by writing
\begin{equation}
N_\mathrm{s}=\int d\omega_{\mathrm
s}\langle\hat{a}^{\dagger}_{\mathrm{s}}\left(\omega_{\mathrm
s}\right)\hat{a}_{\mathrm{s}}\left(\omega_{\mathrm s}\right)\rangle
=\sum_{g=1}^{\infty}\langle\hat{a}^{\dagger}_{\mathrm{s},g}\hat{a}_{\mathrm{s},g}\rangle=\sum_{g=1}^{\infty}|v_g|^2,
\end{equation}
whereas the effective amount of spectral modes, related to the
Schmidt number K, is obtained as
\begin{equation}
K_{\mathrm
UV}=\frac{\left(\sum_{g=1}^{\infty}u_gv_g\right)^2}{\sum_{g=1}^{\infty}
u_g^2v^2_g}.
\end{equation}
Before concluding this section, it is important to remark that
although the theoretical model described above is valid for most
experimental setups and applications, one most keep in mind that,
as any model, it has its limitations; particularly when extremely
high photon fluxes are considered
\cite{christ2013,Perez2014,PerinaJr2016a}.
\section{Interaction of twin beams with matter}
We now consider the interaction of twin beams with an absorbing
medium. For the sake of clarity, we assume a simple energy level
configuration of the medium where two-photon transitions occur
from a ground (initial) state $|\mathrm{g}\rangle$ to a
doubly-excited final state $|\mathrm{f}\rangle$ via non-resonant
intermediate states denoted by $|k\rangle$. For simplicity, we
omit any other degree of freedom connected to vibrational spectra
of the sample, and assume that the lifetimes of intermediate
states are longer than light-matter interaction time. This
approximation, which can be satisfied by selecting a proper
correlation time between photons
\cite{Fei1997Entanglement,Saleh1998Entangled,Leon2013Role,Schlawin2013Suppression},
implies that effects due to dissipation in the single-excitation
manifold (intermediate states) are assumed to be negligible.
The interaction of the electromagnetic field $\hat{E}$ and the
sample, in the dipole approximation, can be expressed as
\begin{equation}
\hat{H}(t)=-\hat{d}(t)\hat{E}(t)+ {\rm h.c.},
\end{equation}
where $\hat{d}$ is the dipole-moment operator, whose time
evolution is given by
\begin{equation}
\hat{d}(t)=\hat{\mu}_{kg}\exp[i(\varepsilon_{k}-\varepsilon_{\mathrm{g}})t]
\end{equation}
with $\hat{\mu}_{kg}$ being the single-excitation transition amplitude
operator from a state $|\mathrm{g}\rangle$ (with energy
$\varepsilon_{\mathrm{g}}$) to a state $|k\rangle$ (with energy
$\varepsilon_{k}$).
By considering that the medium is initially in its ground state
$|\mathrm{g}\rangle$, one can make use of second-order
time-dependent perturbation theory to find that the resulting TPA
signal is given by \cite{Perina1998Multiphoton,Leon2013Role}
\begin{eqnarray}\label{Eq:Probability1}
S_{\mathrm{g}\rightarrow
\mathrm{f}}&=&\frac{1}{\hbar^4}\int_{-\infty}^{\infty}dt_{\mathrm{2}}\int_{-\infty}^{t_{\mathrm{2}}}dt_{\mathrm{1}}\int_{-\infty}^{\infty}dt'_{\mathrm{2}}\int_{-\infty}^{t'_{\mathrm{2}}}dt'_{\mathrm{1}}
M^{*}\left(t_{\mathrm{2}},t_{\mathrm{1}}\right)\nonumber\\
&\times&M\left(t'_{\mathrm{2}},t'_{\mathrm{1}}\right)\langle\hat{E}^{(-)}\left(t_{\mathrm{2}}\right)\hat{E}^{(-)}\left(t_{\mathrm{1}}\right)\hat{E}^{(+)}\left(t'_{\mathrm{2}}\right)\hat{E}^{(+)}\left(t'_{\mathrm{1}}\right)\rangle,
\nonumber\\
\end{eqnarray}
where
$\langle\hat{E}^{(-)}\left(t_{\mathrm{2}}\right)\hat{E}^{(-)}\left(t_{\mathrm{1}}\right)\hat{E}^{(+)}\left(t'_{\mathrm{2}}\right)\hat{E}^{(+)}\left(t'_{\mathrm{1}}\right)\rangle$
corresponds to the four-point correlation function of the optical
field. The electric-field operator amplitude is defined as
\begin{equation}\label{Eq:Elec}
\hat{E}^{(+)}\left(t\right)=\hat{E}_\mathrm{s}^{(+)}\left(t\right)+\hat{E}_\mathrm{i}^{(+)}\left(t\right),
\end{equation}
and
\begin{eqnarray}\label{Eq:M}
M(t_\mathrm{2},t_\mathrm{1})&=&\sum_{k}\mu_{\mathrm{f}k}\mu_{k\mathrm{g}}\exp\left[i\left(\varepsilon_{\mathrm{f}}-\varepsilon_{k}\right)t_\mathrm{2}
\right. \nonumber \\
& & \left. \mbox{}+i\left(\varepsilon_{k}-\varepsilon_{\mathrm{g}}\right)t_\mathrm{1}\right].
\end{eqnarray}
where $\mu_{fk}$ denotes the transition dipole moment from the $k$th
intermediate state to the final doubly-excited state $|f\rangle$ and $\mu_{kg}$
is defined as in Eq.(17). Notice that the sum over the $k$ states in
Eq.~(\ref{Eq:M}) appears because the excitation of the medium occurs through
non-resonant intermediate states.
Upon substitution of Eq.~(\ref{Eq:Elec}) into
Eq.~(\ref{Eq:Probability1}), one finds that the TPA signal is
composed by sixteen different terms:
\begin{widetext}
\begin{eqnarray}\label{Eq:Probability2}
S_{\mathrm{g\rightarrow
f}}\left(\tau_\mathrm{s},\tau_\mathrm{i}\right)&=&\frac{1}{\hbar^4}\int_{-\infty}^{\infty}dt_{\mathrm{2}}\int_{-\infty}^{t_{\mathrm{2}}}dt_{\mathrm{1}}\int_{-\infty}^{\infty}dt'_{\mathrm{2}}\int_{-\infty}^{t'_{\mathrm{2}}}dt'_{\mathrm{1}}
M^{*}\left(t_{\mathrm{2}},t_{\mathrm{1}}\right)M\left(t'_{\mathrm{2}},t'_{\mathrm{1}}\right)\nonumber\\
&&\hspace{3mm}\times\bigg[\langle\hat{E}_{\mathrm{s}}^{(-)}\left(t_{\mathrm{2}}\right)\hat{E}_{\mathrm{s}}^{(-)}\left(t_{\mathrm{1}}\right)\hat{E}_{\mathrm{s}}^{(+)}\left(t'_{\mathrm{2}}\right)\hat{E}_{\mathrm{s}}^{(+)}\left(t'_{\mathrm{1}}\right)\rangle+\langle\hat{E}_{\mathrm{s}}^{(-)}\left(t_{\mathrm{2}}\right)\hat{E}_{\mathrm{s}}^{(-)}\left(t_{\mathrm{1}}\right)\hat{E}_{\mathrm{i}}^{(+)}\left(t'_{\mathrm{2}}\right)\hat{E}_{\mathrm{i}}^{(+)}\left(t'_{\mathrm{1}}\right)\rangle\nonumber\\
&&\hspace{10mm}+\langle\hat{E}_{\mathrm{s}}^{(-)}\left(t_{\mathrm{2}}\right)\hat{E}_{\mathrm{s}}^{(-)}\left(t_{\mathrm{1}}\right)\hat{E}_{\mathrm{s}}^{(+)}\left(t'_{\mathrm{2}}\right)\hat{E}_{\mathrm{i}}^{(+)}\left(t'_{\mathrm{1}}\right)\rangle+\langle\hat{E}_{\mathrm{s}}^{(-)}\left(t_{\mathrm{2}}\right)\hat{E}_{\mathrm{s}}^{(-)}\left(t_{\mathrm{1}}\right)\hat{E}_{\mathrm{i}}^{(+)}\left(t'_{\mathrm{2}}\right)\hat{E}_{\mathrm{s}}^{(+)}\left(t'_{\mathrm{1}}\right)\rangle\nonumber\\
&&\hspace{10mm}+\langle\hat{E}_{\mathrm{s}}^{(-)}\left(t_{\mathrm{2}}\right)\hat{E}_{\mathrm{i}}^{(-)}\left(t_{\mathrm{1}}\right)\hat{E}_{\mathrm{s}}^{(+)}\left(t'_{\mathrm{2}}\right)\hat{E}_{\mathrm{s}}^{(+)}\left(t'_{\mathrm{1}}\right)\rangle+\langle\hat{E}_{\mathrm{s}}^{(-)}\left(t_{\mathrm{2}}\right)\hat{E}_{\mathrm{i}}^{(-)}\left(t_{\mathrm{1}}\right)\hat{E}_{\mathrm{s}}^{(+)}\left(t'_{\mathrm{2}}\right)\hat{E}_{\mathrm{i}}^{(+)}\left(t'_{\mathrm{1}}\right)\rangle\nonumber\\
&&\hspace{10mm}+\left.\langle\hat{E}_{\mathrm{s}}^{(-)}\left(t_{\mathrm{2}}\right)\hat{E}_{\mathrm{i}}^{(-)}\left(t_{\mathrm{1}}\right)\hat{E}_{\mathrm{i}}^{(+)}
\left(t'_{\mathrm{2}}\right)\hat{E}_{\mathrm{s}}^{(+)}\left(t'_{\mathrm{1}}\right)\rangle+\langle\hat{E}_{\mathrm{s}}^{(-)}\left(t_{\mathrm{2}}\right)
\hat{E}_{\mathrm{i}}^{(-)}\left(t_{\mathrm{1}}\right)\hat{E}_{\mathrm{i}}^{(+)}\left(t'_{\mathrm{2}}\right)\hat{E}_{\mathrm{i}}^{(+)}\left(t'_{\mathrm{1}}\right)\rangle\right.\nonumber\\
&&\hspace{10mm}+\left\{{\rm s}\leftrightarrow {\rm i}\right\}\bigg]\nonumber\\
&=&I_{\mathrm{ssss}}+I_{\mathrm{iiii}}+I_{\mathrm{sisi}}+I_{\mathrm{siis}}+I_{\mathrm{isis}}+I_{\mathrm{issi}}.\hspace{7cm}
\label{Eq:Probability2}
\end{eqnarray}
\end{widetext}
Notice that we may write the TPA signal as a function of the
mutual delay between the beams given by
$\tau=\left(\tau_\mathrm{s}-\tau_\mathrm{i}\right)$. This delay
can easily be introduced in Eq.~(\ref{Eq:Probability1}) by making
the substitution
$\hat{E}_{\mathrm{s}}(t)\rightarrow\hat{E}_{\mathrm{s}}(t+\tau)$
for the signal field. The symbol $\{\mathrm{s\leftrightarrow i}\}$
stands for the contributions that are obtained by interchanging
the labels $\mathrm{s}$ and $\mathrm{i}$.
Interestingly, one can show that the TPA signal given by
Eq.~(\ref{Eq:Probability2}) contains only six non-vanishing
contributions, corresponding to the terms with even number of
indices $\mathrm{s,i}$. These are collected in the last line of
Eq.~(\ref{Eq:Probability2}). In the following we will discuss the
explicit form of each of these non-vanishing terms.
We start by describing the first two terms, these correspond to
the case where photons from a single signal (idler) beam are
absorbed. This means that the four-point correlation function
describing this process in the signal beam (and similarly in the
idler beam) is $\langle \hat{E}^{(-)}_{\mathrm{s}}
\hat{E}^{(-)}_{\mathrm{s}} \hat{E}^{(+)}_{\mathrm{s}}
\hat{E}^{(+)}_{\mathrm{s}}\rangle$, whose explicit form is given
by
\begin{widetext}
\begin{eqnarray}
I_{\mathrm{ssss}}&=&\frac{1}{\hbar^4}\int_{-\infty}^{\infty}dt_{\mathrm{2}}\int_{-\infty}^{t_{\mathrm{2}}}dt_{\mathrm{1}}\int_{-\infty}^{\infty}dt'_{\mathrm{2}}\int_{-\infty}^{t'_{\mathrm{2}}}dt'_{\mathrm{1}}M^{*}\left(t_{\mathrm{2}},t_{\mathrm{1}}\right)M\left(t'_{\mathrm{2}},t'_{\mathrm{1}}\right)\langle\hat{E}_{\mathrm{s}}^{(-)}\left(t_{\mathrm{2}}\right)\hat{E}_{\mathrm{s}}^{(-)}\left(t_{\mathrm{1}}\right)\hat{E}_{\mathrm{s}}^{(+)}\left(t'_{\mathrm{2}}\right)\hat{E}_{\mathrm{s}}^{(+)}\left(t'_{\mathrm{1}}\right)\rangle\nonumber\\
&=&\frac{1}{\hbar^2 4 \epsilon^2A^2c^2n_{\mathrm s}^2}\int_{-\infty}^{\infty}\
d\omega_{\mathrm
s}\int_{-\infty}^{\infty}d\omega'_{\mathrm
s}\mathcal{K}^{*}\left(\omega_{\mathrm
s}\right)\mathcal{K}\left(\omega'_{\mathrm
s}\right)\left[F_{1\mathrm s}\left(\varepsilon_{\mathrm f}-\varepsilon_{\mathrm g}-\omega_{\mathrm
s},\omega'_{\mathrm s}\right)F_{1\mathrm s}\left(\omega_{\mathrm
s},\varepsilon_{\mathrm f}-\varepsilon_{\mathrm g}-\omega'_{\mathrm s}\right)\right.+\nonumber\\
&&\left.F_{1\mathrm s}\left(\varepsilon_{\mathrm f}-\varepsilon_{\mathrm g}-\omega_{\mathrm
s},\varepsilon_{\mathrm f}-\varepsilon_{\mathrm g}-\omega'_{\mathrm
s}\right)F_{1\mathrm s}\left(\omega_{\mathrm
s},\omega'_{\mathrm s}\right)\right],
\label{Eq:20}
\end{eqnarray}
\end{widetext}
where the spectral response of the medium is given by the function $\mathcal{K}\left(\omega\right)$,
\begin{equation}
\mathcal{K}\left(\omega\right)=\sum_k\frac{\mu_{\mathrm{f}k}\mu_{k\mathrm{g}}}{\varepsilon_{k}-\varepsilon_{\mathrm{g}}-\omega},
\end{equation}
and the spectral functions of the fields are described by $F_{\mathrm{1i,1s}}$. The spectral functions $F_\mathrm{1j}$, with
$\mathrm{j=i,s}$, contain information about the \emph{classical
correlations} of the photons and they are given by
\cite{torres-company2011}
\begin{equation}
F_{\mathrm{
1j}}\left(\omega,\omega'\right)=\sum_g\sqrt{\omega\omega'}f^*_{\mathrm{j},g}\left(\omega\right)f_{\mathrm{j},g}\left(\omega'\right)|v_{g}|^2.
\end{equation}
Note that, as expected, the first two non-vanishing terms of
Eq.~(\ref{Eq:Probability2}) do not depend on the mutual delay
between the signal and idler beams. This implies that these
contributions represent a background noise for VSS, as they do not
carry spectroscopic information about the sample.
The next contribution, $I_\mathrm{sisi}$, may explicitly be written as
\begin{widetext}
\begin{eqnarray}
I_{\mathrm{sisi}}\left(\tau_\mathrm{s},\tau_\mathrm{i}\right)&=&\frac{1}{\hbar^4}\int_{-\infty}^{\infty}dt_{\mathrm{2}}\int_{-\infty}^{t_{\mathrm{2}}}dt_{\mathrm{1}}\int_{-\infty}^{\infty}dt'_{\mathrm{2}}\int_{-\infty}^{t'_{\mathrm{2}}}dt'_{\mathrm{1}}M^{*}\left(t_{\mathrm{2}},t_{\mathrm{1}}\right)M\left(t'_{\mathrm{2}},t'_{\mathrm{1}}\right)\langle\hat{E}_{\mathrm{s}}^{(-)}\left(t_{\mathrm{2}}\right)\hat{E}_{\mathrm{i}}^{(-)}\left(t_{\mathrm{1}}\right)\hat{E}_{\mathrm{s}}^{(+)}\left(t'_{\mathrm{2}}\right)\hat{E}_{\mathrm{i}}^{(+)}\left(t'_{\mathrm{1}}\right)\rangle\nonumber\\
&=&\frac{1}{\hbar^2 4 \epsilon^2A^2c^2n_{\mathrm s}n_{\mathrm
i}}\int_{-\infty}^{\infty}\
d\omega_{\mathrm
i}\int_{-\infty}^{\infty}d\omega'_{\mathrm
i}\mathcal{K}^{*}\left(\omega_{\mathrm
i}\right)\mathcal{K}\left(\omega'_{\mathrm
i}\right)\exp\left[{i\left(\omega_{\mathrm
i}-\omega'_{\mathrm i}\right)
\left(\tau_\mathrm{i}-\tau_\mathrm{s}\right)}\right]\nonumber\\
&&\hspace{-3mm} \times
\left[F^*_2\left(\varepsilon_{\mathrm f}-\varepsilon_{\mathrm g}-\omega_{\mathrm
i},\omega_{\mathrm
i}\right)F_2\left(\varepsilon_{\mathrm f}-\varepsilon_{\mathrm g}-\omega'_{\mathrm
i},\omega'_{\mathrm i}\right)+
F_{1\mathrm i}\left(\omega_{\mathrm
i},\omega'_{\mathrm i}\right)F_{1\mathrm s}\left(\varepsilon_{\mathrm f}-E_{\mathrm
g}-\omega_{\mathrm
i},\varepsilon_{\mathrm f}-\varepsilon_{\mathrm g}-\omega'_{\mathrm i}\right)\right].
\label{Eq:23}
\end{eqnarray}
\end{widetext}
Notably, this term contains the function $F_2$, which is directly
related to the \emph{quantum correlations} between the fields and
is defined by \cite{torres-company2011}
\begin{equation}
F_{2}\left(\omega,\omega'\right)=\sum_g\sqrt{\omega\omega'}f_{\mathrm{s},g}\left(\omega\right)f_{\mathrm{i},g}\left(\omega'\right)v_{g}u_{g}.
\end{equation}
{\color{blue}}
The fourth term, $I_{\mathrm siis}$, is equal to the cross correlation
$\mathrm{(si)-(is)}$. Here, it is
important to highlight the fact that $ \mathrm{(si)}$ and $ \mathrm{(is)}$ are
not mutually interchangeable as time-ordering must be satisfied. Consequently,
this term writes
\begin{widetext}
\begin{eqnarray}
I_{\mathrm{siis}}\left(\tau_\mathrm{s},\tau_\mathrm{i}\right)&=&\frac{1}{\hbar^4}\int_{-\infty}^{\infty}dt_{\mathrm{2}}\int_{-\infty}^{t_{\mathrm{2}}}dt_{\mathrm{1}}\int_{-\infty}^{\infty}dt'_{\mathrm{2}}\int_{-\infty}^{t'_{\mathrm{2}}}dt'_{\mathrm{1}}
M^{*}\left(t_{\mathrm{2}},t_{\mathrm{1}}\right)M\left(t'_{\mathrm{2}},t'_{\mathrm{1}}\right)\langle\hat{E}_{\mathrm{s}}^{(-)}\left(t_{\mathrm{2}}\right)\hat{E}_{\mathrm{i}}^{(-)}\left(t_{\mathrm{1}}\right)\hat{E}_{\mathrm{i}}^{(+)}\left(t'_{\mathrm{2}}\right)\hat{E}_{\mathrm{s}}^{(+)}\left(t'_{\mathrm{1}}\right)\rangle\nonumber\\
&=&\frac{1}{\hbar^2 4 \epsilon^2A^2c^2n_{\mathrm s}n_{\mathrm
i}}\int_{-\infty}^{\infty}\
d\omega_{\mathrm
i}\int_{-\infty}^{\infty}d\omega_{\mathrm
s}\mathcal{K}^{*}\left(\omega_{\mathrm
i}\right)
\mathcal{K}\left(\omega_{\mathrm s}\right)\exp\left[{i\left(\omega_{\mathrm
i}+\omega_{\mathrm
s}\right)\left(\tau_\mathrm{i}-\tau_\mathrm{s}\right)+i\left(\varepsilon_{\mathrm f}-\varepsilon_{\mathrm g}\right)\left(\tau_\mathrm{s}-\tau_\mathrm{i}\right)}\right]\nonumber\\
&&\hspace{-3mm} \times \left[
F^{*}_{\mathrm {2}}\left(\varepsilon_{\mathrm f}-\varepsilon_{\mathrm g}-\omega_{\mathrm
i},\omega_{\mathrm
i}\right)F_{\mathrm {2}}\left(\omega_{\mathrm s},\varepsilon_{\mathrm f}-\varepsilon_{\mathrm g}-\omega_{\mathrm s}\right)+
F_{1\mathrm{s}}\left(\varepsilon_{\mathrm f}-\varepsilon_{\mathrm g}-\omega_{\mathrm
i},\omega_{\mathrm
s}\right)F_{1\mathrm{i}}\left(\omega_{\mathrm i},\varepsilon_{\mathrm f}-\varepsilon_{\mathrm g}-\omega_{\mathrm
s}\right)\right].
\label{Eq:24}
\end{eqnarray}
\end{widetext}
The remaining terms are easily obtained by interchanging the label
$\mathrm{s}$ and $\mathrm{i}$ in Eqs.~(\ref{Eq:23}) and
(\ref{Eq:24}), respectively.
\section{Virtual-state spectroscopy with entangled beams}
\begin{figure}[b!]
\centering
\includegraphics[width=8cm]{Fig2.eps}
\caption{TPA spectrogram as a function of the number $N_{signal}$ of photons in the
twin beam; the delay range considered is $0\leq\tau\leq 8$ ps,
the length of the nonlinear crystal is L = 1 mm and the pump pulse
duration is set to $\tau_p$ = 1 ps, and the inverse group velocities
are set to $G_s$ = 5.2 ps/m and $G_i$ = 5.6 ps/m. For the sake of simplicity, the energy axis is defined by means of the energy mismatch: $2\varepsilon_{k} - \varepsilon_{\mathrm{f}}$.}
\label{Fig:spectrogram}
\end{figure}
We are now ready to discuss the implementation of the VSS protocol
with intense twin beams. For this, we consider a simple model
system in which the two-photon excitation energy of the medium
$|\mathrm{g}\rangle\rightarrow|\mathrm{f}\rangle$ corresponds to
the pump wavelength $\lambda_\mathrm{p0}=400$ nm
($E_{\mathrm{f}}=3.1$ eV considering $\varepsilon_{\mathrm{g}}=0$
eV). The intermediate-level energies are randomly chosen to be
$\varepsilon_{k}=\left(\varepsilon_{\mathrm{f}}+\{0.05, 0.075,
0.089\}\right)/2$ eV. Following this energy-level configuration,
we consider a nonlinear crystal producing degenerate photon pairs
with a wavelength of 800 nm. Notice that the central frequency of
the down-converted photons does not match any of the intermediate
states, thus making them effectively non-resonant (or virtual)
transitions. Moreover, the energies of these transitions, although
random, are kept close to the central frequency of the photons.
The reason for this lies in the fact that entangled two-photon
absorption is optimal under conditions of near-resonance between
entangled photons and the intermediate states \cite{upton2013}.
Finally, we assume the group velocity matching condition
\cite{keller1997}: $G_{\mathrm p}=(G_{\mathrm s}+G_{\mathrm
i})/2$, with $G_s$, $G_i$ and $G_p$ being in turn the inverse
group velocities of the signal, idler and pump beams. We have
considered this condition because it allows for a simple
interpretation and control of the correlations between the photon
beams.
\begin{figure}[t!]
\begin{tabular}{cc}
\includegraphics[width=8.5cm]{Fig3.eps}
\end{tabular}
\caption{TPA spectrograms, and their corresponding average, for twin beams
carrying (a,b) $N_s=1$, (c,d) $N_s=10$, and (e,f) $N_s=100$ photons.
Average was performed over and ensemble of 100 crystals of different
lengths $L\in\llav{20,22}$ mm. The vertical grey lines indicate the
relative energies, $2\varepsilon_{k} - \varepsilon_{\mathrm{f}}$, of the intermediate levels.}
\label{Fig:average_spectrogram}
\end{figure}
Figure~\ref{Fig:spectrogram} shows the TPA spectrogram
--- Fourier transform w.r.t. the delay between beams, of the TPA
signal --- as a function of the number of photons
$N_\mathrm{signal}\equiv N_{\mathrm{s}}= N_{\mathrm{i}}$ carried
by the twin beam. We can immediately see from
Fig.~\ref{Fig:spectrogram} that several peaks emerge from the
Fourier transform of the TPA signal. These peaks appear as a
result of the interference between different pathways through
which two-photon excitation of the medium can occur
\cite{Saleh1998Entangled,Leon2013Role}. Concurrently, as pointed
out previously \cite{svozilik2016practical}, we can see that the
visibility of the TPA signal is affected as the number of photons
$N_{\text{signal}}$ is increased, thus defining a limit in the
photon flux at which VSS can be implemented. Interestingly, one
can make use of the signal shown in Fig.~\ref{Fig:spectrogram} to
extract information related to the energy level structure of the
medium
\cite{Saleh1998Entangled,Perina1998Multiphoton,Leon2013Role}. To
do so, we perform an average of the normalized TPA spectrograms
over different crystal lengths,
\begin{equation}
\tilde{S}_{g\rightarrow f}\pare{\tau} = \frac{1}{N}\sum_{n=1}^{N} \frac{S_{g\rightarrow f}\pare{\tau;L_n}}{\text{max}\llav{S_{g\rightarrow f}\pare{\tau;L_n}}},
\end{equation}
where $N$ is the number of crystal lengths used to obtain the
corresponding TPA signals. Notice that by changing the crystal
length, one effectively modifies the correlation (entanglement)
time between photons
\cite{Saleh1998Entangled,Perina1998Multiphoton,Leon2013Role},
which means that the average is effectively performed over
different correlation times. Therefore, we can experimentally
obtain the average of the TPA signals by using different
strategies, depending on the configuration of the setup that is
being used. For instance, in type-I SPDC, changing the width of
the pump beam modifies the correlation between photons
\cite{joobeur1994}, whereas in type-II, the configuration used in
this work, the correlation time is linearly proportional to the
crystal length \cite{shih1994}, so a proper set of two
wedge-shaped nonlinear/compensation crystals might be used.
Another alternative to control the correlation time of the photons
is by introducing frequency chirps in either the pump pulse or
down-converted beams \cite{svozilik2016practical}, or by changing
the time duration of the pump, as depicted in Fig.~4.
\begin{figure}[b!]
\begin{tabular}{cc}
\includegraphics[width=8.5cm]{Fig4_new.eps}
\end{tabular}
\caption{Delay-integrated TPA signal (left column) for
spectrally (a) anti-correlated,
(c) uncorrelated, and (e) correlated two-photon states, and their
corresponding Schmidt decomposition (right column). The
symbols $\nu_{\rm s,i}=\omega_{\rm s,i} -
\omega_{\rm s,i}^{0}$ stand for the frequency deviations from the
central
frequency $\omega_{s,i}^0$ of the photon fields. Integration of the
signals was performed over a delay range $\Delta \tau$
of $0 \leq\tau\leq 8$ ps. The length of the nonlinear crystal is
$L=1$~mm, and the pump pulse duration was set to (a) $\tau_{\mathrm p}
= 20$~fs, (c) $\tau_{\mathrm p} = 110$~fs, and (e) $\tau_{\mathrm p} =
1$~ps.}
\label{Fig:Threshold}
\end{figure}
Figure~\ref{Fig:average_spectrogram} shows the TPA spectrograms,
and their corresponding average over $100$ crystal lengths, for
twin beams carrying (a,b) $N_s=1$, (c,d) $N_s=10$, and (e,f)
$N_s=100$ photons. Notice that by averaging the TPA spectrograms
only three peaks remain in the signal, whose locations reveal the
energy of the intermediate states that contribute to the
two-photon excitation of the medium. Interestingly, the results in
Figs.~\ref{Fig:spectrogram} and \ref{Fig:average_spectrogram} show
that although VSS can be implemented with entangled fields
carrying a large number of photons, there exists a threshold in
the photon-pair number, as the height of the peaks with respect to
the background noise (signal-to-noise ratio) gets diminished with
increasingly larger photon fluxes. It is important to remark that
in obtaining the results shown in
Fig.~\ref{Fig:average_spectrogram}, we have assumed that the
temporal walk-off of the photons is much shorter than the lifetime
of the intermediate levels.
To explore the limits on the photon flux that can be used in the
implementation of VSS, we now analyze the terms that contribute to
the overall TPA signal. For the sake of simplicity, we divide all
terms into three different groups. The first group
($I_{\text{noise}}$) contains the terms that are independent of
the delay between the beams, namely the first two terms of
Eq.~(\ref{Eq:Probability2}). As we discussed above, these terms do
not contain spectroscopic information and represent a background
noise of the TPA signal. The second group ($I_{\text{class}}$)
contains the terms related to the classical correlations,
represented by those containing products of the functions
$F_\mathrm{1j}$, with $\mathrm{j=s,i}$ [see Eqs.~(\ref{Eq:23}) and
(\ref{Eq:24})]. Notice that these functions contain single-beam
correlations only. Finally, the third group ($I_{\text{quant}}$),
which depends on products of the functions $F_{2}$, represents the
quantum correlations between the two photon fields. This final
group is the most important one, as it contains the information
about the intermediate-state transitions occurring during the TPA
process.
Figure~\ref{Fig:Threshold} shows the delay-integrated TPA
contributions, considering three different initial states, namely
spectrally (a,b) anti-correlated, (c,d) quasi uncorrelated, and
(e,f) correlated photons. The delay-integrated signals are
obtained by integrating the TPA signal [Eq.
(\ref{Eq:Probability2})] over a delay interval $\Delta\tau$, while
fixing the correlation time between photons by means of the
pump-pulse duration $\tau_p$. Notice that the delay-integrated
signals with varying frequency correlations [depicted in
Figs.~\ref{Fig:Threshold}(b,d,f)] reflect the mutual interplay
between all participating terms (noise, classical, and quantum).
More importantly, they show that quantum contributions (blue solid
line), where spectroscopic information about the sample resides,
dominates in a low-to-moderate photon flux regime for
anti-correlated and quasi uncorrelated photons. This effect can be
understood in terms of the Schmidt modes of the two-photon state
[depicted in Figs.~\ref{Fig:Threshold}(b,d)]. As the number of
photons is increased, the number of effectively populated Schmidt
modes becomes smaller. The reduction of populated Schmidt modes
results in a reduced spectral overlap between the absorbed
entangled photons and the sample under study, thus lowering the
spectroscopic resolution of the system.
Remarkably, when correlated photons interact with the sample, we
find that the signal carrying useful information is completely
suppressed. This demonstrates the fact that entanglement alone is
not the key ingredient for implementing VSS, but rather a
combination of entanglement and anti-correlation of the absorbed
photons \cite{Leon2013Role}. In particular, for our model system,
the use of spectrally anti-correlated photons guarantees that the
transition from the quantum (linear) to the classical (quadratic)
regime occurs around $N_\mathrm{signal} \approx 10^4$ signal
photons. It is important to remark that this photon-number limit
is valid for the model system considered here. As we discussed
above, this limit strongly depends on the number of Schmidt modes
contained in the photon spectra. Indeed, as shown in
Fig.~\ref{Fig:5}, a broader spectrum of anti-correlated photons
will push the limit towards higher values of photon numbers,
whereas a narrower spectrum will reduce the photon flux at which
VSS can be successfully implemented.
\begin{figure}[t]
\begin{tabular}{cc}
\includegraphics[width=8.5cm]{Fig5.eps}
\end{tabular}
\caption{Delay-integrated TPA signal {\color{blue}(left column)} for the
fixed
pump-duration $\tau_{\mathrm p}=1$~ps for different values of the
crystal length (a)
L=0.75~mm and (c) L=5~mm with the corresponding Schmidt
numbers (right column) plotted in (b) and (d). Integration of the signals was
performed over a delay range $\Delta \tau$} of $0
\leq\tau\leq 8$ ps.
\label{Fig:5}
\end{figure}
Finally, notice that the Schmidt number $K_\mathrm{UV}$ is
inversely related to the length of crystal $L$, as depicted in
Fig.~\ref{Fig:5}. From here we can see that the use of shorter lengths of the
crystal produces a broader spectrum, with rich spatial structure, in the produced photon fields. This shows the many knobs that non-classical light provides to emerging nonlinear spectroscopy techniques.
\vspace{4mm}
\section{Conclusions}
We have presented a thorough analysis of the
virtual-state spectroscopy technique implemented with intense twin
beams. We showed that the virtual-state spectroscopy may be
implemented with entangled twin beams carrying up to $10^4$
photon pairs, provided that a proper configuration of the experimental setup
and a particular shape of the spectral correlations between photons is
selected. Our results suggest that by making use of intense twin beams one
might be able to detect two-photon absorption signals up to four orders of
magnitude larger than previously reported, thus paving the way towards the first
experimental implementation of the virtual-state spectroscopy
technique.
\section*{Acknowledgment}
JS thanks Alejandra Catalina Valencia Gonz\'{a}lez and Mayerlin Nu\~{n}ez
Portela for useful and stimulating discussions. JS also acknowledges the
Faculty of Science of Universidad de los Andes. This work was supported by
projects 17-23005Y (JS) and 15-08971S (JP) of the Czech Science
Foundation, and project LO1305 of M\v{S}MT \v{C}R. RJLM gratefully acknowledge financial support from DGAPA-UNAM, Mexico, under the project UNAM-PAPIIT IA100718.
| {
"redpajama_set_name": "RedPajamaArXiv"
} | 733 |
\section{Introduction} \label{s1}
\subsection{Preliminaries} \label{s1.1}
In this paper we consider Maxwellian electromagnetic fields in the
flat Min\-kowski spacetime with the metric tensor $g_{\mu\nu}=
\textnormal{diag}(+1,-1,-1,-1)$, thus taking Cartesian coordinates
(algebraic relations used or deduced here, frequently remain
unaltered also in the framework of general relativity). Greek
indices are four- and Latin, three-dimensional. However we more
frequently use as three-dimensional quantities four-dimensional
vectors (tensors) orthogonal to the timelike unit vector
describing the reference frame (the monad). Different frames may
be simultaneously applied (the test-object property which is
essential in treatment of reference frames in non-quantum theory).
In general, we do not mutually relate reference frames and systems
of coordinates. A comma ($\,_,$) followed by an index is used to
denote partial differentiation with respect to the corresponding
coordinate. We also use natural units in which the velocity of
light in a vacuum is $c=1$. Round brackets mean symmetrization and
square brackets, antisymmetrization in the indices contained in
them (the so-called Bach brackets). In concrete calculations no
approximations are assumed.
This material is essentially the final chapter of my unpublished
one-semester course ``Relativistic Physics'' given to
undergraduate (Licenciatura) students at the Physics Department of
the University of Guadalajara during the last seven years. The
students first have to attend another course on tensor calculus
which also includes the formalism of Cartan forms with some
applications in physics. The subsection \ref{s4.2} was included in
my course only in the last semester.
\subsection{Preview of the paper} \label{s1.2}
More than one hundred years ago, A. Li\'enard \cite{Lien} and E.
Wiechert \cite{Wiech} discovered an exact solution of Maxwell's
equations describing electromagnetic field of a pointlike electric
charge in an arbitrary motion. A frequently used treatment of this
solution can be found in \cite{LanLif}, and its more general
deduction, including the use of an arbitrary mixture of retarded
and advanced potentials, in \cite{SyngeSR}. In section~\ref{s2} we
consider a simple and direct deduction of the Li\'enard--Wiechert
(below abbreviated as LW) solution with the use of the light cone
concept which involves a supposition of lightlike propagation of
information from this pointlike source. Some important general
properties of the LW solution are discussed in section~\ref{s3}.
Here a general classification of electromagnetic fields is
outlined, and it is found that the LW field belongs to the pure
electric type, thus its magnetic part can be transformed away when
one passes to certain non-inertial reference frames. It is well
known that in a vacuum electromagnetic waves propagate with the
fundamental velocity $c$ ($=1$). However, as it is shown in
section~\ref{s4}, a mixture of non-radiative and radiative
electromagnetic fields has another propagation velocity ($<1$).
For this reason, when we speak above and in sections \ref{s2} and
\ref{s5} about `propagation of information,' we do not speak
strictly about propagation of electromagnetic field in the general
sense. In subsection~\ref{s4.2} the general method of finding
reference frames co-moving with electromagnetic fields is
formulated (mostly for the case of pure subtypes of electric or
magnetic types of fields {\it via} transformation away of the
magnetic or electric field, respectively; however also in the
impure subtypes, though there it is impossible to transform away
one or --- asymptotically
--- both fields {\bf E} and {\bf B}, one always may make these
fields mutually parallel, thus transforming away the Poynting
vector in the respective frame). In frames co-moving with the
electromagnetic field, the Poynting vector automatically vanishes.
This method is then applied to the LW field. Relative motion of
different reference frames is considered in subsection~\ref{s4.3},
first in general and then for the LW solution. In section~\ref{s5}
some results obtained in the paper are discussed. In two
appendices, \ref{sA} and \ref{sB}, a short review of the
Ehlers--Zel'manov covariant theory of reference frames (its
algebraic part) is given together with applications to the
description of electric and magnetic fields.
\section{A systematic deduction of the LW
solution} \setcounter{equation}{0} \label{s2}
Let us consider a pointlike charge $Q$ in a motion along a
worldline $L$ parametrically described as \begin{equation} \textnormal{{\bf
r}}'=\textnormal{{\bf r}}'(t'), ~ \mathrm{ equivalently, } ~
x'^i=x'^i(t'), \end{equation} $t'=x'^0$, $i=1, ~ 2, ~ 3$. We shall determine
at an arbitrary, but fixed spacetime point $P$ with coordinates
$x^\mu$ (not on $L$), the electromagnetic field created by the
charge $Q$ being at another point $P'$ on $L$; the coordinates are
chosen to be Cartesian. It is obvious that the electromagnetic
field created by a pointlike charge should have a singularity on
$L$, this is why we exclude here the case of coincidence of the
points $P$ and $P'$. Note that the coordinates of $P$ represent
four independent scalar variables $x^\mu$, and those of $P'$
merely are scalar functions of some parameter (this may be $s'$,
but we shall use the retarded time $t'$) along the worldline $L$,
$x'^\mu(t')$ (there are three equations, the fourth being simply
an identity, $x'^0=t'$). To mutually relate the spacetime points
$P$ and $P'$, we use a hypothesis that the information about
position and state of motion of the charge propagates with the
fundamental velocity (that of light) in an accordance with the
relativistic causality law. If the point $P$ and worldline $L$ are
given, the point $P'$ can be determined as that of intersection of
the past light cone with a vertex at $P$ and the line $L$ (this
simultaneously means that $P$ is on the future light cone with a
vertex at $P'$). This constructive definition is important in the
subsequent calculations, but fortunately the concrete relation
between the position of $P$ and the corresponding retarded time
$t'$ at $P'$ turns out to be of no importance. Thus $t'$ is a
function of all four coordinates of $P$ --- we write it as
$t'(x)$; we shall easily calculate the explicit form of
derivatives of $t'$ with respect to the coordinates $x^\mu$
without an explicit knowledge of $t'(x)$.
We take the Minkowski metric as $g_{\mu\nu}=g^{\mu\nu}=
\textnormal{diag} (+1,-1,-1,-1)$ (in fact, this is the definition
of Cartesian coordinates), thus the tangent vector to $L$,
$u'^\mu=dx'^\mu/ds'$ (the four-velocity of the charge) taken at
the retarded point $P'$, is timelike and unitary ($u'\cdot u'
\equiv u'^\mu u'_\mu=1$), its timelike property being manifested
by the relation $ds'^2>0$ along $L$. Locally, $u'$ determines the
direction of growth of the proper time $s'$, being simultaneously
the projector onto the (retarded) physical time direction of the
(retarded) reference frame (retardedly) co-moving with the charge.
Another projector, now a tensor, can be constructed as
(\ref{bproj}), here \begin{equation} \label{bmunu} b_{\mu\nu}=
g_{\mu\nu}-u'_\mu u'_\nu. \end{equation} It is (a) symmetric ($b_{\mu\nu}=
b_{\nu\mu}$), (b) orthogonal to $u'$, thus realizing projection
onto the subspace $\perp u'$ (the physical three-space of the just
mentioned inertial reference frame at $P'$); (c) it possesses the
property of idempotent ($b^\mu_\lambda b^\lambda_\nu=b^\mu_\nu$
with det\,$b^\mu_\lambda= 0$), and (d) plays the r\^ole of the
three-dimensional metric in the mentioned subspace, with the
signature $(0,-,-,-)$ (zero is inserted in the four-dimensional
sense). Thus $g^\lambda_\lambda \equiv\delta^\lambda_\lambda=4$
and $b^\lambda_\lambda=3$ give dimensionalities of the space-time
and subspace under consideration.
Let us introduce a vector connecting the four-points (events) $P'$
and $P$, \begin{equation} \label{R} R^\mu=x^\mu-x'^\mu(t'). \end{equation} Of course, this
is not a vector under more general transformations than the
Lorentz ones (like the Euclidean `radius vector' is a vector only
in Cartesian systems). Since $R^\mu$ lies on the light cone, \begin{equation}
\label{RR} R^\mu R_\mu=0, \end{equation} this vector is null. Its projection
onto $u'$ is denoted as $D$, and onto the retarded three-space, as
$\textnormal{\bf D}^\mu$: \begin{equation} \label{D} D:=u'^\mu R_\mu\equiv
u'\cdot R, ~ ~ ~ \textnormal{\bf D}^\mu=R^\nu b^\mu_\nu=R^\mu-
Du'^\mu, ~ ~ \textnormal{\bf D}\perp u'. \end{equation} Due to (\ref{bmunu}),
$\Rightarrow \delta^\mu_\nu=b^\mu_\nu+u'^\mu u'_\nu$, and the null
property (\ref{RR}), \begin{equation} \label{D.D} \textnormal{\bf D}^\mu
\textnormal{\bf D}_\mu=-D^2, ~ ~ ~ D=\sqrt{-\textnormal{\bf
D}^\mu\textnormal{\bf D}_\mu}, \end{equation} thus we call $\textnormal{\bf
D}^\mu$ the `retarded spatially projected vector between $P'$ and
$P$.' Similarly, $D$ is interpreted as the retarded
three-dimensional distance between $P'$ and $P$. Recall also that
\begin{equation} \label{uexp} u'^\mu=\frac{dx'^\mu}{ds'}=
\frac{dx'^0}{ds'}\frac{dx'^\mu}{dx'^0}=u'^0\cdot(1,v'^i). \end{equation}
Now we are ready to calculate all necessary derivatives (of $t'$,
$R^\mu$, $D$, $u'^\mu$, and more) with respect to $x^\mu$. The
first step is to write
$$
{R^\mu}_{,\alpha}=\frac{\partial x^\mu}{\partial
x^\alpha}-\frac{\partial x'^\mu}{\partial
x^\alpha}=\delta^\mu_\alpha-\frac{dx'^\mu}{ds'}\frac{ds'}{dt'}
\frac{\partial t'}{\partial x^\alpha},
$$
that is, \begin{equation} \label{t,} {R^\mu}_{,\alpha}=\delta^\mu_\alpha-
\frac{u'^\mu}{u'^0} t'_{,\alpha}. \end{equation} Differentiation of
(\ref{RR}) yields
$$
R_\mu{R^\mu}_{,\alpha}\equiv\frac{1}{2}\left(R_\mu R^\mu
\right)_{,\alpha}=0,
$$
thus \begin{equation} t'_{,\alpha}=\frac{u'^0 R_\alpha}{D}, \end{equation} and its
substitution into (\ref{t,}) yields \begin{equation}
{R^\mu}_{,\alpha}=\delta^\mu_\alpha-\frac{u'^\mu R_\alpha}{D}. \end{equation}
Now, \begin{equation} \label{diffu} {u'^\mu}_{,\alpha}=\frac{du'^\mu}{dt'}
t'_{,\alpha}= \frac{du'^\mu}{ds'}\frac{ds'}{dt'}t'_{,\alpha}=
\frac{a'^\mu R_\alpha}{D} \end{equation} (similar derivatives of all primed
objects are proportional to $R$ with the differentiation
subindex), where \begin{equation} a'^\mu= \frac{du'^\mu}{ds'} \end{equation} is the
acceleration four-vector (at $P'$) obviously possessing the
property of four-orthogonality to $u'$: \begin{equation} u'^\mu a'_\mu\equiv 0.
\end{equation} This use of the acceleration four-vector is more economic than
of the respective three-vector, though their mutual relation is
somewhat indirect; the reader, beginning with (\ref{a4-3}), may
easily reconstruct the corresponding formulae and apply them to
interpretation of the results and to make a comparison with the
treatment of LW problem in \cite{LanLif}. The final step in this
part of calculations is to differentiate $D$: \begin{equation} D_{,\alpha}=(u'
\cdot R)_{,\alpha}=u'_{\mu, \alpha}R^\mu+u'_\mu{R^\mu}_{,\alpha}
=u'_\alpha-\frac{R_\alpha}{D}(1-a'\cdot R) \end{equation} where, of course,
$a'\cdot R:= a'_\mu R^\mu\equiv a'\cdot\textnormal{\bf D}$. Let us
also take into account that \begin{equation} \label{divR} {R^\nu}_{,\nu}=3 ~
\textnormal{ and } {a'^\mu}_{,\nu}= \frac{da'^\mu}{ds'}\,\!
\frac{R_\nu}{D} \end{equation} [see a comment to (\ref{diffu})].
The second, and last, preparatory part of our calculations is to
write down Maxwell's equations. Outside the sources, their
four-dimensional form is \begin{equation} \label{Max} {F^{\mu\nu}}_{,\nu}=0 \end{equation}
where \begin{equation} F_{\mu\nu}=A_{\nu,\mu}-A_{\mu,\nu} \end{equation} is the field
tensor written in terms of the four-potential $A_\mu$, thus
${F^{\mu\nu}}_{,\nu}=\square A^\mu+\left({A^\nu}_{,\nu}\right)^{,
\mu}=0$, the d'Alembertian operator being $\square=\Delta-
\partial^2/\partial t^2$. The ${A^\nu}_{,\nu}$-term can be
eliminated if we use the Lorenz condition\footnote{This condition
is due not to H.A.~Lorentz as admits the majority of physicists,
but to L.V.~Lorenz (born in Elsinore, Denmark, in 1829), see the
footnote related to formula (5.1.47) in \cite{PenRin}, p. 321.}
\begin{equation} \label{LorCond} {A^\nu}_{,\nu}=0 \end{equation} which only fixes global
gauge of the four-potential without any other restrictions. The
alternative form of Maxwell's equations should then include the
Lorenz condition, thus in the form of a system \begin{equation} \label{Maxw}
\square A^\mu=0 ~ ~ \textnormal{and} ~ ~ {A^\nu}_{,\nu}=0. \end{equation} The
well-known Coulomb potential in a vacuum in electrostatics can be
written as $A^\mu=\frac{Q}{r}\delta^\mu_0$ for a pointlike charge
$Q$ located at the spatial origin. One notices that the
four-velocity of the charge at rest is $u'^\mu=u^\mu=
\delta^\mu_0$. This potential exactly satisfies both equations of
(\ref{Maxw}) when $\textnormal{{\bf r}}\neq 0$. We shall now show
that a simple generalization of the Coulomb potential is also an
exact solution of Maxwell's equations, and this is precisely that
of Li\'enard--Wiechert.
The generalization is simply \begin{equation} \label{LW} A^\mu=
\frac{Qu'^\mu}{D}. \end{equation} The proof that this is the exact solution
is quite short for the Lorenz condition:
$$
{A^\nu}_{,\nu}=\frac{Q}{D}\left({u'^\nu}_{,\nu}-\frac{u'^\nu
D_{,\nu}}{D}\right)=\frac{Q}{D^2}\left[a'\cdot R-1+\frac{R_\nu
u'^\nu}{D}\left(1-a'\cdot R\right)\right]\equiv 0,
$$
and for the d'Alembert equation [the first in (\ref{Maxw})], a
little tedious. First, we calculate \begin{equation} \label{Amunu} A_{\mu,
\nu}=\frac{Q}{D^2}\left[a'_\mu R_\nu-u'_\mu\left(u'_\nu
-R_\nu\frac{1-a'\cdot R}{D}\right)\right]. \end{equation} Turning now to the
rest of (\ref{Maxw}), we see that it is necessary to consider
$\square A_\mu=-{A_{\mu,\nu}}^{,\nu}$, taking into account
(\ref{divR}) and the already known derivatives of $u'$, $a'$,
$R^\alpha$, and $D$. The reader can verify after performing
differentiation that for $D\neq 0$ all terms identically cancel:
$$
\left\{\frac{Q}{D^2}\left[a'_\mu R^\nu-u'_\mu\left(u'^\nu-R^\nu
\frac{1-a'\cdot R}{D}\right)\right]\right\}_{,\nu} \equiv 0.
$$
This completes the proof.
Since we shall need the full expression of $F_{\mu\nu}$ in the
subsequent calculations, let us now antisymmetrize the expression
(\ref{Amunu}) (the first term in round brackets is immediately
cancelled): \begin{equation} \label{Fmunu} F_{\mu\nu}=\frac{Q}{D^2}\left[R_\mu
\left( a'_\nu+u'_\nu \frac{1-a'\cdot R}{D}\right)- R_\nu\left(
a'_\mu+u'_\mu \frac{1-a'\cdot R}{D}\right) \right]. \end{equation} This is a
specific type of skew-symmetric tensor sometimes called {\it
simple bivector} since it represents an antisymmetrization of only
two vectors, $R^\mu$ (\ref{R}) and $U^\mu=\frac{Q}{D^2}\left(
a'^\mu+u'^\mu \frac{1-a'\cdot R}{D} \right)$: \begin{equation} \label{FRU}
F_{\mu\nu}=R_\mu U_\nu-U_\mu R_\nu \end{equation} which can be written as a
2-form $F=R\wedge U$, $R=R_\mu dx^\mu$ and $U=U_\mu dx^\mu$.
\section{General properties of the LW field}
\setcounter{equation}{0} \label{s3}
First it is worth mentioning the obvious fact that the Coulomb
field is a special case of the LW solution: one simply has to
consider a pointlike charge at rest, that is $u'^\mu
=\delta^\mu_0$ for any $P'$, thus $a'^\mu=0$. This is the reason
why the LW solution has to be interpreted as the electromagnetic
field of an arbitrarily moving pointlike charge (of course, the
Gauss theorem is here also applicable, for example, in an inertial
frame instantaneously co-moving with the central charge at $P'$).
\subsection{Classification of electromagnetic fields and its
application to the LW solution} \label{s3.1}
The classification of electromagnetic fields is based on existence
of only two invariants built with the field tensor $F_{\mu\nu}$,
while all other invariants are merely algebraic functions of these
two (if not vanish identically). The first invariant is
$I_1=F_{\mu\nu} F^{\mu\nu}=2(\textnormal{{\bf
B}}^2-\textnormal{{\bf E}}^2)$, and the second, $I_2=
F\!\stackrel{\textnormal{\small$\ast$}}{
\textnormal{\scriptsize$\mu\nu$}} F^{\mu\nu}=4 \textnormal{{\bf
E}}\bullet\textnormal{{\bf B}},$ {\it cf.} (\ref{elE}) and
(\ref{magB}); the definition of $I_2$ contains dual conjugation of
$F_{\mu\nu}$, \begin{equation} \label{Fdual}
F\!\stackrel{\textnormal{\small$\ast$}}{
\textnormal{\scriptsize$\mu\nu$}}:=
\frac{1}{2}\epsilon_{\mu\nu\alpha\beta}F^{\alpha\beta}, ~ ~
F\!\stackrel{\textnormal{\scriptsize$\mu\nu$}}{
\textnormal{\small$\ast$}}:=-
\frac{1}{2}\epsilon_{\mu\nu\alpha\beta}F_{\alpha\beta}. \end{equation} Here
$\epsilon_{\mu\nu\alpha\beta}$ is the completely skew-symmetric
object (not exactly a tensor) with $\epsilon_{0123}=+1$, known as
the Levi-Civit\`a symbol. In fact, only the squared $I_2$ is
really invariant, and $I_2$ itself is a pseudo-invariant which
acquires the factor $J/|J|$ by a general transformation of
coordinates, $J$ being the Jacobian of the transformation, thus
the concrete sign of $I_2$ does not matter. In terms of $I_1$ the
invariant classification suggests three types of fields: $I_1<0$
is the electric type (the electric field dominates), $I_1>0$ gives
the magnetic type, and to $I_1=0$ corresponds the null type. On
the pseudo-invariant $I_2$ the further working out in detail of
the classification is based: the additional subtypes are impure
($I_2\neq 0$) and pure ($I_2=0$). It is important that the pure
electric case permits (at least, locally, if one considers only
inertial frames) to completely eliminate the magnetic field, and
similarly, the pure magnetic field permits to completely eliminate
the electric field, while the pure null electromagnetic field in a
vacuum permits to find a coordinate system (reference frame) in
which the electric and magnetic field intensities would take any
desired finite (nonzero and non-infinite) and equal values, but,
of course, the field will continue to pertain to the same pure
null type (in this case, both fields {\bf E} and {\bf B} will be
ever equal in their absolute values and mutually orthogonal, as
can be seen from the structure of both invariants). This last
property is closely related to the Doppler effect (not only in the
sense of the frequency, but --- and more profoundly --- also of
the field intensity), in particular, a complete elimination of the
pure null type field is `possible' only asymptotically (in less
rich-in-content terms, this means `impossible'), since there
cannot exist any reference frame moving with the speed of light
with respect to an arbitrary permissible reference frame. The
impure electric, magnetic, and null types obviously do not permit
such manipulations with the three-dimensional parts {\bf E} and
{\bf B} of the electromagnetic field (in the impure electric and
magnetic cases it is impossible to transform away the counterparts
of these respective fields).
Let us now apply this classification to the LW electromagnetic
field. Since $I_2=\frac{1}{2}\epsilon_{\mu\nu
\alpha\beta}F^{\mu\nu} F^{\alpha\beta}\equiv 0$ for any simple
bivector (\ref{FRU}), even with {\it arbitrary} $R$ and $U$, the
field is pure. Then it is pure electric since \begin{equation} \label{I1} I_1=
-\frac{2 Q^2}{D^4}<0 \end{equation} (remarkably, the structure of $I_1$ is
exactly Coulombian). This means that at any point of the spacetime
(any finite value of the distance $D$, {\it i.e.} not
asymptotically) it is possible to transform away the magnetic part
of the field; moreover, it is possible to find such a global
reference frame in which only electric part of the field will be
present. This possibility can be globally realized for any
concrete choice of the motion of the pointlike charge. In these
specific reference frames which are in general non-inertial, but
naturally admissible in special relativity (like those to which we
are accustomed in non-relativistic physics, the area much more
restricted than special relativity), the Poynting vector of the LW
field will vanish globally. This fact will be discussed in more
concrete details below. Its physical meaning is that at any finite
point of the spacetime the electromagnetic LW field propagates
with sub-luminal velocity.
\section{Propagation of the LW electromagnetic
field} \setcounter{equation}{0} \label{s4}
\subsection{Viewpoint of an inertial observer} \label{s3.2}
This is the least interesting case of the reference frame
application to LW solution while the approach reduces to use of a
monad adapted to Cartesian coordinates. Let the inertial observer
at $P$ measure electric and magnetic fields {\bf E} and {\bf B} as
well as electromagnetic energy density $w$ and Poynting vector
{\bf S} which are two of the three decomposition parts of
(\ref{Tmunu}) (we shall not consider the stress tensor) with
respect to this observer's monad $\tau^\mu=\delta^\mu_0$ (the
observer is at rest with respect to the Cartesian coordinates) and
to the corresponding orthogonal projector
$b^\mu_\nu=\delta^\mu_\nu- \delta^\mu_0\delta_\nu^0
\Leftrightarrow \delta^\mu_i\delta_\nu^j \delta^i_j \Rightarrow
(0,\delta^i_j)$ [see (\ref{bmunu})], \begin{equation} \label{winert} w\equiv
{T_{ \textrm{\scriptsize em}}}^0_0= \frac{1}{4\pi}\left(
\frac{1}{4}F_{\alpha\beta}F^{\alpha\beta}-
F_{0\alpha}F^{0\alpha}\right)= \frac{1}{8\pi}\left(
\textnormal{{\bf E}}^2+\textnormal{{\bf B}}^2\right), \end{equation} \begin{equation}
\label{Poynting} \textnormal{{\bf S}}^i=
{T_{\textnormal{\scriptsize em}}}^i_0=-\frac{1}{4\pi}F_{i\alpha}
F^{0\alpha}=\frac{1}{4\pi}\left(\textnormal{{\bf E}}\times
\textnormal{{\bf B}}\right)^i, \end{equation} {\it cf.} (\ref{Ttau}). Here
\begin{equation} \label{EBinert} \textnormal{\bf E}^i=\frac{Q}{D^3}\left[u'_0
\left(R^i-R_0v'^i \right)(1-a'\cdot R)+D\left(a'_0R^i-R_0a'^i
\right) \right] \end{equation} and $\textnormal{\bf B}^i=\ast(dt\wedge
R\wedge U)\equiv(\textnormal{\bf n}\times \textnormal{\bf E})^i$
where (for the inertial frame) $\textnormal{\bf n}=\textnormal{\bf
R}/R_0$ and the electromagnetic field 2-form $F=R \wedge U$ where
$R$ and $U$ are 1-forms built of the respective covectors found in
(\ref{FRU}); see also the definitions (\ref{EB}) and (\ref{magB}).
Taking into account (\ref{a4-3}) and relations
$D=u'_0\left(R_0-R^iv'^i\right)$ and
$R^i\left(R^i-R_0v'^i\right)=R_0\left(R_0-R^iv'^i\right)$, it is
easy to verify that (\ref{EBinert}) coincides with the expression
given by Landau and Lifshitz (\cite{LanLif}, (63,8)) --- in our
notations, \begin{equation} \label{LLE} \textnormal{\bf E}^i=\frac{Q}{\left(
R_0-R^iv'^i \right)^3}\left\{\frac{1}{{u'_0}^2}
\left(R^i-R_0v'^i\right)+\left[ \textnormal{\bf
R}\times\left((\textnormal{\bf R}-R_0\textnormal{\bf
v}')\times\dot{\textnormal{\bf v}}'\right) \right]\right\}. \end{equation}
However, since the Poynting vector expression is nonlinear in
characteristics of the electromagnetic field (due to
multiplication of electric and magnetic vectors), we prefer our
consideration given in the next subsection to that which splits
(\ref{LLE}) in two parts one of which should describe the outgoing
radiation; this reasoning works only asymptotically, and the
expression (\ref{EBinert}) is in this case more transparent than
(\ref{LLE}) due to the factor $D$ in the corresponding term in
square brackets in (\ref{EBinert}).
Finally, it is worth mentioning that the differential
characteristics of any inertial frame (its acceleration, rotation,
and rate-of-strain tensor), including the frame considered above,
identically vanish, thus of course simplifying the considerations
given in \cite{LanLif}, though at the cost of omission of some
important details.
\subsection{The retarded reference frame co-moving with the
charge} \label{s4.1}
The retarded reference frame at $P$ co-moving with the charge at
$P'$ is determined by the monad $\tau^\mu=u'^\mu$. Thus for
electric and magnetic fields we have \begin{equation} \label{BEretard}
\textnormal{{\bf E}}=\frac{Q}{D^2}\left[(1-a'\cdot
R)\textnormal{{\bf n}}-D\textnormal{{\bf a}}'\right], ~ ~
\textnormal{\bf B}=\frac{Q}{D}\,\textnormal{\bf a}'\!\times\!
\textnormal{\bf n}. \end{equation} However it is more direct to use
projections considered in appendix \ref{sB} which result in the
non-inertial reference frame where the Poynting vector is
$$
S^\mu:=T^\nu_\lambda u'^\lambda b^\mu_\nu,
$$
and projections have to be applied to $F_{\lambda\alpha}
F^{\nu\alpha}$ using (\ref{FRU}) and the relation $R_\mu U^\mu=
Q/D^2$ obvious from $U^\mu$ given just before that expression for
$F_{\mu\nu}$. Then
$$
F_{\lambda\alpha}F^{\nu\alpha} u'^\lambda b^\mu_\nu=
\frac{Q^2}{D^4}\left[D\,\textnormal{\bf D}^\mu\, a'\!\cdot\!a'-D\,
a'^\mu-\frac{\textnormal{\bf D}^\mu}{D}\,a'\!\cdot\!
\textnormal{\bf D}(1-a'\!\cdot\!\textnormal{\bf D})\right].
$$
In order to find a more concise form of the last expression, let
us introduce the unit radial vector $n$ perpendicular to the
monad: \begin{equation} \label{nproj} \textnormal{\bf n}^\sigma:=
\frac{\textnormal{\bf D}^\sigma}{D}, ~ ~ ~ \textnormal{\bf
n}\cdot\textnormal{\bf n}=-1. \end{equation} Then
$$
S^\mu=-\frac{Q^2}{4\pi D^2}\left[\textnormal{\bf n}^\mu\left(a'\!
\cdot\! a'+(\textnormal{\bf n}\!\cdot\! a')^2\right)-\frac{1}{D}
\left( a'^\mu+\textnormal{\bf n}^\mu(\textnormal{\bf n}\!\cdot\!
a')\right)\right].
$$
This expression however takes more transparent form if we also use
the projector onto the two-dimensional surface simultaneously
orthogonal to both $u'$ and $n$. This will be a spherical surface
of radius $D$ not in a hyperplane perpendicular to $u'$, but on
the future light cone with its vertex at $P'$ (a sphere
corresponding to the retarded time in analogy with determination
of the LW field). Thus we introduce the projector \begin{equation}
\label{cproj} c^{\sigma\tau}:= b^{\sigma\tau}+n^\sigma
n^\tau\equiv \eta^{\sigma\tau}-u'^\sigma u'^\tau+n^\sigma n^\tau,
\end{equation}
$$
c^{\sigma\tau}c_{\rho\tau}=c^\sigma_\rho, ~ ~ c^{\sigma\tau}
n_\sigma=0, ~ ~ {c^\sigma}_\sigma=2,
$$
and relations similar to $a^\epsilon\equiv b^{\epsilon\sigma}
a_\sigma$ should be also taken into account. This new projection
tensor plays the r\^ole of metric tensor on the two-dimensional
sphere with the signature $(0,0,-,-)$ involving two zeros, one
with respect to direction of the proper time from the viewpoint of
all four dimensions, and the second, in the sense of the radial
direction ($n$) which corresponds to the sphere. Finally, the
Poynting vector takes the form \begin{equation} \label{simplPoynt} S^\mu=
\frac{Q^2}{4\pi}\left(\frac{1}{D^3} c^{\mu\tau} a'_\tau-
\frac{1}{D^2}n^\mu c^{\sigma\tau}a'_\sigma a'_\tau\right). \end{equation}
This remarkably simple expression of the LW energy flux suggests
the following two conclusions. First, the part proportional to
$1/D^3$ and linear in the retarded four-acceleration $a'$, is
perpendicular to the radial direction {\bf n} ({\it i.e.}, it is
restricted to the corresponding two-sphere on the future light
cone with its vertex at $P'$). Thus it describes a redistribution
of energy at the fixed retarded distance $D$ from the field
source. The integral redistribution flux becomes smaller with more
distant location of the observer and asymptotically ($D
\rightarrow\infty$) tends to zero due to multiplication of
(\ref{simplPoynt}) by the two-dimensional surface element of the
sphere ($\sim D^2$), while the integration is performed only in
the sense of angular coordinates on the sphere. Of course, the
very surface (if taken not on the light cone), as well as the
reference frame's three-space, is non-holonom since in general
this frame possesses rotation \begin{equation} \label{rotu'} \omega=\ast(u'
\wedge du')=\ast(a'\wedge u'\wedge n)= \textnormal{{\bf a}}'\times
\textnormal{{\bf n}}, \end{equation} see (\ref{rot}), (\ref{vecprod}),
(\ref{diffu}), and the final remarks in appendix \ref{sA}. Second,
the part proportional to $1/D^2$ has positive radial direction
(take into account that it gives exactly this contribution since
four-dimensional square of the spacelike vector $a'$ is negative
due to the space-time signature). Thus it describes an energy flux
{\it from} the charge {\it to} spatial infinity. Moreover, all
this part of energy really goes to infinity without being
accumulated or rarefied at any values of $D$. Hence this term
really describes radiation of energy by the accelerated charge.
The non-holonomicity remark is here also relevant, and in this
situation one has to take certain caution; this is why we
mentioned a roundabout approach involving the light cone which
always exists and represents a real hypersurface, though its
normal vector is null, thus at the same time it is on the light
cone itself. This problem goes beyond the bounds of our paper, and
we only mention here that it was successfully treated in last few
decades in general relativity. After all, we are living and
working in the rotating reference frame of our planet, therefore
our three-dimensional physical space certainly is non-holonom, but
this does not prevent us to do physics and to apply it quite well.
In the retarded co-moving reference frame of the pointlike charge
the LW electromagnetic energy flux has no other constituent parts.
Since the problem does not take into account the sources of
acceleration of the charge (the lack of a strict auto-consistency
of the problem), the energy flux does not result here in any
change of the state of motion of charge. One may say that there is
implicitly some kind of engine which prescribes the exact world
line of the charged particle (the LW problem does not involve any
information about the particle's mass and energy), thus this
``engine'' automatically ``takes into account'' the particle's
energy loss due to radiation (which at finite distances is not
ligtlike, see below). Other details follow from the further
consideration of a new reference frame in which the magnetic field
of the LW solution simply vanishes.
\subsection{LW solution in the
reference frame co-moving with electromagnetic field, but not with
the charge} \label{s4.2}
In a reference frame which is co-moving with electromagnetic
field, the Poynting vector should vanish. This can occur for two
alternative reasons (to be realized in this frame): either
electric and magnetic vectors are mutually parallel (this is the
impure classification subcase), or one of them is equal to zero
(the pure subcase). The first case was considered by Wheeler
\cite{Whee} toward other ends. The second case pertains naturally
to the LW field since this is a pure electric one (thus Wheeler's
approach is not applicable, and the magnetic part can be
transformed away {\it via} a proper choice of the reference
frame). In fact, this possibility is scarcely encountered in
literature (I even don't know any references), and it would be
interesting to investigate it in more detail. We shall see that
this task is much simpler than one could expect.
Remember the general form of the LW field tensor, (\ref{FRU}):
$F_{\mu\nu}=R_\mu U_\nu-U_\mu R_\nu$. Let us (algebraically)
regauge the vector $U ~ \rightarrow ~ V=U+kR$ where $k$ is a
scalar function. This does not change the field tensor, \begin{equation}
\label{FRV} F_{\mu \nu}=R_\mu V_\nu-V_\mu R_\nu. \end{equation} Applying now
the 1-form definition of the magnetic vector in a $\tau$-frame
(\ref{magB}) and taking the monad as $\tau=NV$ where the scalar
normalization factor is $N=(V\cdot V)^{-1/2}$, we obviously come
to {\bf B}$=0$ in this frame. The problem is thus reduced to a
proper choice of $k$ such that $V$ will be a suitable real
timelike vector with $V\cdot V>0$. This method should work in our
case (for a pure magnetic field, a similar technique can be
applied, though requiring automatic representation of $\ast F$ as
a simple bivector).
We see that \begin{equation} \label{V1} V^\mu=\frac{Q}{D^2}\left(
a'^\mu+\frac{1-a'\!\cdot\! R}{D}\,u'^\mu+kR^\mu \right), \end{equation} thus
it was natural to include before $k$ the scalar coefficient
$Q/D^2$. Then \begin{equation} V\!\cdot\! V=\left(\frac{Q}{D^2}\right)^2\left[
a'\!\cdot\! a'+ \frac{(1-a'\!\cdot\! R)^2}{D^2}+2k\right]. \end{equation} In
fact, $k$ still remains arbitrary. Let it be \begin{equation} k=
\frac{1}{2}\left[\frac{1}{D^2}-a'\!\cdot\! a'-\frac{(1-a'\!\cdot\!
R)^2}{D^2}\right] \end{equation} (the first term in the square brackets,
$1/D^2$, got its denominator to fit the dimensional
considerations). Finally, \begin{equation} V\cdot V=\left(\frac{Q}{D^3}
\right)^2>0 \end{equation} and \begin{equation} \label{taucomov} \hat{\tau}^\mu=Da'^\mu+
\left(1-a'\!\cdot\! R\right)u'^\mu+\frac{1}{2D}\left[1-D^2a'\!
\cdot\! a'-\left(1-a'\!\cdot\! R\right)^2\right]R^\mu \end{equation} (it is
clear that $\hat{\tau}\cdot\hat{\tau}=+1$). By its definition, the
monad $\hat{\tau}$ describes the reference frame co-moving with
the LW electromagnetic field: in this frame the Poynting vector of
the field vanishes, and the electromagnetic energy flux ceases to
exist due to the absence of magnetic part $\hat{\textnormal{\bf
B}}$ of the field in this frame (applicable at any finite distance
$D$, not asymptotically). Really, (\ref{FRV}) now can be rewritten
as
$$
F_{\mu\nu}=\frac{Q}{D^3}\left(R_\mu\hat{\tau}_\nu-\hat{\tau}_\mu
R_\nu\right),
$$
thus the expression of $\hat{\textnormal{\bf B}}$ (\ref{magB})
contains $\hat{\tau}\wedge R \wedge\hat{\tau}\equiv 0$.
Let us now calculate the electric vector $\hat{\textnormal{\bf
E}}$ in the frame $\hat{\tau}$. A combination of (\ref{taucomov}),
(\ref{V1}), and (\ref{FRV}) gives \begin{equation} \label{FRVCart} F=R\wedge
V=\frac{Q}{D^3}R \wedge\hat{\tau}, \end{equation} see also (\ref{F2form}).
Then the expression (\ref{elE}) yields \begin{equation} \label{Ecomov}
\hat{\textnormal{\bf E}}=\ast(\hat{\tau} \wedge\ast F)=
\frac{Q}{D^3}\ast[\hat{\tau}\wedge\ast(R\wedge\hat{\tau})]=
\frac{Q}{D^2}\hat{\textnormal{{\bf n}}} \end{equation} which is, up to an
understandable reinterpretation of notations, exactly the form
known as the Coulomb field vector. Here $\hat{\textnormal{\bf
n}}^\mu=\hat{\textnormal{\bf D}}^\mu/D$ ($\perp\hat{\tau}$) where
$R^\mu u'_\mu=: D\equiv\hat{D}:=R^\mu\hat{\tau}_\mu$ and
$\hat{\textnormal{\bf D}}^\mu\!\!=\hat{b}^\mu_\nu R^\nu$ with
$\hat{b}^\mu_\nu=\delta^\mu_\nu- \hat{\tau}^\mu\hat{\tau}_\nu$,
hence \begin{equation} \label{Dhat} \hat{\textnormal{\bf D}}^\mu=-D^2a'^\mu-
D\left(1-a'\! \cdot\! R\right)u'^\mu+\frac{1}{2}\left[1+D^2
a'\!\cdot\! a'+ \left(1-a'\!\cdot\! R\right)^2\right]R^\mu, \end{equation}
$\hat{\textnormal{\bf D}}^\mu\neq\textnormal{\bf D}^\mu$; note
that $\hat{\textnormal{\bf D}}^\mu\hat{\textnormal{\bf D}}_\mu=-
D^2$, as this was the case for $\textnormal{\bf D}^\mu$ in
(\ref{D.D}). It is clear that $\hat{\textnormal{\bf D}}^\mu\!\!+D
\hat{\tau}^\mu=R^\mu$.
\subsection{Relative three-velocities of reference frames}
\label{s4.3}
Let us now simultaneously consider three distinct reference frames
and denote them as A, B, and C. Between such frames there can be
established quite a few algebraic relations having a clear and
important physical meaning, and it is interesting that these
relations hold equally in general and special relativity. One
defines the relative three-velocity of frame B with respect to
frame A (and measured in A) as a (co)vector $\textnormal{\bf
v}_{\textnormal{\tiny BA}}$ perpendicular to the monad $\tau_{
\textnormal{\tiny A}}$. According to (\ref{v}), \begin{equation} \label{tau,v}
\tau_{\textnormal{\tiny B}}=(\tau_{ \textnormal{\tiny A}}+
\textnormal{\bf v}_{\textnormal{\tiny BA}})(\tau_{
\textnormal{\tiny A}}\cdot\tau_{\textnormal{\tiny B}})
\textnormal{ and } \textnormal{\bf v}^{\phantom{\textnormal{\tiny
BA}}\mu}_{\textnormal{\tiny BA}}= \frac{\tau^\nu_{
\textnormal{\tiny B}}b^{\phantom{\textnormal{\tiny
A}}\mu}_{\textnormal{\tiny A}\nu}}{\tau_{\textnormal{\tiny
A}}\cdot\tau_{\textnormal{\tiny B}}} \end{equation} (here the relation
$\tau^\mu_{\textnormal{\tiny B}}-\tau^\mu_{ \textnormal{\tiny
A}}(\tau_{\textnormal{\tiny A}}\cdot\tau_{ \textnormal{\tiny
B}})\equiv\tau^\nu_{\textnormal{\tiny
B}}b^{\phantom{\textnormal{\tiny A}}\mu}_{\textnormal{\tiny A}\nu}
$ was used); hence, \begin{equation} \label{tauA.tauB} \tau_{\textnormal{\tiny
A}}\cdot\tau_{\textnormal{\tiny B}}=\frac{1}{\sqrt{1+
\textnormal{\bf v}_{\textnormal{\tiny BA}}\cdot\textnormal{\bf
v}_{\textnormal{\tiny BA}}}}\equiv\frac{1}{\sqrt{1-
\textnormal{\bf v}_{\textnormal{\tiny BA}}\bullet\textnormal{\bf
v}_{\textnormal{\tiny BA}}}}=\frac{1}{\sqrt{1- \textnormal{\bf
v}_{\textnormal{\tiny BA}}^2}}. \end{equation} It is clear that similar
relations exist for any pair of reference frames whatever when the
respective monads are introduced. We see that there is a symmetry
for squared three-velocities between any pair of frames, in
particular, $\textnormal{\bf v}_{\textnormal{\tiny BA}}^2=
\textnormal{\bf v}_{\textnormal{\tiny AB}}^2$. Since these
three-velocities are described as four-vectors perpendicular to
the respective monads (of the frames corresponding to the frame
subindex of $\tau$ and of $b$), they belong to different (local)
three-spatial sections of spacetime and in general cannot be
directly compared by measurements ones with others without further
projections onto alternative subspaces. The inevitability of such
a situation is quite obvious. Even in the generally used
special-relativistic composition-of-velocities formula for
globally inertial frames in motion along ``same spatial
direction,'' this is in fact also the case which is tacitly
assumed, but frequently not properly understood. Its strict
formulation when these velocities are not mutually ``parallel,''
is however more laborious.
Another useful step in our calculations is to apply same procedure
as in (\ref{tau,v}), but taken with respect to the frames C and A,
then to C and B, and further applying it to the free
$\tau_{\textnormal{\tiny B}}$, thus $\tau_{\textnormal{\tiny
C}}=(\tau_{ \textnormal{\tiny A}}+\textnormal{\bf
v}_{\textnormal{\tiny CA}})(\tau_{\textnormal{\tiny
A}}\cdot\tau_{\textnormal{\tiny C}})=(\tau_{\textnormal{\tiny
B}}+\textnormal{\bf v}_{\textnormal{\tiny
CB}})(\tau_{\textnormal{\tiny B}}\cdot\tau_{\textnormal{\tiny
C}})=[(\tau_{\textnormal{\tiny A}}+\textnormal{\bf
v}_{\textnormal{\tiny BA}})(\tau_{\textnormal{\tiny
A}}\cdot\tau_{\textnormal{\tiny B}}) +\textnormal{\bf
v}_{\textnormal{\tiny CB}}](\tau_{\textnormal{\tiny
B}}\cdot\tau_{\textnormal{\tiny C}})$. When this expression is
multiplied by $b_{\textnormal{\tiny A}}$ under a contraction with
the lower (component) index of this factor, we come to \begin{equation}
\label{compABC} \textnormal{\bf v}_{\textnormal{\tiny
CA}}^{\phantom{ \textnormal{\tiny CA}}\nu}=\left[\textnormal{\bf
v}_{\textnormal{\tiny BA}}^{\phantom{ \textnormal{\tiny BA}}\nu}
(\tau_{\textnormal{\tiny A}}\cdot\tau_{\textnormal{\tiny B}})+
\textnormal{\bf v}_{\textnormal{\tiny CB}}^{\phantom{
\textnormal{\tiny BA}}\mu}b^{\phantom{\textnormal{\tiny
A}}\nu}_{\textnormal{\tiny
A}\mu}\right]\frac{\tau_{\textnormal{\tiny
B}}\cdot\tau_{\textnormal{\tiny C}}}{\tau_{\textnormal{\tiny
A}}\cdot\tau_{\textnormal{\tiny C}}}. \end{equation} In fact, this is the
local velocities composition formula $\textnormal{A}\rightarrow
\textnormal{B}\rightarrow\textnormal{C}$ for general (not only
inertial) frames in both relativities, special as well as general
one. Here, of course, one has to take into account the relation
(\ref{tauA.tauB}). In this paper we do not consider further
details of the usual composition formula.
Other relations which are worth being mentioned, are the following
ones: those with projections onto the alternative monads, \begin{equation}
\label{vBAvAB} \textnormal{\bf v}_{\textnormal{\tiny
BA}}^{\phantom{ \textnormal{\tiny BA}}\nu}b^{\phantom{
\textnormal{\tiny B}}\mu}_{\textnormal{\tiny B}\nu}=-
(\tau_{\textnormal{\tiny A}}\cdot\tau_{\textnormal{\tiny B}})
\textnormal{\bf v}_{\textnormal{\tiny AB}}^{\phantom{
\textnormal{\tiny AB}}\mu}\textnormal{ and } \textnormal{\bf
v}_{\textnormal{\tiny AB}}^{\phantom{ \textnormal{\tiny
AB}}\nu}b^{\phantom{ \textnormal{\tiny A}}\mu}_{\textnormal{\tiny
A}\nu}=-(\tau_{\textnormal{\tiny A}}\cdot\tau_{\textnormal{\tiny
B}}) \textnormal{\bf v}_{\textnormal{\tiny BA}}^{\phantom{
\textnormal{\tiny BA}}\mu}; \end{equation} further, due to (\ref{tau,v}) and
(\ref{vBAvAB}), \begin{equation} \textnormal{\bf v}_{\textnormal{\tiny
AB}}\cdot \textnormal{\bf v}_{\textnormal{\tiny BA}}=-\tau_{
\textnormal{\tiny A}}\cdot\textnormal{\bf v}_{\textnormal{\tiny
AB}}=-(\tau_{\textnormal{\tiny A}}\cdot\tau_{\textnormal{\tiny
B}})\textnormal{\bf v}_{\textnormal{\tiny BA}}^2=(\tau_{
\textnormal{\tiny A}}\cdot\textnormal{\bf v}_{\textnormal{\tiny
AB}})^2/\textnormal{\bf v}_{\textnormal{\tiny AB}}^2 \end{equation} (here the
obvious symmetry $\tau_{ \textnormal{\tiny A}}\cdot\textnormal{\bf
v}_{\textnormal{\tiny AB}}=\tau_{ \textnormal{\tiny
B}}\cdot\textnormal{\bf v}_{\textnormal{\tiny BA}}$ was taken into
account); finally, \begin{equation} \textnormal{\bf v}_{\textnormal{\tiny AB}}=
-(\tau_{\textnormal{\tiny A}}\cdot\tau_{\textnormal{\tiny B}})
\textnormal{\bf v}_{\textnormal{\tiny BA}}+(\textnormal{\bf
v}_{\textnormal{\tiny AB}}\cdot\tau_{\textnormal{\tiny A}})\tau_{
\textnormal{\tiny A}} \end{equation} (decomposition with respect to the frame
A). Note that $\textnormal{\bf v}_{\textnormal{\tiny AB}}^2:=
\textnormal{\bf v}_{\textnormal{\tiny AB}}\bullet\textnormal{\bf
v}_{\textnormal{\tiny AB}}=-\textnormal{\bf v}_{\textnormal{\tiny
AB}}\cdot\textnormal{\bf v}_{\textnormal{\tiny AB}}>0$.
Let us globally (at any $P$) denote in the LW problem the
reference frame of inertial observer as A,
$\tau_{\textnormal{\tiny A}}^{\phantom{\textnormal{\tiny
A}}\mu}=\delta^\mu_0$, the retarded frame co-moving with the
charge as B, $\tau_{\textnormal{\tiny B}}^{\phantom{
\textnormal{\tiny B}}\mu}=u'^\mu$, and the frame co-moving with
the field and introduced in subsection \ref{s4.2}, as C ($\tau_{
\textnormal{\tiny C}}^{\phantom{ \textnormal{\tiny
C}}\mu}=\hat{\tau}^\mu$). Then, on the one hand, \begin{equation} (\tau_{
\textnormal{\tiny B}}\cdot\tau_{\textnormal{\tiny C}})=(u'
\cdot\hat{\tau})=1-\frac{1}{2}\left[D^2a'\!\cdot\! a'+ \left( a'\!
\cdot\! R\right)^2\right]. \end{equation} On the other hand, \begin{equation}
\textnormal{\bf v}_{\textnormal{\tiny CB}}=\frac{\hat{\tau}}{(u'\!
\cdot\!\hat{\tau})}-u'. \end{equation}
Rotation of the frame C takes the (not quite easily deducible)
form \begin{equation} \label{omegC} \hat{\omega}=-\frac{1- D\,(\dot{a}'\!\cdot
\! R)}{1-a'\!\cdot\! R}\;\textnormal{\bf a}'\!\times\hat{
\textnormal{\bf n}}+D\,\dot{\textnormal{\bf a}}'\!\times\hat{
\textnormal{\bf n}} \end{equation} where 1-form $\dot{a}'
=(da'_\mu/ds')dx^\mu$ describes the retarded third proper-time
derivative of position of the charge in its motion along the
worldline $L$. It is worth giving some hints for the deduction of
(\ref{omegC}): The exterior product of any odd-rank forms $\alpha$
and $\beta$ is skew-symmetric, thus $\alpha\wedge\alpha\equiv 0$.
The vector product (\ref{vecprod}) is applicable to a pair of
arbitrary vectors, thus it automatically projects each of them
onto the three-dimensional subspace orthogonal to the monad. One
now has to apply the definition of rotation (\ref{rot}) to the
monad $\hat{\tau}$. Some simplifications follow immediately. Then
to complete the simplification one has to take into account a
relation following from the form (not directly from the general
definition) of $\hat{\tau}$ (\ref{taucomov}) and $\hat{
\textnormal{\bf D}}$ (\ref{Dhat}):
$$
\hat{ \textnormal{\bf D}}_\mu=D\hat{\tau}_\mu-2D^2a'_\mu-2D(1-a'
\cdot R)u'_\mu+\left[D^2(a'\cdot a')+(1-a'\cdot R)^2\right]R_\mu
$$
(at each subsequent step only very few terms survive). The final
result is (\ref{omegC}) which should be compared with
(\ref{rotu'}).
\section{Concluding remarks} \setcounter{equation}{0} \label{s5}
We tried to give in this paper a self-sufficient consideration of
the LW solution, from its heuristic deduction to an analysis of
important properties of the obtained field. One of these
properties is that of field's motion with respect to a given
reference frame. In fact, one can relate this motion to the monad
describing the frame in which the electromagnetic field does not
propagate (its Poynting vector, the electromagnetic energy flux
density, vanishes in this frame). It is possible to find such a
frame in all cases with the exception of {\it pure null}
electromagnetic fields: in this latter case both electromagnetic
invariants are equal to zero, consequently there remains only an
{\it asymptotic} possibility to transform away the field's motion,
but then {\it it is transformed away always together with the
field itself} (this is precisely the asymptotic limit of the
Doppler effect). This asymptotic situation does not belong to any
admissible reference frame or system of coordinates since such a
frame (or, of one wishes, a system) is a degenerate one and thus
excluded from consideration (whose region of application is an
open one, and the `boundary' is excluded from it, though we can
approach it as `near' as we wish, making the non-zero field as
weak as we choose it to become). In this pure null case (the
definition see in section \ref{s3.1}) the field by itself
exercises lightlike (null) motion, that with the velocity of
light. But then there cannot exist a co-moving (with this field)
reference frame since its four-velocity should coincide with the
monad of the co-moving frame, and the monad vector is timelike by
its definition. (More physical reasons are related to the fact
that the continuous swarm of observers forming, together with
their measuring equipment, a reference frame, and thus being
co-moving with it, should always possess non-zero rest masses,
though, of course, these masses have to be infinitesimal ones to
guarantee the test property of a classical frame of reference. The
non-zero rest mass means a timelike worldline of the corresponding
object, thus the lightlike motion of any reference frame is
physically impossible.) In all other cases concerning
electromagnetic fields' types a co-moving frame is easily
realizable (in this paper we discussed the pure electric and pure
magnetic types, and all impure subcases should be dealt with
according to the method used by Rainich and Wheeler, see
\cite{Whee}).
Another property is also related to propagation, however {\it not
of the field} but {\it of the information} about its sources, thus
this property belongs to {\it the deduction} of the LW field. This
is a rare case when we encounter in a classical physical context
the concept of information usually alien to it. And here
information propagates with the velocity of light in a vacuum.
\renewcommand{\theequation}{\Alph{section}.\arabic{equation}}
\section*{Appendices}
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Juan Manuel Rodríguez Parrondo (Madrid, 9 de enero de 1964) es un físico español, conocido por la notablemente contraintuitiva paradoja de Parrondo, en la que la elección de estrategias perdedoras puede conducir a una victoria. En 1996, desarrolló los juegos de oportunidad (ahora llamados juegos de Parrondo), que exhibieron este fenómeno aparentemente paradójico. Gran parte de su trabajo afecta a la termodinámica y la información y es conocido por contribuciones a la teoría de los cambios de estado inducidos por ruido, al trinquete browniano, a la física de la información y a la mecánica estadística.
Biografía
Juan Manuel Rodríguez Parrondo nació en Madrid. Obtuvo la licenciatura en Física en 1987 y el doctorado en 1992 por la Universidad Complutense de Madrid. Su tutor de doctorado externo era Javier del la Rubia de la UNED. El tema de la tesis doctoral de Parrondo estaba en el área de las ecuaciones diferenciales estocásticas y la Teoría del paseo aleatorio de fractales.
Después de su tesis doctoral, Parrondo llevó a cabo una investigación postdoctoral que combinó los temas de la teoría de la información y la termodinámica-esto probó la influencia en la dirección de sus investigaciones futuras. Como investigador trabajó en las teorías de los cambios de estado inducidos por ruido con Katja Lindenberg en la UCSD (EE. UU.) en 1992, las redes neuronales con Chris Van den Broeck de la Universidad de Hasselt (Bélgica) en 1993, en el demonios de Maxwell con Thomas M. Cover en Stanford (EE. UU.) en 1995.
En 1996, obtuvo una plaza fija en la Universidad Complutense de Madrid y en este año concibió el concepto de juegos de oportunidad perdedores, que paradójicamente ganan cuando se juega a perder. En 1999, visitó a Marcello O. Magnasco de la Universidad Rockefeller en Nueva York, trabajando en el trinquete Browniano y a Derek Abbott de la Universidad de Adelaida (Australia), trabajando en los juegos de Parrondo. En 2005, Parrondo realizó otra visita de colaboración extensa, esta vez a Carlos Bustamante de la Universidad de Berkeley (EE. UU.) trabajando en los motores moleculares.
En el periodo 2003 - 2004, Parrondo realizó una serie regular de artículos de ciencia para la radio española RNE. Desde 2001 hasta 2013, Parrondo fue el equivalente español de Martin Gardner escribiendo los "Juegos Matemáticos" para la columna de la edición española de Scientific American llamada Investigación y Ciencia. Aunque esta columna en la versión inglesa ha sido discontinua, la columna de Juegos Matemáticos sigue viva, primero bajo la dirección de Parrondo y en la actualidad bajo la dirección de Bartolo Luque.
Génesis de los Juegos de Parrondo
Parrondo concibió inicialmente sus contraintuitivos juegos de oportunidad en 1996 como un ejemplo de cómo el trinquete browniano funcionaba y presentó la idea por primera vez en una diapositiva titulada Cómo Estafar a un Mal Matemático, en un trabajo para la CEE sobre la la Complejidad y el Caos, Turín (Italia). En ese mismo año publicó un artículo criticando el análisis de Richard Feynman del trinquete browniano en el American Journal of Physics. Derek Abbott de la Universidad de Adelaida (Australia) estaba trabajando en un tema relacionado, pero seguía sin resolverlo con respecto al análisis de Feynman. El artículo de Parrondo incitó a Abbott a volar hacia Madrid en 1997 y se encontraron por primera vez-pero el problema demostrado era difícil y hasta [1999]] no publicaron una solución final. Sin embargo, en ese tiempo, Parrondo compartió el concepto de su paradoja—como consecuencia Abbott acuñó las condiciones de la paradoja de Parrondo y los juegos de Parrondo, publicando su verificación del resultado en la revista Nature en 1999.
Otros datos de Parrondo
En varios artículos y fuentes de Internet el nombre de Parrondo se escribe a veces incorrectamente "Parrando". Se puede encontrar en un artículo del 25 de enero de 2000 sobre la la Paradoja de Parrando en el New York Times—debido a la naturaleza influyente de este periódico este error de la mecanografía propagó ampliamente a escritores y periodistas que no verificaron sus fuentes.
Parrondo fue inspirado para estudiar Física cuando estaba en el instituto, después de leer un artículo sobre mecánica cuántica que Douglas Hofstadter publicó en Scientific American. Hofstadter reemplazó a Martin Gardner cuando Gardner se retiró de Scientfic American. Curiosamente, la historia ha completado el círculo cuando Parrondo ha ocupado el puesto de redactor de Juegos Matemáticos para la edición española.
En España tradicionalmente se usan dos apellidos y los científicos españoles suelen usar el primer apellido al publicar en los periódicos en inglés. Así que uno pensaría que el apellido doble "Rodríguez Parrondo" debe acortarse a simplemente "Rodríguez" y no "Parrondo." Sin embargo, en 1992, cuando Parrondo publicó su primer artículo en inglés escogió utilizar su segundo apellido, porque "Rodríguez" es un apelido muy común y no muy distintivo. De nuevo, esto demuestra que de manera fortuita la "paradoja de Rodríguez" no tendría ese halo que le caracteriza.
En 1999, Parrondo asistió a una conferencia dónde los papeles estaban doblemente cegados. "Doblemente cegados" significa que los nombres de los autores no se revelan a los revisores para eliminar prejuicios. Se les solicitó a los revisores que intentaran adivinar de quién eran sus artículos para comprobar la efectividad del proceso. Los cinco revisores de Parrondo confundieron a Parrondo con Rolf Landauer quien, hasta ese momento, era el líder del área de la física de la información. Desconocido por los revisores, Rolf Landauer realmente había muerto unos días antes. Para marcar esta transición, el comité premió a Parrondo con "el premio informal Landauer" durante el banquete de la conferencia.
Físicos de España del siglo XX
Físicos de España del siglo XXI
Nacidos en Madrid | {
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{"url":"http:\/\/mathhelpforum.com\/discrete-math\/189234-showing-equality-via-simple-calculation.html","text":"# Math Help - Showing equality via a simple calculation\n\n1. ## Showing equality via a simple calculation\n\nI'm studying for an introductory course on logic, I'm at the point where I've to show the equality of certain formulas using a calculation with some basic standard equivalences. Like Inversion, True\/False elimination, DeMorgan, distributivity et cetera. I'ce come across a formula that's intuitively very clear, I just don't understand how to work it from A to B.\n\nI'm asked to provide a calculation showing that: $P \\wedge (P \\lor Q) = P$. Intuitively I can see this to be true, drawing the truthtables confirms this, but how can I show this via a simple calculation?\n\nI know I can rewrite this as follows: by distribution I get: $(P \\wedge P) \\lor (P \\wedge Q) = P$, from which by idempotence follows that: $P \\lor (P \\wedge Q) = P$. Which actually leads me to exercise b . To show that is equivalent to P.\n\nThe big question is: how do I eliminate the Q? What rule can I apply here to show the equivalence to P?\n\n2. ## Re: Showing equality via a simple calculation\n\n$P\\lor(P\\land Q)=(P\\land 1)\\lor(P\\land Q)=P\\land(1\\lor Q)=P\\land1=P$.\n\n3. ## Re: Showing equality via a simple calculation\n\nAh I see now, thanks! I haven't seen distributive and true\/false elimination being used like that","date":"2014-09-02 10:22:51","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 0, \"mathjax_display_tex\": 0, \"mathjax_asciimath\": 0, \"img_math\": 0, \"codecogs_latex\": 4, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.8533567190170288, \"perplexity\": 772.9754461723231}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2014-35\/segments\/1409535921872.11\/warc\/CC-MAIN-20140909040124-00381-ip-10-180-136-8.ec2.internal.warc.gz\"}"} | null | null |
\section{Introduction}
The Michelson interferometer was first used in 1887 in the famous experiment by A.~Michelson and E.~Morley \cite{Michelson1887}. Since then, it became a standard tool being routinely employed in high-precision optical measurements. Currently, the most conspicuous devices based on the Michelson interferometer topology are gravitational-wave (GW) detectors, like LIGO \cite{LIGOsite, CQG_32_7_074001_2015}, VIRGO \cite{AdvVIRGOsite, Accadia2012}, and GEO-600 \cite{GEOsite, Grote2010}, which have arm lengths varying form several hundreds of meters to several kilometers.
\begin{figure}
\includegraphics{2015membrane-gw_detector.pdf}
\caption{The dual-recycled Michelson/Fabry-Perot topology of the modern laser GW detectors. PRM: the power recycling mirror; SRM: the signal recycling mirror; ITM: the input test mass; ETM: the end test masses. The optional mirrors are shown by dashed lines (in the real GW detectors, either ITMs, or PRM and/or SRM can be absent).}\label{fig:dual_rec_Michelson}
\end{figure}
The typical optical layout of GW detectors is shown in Fig.\ \ref{fig:dual_rec_Michelson}. In addition to the end mirrors (the end test masses, ETMs), it could include up to four additional ones. Two of them (the input test masses, ITMs), form, together with the ETMs, two Fabry-Perot arm cavities, which increase the light's storage time for improving the interferometer's signal response. Two so-called recycling mirrors, the power- and the signal-recycling mirror (PRM and SRM) allow to independently tune the bandwidths and the detunings of its two optical modes, the common and the differential ones \cite{Vinet_PRD_38_433_1988, Meers1988}. Detuning of the SR mirror can also result in a sensitivity improvement via the so-called `optical spring' \cite{Buonanno2002}. Since it is dynamically unstable, also schemes exploiting two bright light fields were researched in order to provide a stable optical spring \cite{Corbitt2007,Rehbein2008}.
\begin{figure}
\includegraphics{2015membrane-michelson_sagnac}
\caption{The Michelson-Sagnac interferometer. PRM: the power recycling mirror; SRM: the signal recycling mirror. The optional mirrors are shown by dashed lines.}\label{fig:Michelson-Sagnac}
\end{figure}
Several years ago, the Michelson interferometer topology was adopted also for table top quantum optomechanical experiments, with partly translucent silicon-nitride membranes playing the role of the test mass \cite{09a1YaFrWeGoDaScSoDa}. These membranes have very small masses ($m\lesssim100\,{\rm ng}$) and low optical and mechanical losses and provide a suitable platform for quantum optomechanical experiments \cite{Thompson_Nature_452_72_2008}. They have, however, a relatively low reflectivity, which does not allow to use them as end mirrors in high-finesse optical resonators. Instead, the {\it Michelson-Sagnac} topology was proposed in Ref.~\cite{09a1YaFrWeGoDaScSoDa}, see Fig.\,\ref{fig:Michelson-Sagnac}. It can be viewed as a derivative of the dual-recycled (signal- and power-recycled) Michelson topology of laser GW detectors. By folding the Michelson arms towards each other, light that is transmitted through the membrane does not leave the interferometer, and the membrane takes the role of the end mirror of both Michelson arms.
In turn, the Michelson interferometer can be treated as a special case of the Michelson-Sagnac interferometer, when setting the membrane transmissivity equal to zero. The general theory of the dual-recycled Michelson-Sagnac interferometer presented in this article can be applied to all {\it Michelson-type interferometers} -- the Michelson-Sagnac, the pure Michelson and the Michelson-Fabry-Perot interferometer.
The standard and well-explored regime of these interferometers assumes a balanced beam splitter, interferometer arms of identical length and optical loss as well as an operation at (or very close to) a dark fringe. This is what we call `\emph{the symmetric regime}'.
A detailed analysis of the dual-recycled Michelson-Fabry-Perot interferometer in the symmetric regime was presented in \cite{Buonanno2003}. It was shown, that the complete interferometer can be mapped to a single Fabry-Perot cavity with effective parameters (the so-called scaling law theorem).
Later the analysis was extended to the symmetric Michelson-Sagnac interferometer \cite{16a1DaKh}.
The first analysis in the \emph{asymmetric} regime of the Michelson-Sagnac interferometer was performed in \cite{Xuereb_PRL_107_213604_2011}. Here, it was in particular shown that optical ground state cooling is possible even outside good cavity regime \cite{Aspelmeyer_RMP_86_1391_2014}, which is due to a ``Fano resonance'' shape of the radiation pressure noise spectral density \cite{Elste_PRL_102_207209_2009, Weiss_Burder_Nunnen_2012}. In \cite{13a1TaKhKaScHa, 14a1VoVy}, the dynamic back action (that is, the optical spring features \cite{Buonanno2002}) of the asymmetric Michelson-Sagnac was analyzed and it was shown, that in contrast to the symmetric case, both the optical damping and the optical rigidity in an asymmetric Michelson-Sagnac interferometer could acquire a nonzero value on the optical resonance, and additional stability and instability regions exist on either side of the resonance. Later, this non-canonical behavior was demonstrated experimentally \cite{14a1SaKaNiTaKhHaSc}.
Here we present the generalized framework for the analysis of asymmetric cavity-enhanced Michelson-type interferometers that includes not only dynamical optomechanical back-action but also the light's quantum noise. In particular, we assume that both input/output ports of the interferometer can be pumped; this assumption simplifies the analysis of the interferometer and provides insights into the internal structure of the equations obtained in \cite{13a1TaKhKaScHa}. In Sec.\,\ref{sec:modes} we show that the character of the optomechanical coupling in Michelson-type interferometers depends on whether one or two recycling mirrors are present. In Sec.\,\ref{sec:calculations}, we analyze in detail the case of just one (signal-) recycling cavity, using the developed framework to explain the ``anomalous'' features of \cite{13a1TaKhKaScHa, 14a1SaKaNiTaKhHaSc}. In Sec.\,\ref{sec:cooling} we provide the optimization of optical cooling in Michelson-type interferometers. The notations used throughout this paper areis given in Table\,\ref{tab:notations}.
\begin{table}
\begin{ruledtabular}
\begin{tabular}{ll}
Quantity & Description \\ \hline
$c$ & Speed of light \\
$\hbar$ & Reduced Plank constant \\
$\kappa_B$ & Boltzmann constant \\
$\omega = ck$ & Any high (optical) frequency \\
$\omega_p = ck_p$ & Optical pump frequency \\
$\gamma$ & Optical half-bandwidth \\
$\delta=\omega_p-\omega_o$ & Detuning of the pump from the optical resonance
frequency \\
$\Omega$ & Any low (mechanical) frequency; if appears together with $\omega$, then $\Omega=\omega-\omega_p$ \\
$L_S = c\tau_S$ & Optical distance between the SRM and the symmetry position of the membrane \\
$L_P = c\tau_S$ & The same for the PRM \\
$R_{W,S}$ & Amplitude reflectivities of the power (W) and signal (S) recycling mirrors \\
$T_{W,S}$ & Amplitude transmissivities of these mirrors \\
$R_m = \cos\theta$ & Amplitude reflectivity of the membrane \\
$T_m = \sin\theta$ & Amplitude transmissivity of the membrane \\
$R = \cos(\pi/4-\epsilon)$ & Amplitude reflectivity of the beamsplitter \\
$T = \sin(\pi/4-\epsilon)$ & Amplitude transmissivity of the beamsplitter \\
$X = \varkappa/k_p$ & D.C. component of the membrane displacement from the symmetry position\\
$x$ & A.C. component of the membrane displacement from the symmetry position\\
$\mathrm{h.c.}$ & Hermitian conjugate of the previous term \\
$\mathrm{C.C.}$ & Caves-Schumaker conjugate \cite{Caves1985} of the previous term, see Eq.\,\eqref{def_CC}.
\end{tabular}
\end{ruledtabular}
\caption{Main notations used in this paper.}\label{tab:notations}
\end{table}
\section{Optomechanical coupling in Michelson-type interferometers}\label{sec:modes}
In order to provide the starting point for our consideration below, let us start with the well-explored case of a single optical mode whose eigenfrequency depends on the position of the mechanical object. This type of the optomechanical coupling is known as the {\it dispersive} one. The Hamiltonian of this system can be presented in the standard form
\begin{equation}\label{H_cav}
\hat{\mathcal{H}}
= \hbar(\omega_o - g\hat{x})(\hat{{\rm e}}^\dagger\hat{{\rm e}} + \sfrac{1}{2})
+ \hat{\mathcal{H}}_m + \hat{\mathcal{H}}_{\rm rest} \,,
\end{equation}
where $\hat{{\rm e}}$ and $\hat{{\rm e}}^\dagger$ are the annihilation and creation operators of the intracavity field (we reserve the notation $\hat{{\rm a}}$ for the incident field), $\hat{x}$ is the mechanical coordinate, $\omega_o$ and $g$ are the optical eigenfrequency and the optomechanical coupling factor, $\mathcal{H}_m$ is a mechanical Hamiltonian and $\mathcal{H}_{\rm rest}$ is the Hamiltonian describing all other optical degrees of freedom, including the optical pump(s) and the optical losses. Note that the Fabry-Perot cavity treatment can be reduced to this lumped mode model, provided that one of its optical modes is selected by the strong classical pump with the frequency $\omega_p$ close to this mode eigenfrequency.
Following Sec.\,III of the review paper \cite{Aspelmeyer_RMP_86_1391_2014}, we
rewrite the Hamiltonian \eqref{H_cav} in the frame rotating with the frequency $\omega_p$:
\begin{equation}\label{H_cav_RW}
\hat{\mathcal{H}}
= -\hbar(\delta + g\hat{x})(\hat{{\rm e}}^\dagger\hat{{\rm e}} + \sfrac{1}{2})
+ \hat{\mathcal{H}}_m + \hat{\mathcal{H}}_{\rm rest} \,,
\end{equation}
where $\delta=\omega_p-\omega_o$ is the detuning of the pump from cavity resonance. Then we extract explicitly from the field $\hat{{\rm e}}$ the classical mean part ${\rm E}$ created by the optical pump, $\hat{{\rm e}}\to{\rm E}+\hat{{\rm e}}$:
\begin{equation}
\hat{\mathcal{H}}
= -\hbar(\delta + g\hat{x})(
|{\rm E}|^2 + {\rm E}^*\hat{{\rm e}} + {\rm E}\hat{{\rm e}}^\dagger
+ \hat{{\rm e}}^\dagger\hat{{\rm e}} + \sfrac{1}{2}
)
+ \hat{\mathcal{H}}_m + \hat{\mathcal{H}}_{\rm rest} \,.
\end{equation}
The term $-\hbar(\delta + g\hat{x})|{\rm E}|^2$ here just create a static radiation pressure on the mechanical object, which can be compensated by some means; the term $-\hbar\delta({\rm E}^*\hat{{\rm e}} + {\rm E}\hat{{\rm e}}^\dagger)$ does not depend on $\hat{x}$ and we absorb it into $\mathcal{H}_{\rm rest}$; and the term $-\hbar g\hat{x}(\hat{{\rm e}}^\dagger\hat{{\rm e}} + \sfrac{1}{2})$ is of the second order of smallness and can be neglected. The remaining terms form the following canonical linearized optomechanical Hamiltonian:
\begin{equation}\label{H_cav_lin}
\hat{\mathcal{H}}
= -\hbar\delta(\hat{{\rm e}}^\dagger\hat{{\rm e}} + \sfrac{1}{2})
- \hbar g({\rm E}^*\hat{{\rm e}} + \mathrm{h.c.})\hat{x}
+ \hat{\mathcal{H}}_m + \hat{\mathcal{H}}_{\rm rest} \,.
\end{equation}
As the next step, consider the Michelson/Fabry-Perot interferometer shown in Fig.\,\ref{fig:dual_rec_Michelson}, {\it assuming the symmetry condition} (the consideration below actually reproduces in a simplified form the scaling law theorem of \cite{Buonanno2003}). Suppose here for simplicity that both recycling mirrors are absent. This scheme can be described by the sum of two single-mode Hamiltonians \eqref{H_cav} of the arm Fabry-Perot cavities:
\begin{equation}\label{H_MFP}
\hat{\mathcal{H}}
= \hbar\bigl[
(\omega_o - g\hat{x}_N)(\hat{{\rm e}}_N^\dagger\hat{{\rm e}}_N + \sfrac{1}{2})
+ (\omega_o - g\hat{x}_E)(\hat{{\rm e}}_E^\dagger\hat{{\rm e}}_E + \sfrac{1}{2})
\bigr]
+ \hat{\mathcal{H}}_m + \hat{\mathcal{H}}_{\rm rest} \,,
\end{equation}
where the subscripts $N$ and $E$ stand for the ``north'' and the ``east'' (as shown in Fig.\,\ref{fig:dual_rec_Michelson}) arms, respectively. This Hamiltonian, similar to \eqref{H_cav}, describes dispersive coupling.
Then introduce the common and the differential optical modes as follows:
\begin{align}\label{e_pm}
\hat{{\rm e}}_\pm &= \frac{\hat{{\rm e}}_N \pm \hat{{\rm e}}_E}{\sqrt{2}} \,, &
\hat{{\bf e}} &= \svector{\hat{{\rm e}}_+}{\hat{{\rm e}}_-} .
\end{align}
In these notations,
\begin{equation}\label{H_MFP_pm}
\hat{\mathcal{H}}
= \hbar\bigl[
(\omega_o - g\hat{y})(\hat{{\bf e}}^\dagger\hat{{\bf e}} + 1)
- g\hat{x}\hat{{\bf e}}^\dagger\mathbb{X}\hat{{\bf e}}
\bigr]
+ \hat{\mathcal{H}}_m + \hat{\mathcal{H}}_{\rm rest} \,,
\end{equation}
where
\begin{align}
y &= \frac{x_N + x_E}{2} \,, & x &= \frac{x_N - x_E}{2}
\end{align}
are coordinates of the common (symmetric) and the differential (antisymmetric) mechanical modes, and $\mathbb{X}$ is the Pauli $x$-matrix [see Eq.\,\eqref{2x2}]. For the common mode $y$, this Hamiltonian still retains the dispersive coupling structure. But the optomechanical coupling with the differential mode $x$ is of a different nature: in this case, the {\em coupling} of the two modes $\hat{{\rm e}}_+$ and $\hat{{\rm e}}_-$ is proportional to the mechanical displacement $x$. We will refer to this term as {\it coherent optomechanical coupling}. Note that opposite to \eqref{H_MFP}, the Hamiltonian \eqref{H_MFP_pm} is valid in the case of the general dual recycled interferometer as well \cite{Meers1988, Buonanno2003} and, in particular, in the case of the pure Michelson interferometer (without the ITM mirrors). In the particular case of a very broadband common optical mode, that is with the bandwidth much broader than all other characteristic frequencies of the system (with the evident exception of $\omega_o$, $\omega_p$), the common optical mode degenerates to an (almost) free space optical field. In this case, the bandwidth of the differential optical mode becomes dependent of $x$. This is the so-called {\it dissipative} optomechanical coupling \cite{Elste_PRL_102_207209_2009, Weiss_Burder_Nunnen_2012}. This simple example shows, that in multi-mode systems the type of the optomechanical coupling can not be categorized in a simple and unique way; it depends on a non-unique choice of the optical modes.
Now, following the above treatment of the Fabry-Perot cavity, we introduce explicitly the classical pumping fields by replacing $\hat{{\rm e}}_\pm \to {\rm E}_\pm + \hat{{\rm e}}_\pm$ and retrace the equations (\ref{H_cav_RW}-\ref{H_cav_lin}). This gives the following linearized Hamiltonian
\begin{equation}\label{H_MFP_pm_lin}
\hat{\mathcal{H}} = -\hbar\delta
(\hat{{\bf e}}^\dagger\hat{{\bf e}} + 1)
- \hbar g\hat{y}({\bf E}^\dagger\hat{{\bf e}} + \mathrm{h.c.})
- \hbar g\hat{x}({\bf E}^\dagger\mathbb{X}\hat{{\bf e}} + \mathrm{h.c.})
+ \hat{\mathcal{H}}_m + \hat{\mathcal{H}}_{\rm rest} \,,
\end{equation}
where
\begin{equation}
{\bf E} = \svector{{\rm E}_+}{{\rm E}_-} .
\end{equation}
Note the similarity between this Hamiltonian and the one for the Fabry-Perot interferometer \eqref{H_cav_lin}.
Moreover, if the differential optical mode is not excited, ${\rm E}_-=0$ (which corresponds to the canonical regime of both the GW detectors and membrane interferometers), then the common optical mode is coupled only with the common mechanical one and the differential optical mode --- only with the differential mechanical one
\begin{equation}\label{H_MFP_pm_diag}
\hat{\mathcal{H}} = -\hbar\delta
(\hat{{\bf e}}^\dagger\hat{{\bf e}} + 1)
- \hbar g\hat{y}({\rm E}_+^\dagger\hat{{\rm e}}_+ + \mathrm{h.c.})
- \hbar g\hat{x}({\rm E}_+^\dagger\hat{{\rm e}}_- + \mathrm{h.c.})
+ \hat{\mathcal{H}}_m + \hat{\mathcal{H}}_{\rm rest} \,.
\end{equation}
Of these two mechanical modes, only the differential one is of interest in both the laser GW detectors and in the small-scale membrane interferometers. In the former case, it is this mode that is coupled with the gravitational waves. In the latter case, the mechanical common mode corresponds to the membrane thickness oscillations, which are characterized by very high (hundreds of gigahertz) eigenfrequency and low $Q$-factor and hardly can be used in optomechanical experiments. Therefore, the part of the Hamiltonian \eqref{H_MFP_pm_diag} referring to common modes can be omitted, which gives the following Hamiltonian
\begin{equation}\label{H_MFP_pm_diff}
\hat{\mathcal{H}} = -\hbar\delta(\hat{{\rm e}}_-^\dagger\hat{{\rm e}}_- + \sfrac{1}{2})
- \hbar g\hat{x}({\rm E}_+^\dagger\hat{{\rm e}}_- + \mathrm{h.c.})
+ \hat{\mathcal{H}}_m + \hat{\mathcal{H}}_{\rm rest} \,.
\end{equation}
Up to the notations, it is identical to the Hamiltonian \eqref{H_MFP_pm_diff}, despite the completely different types of the optomechanical coupling --- the dispersive one in \eqref{H_cav_lin} and the coherent or the dissipative one in \eqref{H_MFP_pm_diff}.
\section{Analysis of the asymmetric interferometer}\label{sec:calculations}
Now, having discussed the various types of optomechanical coupling in Michelson-type interferometers, we are in position to consider in depth the asymmetric case. In the rest of this paper, we focus on the above mentioned case of a very broadband common optical mode, which is characterized by the dissipative (in contrast to coherent) optomechanical coupling. This case is typical for table-top interferometers researching fundamental optomechanics, because in this case much lower optical powers than in the large-scale gravitational-wave detectors is required. Due to this reason, we do not consider here the common mechanical mode. At the same time, both common and differential optical modes will be taken into account.
In the calculations below, we will use the Heisenberg picture (or input/output relations) approach which is more conveninent for analysis of sophisticated optomechanical systems, see {\it e.g.}\, \cite{Caves1981, Buonanno2003, 12a1DaKh}. In this picture, the linearized dynamics of a two-port optomechanical system can be described by two matrix equations. The first one is the optical input/output relation:
\begin{equation}\label{in_out}
\hat{{\bf b}}(\omega) = \mathbb{R}_{\rm ifo}(\omega)
\bigl[\hat{{\bf a}}(\omega) + ik_p\mathbb{G}(\Omega){\bf E}\hat{x}(\Omega)\bigr]\,,
\end{equation}
where $\mathbb{R}_{\rm ifo}$ and $\mathbb{G}$ are $2\times2$ matrices and
\begin{align}
\hat{{\bf a}} &= \svector{\hat{{\rm a}}_+}{\hat{{\rm a}}_-} , &
\hat{{\bf b}} &= \svector{\hat{{\rm b}}_+}{\hat{{\rm b}}_-}
\end{align}
are two-components vectors for the input and output optical fields in the ``west'' and the ``south'' (as shown in Fig.\,\ref{fig:Michelson-Sagnac}) ports of the interferometer. The second equation describes the radiation pressure force acting on the mechanical object:
\begin{equation}\label{F}
\hat{F}(\Omega) = \hat{F}_{\rm fl}(\Omega) - K(\Omega)\hat{x}(\Omega) \,,
\end{equation}
where
\begin{equation}\label{F_fl}
\hat{F}_{\rm fl}(\Omega)
= \hbar k_p{\bf E}^\dagger\mathbb{F}(\Omega)\hat{{\bf a}}(\omega) + \mathrm{C.C.}
\end{equation}
is the stochastic part of the radiation pressure force,
\begin{equation}\label{K}
K(\Omega) = \hbar k_p^2{\bf E}^\dagger\mathbb{K}(\Omega){\bf E}
\end{equation}
is the optical rigidity, and $\mathbb{F}$, $\mathbb{K}$ are $2\times2$ matrices. The explicit equations for the matrices $\mathbb{R}_{\rm ifo}$, $\mathbb{G}$, $\mathbb{F}$, and $\mathbb{K}$ are quite cumbersome; they are derived in the Appendix, see Eqs.\,(\ref{bbR_ifo}, \ref{bbG}, \ref{bbF}, \ref{bbK}), respectively. The non-symmetrized spectral density $\tilde{S}_F$ of the force $\hat{F}_{\rm fl}$ can be obtained from Eq.\,\eqref{F_fl} using directly the definition \eqref{tilde_S}. In particular, if the incident quantum fields are in vacuum, then the spectral density is equal to
\begin{equation}\label{tilde_S_F}
\tilde{S}_F(\Omega)
= \hbar^2k_p^2{\bf E}^\dagger\mathbb{F}(\Omega)\mathbb{F}^\dagger(\Omega){\bf E}\,.
\end{equation}
An interesting feature of Eqs.\,\eqref{in_out} and \eqref{F} is the following symmetry condition [see Eqs.\,(\ref{bbG}, \ref{bbF})]:
\begin{equation}\label{G_F}
\mathbb{G}(\Omega) = \mathbb{F}^\dagger(\Omega) \,.
\end{equation}
It is the two-port analog of the well-known relation between the measurement noise and the radiation pressure noise in ordinary (single-port) interferometers \cite{Caves1981, 02a1KiLeMaThVy, Buonanno2003}, which gives rise to the uncertainty relation between the radiation pressure noise and the measurement noise spectral densities of these devices \cite{Buonanno2003, 12a1DaKh} (which, in turn, is a particular case of the general uncertainty relation for the continuous linear quantum measurement \cite{92BookBrKh}).
As we have mentioned, in this paper we focus on the case without power-recycling,
\begin{equation}\label{no_pr}
R_W=0 \,.
\end{equation}
In addition, we assume the lumped mode approximation (that is, the high finesse limit), which is a good approximation in common setups and significantly simplify the equations. Namely, we suppose that: (i) the transmissivity of the signal recycling mirror is small
\begin{subequations}\label{sm_app}
\begin{gather}
T_S^2 = 1-R_S^2 = 4\gamma_S\tau_S \ll 1 \,,
\intertext{(ii) the signal recycling cavity is tuned close to the resonance:}
e^{i\omega\tau_S} = e^{i(\delta_S+\Omega)\tau_S + i\theta} \,,\quad
|\delta_S+\Omega|\tau_S \ll 1 \,, \\
\intertext{where $\delta_S$ is the detuning of the ``south'' arm, and (iii) the asymmetry of the interferometer is small:}
p^2 = \epsilon^2 + \varkappa^2 \ll 1 \,.
\end{gather}
\end{subequations}
We assume the following relations between these small values:
\begin{equation}\label{nopr_sm_2}
\gamma_S\tau_S \sim |\delta_S+\Omega|\tau_S \sim p^2 \,.
\end{equation}
Then, keeping {\it in each component} of the matrices $\mathbb{F}$ and $\mathbb{K}$ [see Eqs.\,(\ref{bbF}, \ref{bbK})] only the leading non-vanishing terms, we obtain that
\begin{gather}
\mathbb{G}^\dagger(\Omega) = \mathbb{F}(\Omega) = \frac{2R_m}{\tau_S\ell(\Omega)}
\smatrix{ip\sin(\alpha-\theta)}{\sqrt{\gamma_S\tau_S}\,e^{-i\theta}}
{[\tau_S\ell_S(\Omega) + ip^2\sin2\alpha/2]e^{i\theta}}
{-\sqrt{\gamma_S\tau_S}\,pe^{i(\theta-\alpha)}} , \label{bbF_nopr_sm} \\
\mathbb{K}(\Omega) = -\frac{2iR_m}{\tau_S\ell(\Omega)}
\smatrix{R_m}{-R_mpe^{-i\alpha}}{-R_mpe^{2i(\theta-\alpha)}}
{[\tau_S\ell_S(\Omega) + \epsilon^2]e^{i\theta}}
+ \mathrm{C.C.} , \label{bbK_nopr_sm}
\end{gather}
where
\begin{subequations}
\begin{gather}
\ell(\Omega) = \gamma - i(\delta+\Omega) \,, \\
\ell_S(\Omega) = \gamma_S - i(\delta_S+\Omega) \,,
\end{gather}
\end{subequations}
\begin{subequations}
\begin{gather}
\gamma = \gamma_S + \gamma_m \,, \\
\delta = \delta_S + \delta_m
\end{gather}
\end{subequations}
are the total bandwidth and the detuning of the interferometer,
\begin{subequations}\label{gd_m}
\begin{gather}
\gamma_m = \frac{p^2\sin^2(\theta-\alpha)}{\tau_S} \,, \\
\delta_m = \frac{p^2R_m\sin(\theta-2\alpha)}{\tau_S}
\end{gather}
\end{subequations}
are the components of $\gamma$, $\delta$ due to the asymmetry of the interferometer, and the angle $\alpha$ is defined as follows:
\begin{align}
\epsilon &= p\cos\alpha \,, & \varkappa &= p\sin\alpha \,.
\end{align}
The dispersive and dissipative coupling factors can be readily derived from Eqs.\,\eqref{gd_m}:
\begin{subequations}\label{g_disp_diss}
\begin{gather}
g_{\rm disp} = -k_p\partd{\delta_m}{\varkappa}
= \frac{2k_pR_mp}{\tau_S}\cos(\theta-\alpha) \,, \\
\frac{g_{\rm diss}}{\sqrt{2\gamma_m}} = k_p\partd{\sqrt{2\gamma_m}}{\varkappa}
= \frac{2k_pR_m}{\sqrt{\tau_S}}\mathop{\rm sign}\nolimits(\theta-\alpha) \label{g_diss}
\end{gather}
\end{subequations}
(note that it is the combination \eqref{g_diss}, but not just $g_{\rm diss}$ appears in the dissipative coupling Hamiltonian, see {\it e.g.}\, Eq.\,(1) of \cite{Xuereb_PRL_107_213604_2011}).
The upper row terms in the matrix \eqref{bbF_nopr_sm} has the order of magnitude of $\mathcal{O}(p^{-1})$, while the lower row ones --- of $\mathcal{O}(1)$. Correspondingly, the matrix $\mathbb{F}\mathbb{F}^\dagger$, which appears in Eq.\,\eqref{tilde_S_F}, has the following structure:
\begin{equation}\label{smallnesses}
\mathbb{F}(\Omega)\mathbb{F}^\dagger(\Omega) \sim
\smatrix{\mathcal{O}(p^{-2})}{\mathcal{O}(p^{-1})}{\mathcal{O}(p^{-1})}{\mathcal{O}(1)}
.
\end{equation}
Suppose now that either the classical field amplitudes ${\rm E}_\pm$ are of the same order of magnitude, or ${\rm E}_+$ dominates:
\begin{equation}\label{equalEs}
{\rm E}_+ \gtrsim {\rm E}_- \,.
\end{equation}
In this case, the spectral density \eqref{tilde_S_F} is dominated by the term proportional to $|{\rm E}_+|^2$, with the other terms being small corrections which have to be neglected for the sake of consistency with the already made approximations. This consideration gives the following equations for the non-symmetrized and symmetrized [see Eq.\,\eqref{S}] radiation pressure noise spectral densities:
\begin{subequations}\label{S_F_can}
\begin{gather}
\tilde{S}_F(\Omega)
= \frac{4\hbar^2k_p^2R_m^2|{\rm E}_+|^2\gamma}{\tau_S|\ell(\Omega)|^2} \,, \\
S_F(\Omega) = \frac{4\hbar^2k_p^2R_m^2|{\rm E}_+|^2\gamma}{\tau_S}\,
\frac{\gamma^2+\delta^2+\Omega^2}{|\ell(\Omega)|^2|\ell(-\Omega)|^2} \,.
\end{gather}
\end{subequations}
The matrix \eqref{bbK_nopr_sm} also has the structure \eqref{smallnesses}. Therefore, the above consideration is valid for the optical rigidity as well, giving:
\begin{equation}\label{K_can}
K(\Omega)
= \frac{4\hbar^2k_p^2R_m^2|{\rm E}_+|^2\delta}{\tau_S\ell(\Omega)\ell^*(-\Omega)} \,.
\end{equation}
Equations (\ref{S_F_can}, \ref{K_can}) do not depend on the interferometer asymmetry and differ from the well-know ``canonical'' ones \cite{Buonanno2003, 12a1DaKh} only by the well-expected factor $R_m^2$.
It follows from this consideration, that the ``non-canonical'' features, predicted in \cite{Xuereb_PRL_107_213604_2011, 13a1TaKhKaScHa} and observed in \cite{14a1SaKaNiTaKhHaSc}, evidently, originates from a violation of the assumption \eqref{equalEs}. In fact, it follows from Eq.\,\eqref{bf_E}, with account of the assumption \eqref{no_pr} and approximations \eqref{sm_app}, that the classical amplitudes of the intracavity fields are equal to
\begin{multline}
{\bf E} = \frac{1}{\tau_S\ell(0)}
\smatrix{\tau_S\ell_S(0) + ip^2\sin2\alpha/2}{-\!\sqrt{\gamma_S\tau_S}\,pe^{-i\alpha}}
{ipe^{i\theta}\sin(\alpha-\theta)}{\sqrt{\gamma_S\tau_S}}
\svector{{\rm A_W}e^{i\omega_p\tau_W}}{{\rm A_S}e^{i\omega_p\tau_S}} \\
\sim\smatrix{\mathcal{O}(1)}{\mathcal{O}(1)}{\mathcal{O}(p^{-1})}{\mathcal{O}(p^{-1})}
\svector{{\rm A_W}e^{i\omega_p\tau_W}}{{\rm A_S}e^{i\omega_p\tau_S}} ,
\end{multline}
which means that {\it typically}, instead of \eqref{equalEs},
\begin{equation}\label{differentEs}
{\rm E}_- \sim \frac{{\rm E}_+}{p} \gg {\rm E}_+ \,.
\end{equation}
This resonance-enhanced value of ${\rm E}_-$ emphasizes the smaller terms in the matrices (\ref{bbF_nopr_sm}, \ref{bbK_nopr_sm}), making their contribution comparable with one of the ``canonical'' terms.
In particular, in the case of ${\rm A}_-=0$, which was considered in \cite{Xuereb_PRL_107_213604_2011, 13a1TaKhKaScHa},
\begin{equation}
\tilde{S}_F(\Omega)
= \frac{4\hbar^2k_p^2R_m^2|{\rm A}_+|^2}{\tau_S|\ell(0)|^2|\ell(\Omega)|^2}\Bigl\{
\gamma_m(2\delta_S - 2\epsilon\varkappa/\tau_S + \Omega)^2
+ \gamma_S\bigl[\gamma^2 + (\delta_S-\delta_m-2\epsilon\varkappa/\tau_S)^2\bigr]
\Bigr\} .
\end{equation}
Note the ``non-canonical'' Fano-resonance term, discussed in \cite{Elste_PRL_102_207209_2009, Xuereb_PRL_107_213604_2011}, which provides a minimum of $\tilde{S}_F(\Omega)$ at $\Omega=-2\delta_S+2\epsilon\varkappa/\tau_S$. It is evident, however, that by fine tuning of the values of ${\rm A}_{W,S}$, any ratio of ${\rm E}_+/{\rm E}_-$ can be obtained. In particular, as we show in the next section, the most effective optical cooling can be achieved by the ideally symmetric field, ${\rm E}_-=0$.
\section{Optimal optical cooling in Michelson-type interferometers}\label{sec:cooling}
In the recent experimental work \cite{14a1SaKaNiTaKhHaSc} optical cooling in the regime of interfering dispersive and dissipative coupling in an asymmetric Michelson-Sagnac interferometer was observed. Here we use our general framework to calculate the optimal cooling regime in the asymmetric Michelson-type interferometers for a given, fixed value of the optical power circulating in the interferometer.
We start with the two well known fundamental interrelations between any source of dissipation and the thermal noise $\hat{F}_T$ associated with it. The first one is the Fluctuation-Dissipation Theorem (FDT) \cite{Callen1951}:
\begin{equation}\label{FDT}
S_T(\Omega) = \hbar|\Omega H|(2n_T + 1) \,,
\end{equation}
where
\begin{equation}
S_T(\Omega) = \frac{\tilde{S}_T(\Omega) + \tilde{S}_T(-\Omega)}{2}
\end{equation}
is the symmetrized spectral density of this noise, $\tilde{S}_T(\Omega)$ is the corresponding non-symmetrized spectral density, see Eqs.\,(\ref{tilde_S}, \ref{S}), $H$ is the friction factor, $n_T$ is the effective number of thermal quanta defined by
\begin{equation}
2n_T + 1 = \coth\frac{\hbar|\Omega|}{2\kappa_BT} \,,
\end{equation}
and $T$ is the temperature. The second one is the Kubo theorem \cite{Kubo1956}:
\begin{equation}\label{Kubo}
\Omega H = \frac{\tilde{S}_T(\Omega) - \tilde{S}_T(-\Omega)}{2\hbar} \,.
\end{equation}
Assuming that $H>0$ (stable system dynamics) and $\Omega>0$, it is easy to get from Eqs.\,(\ref{FDT}, \ref{Kubo}), that
\begin{equation}
\frac{1}{n_T} +1 = \frac{\tilde{S}_T(\Omega)}{\tilde{S}_T(-\Omega)} \,.
\end{equation}
In optical cooling experiments, the ``native'' mechanical heat bath is supplemented by the low temperature optomechanical one. In this case, the steady state mean number of phonons in the mechanical oscillator is given by
\begin{equation}
2\mean{n} + 1 = \frac{S_T(\Omega_m) + S_F(\Omega_m)}{\hbar\Omega_m(H + H_{\rm opt})} \,,
\end{equation}
where $S_F$ is the symmetrized spectral density of the radiation pressure noise, $H_{\rm opt}$ is the optical damping:
\begin{equation}
\Omega H_{\rm opt} = -\Im K \,,
\end{equation}
and we absorbed the shift of the mechanical resonance frequency imposed by the optical spring into $\Omega_m$.
Rewriting the Kubo theorem for the optical damping:
\begin{equation}
\Omega H_{\rm opt} = \frac{\tilde{S}_F(\Omega) - \tilde{S}_F(-\Omega)}{2\hbar} \,,
\end{equation}
it is is easy to show that
\begin{equation}\label{mean_n}
\frac{1}{\mean{n}} + 1 = \frac{\tilde{S}_T(\Omega_m) + \tilde{S}_F(\Omega_m)}
{\tilde{S}_T(-\Omega_m) + \tilde{S}_F(-\Omega_m)} \,.
\end{equation}
In the Michelson-Sagnac interferometer, the explicit form of $\tilde{S}_F$ is rather sophisticated, see Eqs.\,(\ref{tilde_S_F}, \ref{bbF_nopr_sm}), and the direct analytical optimization of \eqref{mean_n} is hardly possible. However, under common experimental conditions the spectral densities $\tilde{S}_F$ and $\tilde{S}_T$ satisfy strong inequalities which significantly simplify this task. Really, starting values of the thermal occupation number of the real mechanical resonators are big, even in the cryogenic microwave experiments; correspondingly, asymmetry of the thermal noise spectral density is small:
\begin{equation}
\tilde{S}_T(\Omega_m) - \tilde{S}_T(-\Omega_m) \ll \tilde{S}_T(\pm\Omega_m) \,.
\end{equation}
Therefore, in order to provide effective optical cooling, asymmetry of the radiation pressure noise spectral density has to be strong:
\begin{equation}
\tilde{S}_F(\Omega_m) \gg \tilde{S}_F(-\Omega_m) \,.
\end{equation}
At the same time, due to technical constrains in contemporary optical cooling experiments, while $\tilde{S}_F(\Omega_m)$ could be close or even exceeds the thermal noise spectral density, its negative-frequency counterpart is small:
\begin{equation}
\tilde{S}_F(-\Omega_m) \ll \tilde{S}_T(\pm\Omega_m) \,.
\end{equation}
(this inequality was fulfilled with very good margin even in the record-breaking works \cite{Teufel_Nature_475_359_2011, Chan_Nature_478_89_2011}). These assumptions simplify Eq.\,\eqref{mean_n} to
\begin{equation}\label{mean_n_opt}
\mean{n} = \frac{\tilde{S}_T(-\Omega_m)}{\tilde{S}_F(\Omega_m)} \,.
\end{equation}
In this case, minimization of $\mean{n}$ is simply equivalent to maximization of $\tilde{S}_F(\Omega)$.
Of the mentioned above technical constrains, the most serious ones are limitations on the value of the optical power inside the interferometer imposed by various undesirable effects, like heating, mechanical nonlinearities, instabilities {\it etc}. Therefore consider maximization of $\tilde{S}_F(\Omega)$, assuming a given optical energy in the interferometer, which is proportional to
\begin{equation}\label{sum_E}
\mathcal{E} \propto |{\rm E}_+|^2 + |{\rm E}_-|^2 \,.
\end{equation}
It follows form Eqs.\,(\ref{tilde_S_F}, \ref{smallnesses}), that this spectral density has the following structure:
\begin{equation}
\tilde{S}_F \propto \mathcal{O}(p^{-2})|{\rm E}_+|^2
+ 2\mathcal{O}(p^{-1})\Re({\rm E}_+^*{\rm E}_-) + \mathcal{O}(1)|{\rm E}_-|^2 \,,
\end{equation}
that is, the symmetric field ${\rm E}_+$ provides the largest value of $\tilde{S}_F$ and therefore the most effective cooling. Therefore, with account of the optical energy constrain, the antisymmetric field has to be canceled, ${\rm E}_-=0$. In this case, the radiation pressure noise spectral density reduces to the canonical Lorentzian form \eqref{S_F_can}.
\section{Summary}\label{sec:summary}
We have shown that the standard description of the radiation-pressure induced optomechanical coupling as either ``dispersive'' or ``dissipative'' is univocal only in the simplest case of a single lumped electromagnetic mode. In the general multi-mode case, in particular in Michelson-type interferometers, the coupling type depends on the non-unique choice of its optical modes.
The most convenient choice, broadly used by the GW community, uses the common and differential optical modes of the interferometer, where the differential optical mode couples to the conventional signal output port. For these modes, the type of the optomechanical coupling further depends on whether the power recycling technique (in addition to signal-recycling) is used or not. In the latter case, the coupling is dissipative, with a dispersive contribution if the interferometer is not perfectly \emph{symmetric}. In the former one, a more sophisticated behavior emerges, where the coupling between two optical modes depends on the mechanical displacement, which we coined as the ``coherent optomechanical coupling''.
We have developed a general framework to calculate the optomechanical properties of the Michelson-type interferometers in the \emph{asymmetric} regime. It covers the possibility of the injection of carrier light into both ports of the interferometer. We used this framework for in depth analysis of the radiation pressure features (both dynamic and stochastic) of the Michelson-type interferometers without the power recycling, leaving the power-recycled configuration, with its different modes and optomechanical coupling structure, for future work.
Our analysis has shown that the ``anomalous'' features originate from the small second-order terms in the Taylor expansion of the (non-symmetrized) radiation pressure noise spectral density in the interferometer length and its asymmetry, see Eqs.\,(\ref{sm_app}, \ref{nopr_sm_2}). Usually, these terms are ignored in the lumped modes approximation routinely used in the analysis in the quantum optomechanical setups. In unbalanced Michelson-type interferometers these corrections are strongly amplified by the resonance-enhanced optical power in the differential optical mode of the interferometer and therefore change significantly the interferometer behavior.
Finally, we have shown that under common experimental conditions, and for a given optical power {\em inside} a cavity-enhanced Michelson interferometer, the lowest steady state mean phonons number $\mean{n}$ can be achieved by exciting the common optical mode alone with balanced light power in both arms. In this case the operation regime of the interferometer is ``canonical'' and fully corresponds to optical cooling in a Fabry-Perot cavity with dispersive coupling. At the same time, both dispersive and dissipative type of coupling could coexist in this case (however, optimal cooling regimes for the two-mode dual recycled interferometers and/or for a given \emph{injected} light power, could differ from this).
\acknowledgments
This work was supported by the Marie Curie Initial Training Network cQOM, by the ERC Advanced Grant MassQ, by the International Max Planck Research School for Gravitational Wave Astronomy (IMPRS), and by DFG through Research Training Group 1991 {\em Quantum mechanical noise in complex systems}. The work of F. Khalili was supported by LIGO NSF Grant No\,PHY-1305863 and Russian Foundation for Basic Research Grant No.\,14-02-00399.
The authors thank Haixing Miao for useful remarks.
The paper has been assigned LIGO document number P1600065.
| {
"redpajama_set_name": "RedPajamaArXiv"
} | 76 |
\section{Introduction}
Atomic vibrations in solids are inevitably affected by the shape of the interatomic potential. For all real materials, the shape of the interatomic potential is far from being quadratic, i.e. harmonic. The intrinsic anharmonicity of solids has many well known consequences such as thermal expansion, soft modes and instabilities, sound absorption, identification of stable crystalline phases etc.~\cite{Khomskii}
A well established approach to anharmonicity is the self-consistent method introduced by Born and Hooton~\cite{Born}, leading to the concept of renormalization of phonon frequencies in the quasiharmonic or self-consistent phonon approximation, where the renormalized phonon frequencies arise from an effective vibrational dynamics within a region about equilibrium, which takes anharmonic terms of the potential into account via adjustable parameters obtained from a self-consistent solution to the many-body problem~\cite{Klein1972}.
However, the effect of anharmonicity extends to far greater areas, including electron-phonon coupling, where traditionally the effect of \textcolor{black}{anharmonic damping} has always been neglected, and where instead recent first-principle calculations demonstrate an important effect of anharmonicity on band-structure~\cite{Montserrat,Cohen}.
\textcolor{black}{In the context of high $T_c$ superconductors, the effect of anharmonic enhancement on $T_c$ has been studied in the early days following the discovery of high-$T_c$ superconductivity in the cuprates. In particular, several works by Plakida and others have studied the effect of anharmonicity on $T_c$ for the case of structurally unstable lattices or deformed lattice potentials~\cite{Plakida_1987,Zacher_1987,Plakida_1989}. Even more recent works on the high-$T_c$ hydrides~\cite{Mauri2015,Bergara2010, Mauri2013, Mauri2014, Mauri2016, Arita2016, Errea2016, Bergara2016,szcesniak2015high,errea2020quantum,camargomartnez2020higher} only take into consideration phonon energy renormalizations due to anharmonicity but neglect anharmonic damping.}
However, a fundamental understanding of the effect of \textcolor{black}{anharmonic damping} on phonon-mediated superconductivity and e.g. on $T_{c}$ is absent due to the lack of analytical approaches to this problem. Yet, this is a fundamental issue in the context of high-T superconductors where anharmonicity becomes important due to the significant temperature values, since in general anharmonicity in solids grows roughly linear in $T$~\cite{Khomskii}. Even more urgent is the problem of the effect of anharmonicity in hydrogen-based materials, which have recorded the highest $T_{c}$ values so far: in these systems the presence of a light element such as hydrogen induces a huge anharmonicity due to the large oscillation amplitudes of the hydrogen atoms~\cite{Pickard2007,Pickard2015,Eremets2015,Pickard_review,Mauri2016, errea2020quantum}.
Numerical studies and first-principle calculations can assess the effect of anharmonicity in an empirical way for a specific material by benchmarking against harmonic calculations, but a systematic fundamental understanding of the role of \textcolor{black}{anharmonic damping} on conventional superconductivity is missing. This would be highly beneficial to obtain system-independent guidelines to not only estimate the effect of \textcolor{black}{anharmonic damping} in general cases, but also to develop generic guidelines for material design.
For example, by relating \textcolor{black}{anharmonic damping} to the interatomic potential it could become possible to design materials with ad-hoc or tunable electron-phonon coupling and superconducting properties.
Here we take a first step in this direction by studying the effect of \textcolor{black}{phonon Akhiezer and Klemens damping} on superconductivity beyond the quasi-harmonic approximation. We do this by explicitly taking into account the phonon damping due to anharmonicity in the mediator for the electron pairing. The theory shows that, unexpectedly, the effect of the anharmonicity (as represented by the damping coefficient) on $T_{c}$ is non-monotonic, i.e. $T_{c}$ first increases then goes through a maximum and then decreases upon increasing the anharmonic damping. This occurs because electron-phonon scattering processes involving energy-loss and energy-gain (Stokes and anti-Stokes) act constructively to increase the effective attraction driving the formation of Cooper pairs. The enhancement is most efficient for a window of critical damping parameter ($D_{max}$) set by the bosonic velocity and correlated with the Ioffe-Regel scale. Outside this window, the strength of pairing deteriorates leading a reduction in $T_c$. \textcolor{black}{These results are valid for both cases of acoustic and optical phonons, as shown in in the Appendix A.3 below.} \\
\section{The theoretical framework}
The displacement field of an anharmonic solid obeys the following dynamical equation~\cite{Maris}:
\begin{equation}
\rho \,\frac{\partial^{2} u_{i}}{\partial t^{2}}=C^{T}_{ijkl}\, \frac{\partial^{2} u_{k}}{\partial x_{j}\partial x_{l}} - C^{T}_{ijkl}\, \alpha_{kl}\,\frac{\partial \Delta T}{\partial x_{j}} + \,\nu_{ijkl}\,\frac{\partial^{2} \dot{u}_{k}}{\partial x_{j}\partial x_{l}}
\label{DEquation}
\end{equation}
which is coupled to Fourier's law for heat transfer and to the energy balance equation for the thermal gradient $\Delta T$.
In Eq.~\eqref{DEquation} , $u_{i}$ denotes the $i$-th Cartesian component of the atomic displacement field, $C^{T}_{ijkl}$ is the isothermal elastic constant tensor, $\alpha_{kl}$ is the thermal expansion tensor, and $\nu_{ijkl}$ is the viscosity tensor. The dot indicates derivative with respect to time of the elastic field $u_{k}$ in the last dissipative term.
For solids, where acoustic excitations can be split into longitudinal (LA) and transverse (TA), Eq.~\eqref{DEquation} can be split into two decoupled equations for LA and TA displacements, leading to the following Green's function in Fourier space ~\cite{Chaikin}:
\begin{equation}\label{GFReal}
G_{\lambda}(\omega,q)\,=\,\frac{1}{\omega^2\,-\,\Omega_{\lambda}^{2}(q)\,+\,i\,\omega\,\Gamma_{\lambda}(q)}
\end{equation}
where $\lambda= TA, LA$ is the branch label, and $\Gamma_{\lambda}(q)=D q^{2}$ represents the \textcolor{black}{Akhiezer} damping, which
coincides with the acoustic absorption coefficient~\cite{Maris}, while $\Omega_{\lambda}(q)=v_{\lambda}q$ is the acoustic eigenfrequency, already renormalized to account for the shift induced by anharmonicity~\cite{Dove}, with $v_{\lambda}$ the speed of sound for branch $\lambda$.
The quadratic dependence $\Gamma_{\lambda}(q)=D q^{2}$ of the damping stems directly from the viscous term in Eq.~\eqref{DEquation} and is typical of Akhiezer damping~\cite{Akhiezer,Maris}. In particular, it has been shown \cite{Akhiezer} that $\Gamma$ takes the following general form for longitudinal excitations (see also \cite{Landau}):
\begin{equation}
\Gamma_{L}=\frac{q^{2}}{2\rho }\left[ \left(\frac{4}{3}\eta + \zeta\right) + \frac{\kappa T \alpha^{2}\rho^{2} v_{L}^{2}}{C_{p}^{2}}\left( 1 - \frac{4 v_{T}^{2}}{3 v_{L}^{2}}\right)^{2}\right].
\label{Damping}
\end{equation}
where $\eta \equiv \nu_{xyxy}$ is the shear viscosity, $\zeta $ is the bulk viscosity, $\rho$ is the solid density, $\kappa$ is the thermal conductivity, $\alpha$ is the longitudinal thermal expansion coefficient, and $C_{p}$ is the specific heat at constant pressure.
The second term in Eq.~\eqref{Damping}, $\sim \alpha^2$, represents the phonon damping due to heat exchange between the compressed and the rarefied regions of the longitudinal wave. This second contribution, in practice, represents only a few percent of the first viscous contribution in Eq.~\eqref{Damping} and is therefore negligible.
The above derivation follows a hydrodynamic approach \cite{landau2013fluid}; by comparing with the result of a microscopic approach based on the Boltzmann transport equation for phonons, it has been shown that~\cite{Maris}
\begin{equation}\label{DiffusionConstant-2}
D_{L} = \frac{C_{v} T \tau}{2\rho} \left(\frac{4}{3}\langle \gamma_{xy}^{2}\rangle -\langle \gamma_{xy} \rangle^{2} \right) \approx \frac{C_{v} T \tau}{2\rho} \langle \gamma_{xy}^{2}\rangle
\end{equation}
where we neglected the contribution from bulk viscosity $\zeta$, since normally $\eta \gg \zeta$. Furthermore,
$\langle...\rangle$ indicates averaging with respect to the Bose-Einstein distribution as a weight, while
$\gamma_{xy}$ is the $xy$ component of the tensor of Gr{\"u}neisen constants. Also, $C_{v}$ is the specific heat at constant volume, while $\tau$ is the phonon life-time. Since $\tau \sim T^{-1}$ (which is an experimental observation for most solids~\cite{Boemmel,Maris}), the diffusion constant $D_L$ is independent of temperature, i.e. a well-known experimental fact~\cite{Boemmel}.
A substantially equivalent expression for the damping of longitudinal phonons, in terms of an average Gr{\"u}neisen constant of the material $\gamma_{av}$, was derived by Boemmel and Dransfeld~\cite{Boemmel}
\begin{equation}\label{DiffusionConstant-3}
D_{L} \approx \frac{C_{v} T \tau}{2\rho} \gamma_{av}^{2}
\end{equation}
and provides a good description of the Akhiezer damping measured experimentally in quartz at $T > 60K$ \cite{Boemmel}.
In turn, the Gr{\"u}neisen constant $\gamma$, or at least the leading term~\cite{Krivtsov2011} of $\gamma_{av}$ or $\gamma_{xy}$ above, can be directly related to the anharmonicity of the interatomic potential. For perfect crystals with pairwise nearest-neighbour interaction, the following relation holds \cite{Krivtsov2011}
\begin{equation}
\gamma= -\frac{1}{6}\frac{V'''(a)a^{2} +2 [V''(a)a -V'(a)]}{V''(a) a+2 V'(a)}
\label{AtomicPotential}
\end{equation}
where $a$ is the equilibrium lattice spacing between nearest-neighbours, and $V'''(a)$ denotes the third derivative of the interatomic potential $V(r)$ evaluated in $r=a$.
Hence, the phonon damping coefficient $D_{L}$ can be directly related to the anharmonicity of the interatomic potential via the Gr{\"u}neisen coefficient and Eq. \eqref{AtomicPotential}.\\
\section{Results}
Because in crystals momentum is always conserved during electron-phonon scattering events, only longitudinal phonons contribute to pairing \cite{Lee,Gorkov}, therefore we will focus on the LA phonon, $\lambda = LA$, and we will drop the $\lambda$ index in the following.
According to Eq.~\eqref{GFReal} we thus choose a phonon propagator written in Matsubara frequency of the form
\begin{eqnarray}
\Pi(i \Omega_n,\textbf{q}) = \frac{1}{v^{2}q^2 +\Omega_n^2+\Gamma(\textbf{q})\,\Omega_n},
\end{eqnarray}
with $\Gamma(\textbf{q}) = D q^2$ being the Akhiezer damping discussed above, and $v$ is the phonon velocity.
We define the Bosonic Matsubara frequency $\Omega_n = 2n\pi T$ where $n$ is an integer number and $T$ the temperature. The superconducting gap equation for a generic gap at momentum $\textbf{k}$ and Fermionic Matsubara frequency $\omega_n = (2n+1)\pi T$ takes the form (see Ref.~\cite{Carbotte2008} or ~\cite{Kleinert})
\begin{eqnarray} \nonumber
\Delta(i\omega_n, \textbf{k}) &=& \frac{g^2}{\beta V} \sum_{\textbf{q}, \omega_m} \frac{\Delta(i\omega_m, \textbf{k}+ \textbf{q}) \Pi(\textbf{q}, i\omega_n - i \omega_m)}{\omega_m^2 + \xi_{\textbf{k} + \textbf{q}}^2 + \Delta(i\omega_m, \textbf{k}+ \textbf{q})^2}\,,\\
&&
\label{Sum-GapEqn}
\end{eqnarray}
for a constant attractive interaction $g$ and volume $V$.
Here $\xi_{\textbf{k}}$ is the free electron dispersion which we choose to be quadratic with a chemical potential $\mu$. The inverse temperature is denoted by $\beta$ and we work in simplified units where twice the electron mass is set to unity. For analytical tractability, we also choose an isotropic gap function independent of frequency, i.e., $\Delta(i\omega_m, \textbf{k}+ \textbf{q}) \equiv \Delta$.
Converting the momentum summation into energy integral with variable $\xi$ and assuming a constant density of states, the gap equation reduces to
\begin{eqnarray} \nonumber
1 &=& \sum_{\omega_m} \int_{-\mu}^{\infty}\frac{\lambda T d\xi}{\left[ (v^{2} - D \omega_m)(\xi + \mu)+ \omega_m^2 \right] \left[\omega_m^2 + \xi^2 + \Delta^2\right]}\\
&&
\label{Integral-GapEqn}
\end{eqnarray}
where $\lambda = N(0) g^2$ and $N(0)$ is the density of states at the Fermi level. To begin the discussion, we confine ourselves to small $D$ so that we can ignore $D\mu \ll T \sim T_c$ even though the chemical potential is allowed to be large compared to $T_c$. This implies that the linear term in $\omega_m$ can be neglected. The remaining constant $\mu v^{2}$ acts like a mass term and reduces $T_c$ for all $D$~\cite{Setty2019}. As this effect is only quantitative, this term can also be ignored, as a first approximation, without affecting the central claims of the paper. The full effect of the chemical potential term will be included in the upcoming paragraphs. With these assumptions and using the energy integral identity $\int_{-\infty}^{\infty} \frac{d \xi}{(z \xi + s) (\xi^2 + r^2)} = \frac{\pi s}{r(s^2 + z^2 r^2)}$, we obtain
\begin{eqnarray} \nonumber
1&=& \sum_{\omega_m}\frac{\lambda \pi T \omega_m^2}{\sqrt{\omega_m^2 + \Delta^2} \Big( \omega_m^4 + (\omega_m^2 + \Delta^2)(v^{2} - D \omega_m)^2 \Big)}.\label{pro}\\
&&
\label{MatsubaraSum-NoCP}
\end{eqnarray}
\begin{figure}[h!]
\includegraphics[width=0.8 \linewidth]{fig1.pdf}
\vspace{0.4cm}
\includegraphics[width=0.8 \linewidth]{fig1b.pdf}
\caption{\textbf{Top: } The dimensionless critical temperature $\bar{T}_c$ as a function of the damping constant $D$ at different dimensionless speeds $\bar{v} \in [0.5,1.4]$. \textbf{Bottom: } The position of the maximum temperature as a function of the dimensionless longitudinal sound speed. In both plots we fixed $\bar{\mu}=0.1$.
} \label{TcVsD}
\end{figure}
\noindent To determine the condition for $T_c$, we set the superconducting gap $\Delta =0$.
We can then perform the infinite sum over Matsubara frequencies (see the Appendix A.1 for more details) to obtain the simplified gap equation
\begin{eqnarray} \nonumber
1&=& \frac{-1}{\bar{v}^4}\Bigg[ \psi\left(\frac{1}{2}\right) + \frac{i (i + D)}{4}\psi\left(\frac{1}{2}- \frac{\bar{v}^{2}}{2 \pi \bar{T}_c (i+D)}\right)\\
&& + \frac{i (i + D)}{4}\psi\left(\frac{1}{2}+ \frac{\bar{v}^2}{2 \pi \bar{T}_c (i+D)}\right) + c.c \Bigg],
\label{NoCP}
\end{eqnarray}
\begin{figure}[hbt]
\includegraphics[width=0.8 \linewidth]{fig2.pdf}
\vspace{0.4cm}
\includegraphics[width=0.8 \linewidth]{fig2b.pdf}
\caption{\textbf{Top: } The dimensionless critical temperature $\bar{T}_c$ in function of the diffusion constant $D$ at different dimensionless chemical potentials $\bar{\mu} \in [0.01,1.5]$. \textbf{Bottom: } The position of the maximum temperature in function of the dimensionless chemical potential. In both plots we fixed $\bar{v}=1.2$.
}\label{CPEffect}
\end{figure}
where, henceforth, the barred quantities are normalized by $\sqrt{\lambda}$, i.e., $\bar{v} = v/\sqrt{\lambda}$ and $\psi(x)$ is the digamma function. A solution for $\bar{T}_c$ can be obtained from Eq.~\eqref{NoCP} and is plotted in Fig.~\ref{TcVsD} (Top) as a function of the anharmonic damping parameter $D$. The plot shows that $\bar{T}_c$ is enhanced quadratically for small $D$, reaches a maximum at an optimal anharmonicity parameter $D_{max}$ (set by the dimensionless phonon velocity $\bar{v}$), and falls off as a power law for larger $D$. The optimal parameter $D_{max}$ increases with $\bar{v}$ as shown in Fig.~\ref{TcVsD} (Bottom). In the Appendix A.2 (see also Refs.~\cite{Parshin1, Schirmacher,baggioli2019unified,Milkus,Jezowski,baggioliPRL} quoted therein), we discuss the behavior of $D_{max}$ for larger values of $\bar{v}$ where it saturates to a value $D_{max}\sim v^2/T_c$ (not shown in Fig.~\ref{TcVsD}). This condition for \textit{resonance} can be obtained from the denominator in Eq.~\ref{MatsubaraSum-NoCP}. Note that the enhancement of the transition temperature occurs only above a critical value of the phonon velocity that is set by the interaction parameter $\sqrt{\lambda}$. The reason for the non-monotonic behavior of $\bar{T}_c$ can be understood from Eq.\eqref{pro} and the anti-symmetry in $\omega$ of the phonon damping term. Because of this property, Stokes and anti-Stokes processes ($\omega_m < \,\text{and}\, > 0$, respectively) add up constructively to increase the effective attraction driving the formation of Cooper pairs. This constructive interference grows with $D$ which gets to the numerator upon adding the two processes. Eventually, however, for sufficiently large anharmonic damping $D\gg v^2/\omega_m$, the quadratic term $\sim D^{2} \omega_m^2$ in the denominator of Eq.\eqref{pro} becomes the dominant contribution, the Stokes and anti-Stokes processes now add up in a destructive way and superconductivity gets suppressed. In the regime where $v$ is very small, the last term in the denominator of Eq.\eqref{pro} can be approximated as $(v^2-D \omega_m)^2\,\sim D^2 \omega_m^2$ and the non-monotonicity is absent even at small $D$ values (see dark lines in Fig.\ref{TcVsD}).\\
\section{Chemical potential effects}
In the following paragraphs, we relax the assumptions made previously on the chemical potential.
We restrict ourselves to the BCS/quasi-BCS regime where the chemical potential is positive and not below the band bottom. This assumption ignores effects where the pairing scale becomes comparable to the band-width and hence keeping the BCS-BEC cross-over regime inaccessible.
Following the same steps of the previous section, we obtain the simplified formula
\begin{eqnarray} \nonumber
1 &=& \sum_{\omega_m}\frac{ \lambda \pi T_c \left(\omega_{mc}^2 + (v^{2} - D \omega_{mc}) \mu\right) |\omega_{mc}|^{-1}}{\left(\omega_{mc}^2 + (v^{2} - D \omega_{mc}) \mu\right)^2 + \omega_{mc}^2 (v^{2} - D\omega_{mc})^2}\\
&&
\label{MatsubaraSum-WithMu}
\end{eqnarray}
where $\omega_{mc}$ is the Fermionic Matsubara frequency at $T=T_c$.
After algebraic manipulations of the Matsubara sum, as shown in the Appendix A.1, the final equation for $\bar{T}_c$ with a finite chemical potential reduces to
\begin{widetext}
\begin{eqnarray}\label{WithMu}
1 &=& \frac{1}{2\bar{v}^{2}\bar{\mu}} \Bigg[ -\psi\left(\frac{1}{2}\right) + \Bigg\{ \frac{b_+ - a^*}{2(b_+ - b_-)}\psi\left(\frac{1}{2} - b_+\right)+ \frac{a^* - b_-}{2(b_+ - b_-)}\psi\left(\frac{1}{2} - b_-\right) + c.c \Bigg\}\Bigg] + \left[D \leftrightarrow -D\right],
\end{eqnarray}
\end{widetext}
where we have the definitions $a \equiv \frac{z}{D+ i}$, $b_{\pm} \equiv \frac{z^* \pm \sqrt{z^2 + \frac{4 \bar{v}^{2} \bar{\mu}}{(2 \pi \bar{T}_c)^2}}}{2 (D-i)}$ and $z \equiv \frac{\bar{v}^{2}}{2\pi \bar{T}_c} + i D \frac{\bar{\mu}}{2\pi \bar{T}_c}$. A plot of the numerical solution for $\bar{T}_c$ versus $D$ is shown in Fig.~\ref{CPEffect} (Top). Many of the features appearing in Fig.~\ref{TcVsD} (Top) are reproduced when the chemical potential is introduced -- a non-monotonic dependence on the anharmonicity parameter, a quadratic rise and power-law fall off for small and large $D$ respectively. This reaffirms the assumptions made on the chemical potential in deriving Eq.~\eqref{NoCP}. However, the chemical potential has an additional non-trivial effect of reducing $\bar{T}_c$ at small and large $D$, but enhances its peak value at optimal $D$. Furthermore, the $\bar{T}_c$ peak position ($D_{max}$) changes substantially for small $\bar{\mu}$ and remains virtually unchanged for larger $\bar{\mu}$. A plot of $D_{max}$ as a function of $\bar{\mu}$ is shown in Fig.~\ref{CPEffect} (Bottom).\\
\section{Discussion}
Much attention has been devoted to the role of disorder induced damping on superconducting $T_c$ (see~\cite{Zhu2006} and references therein); however, only a few theoretical works have examined directly the effects of damping on the superconducting properties, mostly in terms of glassiness~\cite{Seki1995, Larkin2002, Setty2019, BSZ2020}. Ref.~\cite{Larkin2002} finds an enhancement of superconducting transition driven by a spin-glass phase formed from paramagnetic spins interacting through Ruderman-Kittel-Kasuya-Yosida exchange couplings. On the other hand, Ref.~\cite{Seki1995} finds that a glassy phase leads to monotonically decreasing $T_c$ but does not take into account the role of anharmonic phonon damping explicitly. The dissipative aspect of the glass phase was considered at a phenomenological level in Ref.~\cite{Setty2019} in the context of the under-doped high-$T_c$ cuprates. While a similar non-monotonic behavior in $T_c$ is found, its mechanism does not arise from the time-reversal symmetry breaking in the dissipation term. This is reflected in the linear rise of $\bar{T}_c$ for small damping as opposed to the quadratic rise as found in this work. Furthermore, as alluded to earlier, the parameter $D$ is a characteristic of anharmonic damping and originates from the viscous damping term in Eq.~\eqref{DEquation} describing anharmonic phonons. It can be directly related to the Gr{\"u}neisen constant, which, in turn, can be determined via first-principle calculations of the inter-atomic potential through Eq.~\eqref{AtomicPotential}; therefore, this relation provides a microscopic handle for tuning $D$ giving one significant control in designing real materials. \par
\section{Conclusion}
To conclude, we have developed superconducting gap equations which account for the effect of \textcolor{black}{anharmonic damping} of phonons. The phonon viscosity parameter $D$ can be related directly to the Gr{\"u}neisen coefficient and to the shape of the interatomic potential. Upon solving the gap equation, it is found that the $T_c$ depends non-monotonically upon the anharmonic damping parameter $D$ and features a maximum as a function of $D$. The value of the critical damping parameter ($D_{max}$) around which Cooper pairing is the strongest is set by the velocity $v$ of the phonon. Within this optimal range of damping, Stokes and anti-Stokes electron-phonon scattering processes act constructively to increase the effective coupling constant. Outside this window, the strength of pairing deteriorates leading to a reduction in $T_c$. The prominence of the peak is enhanced when the Fermi energy is large compared to the electron-phonon coupling. Since the phonon damping corresponds to the phonon linewidth, these predictions may be further tested and investigated experimentally. \textcolor{black}{The same results (anharmonic enhancement of $T_c$ and non-monotonicity with damping) and the same resonance mechanism (this time due to Klemens damping~\cite{Klemens}) apply in the case of pairing mediated by optical phonons, as shown in the Appendix A.3 below.} Hence, the presented framework may lead to new guidelines for material design to optimize $T_c$ in conventional superconductors, including high-T hydrides. \\
\textit{Acknowledgements -- } Useful discussions with Boris Shapiro are gratefully acknowledged.
M.B. acknowledges the support of the Spanish MINECO's ``Centro de Excelencia Severo Ochoa'' Programme under grant SEV-2012-0249. CS is supported by the U.S. DOE grant number DE-FG02-05ER46236.
\begin{appendix}
\section{Details of the derivations}
\subsection{Theoretical framework}
To obtain Eq.~\ref{Integral-GapEqn} from the gap equation (Eq.~\ref{Sum-GapEqn}; see Fig.~\ref{Feynman} for the associated self-energy diagram) we make the assumption of an isotropic gap function independent of frequency, i.e., $\Delta(i\omega_m, \textbf{k}+ \textbf{q}) \equiv \Delta$. This allows us to cancel the order parameter in the numerator on both sides of Eq.~\ref{Sum-GapEqn} and eliminate the $\omega_n$ dependence to yield
\begin{eqnarray} \nonumber
1 &=& \frac{g^2}{\beta V} \sum_{\textbf{q}, \omega_m} \frac{1}{\left( (v^{2} - D \omega_m) q^2 + \omega_m^2\right) (\omega_m^2 + \xi_{\textbf{q}}^2+ \Delta^2)}.\\
&&
\end{eqnarray}
We can now convert the $\textbf{q}$ momentum sum into an integral by replacing $\frac{1}{V}\sum_{\textbf{q}} \rightarrow \frac{1}{(2 \pi)^d}\int d^d\textbf{q} \rightarrow \int N(\xi)d\xi$, where $N(\xi)$ is the density of states at energy $\xi$. For quadratic bands with chemical potential $\mu$, we have $\xi_{\textbf{q}} = q^2 - \mu$ written in units stated in the main text. We now further assume a featureless density of states and approximate $N(\xi) \simeq N(0)$ as in a BCS superconductor. This is exact in two dimensions and works well when the chemical potential is far away from the band bottom in three dimensions. Defining $\lambda = g^2 N(0)$, we finally obtain Eq.~\ref{Integral-GapEqn}. \par
To obtain Eq.~\ref{NoCP} from Eq.~\ref{MatsubaraSum-NoCP}, we can simplify the Matsubara sum by summing over only positive frequencies and writing the equation for $T_c$ as
\begin{eqnarray} \nonumber
1 &=& \frac{\lambda}{2(2\pi T_c)^2} \sum_{m=0}^{\infty}\Bigg[ \frac{1}{x \left(x^2 + (v^{2'} + D x)^2\right)} \\
&&+ \frac{1}{x \left(x^2 + (v^{2'} - D x)^2\right)} \Bigg]
\end{eqnarray}
where $x\equiv m+\frac{1}{2}$ and the primed quantities are dimensionless variables normalized by $2\pi T_c$ (i.e, $v^{2'} = v^2/2\pi T_c$). One can then use partial fractions to simplify the denominators and use the identity $\psi(z) = \lim_{k \rightarrow \infty} \left\{- \sum_{n=0}^{k-1} \frac{1}{n+z} + \ln k\right\}$. The logarithmic terms cancel to yield Eq.~\ref{NoCP}. Similarly, one can obtain Eq.~\ref{WithMu} from Eq.~\ref{MatsubaraSum-WithMu} by shifting the summation over positive frequencies and writing the equation for $T_c$ as
\begin{widetext}
\begin{eqnarray}
1 &=& \frac{\lambda \pi T_c}{(2\pi T_c)^3} \sum_{m=0}^{\infty}\Bigg[ \frac{\left(x^2 + (v^{2'} - D x)\mu'\right)x^{-1}}{\left[\left(x^2 + (v^{2'} - D x)\mu'\right)^2 + x^2 (v^{2'} - D x)^2\right]} + \frac{\left(x^2 + (v^{2'} + D x)\mu'\right)x^{-1}}{\left[\left(x^2 + (v^{2'} + D x)\mu'\right)^2 + x^2 (v^{2'} + D x)^2\right]} \Bigg]. \label{full}
\end{eqnarray}
\end{widetext}
We again expand the summand above in partial fractions by factoring the denominators. Performing the remaining integer summations using the identity for $\psi(x)$ defined above, we obtain Eq.~\ref{WithMu}.
\begin{figure}
\centering
\begin{tikzpicture}
\node[] at (3.8,2.4) {$\Pi(\textbf{q}, i\omega_n - i\omega_m)$};
\node[] at (3.8,0.4) {$ g(\textbf{k}+\textbf{q}, i\omega_m)$};
\draw [line width=0.5mm] []
(2,0) -- (6,0);
\draw [decorate,decoration={zigzag,amplitude=.8mm,segment length=2mm}](2,0) arc (180:0:2);
\end{tikzpicture}
\caption{Feynman diagram for the anomalous self-energy. In the weak coupling BCS limit, the anomalous self-energy reduces to the gap function. The solid (zig-zag) line is the electron (boson) Green function in the superconducting state.} \label{Feynman}
\end{figure}\\[1cm]
\subsection{The resonance condition}
In this paragraph, we provide more details about the resonance condition discussed in the main text. The idea is that at a specific frequency, sometimes referred to as the \textit{Ioffe-Regel frequency} \cite{Parshin1}, the boson mediator for the phonons undergoes a crossover from a ballistic propagation to a diffusive incoherent motion. More precisely, this happens at:
\begin{equation}
\omega_{IR}\,\sim\,\frac{v^2}{\pi\,D}
\end{equation}
This value is of fundamental importance in the realm of amorphous systems, because of its correlation with the boson peak frequency, where the vibrational density of states (VDOS), normalized by the Debye law $\sim \omega^2$, displays a maximum value \cite{Schirmacher,baggioli2019unified,Milkus}. The same boson peak phenomenology, however, is also at play in strongly anharmonic crystals ~\cite{Jezowski,baggioliPRL}.
Physically, this means that the density of the boson mediators is maximal around the boson peak frequency. As a consequence, one would expect the effects of the mediators to be enhanced at such energy scale. By estimating that:
\begin{equation}
\omega_{IR}\,\sim\,T_c
\end{equation}
we arrive at the following phenomenological resonance condition:
\begin{equation}
T_c\,\sim\,\frac{v^2}{\pi\,D_{max}}\label{res}
\end{equation}
which is quoted in the main text. Here $D_{max}$ is the value of the phonon viscosity at which $T_c$ is maximized.\\
In order to validate this expression, we plot the ratio $\pi D T_c/v^2$ in figure \ref{figlast} for the same curves shown in the main text in fig.\ref{TcVsD}. We observe, that, especially for large values of the sound speed (compared to the phonon viscosity $D$), the resonance condition \eqref{res} holds to good accuracy. This observation provides a useful correlation between the energy scale of the boson peak (induced by anharmonicity) and the maximum critical temperature that can be reached.
\begin{figure}
\centering
\includegraphics[width=0.7\linewidth]{new2.pdf}
\caption{A validation of the resonance condition \eqref{res} using the data of fig.\ref{TcVsD}.}
\label{figlast}
\end{figure}
\par
\subsection{Pairing mediated by anharmonic optical phonons}
In the main text we focused our attention on the case of pairing mediated by acoustic phonons, where the anharmonic damping is diffusive, $\Gamma \sim q^{2}$, according to the Akhiezer mechanism.
In this section, we consider the case of pairing mediated by optical phonons. In the case of optical phonons, the anharmonic damping is mainly related to the decay process of the optical phonon into two acoustic phonons.
The damping coefficient $\Gamma$ is independent of $q$, in this case, and was famously calculated by Klemens using perturbation theory~\cite{Klemens}.
As shown by Klemens, the damping parameter $\Gamma$ for optical phonons is proportional to the square of the Gr{\"u}neisen constant $\gamma$ of the material.
Hence, also in this case the $T_c$-enhancement could be tuned via the interatomic potential of the parameter through $\gamma$, in a material-by-design perspective.
Hence, we take a typical dispersion relation for optical phonons,
\begin{equation}
\Omega_{opt}(q)=\omega_0 +\,\alpha\, q^{2}
\end{equation}
with Klemens damping given a constant $\Gamma$.
We implement this model of optical phonons into the Green's function Eq. (2) of the main article, this time with damping $\Gamma = const$ independent of $q$~\cite{Klemens}, leading to the following form of the Bosonic propagator:
\begin{equation}
\Pi(i \Omega_n,\textbf{q}) = \frac{1}{\left[\omega_{0}^2 +2 \,\omega_0\,\alpha \,q^{2}+\mathcal{O}(q^4)\,\right] +\Omega_n^2-\Gamma\,\Omega_n}.
\end{equation}
Upon implementing this propagator in the theoretical framework above, we obtain the theoretical predictions for $T_c$ as a function of anharmonic damping constant $\Gamma$ for pairing mediated by optical phonons, reported in Fig.\ref{figopt} above.
\begin{figure}
\centering
\includegraphics[width=0.7\linewidth]{opt1.pdf}
\vspace{0.2cm}
\includegraphics[width=0.7\linewidth]{opt2.pdf}
\caption{The dimensionless critical temperature $\tilde{T}_c\equiv 2\pi T_c/\sqrt{\lambda}$ in function of the constant damping $\Gamma$. \textbf{Top: } Increasing the mass gap of the optical mode $\omega_0^2$ from orange to purple. \textbf{Bottom:} Increasing the curvature of the optical dispersion relation $\alpha$ from yellow to black.}
\label{figopt}
\end{figure}
These predictions align well with the effect of $T_c$-enhancement due to anharmonic damping at low damping, followed by a peak and subsequent decrease of $T_c$, that was shown in the main article for acoustic phonons.
Also, in this case, clearly, the anharmonic damping can lead to a substantial increase of $T_c$, by at least a factor three.
Furthermore, theory predicts that the damping-induced enhancement, and the peak, become larger upon increasing the optical phonon energy gap $\omega_0$, as shown in the top panel of Fig.\ref{figopt}.
Finally, also the curvature coefficient $\alpha$ in the optical dispersion relation has an effect on the enhancement and on the peak, they both become larger as $\alpha$ becomes smaller, hence upon approaching flat-looking optical dispersion relations, which are typically seen in DFT calculations of optical phonons in hydride materials~\cite{Pickard2015}.
\end{appendix}
\bibliographystyle{apsrev4-1}
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"redpajama_set_name": "RedPajamaWikipedia"
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{"url":"https:\/\/www.aimsciences.org\/article\/doi\/10.3934\/dcdsb.2006.6.1097","text":"Article Contents\nArticle Contents\n\n# A qualitative study of the damped duffing equation and applications\n\n\u2022 In this paper, we analyze the damped Duffing equation by means of qualitative theory of planar systems. Under certain parametric choices, the global structure in the Poincar\u00e9 phase plane of an equivalent two-dimensional autonomous system is plotted. Exact solutions are obtained by using the Lie symmetry and the coordinate transformation method, respectively. Applications of the second approach to some nonlinear evolution equations such as the two-dimensional dissipative Klein-Gordon equation are illustrated.\nMathematics Subject Classification: Primary: 34C05, 34C14, 34C20; Secondary: 35B40.\n\n Citation:","date":"2023-03-27 19:23:19","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 0, \"mathjax_display_tex\": 0, \"mathjax_asciimath\": 0, \"img_math\": 0, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 1, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.3766891062259674, \"perplexity\": 667.1643939377143}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2023-14\/segments\/1679296948684.19\/warc\/CC-MAIN-20230327185741-20230327215741-00566.warc.gz\"}"} | null | null |
»AAMI Drive In Gallery« is a 5-year project in cooperation with institute partner company GH Park. It offers an exhibition space in a parking garage in the centre of Maribor, Slovenia's second biggest city. "Drive In Gallery" is a new and unique concept of exhibiting, manifested only by Institute AAMI on Slovenian ground, where artists display and promote their work for 5 years in this 30.000 m2 parking garage with an average daily visit of over 5.000 costumers, which presents an excellent opportunity also for artwork sale. The artists provide their artworks printed on comatex material, so it is appropriate for this semi-outdoor exhibition. Being a part of this project is surely a great promotion for the artists and for the visitors and tourists as well, because we somehow integrate art in people`s everyday lives. | {
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} | 592 |
Finely powder all drugs dissolve sugar in milk to make syrup. To this syrup, add powdered drugs in small quantities and mix well. When completed and cool, add ghee and mix to homogenity.
Improve memory power, blood purification, nervous weakness and epilepsy. | {
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Biografia
Di famiglia nobile appartenente alla ricca borghesia cutrese, scelse tuttavia la carriera ecclesiastica arrivando ad essere ordinato presbitero e a ricevere la nomina a vicario generale della diocesi di Sutri.
Il 25 giugno 1706 venne nominato vescovo di Strongoli da papa Clemente XI; ricevette l'ordinazione episcopale a Roma il successivo 27 giugno. Il fratello minore, Camillo, sarà anch'egli futuro prelato.
Come vescovo resse la diocesi calabrese per 12 anni; ivi rimase fino alla morte, avvenuta nel febbraio 1719.
Note
Voci correlate
Diocesi di Strongoli
Collegamenti esterni
Vescovi di Strongoli | {
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} | 1,886 |
The course will provide students with a foundation in the principles of group dynamics, with an emphasis on small-group dynamics. Key aspects and principles of group functioning will be addressed including group formation, conflict, structure, influence, and power. Applications of these principles to the functioning of small groups in psychology will also be addressed. | {
"redpajama_set_name": "RedPajamaC4"
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\section{Introduction}
\label{Introduction}
$~~\,~$ Different aspects of higher spin field theory
in various dimensions attract
considerable attention currently.
${}$First of all, higher spin fields and their
possible interactions bring about numerous
challenges for theoreticians.
More importantly, massive higher spin states
are known to be present in the spectra of the
string and superstring theories.
It is therefore quite natural to expect that,
in a field theory limit, the superstring theory
should reduce to a consistent
interacting supersymmetric theory of
higher spin fields.
In four space-time dimensions,
Lagrangian formulations for massive fields
of arbitrary spin were constructed thirty years
ago \cite{SH}. A few years later, the massive
construction of \cite{SH} was used to derive
Lagrangian formulations for gauge massless fields
of arbitrary spin \cite{Fronsdal}.
Since then, there have been published hundreds
of papers in which the results of \cite{SH,Fronsdal}
were generalized, (BRST) reformulated, extended,
quantized, and so forth.
Here it is hardly possible to comment
upon these heroic follow-up activities.
We point out only several reviews \cite{REW} and
some recent papers \cite{DEV}.
One of the interesting directions in higher
spin field theory is the construction of
manifestly supersymmetric extensions
of the models given in \cite{SH,Fronsdal}.
In the massless case, the problem has actually
been solved in \cite{KSP,KS} (see \cite{BK}
for a review and \cite{KSG} for generalizations).
${}$For each superspin $Y>3/2$, these
publications provide two dually equivalent off-shell
realizations in 4D, ${\cal N }= 1$ superspace.
At the component level, each of the
two superspin-$Y$ actions
\cite{KSP,KS} reduces to a sum of the spin-$Y$
and spin-$(Y+1/2)$ actions \cite{Fronsdal}
upon imposing a Wess-Zumino-type
gauge and eliminating the auxiliary fields.
On the mass shell, the only independent
gauge-invariant field strengths in these models
are exactly the higher spin on-shell field strengths
first identified in ``Superspace'' \cite{GGRS}.
As concerns the massive case, off-shell higher spin
supermultiplets have never been constructed
in complete generality.
In 4D, ${\cal N}=1$ Poincar\'e
supersymmetry,
a massive multiplet of superspin $Y$
describes four propagating fields
with the same mass but different
spins $s$ $=$ $(Y-1/2, Y, Y, Y+1/2)$,
see, e.g., \cite{BK,GGRS} for reviews.
${}$The first attempts\footnote{Some preliminary results
were also obtained in \cite{BL}.}
to attack the problem of constructing
free off-shell massive higher spin supermultiplets
were undertaken in recent works
\cite{BGLP1,BGLP2,GSS} that
were concerned with deriving off-shell
realizations for the massive
{\it gravitino multiplet} ($Y$ = 1)
and the massive {\it graviton multiplet}
($Y$ = 3/2). This led to two $Y$ = 3/2 formulations
constructed in \cite{BGLP1}
and one $Y$ = 1 formulation
derived in \cite{BGLP2}.
The results of \cite{BGLP1} were soon
generalized \cite{GSS} to produce
a third $Y$ = 3/2 formulation.
In the present letter, we continue the research
started in \cite{BGLP1,BGLP2}
and derive two
new off-shell realizations for the massive gravitino
multiplet, and three new off-shell realizations
for the massive graviton multiplet.
Altogether, there now occur
four massive $Y$ = 1 models
(in conjunction with the massive
$Y$ = 1 model constructed by
Ogievetsky and Sokatchev years ago \cite{OS2})
and six massive $Y$ = 3/2 models.
We further demonstrate that these realizations
are related to each other by duality transformations
similar to those which relate massive
tensor and vector multiplets, see \cite{K}
and references therein.
It is interesting to compare the massive
and massless results in the case of the $Y$ = 3/2
multiplet. In the massless case, there are three
building blocks to construct {\it {minimal}} \footnote{To
our knowledge, no investigations have occured for
the possible existence of
\newline $~~~~~~$ a massive
{\it {non-minimal}}
$Y$ = 3/2 theory.} linearized
supergravity \cite{GKP}. They correspond to
(i) old minimal supergravity
(see \cite{BK,GGRS} for reviews);
(ii) new minimal supergravity
(see \cite{BK,GGRS} for reviews);
(iii) the novel formulation derived in \cite{BGLP1}.
These off-shell $(3/2,2)$ supermultiplets,
which comprise all the supergravity
multiplets with $12+12$ degrees of freedom,
will be called type I, type II and type III
supergravity multiplets\footnote{In the case
of type III supergravity, a nonlinear formulation
is still unknown.}
in what follows,
in order to avoid the use of unwieldy
terms like ``new new minimal''
or ``very new'' supergravity.
As is demonstrated below, each of the
massless type I---III
formulations admits a massive
extension, and the latter turns out to possess
a nontrivial dual. As a result, we have now
demonstrated that there occur {\it {at}} {\it {least}}
six off-shell distinct massive $Y$ = 3/2
minimal realizations.
This paper is organized as follows.
In section 2 we derive two new
(dually equivalent) formulations
for the massive gravitino multiplet.
They turn out to be massive extensions
of the two standard off-shell formulations
for the massless spin $(1,3/2)$ supermultiplet
discovered respectively in \cite{FV,deWvH,GS}
and \cite{OS}. In section 3 we derive three new
formulations for the massive graviton multiplet.
Duality transformations are also worked out
that relate all the massive $Y$ = 3/2 models.
A brief summary of the results obtained is given
in section 4. The paper is concluded by a technical
appendix. Our superspace conventions mostly follow
\cite{BK} except the following two from
\cite{GGRS}: (i) the symmetrization of $n$ indices
does not involve a factor of $(1/n!) $;
(ii) given a four-vector
$v_a$, we define $v_{\un a} \equiv v_{\alpha {\dot{\alpha}}}
=(\sigma^a)_{\alpha {\dot{\alpha}} } v_a$.
\section{Massive Gravitino Multiplets}
\label{Massive Gravitino Multiplets}
$~~\,~$ We start by recalling the off-shell formulation
for massless (matter) gravitino multiplet
introduced first in \cite{FV,deWvH}
at the component level and then formulated
in \cite{GS} in terms of superfields
(see also \cite{GG}).
The action derived in \cite{GS} is
\begin{eqnarray}
S_{(1,\frac 32)}[\Psi , V]
&=& \hat{S}[\Psi ]
+ \int d^8z\,\Big\{ \Psi^\alpha W_\alpha + {\Bar \Psi}_{\dot{\alpha}}
{\Bar W}^{\dot{\alpha}} \Big\}
- {1\over 4} \int d^6z \,W^\alpha W_\alpha~,
\label{tino}\\
&& \qquad \qquad
W_\alpha = -{1 \over 4} \Bar D^2D^\alpha V~,
\nonumber
\end{eqnarray}
where
\begin{eqnarray}
\hat{S}[\Psi ]
&=& \int d^8z\, \Big\{
D^\alpha\Bar \Psi^{\dot\alpha}\Bar D_{\dot\alpha}\Psi_\alpha
-\frac 14\Bar D^{\dot\alpha}\Psi^\alpha\Bar D_{\dot\alpha}\Psi_\alpha
-\frac 14 D_\alpha \Bar \Psi_{\dot\alpha} D^\alpha \Bar \Psi^{\dot\alpha}
\Big\}~.
\label{S-hat}
\end{eqnarray}
This massless $Y$ = 1 model
is actually of some interest in the context of
higher spin field theory. As mentioned in
the introduction, there exist two dually
equivalent gauge superfield formulations
(called longitudinal and transverse) \cite{KS}
for each massless {\it integer} $Y$
$\geq 1$, see \cite{BK} for a review.
The longitudinal series\footnote{The
transverse series terminates at a non-minimal
gauge formulation for the massless \newline
$~~~~~~$ gravitino multiplet
realized in terms of an unconstrained real scalar
$V$ and Majorana \newline
$~~~~~~$ $\gamma$-traceless
spin-vector ${\bf \Psi}_a=
(\Psi_{a \beta}, \Bar \Psi_{a}{}^{\dot{\beta}})$,
with $\gamma^a {\bf \Psi}_a=0$.}
terminates, at $Y =1$, exactly at the action (\ref{tino}).
To describe a massive gravitino multiplet,
we introduce an action
$S=S_{(1,\frac 32)}[\Psi , V] + S_m[\Psi ,V]$,
where $S_m[\Psi ,V]$ stands for
the mass term
\begin{eqnarray}
S_m[\Psi,V]=m \int d^8z\,\Big\{
\Psi^2
+\Bar \Psi^2
+\alpha m V^2
+ V\Big(\beta D^\alpha \Psi_\alpha
+\beta^* \Bar D_{\dot\alpha} \Bar \Psi^{\dot\alpha}\Big)
\Big\}~,
\label{S-m}
\end{eqnarray}
where $\alpha$ and $\beta$ are respectively real and complex
parameters. These parameters should be fixed by the
requirement that the equations of motion be equivalent
to the constraints
\begin{equation}
i \pa_{\un a} \Bar \Psi^{\dot{\alpha}} + m \Psi_\alpha = 0~, \qquad
D^\alpha \Psi_{\alpha}=0~, \qquad
\Bar D^2 \Psi_{\alpha}=0~~,~~
\label{mass-shell}
\end{equation}
required to describe an irreducible on-shell multiplet
with $Y$ = $1$, see \cite{BK,BGLP2}.
In the space of spinor superfields
obeying the Klein-Gordon equation,
$(\Box -m^2) \Psi_\alpha =0$,
the second and third constraints
in (\ref{mass-shell}) are known to select
the $Y$ = 1 subspace \cite{BK}
(see also \cite{Sok}).
Without imposing
additional constraints
(such as the first one in \ref{mass-shell}),
the superfields $\Psi_\alpha $ and $\Bar \Psi_{\dot{\alpha}}$
describe two massive $Y$ = 1
representations. Generally, an irreducible representation
emerges if these superfields are also subject to
a reality condition of the form
\begin{equation}
\pa_{\un a} \Bar \Psi^{\dot{\alpha}} + m \,e^{i \varphi}\,
\Psi_\alpha = 0~, \qquad |e^{i \varphi} | =1~,
\end{equation}
where $\varphi$ a constant real parameter.
As is obvious, the latter constraint implies
the Klein-Gordon equation. Applying a
phase transformation to $\Psi_\alpha$, allows
us to make the choice $e^{i \varphi} =-i$
corresponding to the Dirac equation.
The equations of motion
corresponding to
$S=S_{(1,\frac 32)}[\Psi , V] + S_m[\Psi ,V]$
are:
\begin{eqnarray}
-\Bar D_{\dot\alpha}D_\alpha\Bar \Psi^{\dot\alpha}
+\frac 12\Bar D^2 \Psi_\alpha
+2m\Psi_\alpha
+W_\alpha
-\beta m D_\alpha V&=&0~,
\label{y1newVeom} \\
\frac 12 D^\alpha W_\alpha
+\Big( \frac 14D^\alpha\Bar D^2 \Psi_\alpha
+\beta mD^\alpha \Psi_\alpha
+c.c.\Big)
+2\alpha m^2V &=&0~.
\label{y1newHeom}
\end{eqnarray}
Multiplying (\ref{y1newVeom}) and
(\ref{y1newHeom}) by $\Bar D^2$ yields:
\begin{eqnarray}
\Bar D^2\Psi_\alpha=
-2\beta W_\alpha~, \qquad
\Bar D^2D^\alpha \Psi_\alpha =-2{ \alpha \over \beta }\, m\Bar D^2V~.
\end{eqnarray}
Next, substituting these relations into the contraction of $D^\alpha$
on (\ref{y1newVeom}) leads to:
\begin{eqnarray}
mD^\alpha \Psi_\alpha = \frac 12 (\beta+\beta^*-1)D^\alpha W_\alpha
+\frac \b2\Big(1+{\alpha\over |\beta|^2}\Big)mD^2V~.
\end{eqnarray}
Substitute these three results into (\ref{y1newHeom})
gives
\begin{eqnarray}
\frac 12 (1-\beta-\beta^*)^2D^\alpha W_\alpha
+\frac 12m\Big(1+{\alpha\over |\beta|^2}\Big)[\beta^2D^2
+(\beta^*)^2\Bar D^2]V
+2\alpha m^2 V =0~.
\end{eqnarray}
This equation implies that
$V$ is auxiliary, $V=0$, if
\begin{equation}
\beta+\beta^*=1~, \qquad
\alpha=-|\beta|^2~.
\label{conditions}
\end{equation}
Then, the mass-shell conditions
(\ref{mass-shell})
also follow.\footnote{One can consider
more general action in which the term
$m ( \Psi^2 + \Bar \Psi^2) $
in (\ref{S-m})
is replaced \newline
$~~~~\,~$ by
$ ( \mu \, \Psi^2
+\mu^*\,\Bar \Psi^2) $,
with $\mu$ a complex mass parameter,
$|\mu|=m$. Then, the first equation in \newline
$~~~~\,~$
(\ref{conditions}) turns into
$\beta/\mu + (\beta/\mu)^* = 1/m$.}
The final action takes the form:
\begin{eqnarray}
S[ \Psi,V] &=&
\hat{S}[\Psi ]
+ \int d^8z\,\Big\{ \Psi \, W
+ {\Bar \Psi} \, {\Bar W} \Big\}
- {1\over 4} \int d^6z \,W^2
\label{ss1final}
\\
&~& ~~+~m \int d^8z\,\Big\{
\Psi^2
+\Bar \Psi^2
-|\beta|^2 m V^2
+ V\Big(\beta D \, \Psi
+\beta^* \Bar D \, \Bar \Psi \Big)
\Big\}~,
\nonumber
\end{eqnarray}
where $\beta+\beta^*=1$.
A superfield redefinition
of the form
$\Psi_\alpha\rightarrow \Psi_\alpha+ \delta \, \Bar D^2\Psi_\alpha$
can be used to change some coefficients
in the action.
The Lagrangian constructed turns out
to possess a dual formulation. For simplicity,
we choose $\beta =1/2$ in (\ref{ss1final}).
Let us consider, following \cite{K},
the ``first-order'' action
\begin{eqnarray}
S_{Aux} &=& \hat{S}[\Psi ]
+ \int d^8z\,\Big\{ m(\Psi^2 + {\Bar \Psi}^2)
+\Psi \, W + {\Bar \Psi}\, {\Bar W}
-{m^2\over 4} V^2
+ {m\over 2} V( D\, \Psi
+ \Bar D\, \Bar \Psi ) \Big\}
\nonumber \\
&~& ~+~
{ 1 \over 2} \left\{
m \int d^6z \, \eta^\alpha \Big(W_\alpha
+ {1 \over 4} \Bar D^2D^\alpha V\Big)
- {1 \over 4} \int d^6z \,W^2 ~+~ c.c. \right\}~.
\label{aux1}
\end{eqnarray}
Here $W_\alpha$ and $\eta_\alpha$ are unconstrained chiral
spinor superfield, and there is no relationship
between $V$ and $W_\alpha$.
Varying $S_{Aux} $ with respect to $\eta_\alpha$
brings us back to (\ref{ss1final}).
On the other hand, if we vary
$S_{Aux} $ with respect to $V$
and $W_\alpha$ and eliminate these superfields,
we then arrive at the following action:
\begin{eqnarray}
\tilde{S} = \hat{S}[\Psi ]
&+& \int d^8z\,\Big\{ m(\Psi^2 + {\Bar \Psi}^2)
+{1\over 4} \Big( D(\Psi+\eta) +
{\Bar D} ({\Bar \Psi} + \Bar \eta ) \Big)^2
\Big\} \nonumber \\
&+& {1\over 8}
\left\{ \int d^6z \, \Big( 2m \eta
- \Bar D^2 \Psi \Big)^2
~+~ c.c. \right\}~.
\label{14}
\end{eqnarray}
Implementing here the shift
\begin{equation}
\Psi_\alpha ~\to~ \Psi_\alpha - \eta_\alpha~~,~~
\end{equation}
brings the action to the form
\begin{eqnarray}
\tilde{S} = \hat{S}[\Psi ]
&+&{1\over 4} \int d^8z\,
\Big( D\,\Psi +
{\Bar D} \,{\Bar \Psi} \Big)^2
- {1\over 2} \int d^8z\,\Big\{ \Psi^\alpha \Bar D^2 \Psi_\alpha
+ \Bar \Psi_{\dot{\alpha}} D^2 \Bar \Psi^{\dot{\alpha}} \Big\}
\nonumber \\
&+& m \int d^8z\,\Big\{\Psi^2 + {\Bar \Psi}^2\Big\}
+ {m^2\over 2}
\left\{ \int d^6z \, \eta^2
~+~ c.c. \right\}~.
\end{eqnarray}
As is seen, the chiral spinor superfield $\eta_\alpha$
has completely decoupled! Therefore,
the dynamical system obtained is equivalent
to the following theory
\begin{eqnarray}
S[\Psi] = \hat{S}[\Psi ]
&+&{1\over 4} \int d^8z\,
\Big( D\,\Psi +
{\Bar D} \,{\Bar \Psi} \Big)^2
-{1\over 2} \int d^8z\,\Big\{ \Psi^\alpha \Bar D^2 \Psi_\alpha
+ \Bar \Psi_{\dot{\alpha}} D^2 \Bar \Psi^{\dot{\alpha}} \Big\}
\nonumber \\
&+& m \int d^8z\,\Big\{\Psi^2 + {\Bar \Psi}^2\Big\}~~,~~
\label{mgravitino2}
\end{eqnarray}
formulated solely in terms of
the unconstrained spinor $\Psi_\alpha$
and it conjugate.
Applying the phase transformation
$\Psi_a \to i\, \Psi_\alpha$, it is seen
that the action obtained is actually equivalent to
\begin{eqnarray}
S[\Psi] = \hat{S}[\Psi ]
&-&{1\over 4} \int d^8z\,
\Big( D\,\Psi -
{\Bar D} \,{\Bar \Psi} \Big)^2
+ m \int d^8z\,\Big\{\Psi^2 + {\Bar \Psi}^2\Big\}~.
\label{mgravitino3}
\end{eqnarray}
It is interesting to compare (\ref{mgravitino3})
with the action for massive $Y$ = 1 multiplet
obtained by Ogievetsky and Sokatchev \cite{OS2}.
Their model is also formulated solely
in terms of a spinor superfield. The
corresponding action\footnote{Setting
$m=0$ in (\ref{OS-action-2})
gives the model for massless gravitino
multiplet discovered in \cite{OS}.}
is
\begin{eqnarray}
S_{OS} [\Psi]
= \hat{S}[\Psi ]
+ {1\over 4} \int d^8z\,
\Big( D\Psi + {\Bar D} {\Bar \Psi}
\Big)^2
+ i \, m \int d^8z\,
\Big( \Psi^2 - {\Bar \Psi}^2
\Big)~,
\label{OS-action-2}
\end{eqnarray}
see Appendix A for its derivation.\footnote{It
was argued in \cite{BGLP2}
that there are no Lagrangian formulations
for massive superspin-1 \newline
$~~~\,~~$ multiplet
solely in terms of an unconstrained
spinor superfield and its conjugate.
The \newline
$~~~\,~~$ ``proof'' given in \cite{BGLP2}
is incorrect, as shown by the two
counter-examples (\ref{mgravitino3}) and
(\ref{OS-action-2}).}
The actions (\ref{mgravitino3}) and
(\ref{OS-action-2}) look similar,
although it does not seem possible
to transform one to the other off
the mass shell.
In fact, the model (\ref{14}),
which is equivalent to (\ref{mgravitino3}),
can be treated as a massive extension
of the Ogievetsky-Sokatchev model for
massless gravitino multiplet \cite{OS}.
Indeed, implementing in (\ref{14}) the shift
\begin{equation}
\Psi_\alpha ~\to \Psi_\alpha + {i \over 2m} \Bar D^2 \Psi_\alpha
~, \qquad
\eta_\alpha ~\to \eta_\alpha - {i \over 2m}
\Bar D^2 \Psi_\alpha~,
\end{equation}
which leaves $\hat{S}[\Psi ] $ invariant,
we end up with
\begin{eqnarray}
S[\Psi, \eta ] =
S_{(1,\frac 32)}[\Psi , G]
&+& m \int d^8z\,\Big\{ \Psi^2 + {\Bar \Psi}^2
+2(1 + i) \Psi \eta + 2(1 - i)\Bar \Psi \Bar \eta \Big\}
\nonumber \\
&+& {m^2 \over 2} \left\{ \int d^6z \, \eta^2
~+~ c.c. \right\}~,
\end{eqnarray}
where
\begin{eqnarray}
S_{(1,\frac 32)}[\Psi , G]
= \hat{S}[\Psi ]
&+& \int d^8z\,
\Big( G +
{1\over 2} ( D\, \Psi + {\Bar D}\, {\Bar \Psi} )
\Big)^2 ~, \\
G &=&{1\over 2} ( D^\alpha \eta _\alpha
+ \Bar D_{\dot{\alpha}} \Bar \eta^{\dot{\alpha}} )~.
\nonumber
\end{eqnarray}
Here $G$ is the linear superfield,
$D^2 G= \Bar D^2 G =0$, associated with
the chiral spinor $\eta_\alpha$ and its conjugate.
The action $S_{(1,\frac 32)}[\Psi , G] $ corresponds
to the Ogievetsky-Sokatchev formulation for
massless gravitino multiplet \cite{OS} as presented
in \cite{BK}.
Before concluding this section,
it is worth recalling one more possibility
to describe
the massless gravitino multiplet \cite{BK,GS}
\begin{eqnarray}
S_{(1,\frac 32)}[\Psi , \Phi]
&=& \hat{S}[\Psi ]
-{1\over 2} \int d^8z\,\Big\{
\Bar \Phi \Phi +
( \Phi +\Bar \Phi) ( D\, \Psi +
\Bar D \, \Bar \Psi )
\Big\}~,
\label{g-fixed}
\end{eqnarray}
with $\Phi$ a chiral scalar, $\Bar D _{\dot{\alpha}} \Phi =0 $.
The actions (\ref{tino}) and (\ref{g-fixed})
can be shown to correspond
to different partial gauge
fixings in the mother theory
\begin{eqnarray}
S_{(1,\frac 32)}[\Psi , V, \Phi]
= \hat{S}[\Psi ]
&+& \int d^8z\,\Big\{ \Psi \, W
+ {\Bar \Psi} \, {\Bar W} \Big\}
- {1\over 4} \int d^6z \,W^2
\nonumber \\
&-&{1\over 2} \int d^8z\,\Big\{
\Bar \Phi \Phi + (\Phi +\Bar \Phi)
( D \, \Psi + \Bar D \, \Bar \Psi )
\Big\}~~,~~
\end{eqnarray}
possessing a huge gauge freedom,
see \cite{BK,GS} for more
details. The massive extension of (\ref{g-fixed})
was derived in \cite{BGLP2} and
the corresponding action is
\begin{eqnarray}
S[\Psi , \Phi] = S_{(1,\frac 32)}[\Psi , \Phi]
+m\int d^8z\,(\Psi^2 + {\Bar \Psi}^2)
-{m\over 4} \Big\{ \int d^6z \, \Phi^2
+ c.c. \Big\}~.
\end{eqnarray}
Unlike its massless limit,
this theory does not seem to admit
a nice dual formulation.
\section{Massive Graviton Multiplets}
\label{Massive Graviton Multiplets}
$~~\,~$ The massive $Y$ = 3/2 multiplet
(or massive graviton multiplet)
can be realized in terms of a real (axial) vector
superfield $H_a$ obeying the equations
\cite{BK,BGLP1,Sok}
\begin{eqnarray}
\label{32irrepsp}
(\Box-m^2)H_a=0~, \quad
D^\alpha H_{\un a}=0~, \quad
\Bar D^{\dot\alpha} H_{\un a}=0 \quad
\longrightarrow \quad \pa^{\un a}H_{\un a}=0~.
\end{eqnarray}
We are interested in classifying those supersymmetric
theories which generate these equations
as the equations of motion.
In what follows, we will use
a set of superprojectors \cite{SG}
for the real vector superfield $H_{\un a}$:
\begin{eqnarray}
(\Pi^T_{1})H_{\un a}&:=&\frac 1{32}
\Box^{-2}\pa_{\dot\alpha}{}^\beta
\{\Bar D^2,D^2\}\pa_{(\alpha}{}^{\dot\beta}H_{\beta)\dot\beta}~, \\
(\Pi^T_{1/2})H_{\un a}&:=&
\frac 1{8\cdot3!}\Box^{-2}\pa_{\dot\alpha}{}^\beta
D_{(\alpha}\Bar D^2D^\gamma
(\pa_{\beta)}{}^{\dot\beta}H_{\gamma\dot\beta}
+\pa_{|\gamma|}{}^{\dot\beta}H_{\beta)\dot\beta})~, \\
\label{trans}
(\Pi^T_{3/2})H_{\un a}&:=&
-\frac 1{8\cdot3!}\Box^{-2}\pa_{\dot\alpha}{}^\beta
D^\gamma\Bar D^2D_{(\gamma}
\pa_{\alpha}{}^{\dot\beta}H_{\beta)\dot\beta}~, \\
(\Pi^L_{0})H_{\un a}&:=&
-\frac 1{32}\pa_{\un a}
\Box^{-2}\{\Bar D^2,D^2\}
\pa^{\un c}H_{\un c}~, \\
\label{long}
(\Pi^L_{1/2})H_{\un a}&:=&
\frac 1{16}\pa_{\un a}\Box^{-2}D^\beta\Bar D^2
D_\beta\pa^{\un c}H_{\un c}~.
\end{eqnarray}
In terms of the superprojectors introduced,
we have \cite{GKP}
\begin{eqnarray}
D^\gamma {\Bar D}^2 D_\gamma H_{\un a} &=&
-8\Box ( \Pi^L_{1/2} + \Pi^T_{1/2} +\Pi^T_{3/2})
H_{\un a} ~, \\
\pa_{\un a}\, \pa^{\un b} H_{\un b} &=&
-2 \Box ( \Pi^L_{0} + \Pi^L_{1/2} ) H_{\un a}~,
\label{id2}\\
\left[D_\alpha , {\Bar D}_{\dot{\alpha}} \right]
\left[D_\beta , {\Bar D}_{\dot{\beta}} \right]
H^{\un b} &=& \Box (8 \Pi^L_{0}
- 24 \Pi^T_{1/2} ) H_{\un a}~.
\label{id3}
\end{eqnarray}
\subsection{Massive Extensions of Type I Supergravity}
\label{Massive Extensions of Type I Supergravity}
$~~\,~$ Consider the off-shell massive supergravity
multiplet derived in \cite{GSS}
\begin{eqnarray}
S^{({\rm IA})} [H, P] =
S^{({\rm I})} [H, \Sigma]
- {1\over 2} m^2\int d^8z \,
\Big\{H^{\un a} H_{\un a}
-\frac 92 P^2 \Big\}~,
\label{IA}
\end{eqnarray}
where the massless part of the action takes the form
\begin{eqnarray}
S^{({\rm I})} [H, \Sigma] &=& \int d^8z \,
\Big\{
H^{\un a}\Box(
- \frac 13 \Pi^L_{0}+ \frac 12 \Pi^T_{3/2})H_{\un a}
-i(\Sigma -\Bar \Sigma ) \pa^{\un a} H_{\un a}
- 3 \Bar \Sigma \Sigma
\Big\}~, \\
&& \qquad
\Sigma = -{1\over 4} \Bar D^2 P~, \qquad
\Bar P = P~~,~~
\nonumber
\end{eqnarray}
and this corresponds to a linearized form of type I (old minimal)
supergravity that has only appeared in the research literature
\cite{VariantSG}. It has not been discussed in textbooks such as
\cite{BK,GGRS}. The distinctive feature {\it {unique}} to this theory
is that its set of auxiliary fields contains one axial vector, one
scalar
and one three-form ($S$, $C_{{\un a} \, {\un b} \, {\un c}} $,
$A_{\un a}$). Interestingly enough and to our knowledge,
there has {\it {never}} been constructed a massive theory that contains
the standard auxiliary fields of minimal supergravity ($S$, $P$,
$A_{\un a}$). This fact may be of some yet-to-be understood
significance.
The theory with action $S^{({\rm IA})} [H, P]$
turns out to possess a dual formulation.
Let us introduce the ``first-order'' action
\begin{eqnarray}
S_{Aux} &=& \int d^8z \, \Big\{
H^{\un a}\Box( - \frac 13 \Pi^L_{0}
+ \frac 12 \Pi^T_{3/2})H_{\un a}
-\frac 12 m^2 H^{\un a}H_{\un a} -U \pa^{\un a} H_{\un a}
\nonumber \\
&& ~~~~~~~~~~~
-\frac 32 U^2 + \frac 94 m^2 P^2
+3m V\Big( U + \frac14 \Bar D^2 P + \frac 14 D^2 P \Big)
\Big\}~,
\end{eqnarray}
where
$U$ and $V$ are real unconstrained superfields.
Varying $V$ brings us back to (\ref{IA}).
On the other hand, we can eliminate $U$ and
$P$ using their equations of motion.
With the aid of (\ref{id2}),
this gives
\begin{eqnarray}
S^{({\rm IB})} [H, P] &=& \int d^8z \, \Big\{
H^{\un a}\Box( \frac 13 \Pi^L_{1/2}
+ \frac 12 \Pi^T_{3/2})H_{\un a}
-\frac 12 m^2 H^{\un a}H_{\un a}
\nonumber \\
&&~~~~~~~~~~- \frac{1}{16} V \{ \Bar D^2 , D^2 \} V
- m V \pa^{\un a} H_{\un a}
+\frac 32 m^2 V^2 \Big\}~.
\label{IB}
\end{eqnarray}
This is one of the two formulations
for the massive $Y$ = 3/2 multiplet
constructed in \cite{BGLP1}.
\subsection{Massive Extensions of Type II Supergravity}
\label{Massive Extensions of Type II Supergravity}
$~~\,~$ Let us now turn to type II
(or new minimal) supergravity.
Its linearized action is
\begin{eqnarray}
S^{({\rm II})} [H, {\cal U}] &=&\int d^8z\,
\Big\{H^{\un a}\Box(-\Pi^T_{1/2}+\frac 12\Pi^T_{3/2})H_{\un a}
+\frac 12{\cal U} [D_\alpha,\Bar D_{\dot\alpha}]H^{\un a}
+\frac 32{\cal U}^2\Big\}~,~~
\label{II}\\
&& \quad
{\cal U}=D^\alpha \chi_\alpha+\Bar D_{\dot\alpha}\Bar \chi^{\dot\alpha}~,
\qquad \Bar D_{\dot{\alpha}} \chi_\alpha = 0~,
\nonumber
\end{eqnarray}
with $\chi_\alpha$ an unconstrained chiral spinor.
It possesses a unique massive extension
\begin{eqnarray}
S^{({\rm IIA})} [H, \chi] &=&
S^{({\rm II})} [H, {\cal U}] - {1\over 2} m^2\int d^8z\,
H^{\un a}H_{\un a}
+3m^2 \left\{ \int d^6z \, \chi^2
+c.c. \right\}
\label{IIA}
\end{eqnarray}
which is derived in Appendix B.
The theory (\ref{IIA}) admits a dual formulation.
Let us consider the following ``first-order'' action
\begin{eqnarray}
S_{Aux} =\, \int d^8z\,
\Big\{H^{\un a}\Box(-\Pi^T_{1/2}+\frac 12\Pi^T_{3/2})H_{\un a}
-\frac 12 m^2 H^{\un a}H_{\un a}
+\frac 12{\cal U} [D_\alpha,\Bar D_{\dot\alpha}]H^{\un a}
+\frac 32{\cal U}^2
\nonumber\\
~~~~~~~~~~~- 6m V \Big( {\cal U} - D^\alpha \chi_\alpha
- \Bar D_{\dot\alpha}\Bar \chi^{\dot\alpha} \Big) \Big\}
+3m^2 \Big\{ \int d^6z \, \chi^\alpha \chi_\alpha
+c.c. \Big\}~,~~~
\end{eqnarray}
in which ${\cal U}$ and $V$ are real unconstrained
superfields. Varying $V$ gives the original action
(\ref{IIA}). On the other hand, we can eliminate
the independent real scalar ${\cal U}$ and chiral spinor
$\chi_\alpha$ variables using their equations of motion.
With the aid of (\ref{id3}) this gives
\begin{eqnarray}
S^{({\rm IIB})} [H, V] &=&\int d^8z\,
\Big\{H^{\un a}\Box(- \frac 13
\Pi^L_{0}+\frac 12\Pi^T_{3/2})H_{\un a}
-\frac 12 m^2 H^{\un a}H_{\un a}
\nonumber \\
&& \quad +mV [D_\alpha,\Bar D_{\dot\alpha}]H^{\un a}
-6m^2 V^2\Big\}
-6 \int d^6z \, W^\alpha W_\alpha~,
\label{IIB}
\end{eqnarray}
where $W_\alpha$
is the vector multiplet field strength
defined in (\ref{tino}).
The obtained action (\ref{IIB}) constitutes
a new formulation
for massive supergravity multiplet.
\subsection{Massive Extensions of Type III Supergravity}
\label{Massive Extensions of Type III Supergravity}
$~~\,~$ Let us now turn to linearized type III
supergravity \cite{BGLP1}
\begin{eqnarray}
S^{({\rm III})} [H, {\cal U}] &=&\int d^8z\,
\Big\{H^{\un a}\Box(\frac 13
\Pi^L_{1/2}+\frac 12\Pi^T_{3/2})H_{\un a}
+ {\cal U} \pa_{\un a} H^{\un a}
+\frac 32{\cal U}^2\Big\}~,
\label{III}\\
&& \quad
{\cal U}=D^\alpha \chi_\alpha+\Bar D_{\dot\alpha}\Bar \chi^{\dot\alpha}~,
\qquad \Bar D_{\dot{\alpha}} \chi_\alpha = 0~,
\nonumber
\end{eqnarray}
with $\chi_\alpha$ an unconstrained chiral spinor.
It possesses a unique massive extension
\begin{eqnarray}
S^{({\rm IIIA})} [H, \chi] &=&
S^{({\rm III})} [H, {\cal U}] - {1\over 2} m^2\int d^8z\,
H^{\un a}H_{\un a}
-9m^2 \left\{ \int d^6z \, \chi^2
+c.c. \right\}~,~~~
\label{IIIA}
\end{eqnarray}
and its derivation is very similar to that
of (\ref{IIA}) given in Appendix B.
Similarly to the type II case considered earlier,
the theory (\ref{IIIA}) admits a dual formulation.
Let us introduce the ``first-order'' action
\begin{eqnarray}
S_{Aux} &=& \int d^8z\,
\Big\{H^{\un a}\Box(\frac 13
\Pi^L_{1/2}+\frac 12\Pi^T_{3/2})H_{\un a}
-\frac 12 m^2 H^{\un a}H_{\un a}
+ {\cal U} \pa_{\un a} H^{\un a}
+\frac 32{\cal U}^2
\nonumber \\
&& +3m V \Big( {\cal U} - D^\alpha \chi_\alpha
- \Bar D_{\dot\alpha}\Bar \chi^{\dot\alpha} \Big) \Big\}
-9m^2 \Big\{ \int d^6z \, \chi^\alpha \chi_\alpha
+c.c. \Big\}~,
\end{eqnarray}
in which ${\cal U}$ and $V$ are real unconstrained
superfields. Varying $V$ gives the original action
(\ref{IIIA}).
On the other hand, we can eliminate
the independent real scalar ${\cal U}$ and chiral spinor
$\chi_\alpha$ variables using their equations of motion.
With the aid of (\ref{id2}) this gives
\begin{eqnarray}
S^{({\rm IIIB})} [H, V] &=&\int d^8z\,
\Big\{H^{\un a}\Box(- \frac 13
\Pi^L_{0}+\frac 12\Pi^T_{3/2})H_{\un a}
-\frac 12 m^2 H^{\un a}H_{\un a}
\nonumber \\
&& \quad ~~~~~~~~-mV \pa_{\un a} H^{\un a}
- \frac 32 m^2 V^2\Big\}
+{1\over 2} \int d^6z \, W^\alpha W_\alpha~,
\label{IIIB}
\end{eqnarray}
with the vector multiplet field strength
$W_\alpha$ defined in eq. (\ref{tino}).
This is one of the two formulations
for the massive $Y$ = 3/2 multiplet
constructed in \cite{BGLP1}. The other formulation is given
by the action (\ref{IB}).
\section{Summary}
\label{Summary}
$~~\,~$ We have formulated new free superfield
dynamical theories for massive multiplets of superspin
$Y$ = 1 and $Y$ = 3/2. We have shown that these new theories
are dually equivalent to the theories with corresponding superspin
given previously in the literature \cite{BGLP1,BGLP2,GSS}.
Although the theories with a fixed and specific value of $Y$
are on-shell equivalent, they differ from one another by distinctive
sets of auxiliary superfields (see discussion of this point in \cite{BGLP1}).
The existence of their varied and distinctive off-shell structures
together with their on-shell equivalence comes somewhat as
a surprise.
This surprise suggests that there is much remaining work to be done
in order to understand and classify the distinct off-shell representations
for all multiplets with higher values of $Y$
in both the massless and massive cases.
Our results raise many questions. For example, for a fixed value
of $Y$ what massless off-shell representations possess massive
extensions? How does the number of such duality related formulations
depend on the value of $Y$?
Are there even more off-shell possibilities
for the massless theories uncovered in the works of \cite{KSP,KS}?
Another obvious question relates to the results demonstrated
in the second work of \cite{KSG}. In this past work, it was shown
that there is a natural way to combine 4D, $\cal N$ = 1 massless
higher spin supermultiplets into 4D, $\cal N$ = 2 massless
higher spin supermultiplets. Therefore, we are led to expect that
it should be possible to combine 4D, $\cal N$ = 1 massive
higher spin supermultiplets into 4D, $\cal N$ = 2 massive
higher spin supermultiplets. As we presently only possess
{\it {four}} $Y$ = 1 and {\it {six}} $Y$ = 3/2 4D, $\cal N$ = 1
supermultiplets, the extension to 4D, $\cal N$ = 2 supersymmetry
promises to be an interesting study for the future.
All of these questions bring to the fore the need for
a comprehensive understanding of the role of duality
for arbitrary $Y$ supersymmetric
representations, of both the massless and massive varieties.
In turn this raises the even more daunting specter
of understanding the role of duality within the context
of superstring/M-theory. To our knowledge
the first time the question was raised about the possibility
of dually related superstrings was in 1985 \cite{GNi} and
there the question concerns on-shell dually related theories.
So for both on-shell and off-shell theories we lack
a complete understanding of duality.
The most successful descriptions of superstrings are of the
type pioneered by Berkovits (see \cite{BL} and references
therein). As presently formulated, there is no sign of duality
in that formalism. So does the superstring uniquely pick
out representations among the many
dual varieties suggested by our work?
\vskip.5cm
\noindent
{\bf Acknowledgments:}\\
The work of ILB was supported in part by the RFBR grant,
project No 03-02-16193, joint RFBR-DFG grant, project
No 02-02-04002, the DFG grant, project No 436 RUS 113/669,
the grant for LRSS, project No 125.2003.2 and INTAS grant,
project INTAS-03-51-6346.
The work of SJG and JP is
supported in part by National Science Foundation
Grant PHY-0099544.
The work of SMK is supported in part by the
Australian Research Council.
\begin{appendix}
\section{Derivation of (\ref{OS-action-2})}
$~~\,~$ Let us start with the action
\begin{eqnarray}
S [\Psi]
= \hat{S}[\Psi ]
+ {1\over 4} \int d^8z\,
\Big( D\, \Psi + {\Bar D} \,{\Bar \Psi}
\Big)^2
+ \int d^8z\,
\Big( \mu \Psi^2 + \mu^* \, {\Bar \Psi}^2
\Big)~,
\label{OS-action}
\end{eqnarray}
where the functional $\hat{S}[\Psi]$ is
defined in (\ref{S-hat}), and
$\mu$ is a complex mass parameter
to be specified later. The action
(\ref{OS-action}) with $\mu=0$
describes the Ogievetsky-Sokatchev
model for the massless gravitino
multiplet \cite{OS}.
We are going to analyze whether this action
with $\mu \neq 0$ can be used to consistently describe
the massive gravitino multiplet dynamics.
The equation of motion for $\Psi^\alpha$ is
\begin{eqnarray}
-\Bar D_{\dot\alpha}D_\alpha\Bar \Psi^{\dot\alpha}
+\frac 12\Bar D^2 \Psi_\alpha
-\frac 12 D_\alpha ( D\, \Psi + {\Bar D}\, {\Bar \Psi} )
+2\mu\,\Psi_\alpha
&=&0~.
\label{OS-em1}
\end{eqnarray}
It implies
\begin{eqnarray}
-\frac 14\Bar D^2 D_\alpha ( D\, \Psi + {\Bar D} \, {\Bar \Psi} )
+\mu \,\Bar D^2 \Psi_\alpha =0~,
\label{OS-em2}
\end{eqnarray}
and therefore
\begin{eqnarray}
0&=& -\frac 14 D^\alpha\Bar D^2 D_\alpha
( D\, \Psi + {\Bar D} \, {\Bar \Psi} )
+\mu \,D^\alpha \Bar D^2 \Psi_\alpha
\label{OS-em3} \\
&=& -\frac 14 D^\alpha\Bar D^2 D_\alpha
( D\, \Psi + {\Bar D} \, {\Bar \Psi} )
+\mu \,\Bar D^2 ( D\, \Psi + {\Bar D}\, {\Bar \Psi} )
+4i \mu \,\pa^{\un a} \Bar D_{\dot{\alpha}} \Psi_\alpha ~.
\nonumber
\end{eqnarray}
Since the first term on the right is real and linear,
we further obtain
\begin{eqnarray}
\mu \,D^\alpha \Bar D^2 \Psi_\alpha &=&
\mu^* \, \Bar D_{\dot{\alpha}} D^2 \Bar \Psi^{\dot{\alpha}}~,
\label{OS-em4} \\
D^2 \Bar D^2 ( D\, \Psi + {\Bar D}\, {\Bar \Psi} )
&+& 4i \mu \,\pa^{\un a}
D^2 \Bar D_{\dot{\alpha}} \Psi_\alpha =0~.
\label{OS-em5}
\end{eqnarray}
Since the operator $\Bar D^2 D^\alpha $
annihilates chiral superfields, applying
it to (\ref{OS-em1}) and making use of
(\ref{OS-em5}), we then obtain
\begin{equation}
\Bar D^2 ( D\, \Psi + {\Bar D}\, {\Bar \Psi} )
=D^2 ( D\, \Psi + {\Bar D} \, {\Bar \Psi} )
=0~.
\label{OS-em6}
\end{equation}
Next, contracting $D^\alpha$ on (\ref{OS-em1})
and making use of
(\ref{OS-em6}) gives
\begin{equation}
i \pa^{\un a}
( \Bar D_{\dot{\alpha}} \Psi_\alpha + D_\alpha \Bar \Psi_{\dot{\alpha}})
+\mu \, D\,\Psi =0~.
\label{OS-em7}
\end{equation}
We also note that, due to (\ref{OS-em6}),
the equation (\ref{OS-em4}) is now
equivalent to
$ \pa^{\un a}
( \mu \, \Bar D_{\dot{\alpha}} \Psi_\alpha -
\mu^* \, D_\alpha \Bar \Psi_{\dot{\alpha}}) =0$.
Therefore, with the choice
$ \mu = i\, m$, where $m$ is real,
we end up with
\begin{equation}
D \,\Psi = \Bar D \,\Bar \Psi =0~.
\label{OS-em8}
\end{equation}
Then, eq. (\ref{OS-em2}) becomes
\begin{equation}
\Bar D^2 \Psi_\alpha = 0~.
\label{OS-em9}
\end{equation}
Finally, the equation of motion
(\ref{OS-em1}) reduces to
\begin{equation}
\pa_{\un a} \Bar \Psi^{\dot{\alpha}} + m \,
\Psi_\alpha = 0~.
\label{OS-em10}
\end{equation}
Eqs. (\ref{OS-em8}) -- (\ref{OS-em10})
define an irreducible $Y$ = 1 massive
representation.
They are equivalent to the equations
of motion in the Ogievetsky-Sokatchev model
(\ref{OS-action-2}).
\section{Derivation of (\ref{IIA})}
$~~\,~$ Let us consider an action
$S = S^{({\rm II})} [H, {\cal U}] + S_m [H, \chi]$,
where $S^{({\rm II})} [H, {\cal U}] $ is the
type II supergravity action, eq. (\ref{II}),
and $S_m [H, \chi]$ stands for the mass term
\begin{eqnarray}
S_m[H, \chi]=
-\frac 12m^2\int d^8z\, H^{\un a}H_{\un a}
+\frac 12\gamma m^2\int d^6z \,
\chi^\alpha\chi_\alpha
+\frac 12\gamma^* m^2\int d^6\bar z \,
\bar \chi_{\dot\alpha}\bar\chi^{\dot\alpha}~,
\end{eqnarray}
with $\gamma$ a complex parameter.
The latter should be determined from
the requirement that
the equations of motion
\begin{eqnarray}
\label{sweet}
\Box\Big[
\Pi_{3/2}^T
-2\Pi_{1/2}^T
\Big]H_{\un a}
-m^2H_{\un a}
+\frac 12[D_\alpha,\Bar D_{\dot\alpha}]{\cal U}
&=&0~, \\
\label{tasty}
\frac 18\Bar D^2D_\alpha[D_\beta,\Bar D_{\dot\beta}]
H^{\un b}
+\frac 34\Bar D^2D_\alpha{\cal U}
+m^2\gamma\chi_\alpha
&=&0~,~~
\end{eqnarray}
be equivalent to (\ref{32irrepsp}).
Since ${\cal U}$ is linear,
(\ref{sweet}) implies that $H_{\un a}$ is linear,
$D^2H_{\un a}=0$.
It is then possible to show
that $\Bar D^{\dot\alpha}H_{\un a}\propto \chi_\alpha$
on-shell.
To prove this proportionality,
first contract $\Bar D^{\dot\alpha}$ on (\ref{sweet})
and use the following identities:
\begin{eqnarray}
\label{goodvibes}
\Bar D^2 D_\beta [D_\alpha, \Bar D_{\dot\alpha}]H^{\un a}
&=&2i\Bar D^2 D^\alpha\pa_{(\alpha}{}^{\dot\alpha}H_{\beta)\dot\alpha}~, \\
\Box\Bar D^{\dot\alpha}\Pi_{1/2}^T H_{\un a}&=&
-\frac i8\Bar D^2D^\delta\pa_{(\alpha}{}^{\dot\beta} H_{\delta)\dot\beta}
=-\frac 1{16}\Bar D^2 D_\beta
[D_\alpha, \Bar D_{\dot\alpha}]H^{\un a}~,~
\end{eqnarray}
to arrive at:
\begin{eqnarray}
+\frac 18\Bar D^2 D_\beta [D_\alpha, \Bar D_{\dot\alpha}]H^{\un a}
+\frac 34\Bar D^2D_\alpha{\cal U}
- m^2 \Bar D^{\dot\alpha}H_{\un a}
=0~.
\end{eqnarray}
Substituting the first two terms
with (\ref{tasty}) leads to:
\begin{eqnarray}
\label{thebomb}
\gamma\chi_\alpha
+ \Bar D^{\dot\alpha}H_{\un a}=0~,
\end{eqnarray}
an upon substituting for ${\cal U}$ in (\ref{tasty})
by substituting (\ref{thebomb}) back in yields:
\begin{eqnarray}
+\frac 18\Bar D^2D_\alpha[D_\beta,\Bar D_{\dot\beta}]H^{\un b}
-\frac 34\frac 1\gamma\Bar D^2D_\alpha[D^\beta\Bar D^{\dot\beta}
-\frac \gamma{\gamma^*}\Bar D^{\dot\beta}D^\beta]H_{\un b}
+m^2\gamma\chi_\alpha
=0~~.~~
\end{eqnarray}
This means that $\chi_\alpha$ will vanish if $\gamma$
is real and $\gamma=6$. Equation (\ref{thebomb}) implies
that $H_{\un a}$ is irreducible when $\chi_\alpha$ vanishes.
This means that $\Pi^T_{3/2}H_{\un a}=H_{\un a}$
and the Klein-Gordon equation
is obtained from (\ref{sweet}).
We therefore obtain (\ref{IIA}).
\end{appendix}
| {
"redpajama_set_name": "RedPajamaArXiv"
} | 7,104 |
{"url":"https:\/\/puzzling.stackexchange.com\/questions\/65008\/the-soldiers-march-25-miles\/65011","text":"The soldiers march 25 miles [closed]\n\nAn infantry platoon marches across the barren landscape. Says the captain, \"We will march 25 miles today, soldiers!\" And indeed, by nightfall, they have marched 25 miles. But when they prepare to set up their sleeping quarters, they find that they are in exactly the same place they started! They marched in an exactly straight line, and no other transportation was used.\n\nHint:\n\nIt is necessary for the soldiers to wear special clothing to survive here, and there is a specific place I am talking about\n\nAnother hint: (Don't read unless necessary)\n\nThe distance of 25mi matters\n\nclosed as too broad by ffao, QuantumTwinkie, Glorfindel, Beastly Gerbil, NL628Apr 27 '18 at 22:40\n\nPlease edit the question to limit it to a specific problem with enough detail to identify an adequate answer. Avoid asking multiple distinct questions at once. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.\n\n\u2022 You're maybe giving hints a little too fast. Don't hesitate to wait a few hours (some will say a day) before giving an hint. \u2013\u00a0Sae\u00efdryl Apr 27 '18 at 13:40\n\u2022 Maybe the soldiers should be following a tank whose treads both moved at exactly the same speed (and thus traveled the same distance) without slippage. If the tank were going around the pole of a planet that was much more than 25 miles in circumference, the distance traveled by the treads would differ by almost as much as if the tank made a much smaller circle. \u2013\u00a0supercat Apr 27 '18 at 20:17\n\nWe are in the future : the soldiers are marching on a 8 miles diameter asteroid and they need special clothing to be able to breathe\n\n(EDIT) and to be more precise\n\nwe're on Ijiraq one of Saturn's moons (approx 8 miles diameter)\n\nOr\n\nDeimos one of Mars' moon works too\n\n\u2022 Close, but I'm thinking of a specific place \u2013\u00a0Redwolf Programs Apr 27 '18 at 13:36\n\u2022 Please hide your answers with a spoiler tag (\">!\") \u2013\u00a0Sae\u00efdryl Apr 27 '18 at 13:39\n\u2022 sry i forgot the spoiler \u2013\u00a0Kant1 Apr 27 '18 at 13:40\n\u2022 Third idea is correct! \u2013\u00a0Redwolf Programs Apr 27 '18 at 13:59\n\u2022 I'm not sure such a place would have sufficient gravity to be able to \"march\". \u2013\u00a0Alexis Olson Apr 27 '18 at 22:03\n\nI think they are\n\nEither in the North or the South pole, and they made a big circle. They need special clothing because it's quite cold\n\n\u2022 What about the straight line part? \u2013\u00a0Redwolf Programs Apr 27 '18 at 13:35\n\u2022 in a straight line \u2013\u00a0TinyTRex72 Apr 27 '18 at 13:35\n\u2022 @Sae\u00efdryl I think the point is that there is a point, somewhere just south of the North Pole (probably only a few miles), where walking due east (c.f. west) for 25 miles will return you to your starting point. The same will be true of the south pole. \u2013\u00a0MD-Tech Apr 27 '18 at 14:14\n\u2022 @user2357112 True, so the accepted answer is just as \"curved\" as this solution\u2014it's just that the soldiers' bodies are oriented differently with respect to the curve in each scenario (walking around a sphere curves down, while this solution curves the same amount but just left or right) \u2013\u00a0maxathousand Apr 27 '18 at 18:00\n\u2022 @maxathousand: Both answers are curved from the perspective of the ambient space, but the accepted answer is straight in the (generalized) sense of being a geodesic of the space formed by the surface of the celestial body the soldiers are marching on, which this answer isn't. \u2013\u00a0user2357112 Apr 27 '18 at 18:11\n\nAre they\n\n\u2022 You should spoiler your answer by starting the line with >! \u2013\u00a0Laurel Apr 27 '18 at 19:04\n\u2022 ohhh okay ... will do \u2013\u00a0MrClan May 1 '18 at 4:03\n\u2022 That's one big piece of exercise equipment \u2013\u00a0Redwolf Programs May 9 '18 at 12:17\n\nMy first thought was\n\nthey are future soldiers marching along the inside of a ringworld (or halo, or dyson sphere)\n\nMay be this:\n\nThey walked 25 miles from their camp A in a straight line and arrived in a camp B. The camp B is built exactly the same as camp A. The landscape is barren and so as a result, it is very difficult to tell that the location is different; only the camp can provide clues but here they are exactly the same.\n\n\u2022 Welcome to Puzzling! Unfortunately, since the question states that they ended \"exactly where they started\" (and not that it only looked like the place they started in), this does not seem like a valid answer to me. \u2013\u00a0ffao Apr 27 '18 at 20:06","date":"2019-10-16 00:50:21","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 0, \"mathjax_display_tex\": 0, \"mathjax_asciimath\": 1, \"img_math\": 0, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.4354095160961151, \"perplexity\": 1292.137391160783}, \"config\": {\"markdown_headings\": false, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2019-43\/segments\/1570986660829.5\/warc\/CC-MAIN-20191015231925-20191016015425-00548.warc.gz\"}"} | null | null |
North Austin hooks first local outpost of Cajun seafood chain
Marijuana-themed sandwich joint sparks up first Austin location on the Drag
Cheba Hut specializes in "toasted" sandwiches, salads, and snacks. Cheba Hut/Facebook
Though new Austinites may not know it from the current array of chain restaurants, The Drag was once a large part of what kept Austin weird. Perhaps it was inevitable that years after Guadalupe Street's heyday in the '70s and '80s, a national franchise is moving in that appropriates that counter culture cool.
A rep for Fort Collins, Colorado-based sandwich shop Cheba Hut confirms that an Austin location will open at 3016 Guadalupe St., Ste. 200, in early 2020. Though the branding of local concepts like Thundercloud Subs hint at la vie boheme, the restaurant goes full out with a cannabis theme and trippy murals plucked out of a head shop.
Specializing in "toasted" subs, Cheba's sandwich offerings are mostly named after marijuana strains like Jamaica Red, Acapulco Gold, and — the perhaps ill-advised — AK-47. Though stoner foods like pizza nachos and ramen-wrapped hot dogs have become a celebrated category over the last few years, the shop keeps the offerings fairly regulation with an assortment of chicken, turkey, roast beef, veggies, and cheeses.
Cheba does go buck-wild with its Loaded Not'chos, nacho cheese Doritos topped with melted cheddar, jalapeños, red onion, black olives, and ranch dressing. Other munchies include a hummus platter; meatballs; pretzel bits; garlic cheese bread; and, inexplicably, French onion soup. There are also salads, though the team seems to have sobered up when naming those.
For drinks, Cheba offers a variety of nonalcoholic "cottonmouth cures," local craft beer, and a full cocktail menu. Naturally, there's Gin n Juice and a Bloody Mary Jane with "stuff on a stick." The other drinks range from the Dirty Hippie with muddled cucumbers, Deep Eddy Vodka, and lemonade to the Brass Monkey, a combination of Pabst Blue Ribbon, orange juice, and regret.
Though no interior details are available for the Austin shop just yet, most of the newer locations feature large-scale psychedelic art, beach scenes, or portraits of stoners like Cheech Marin, Hunter S. Thompson, and Willie Nelson. The staff wears tie-dyed T-shirts and the social media strategy seems to lean toward dank memes.
The Guadalupe location will be the chain's first in Texas. Cheba was developed in Tempe, Arizona, in 1998 by then-Arizona State University student Scott Jennings. Since then it has spread to 26 locations, mostly clustered in the Southwest. | {
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} | 3,651 |
The first Xiaomi smartphones to receive this version
Chris Skeldon August 29, 2021 2 min read
Xiaomi is not slowing down the speed with which it releases new versions of its Android version, with MIUI 12.5 Enhanced almost ready now. This version is being prepared for release and delivery to users.
With this version almost ready, it's time for Xiaomi to show where this version will go first. The list of the first smartphones that will receive MIUI 12.5 Enhanced was known and left many users of these smartphones satisfied. See if your Xiaomi is on this list.
Not many were expecting MIUI 12.5 Enhanced, as it was considered a preview version of Xiaomi's next big update. This is an improved version of the previous version, which is also intended to correct some issues that this Android customization ended up with.
Of course, the classic question of these moments immediately appeared. All users want to know if and when their Xiaomi smartphone will receive MIUI 12.5 Enhanced and when it will arrive to be installed in devices.
The above list is official and It was an introduction By Xiaomi to show which of their smartphones receive the improved MIUI 12.5 first, but now on the global market. This version is now available in China for a wide range of smartphones.
With a long list of improvements, this release focuses on providing better and more efficient management of available memory and storage. There is also the use of more efficient algorithms that can achieve more from each smartphone.
The thing that was expected to be known and which turned out to be not revealed yet is the release date of this version. Xiaomi indicates that MIUI 12.5 Enhanced will arrive in the global market in the last quarter of 2021, but without providing a specific date.
This is great news for anyone with a Xiaomi smartphone. The improved MIUI 12.5 promises to bring more features to these devices, with better and more accurate resource management, something that everyone has come to expect.
Chris Skeldon
"Coffee trailblazer. Social media ninja. Unapologetic web guru. Friendly music fan. Alcohol fanatic."
See also Square Enix at E3 2021 | Where to watch, what time to start and what to expect
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Wall Street is on a volatility path once again. But Biden still has a positive credit – Bolsa
Andrea Hargraves
Copyright © All rights reserved. |
Newsever by AF themes. | {
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} | 33 |
Hand-Made in Italy and designed in London, Sienna Alexander started in 2016 with the aim to combine eminent quality with timeless design. Every style we create brings all the design elements together into a light, wearable and fashionable frame, designed for women to make a statement about themselves when they wear it because eye-wear is the only accessory that we wear on our face. Our collection was inspired by the multicultural and vibrant city of London and every model was given its name after an iconic area postcode in London. Our sunglasses are produced using the highest quality materials in family-run factories in Northern Italy. | {
"redpajama_set_name": "RedPajamaC4"
} | 3,282 |
How to disperse nanoparticles / nanopowders (nanomaterials)? How to disperse nano-materials and mix with other powder?
Disperse nanoparticles: 1) If used in the aqueous phase, may use ultrasonic treatment to disperse; 2) If used in the oil phase, may use high shear mixing instrument to disperse. 3) If directly used as dry powder form, may use ball mill treatment to disperse.
How to disperse nano-materials and mix with other powder? There is no specific method of the world. It is still a research topic. In general, if one nanomaterial will be mixed with other powder (for example, your ceramic powder), the first step is to put the nanomaterial into water or ethanol in the high-speed mixing instrument, add 1% dodecyl benzene sulfonate (detergent main ingredients), Instantly after mixing, then put the dispersed nanomaterial into the other powder (your ceramic powder) and continue to mix by still using high-speed mixing instrument, stirring rate the higher the better, time the longer the better as well, and then heating the mixed liquid material to be evaporated completely. | {
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Q: Java array manipulation, invert an int[][] array I am trying to flip each col in this array to invert the image. However, when I run my code, I get a mirror image of the second half of the image, for some ridiculous reason, that I cannot figure out. Can someone please tell me why this only works half-way?
public void invert() {
int[][] tempArray= someArray;
for(int row = 0; row < someArray.length; ++row)
{
int x = someArray[row].length - 1;
for(int col = 0; col < someArray[i].length; ++col, --x)
{
tempArray[row][col] = someArray[row][x];
}
}
someArray = tempArray;
}
someArray is an int[][] array defined elsewhere in my class of size 328x500
int x is a counter variable to decrement through the columns backwards
A: After you have reversed half of them, you have lost the original values in the first half, then the rest of the loop just copies those replaced values back into themselves.
A: Make a method:
public static int[] reversArray(int[] array){
for(int i = 0; i < Math.ceil(array.length/2); i++){
int temp = array[i];
array[i] = array[array.length - (i+1)];
array[array.length - (i+1)] = temp;
}
return array;
}
Then:
for(int i = 0; i < someArray.length; i++{
someArray[i] = reverseArray(someArray[i]);
}
reverseArray(someArray);
A: The problem is because you are manipulating the same array.
Remember java arrays are reference types. So your tempArray and someArray is referring to the same array.
Now, let's say row 1 of your array is {1,2,3} and your output should be {3,2,1}.
But since it's the same array, during the first iteration, the array will become {3,2,3}. And in the third iteration you are reading the same array and trying to replace 3 in col=2 with the 3 in col=0. So your result is 3,2,3.
You should instead create a new array.
replace:
int[][] tempArray= someArray;
with
int[][] tempArray = new int[someArray.length][someArray[0].length];
// If you have variable length column, you may want to intialize it inside the loop.
| {
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Q: convert bash pipeline into a function with parameter I have a pipeline I use to preview csv files:
cat file_name.csv | sed -e 's/,,/, ,/g' | column -t -s ","| less -s
But i want to create an alias viewcsv that will allow to just replace the filename.
I tried viewcsv="cat $1 | sed -e 's/,,/, ,/g' | column -t -s ","| less -s" but that didn't work. Googling turned up that I need to convert this pipeline to a function? How can i convert this to a function so that viewcsv file_name.csv will return same output as cat file_name.csv | sed -e 's/,,/, ,/g' | column -t -s ","| less -s does?
A: Function syntax looks like this:
viewcsv() {
sed -e 's/,,/, ,/g' "$1" | column -t -s ","| less -s
}
Notice that I have replaced cat "$1" | sed with sed "$1".
csvkit has a CSV previewer, by the way:
$ csvlook <<< $'a,b,c\n10,20,30'
| a | b | c |
| -- | -- | -- |
| 10 | 20 | 30 |
| {
"redpajama_set_name": "RedPajamaStackExchange"
} | 9,035 |
\subsection{Reference galaxy sample}
We use the New York University Value Added Galaxy Catalogue (NYU-VAGC)
\footnote{http://wassup.physics.nyu.edu/vagc/} to construct a
reference sample of galaxies, which are cross-correlated with the AGN
sample. The original NYU-VAGC is a catalogue of local galaxies
(mostly below $z\approx0.3$) constructed by \citet{blanton05} based on
the SDSS DR2. Here we use a new version of the NYU-VAGC ({\tt Sample
dr4}), which is based on SDSS DR4. The NYU-VAGC is described in detail
in \citet{blanton05}.
We have constructed two reference samples: 1) a {\em spectroscopic}
reference sample , which is used to compute the projected AGN-galaxy
cross-correlation function $w(r_p)$; 2) a {\em photometric} reference
sample, which is used to calculate counts of close neighbours around
AGN
The spectroscopic reference sample is constructed by selecting from
{\tt Sample dr4} all galaxies with $14.5 < r < 17.6 $ that are
identified as galaxies from the Main sample (note that $r$-band
magnitude has been corrected for foreground extinction). The galaxies
are also restricted to the redshift range $0.01\leq z\leq0.3$, and the
absolute magnitude range $-23<M_{^{0.1}r}<-17$. The spectroscopic
reference sample contains 292,782 galaxies. We do not consider
galaxies fainter than $M_{^{0.1}r}=-17$, because the volume covered by
such faint samples is very small and the results are subject to large
errors as a result of cosmic variance \citep[see for example Fig. 6
of][]{li06}. The faint apparent magnitude limit of 17.6 is chosen to
yield uniform galaxy sample that is complete over the entire area of
the survey.
The photometric reference sample is also constructed from {\tt Sample
dr4} by selecting all galaxies with $14.5<r<19$. The resulting sample
includes 1,065,183 galaxies. Throughout this work we adopt standard
$\lambda$CDM cosmological parameters: $\Omega = 0.3$,
$\Omega_{\Lambda} = 0.7$, and H$_0$ = 70 km~s$^{-1}$ Mpc$^{-1}$.
\section {Mock Catalogues}
In this section we describe how we construct a large set of mock
galaxy samples with the same geometry and selection function as the
spectroscopic samples described in the previous section . We will use
these mock catalogues to test our method for correcting for the effect
of fibre collisions on the measurement of the AGN-galaxy
cross-correlation function on small scales. We will also use these
mock catalogues to construct models of AGN clustering for comparison
with the observations.
\subsection{Galaxy properties in the Millennium Simulation }
Our mock catalogues are constructed using the Millennium Simulation
\citep{springel05}, a very large simulation of the concordance
$\Lambda$CDM cosmogony with $10^{10}$ particles. The chosen
simulation volume is a periodic box of size $L_{box}=500 h^{-1}$ Mpc
on a side, which implies a particle mass of $8.6\times10^8$ 4$h^{-1}
M_{\odot}$. Haloes and subhaloes at all output snapshots are
identified using the {\tt subfind} algorithm described in
\citet{springel01} and merger trees are then constructed that describe
how haloes grow as the Universe evolves. \citet{croton06} implemented
a model of the baryonic physics in these simulations in order to
simulate the formation and evolution of galaxies and their central
supermassive black holes \citep[see][for more details]{croton06}.
This model produced a catalogue of 9 million galaxies at $z=0$ down to
a limiting absolute magnitude limit of $M_r-5\log h=-16.6$. This
catalogue is well-matched to many properties of the present-day galaxy
population (luminosity-colour distributions, clustering etc.). It is
publically available at
http://www.mpa-garching.mpg.de/galform/agnpaper. In our work, we
adopt the positions and velocities of the galaxies given in the Croton
et al. catalogue. The $r$-band luminosities and stellar masses are
assigned to each model galaxy, using the parametrized functions
described by \citet{wang06}. These functions relate the physical
properties of galaxies to the quantity $M_{infall}$, defined as the
mass of the halo at the epoch when the galaxy was last the central
dominant object in its own halo. They were chosen so as to give close
fits to the results of the physical galaxy formation model of
\citet{croton06}, but their coefficients were adjusted to improve the
fit to the SDSS data, in particular the galaxy mass function at the low
mass end. Extensive tests have shown that the adopted parametrized
relations allow us to accurately match the luminosity and stellar mass
functions of galaxies in the SDSS, as well as the shape and amplitude
of the two point correlation function of galaxies in different
luminosity and stellar mass ranges \citep{li06,wang06}.
\subsection{Constructing the catalogues}
Our aim is to construct mock galaxy redshift surveys that have the
same geometry and selection function as the SDSS DR4. A detailed
account of the observational selection effects accompanies the
NYU-VAGC release. The survey geometry is expressed as a set of
disjoint convex spherical polygons, defined by a set of ``caps''. This
methodology was developed by Andrew Hamilton to deal accurately and
efficiently with the complex angular masks of galaxy surveys
\citep{ht02}
\footnote{http://casa.colorado.edu/$^\sim$ajsh/mangle/}. The
advantage of using this method is that it is easy to determine whether
a point is inside or outside a given polygon \citep{tegmark02}. The
redshift sampling completeness is then defined as the number of
galaxies with redshifts divided by the total number of spectroscopic
targets in the polygon. The completeness is thus a dimensionless
number between 0 and 1, and it is constant within each of the
polygons. The limiting magnitude in each polygon is also provided (it
changes slightly across the survey region).
We construct our mock catalogues using the methods described in
\citet{yang04}, except that we position the virtual observer randomly
inside the simulation and not at the centre of the box. Because the
survey extends out to $z \sim 0.3$, this implies that we need to cover
a volume that extends to a depth of $900 h^{-1}$ Mpc, i.e. twice that
of the Millennium catalogue. We thus create $5\times 5\times 5$
periodic replications of the simulation box and place the observer
randomly within the central box, so that the required depth can be
achieved in all directions for the observer.
We produce 20 mock catalogues by following the procedure described
below:
\begin{enumerate}
\item We randomly place a virtual observer in the stack of boxes
described above. We define a ($\alpha$,$\delta$)-coordinate frame and
remove all galaxies that lie outside the survey region.
\item For each galaxy we compute the redshift as "seen" by the virtual
observer. The redshift is determined by the comoving distance and the
peculiar velocity of the galaxy.
\item We compute the $r$-band apparent magnitude of each galaxy from
its absolute magnitude $M_r$ and its redshift, applying a (negative)
K-correction but neglecting any evolutionary correction. We then
select galaxies according to the position-dependent magnitude limit
(provided in the {\tt Sample dr4}) and apply a (positive) K-correction
to compute $M_{^{0.1}r}$, the $r$-band absolute magnitude of the
galaxy at $z=0.1$.
\item To mimic the position-dependent completeness, we randomly
eliminate galaxies using the completeness masks provided in {\tt
Sample dr4}.
\item Finally, we mimic the actual selection criteria of our own
reference sample by restricting galaxies in the mock catalogue to
$0.01<z<0.3$, $14.5<r<17.6$ and $-23< M_{^{0.1}r}<-17$.
\end{enumerate}
Figure~\ref{fig:mock} shows the equatorial distribution of galaxies in
one of our mock catalogues, compared to that in the observational
sample. The average number of galaxies in our mock catalogues is
$\sim$320,000, with a r.m.s. dispersion of $\sim9000$, in good
agreement with the observed number.
\begin{figure*}
\centerline{
\psfig{figure=f1a.ps,width=0.8\hssize}
\psfig{figure=f1b.ps,width=0.8\hssize}}
\caption{Equatorial distribution of right ascension and redshift for
galaxies within 6$^\circ$ of the equator in the SDSS (left) and in one
of our mock catalogues (right).}
\label{fig:mock}
\end{figure*}
\subsection{Fibre collisions}
The procedure described above does not account for the fact that the
spectroscopic target selection becomes increasingly incomplete in
regions of the sky where the galaxy density is high, because two
fibres cannot be positioned closer than 55 arcseconds from each other.
In order to mimic these fibre ``collisions'', we modify step (4)
above. We no longer randomly sample galaxies using the completeness
masks. Instead, we assign fibres to our mock galaxies using a
procedure that is designed to mimic the tiling code that assigns
spectroscopic fibres to SDSS target galaxies \citep{blanton03}. We run
a friends-of-friends grouping algorithm on the mock galaxies with a
55$^{\prime\prime}$ linking length. Isolated galaxies, i.e. those in
single-member groups, are are always assigned fibres. If two targets
collide, we simply pick one at random to be the spectroscopically
targeted galaxy. For groups with more than two members, we need to
determine which members will be assigned fibres and which will not.
The resulting groups are almost always of sufficiently low
multiplicity so that in principle, one could simply check all
possibilities to find the best possible combination of galaxies that
would eliminate fibre collisions (this is the procedure adopted in the
SDSS target selection). In our work we use a somewhat more efficient
method. For each group, we calculate the geometric centre. The group
members located closer to the center are preferentially eliminated.
For example, in a triple collision this algorithm will keep the outer
two members rather than the middle one.
This procedure is complicated by the fact that some fraction of the
sky will be covered with overlaps of different tiles (Each
spectroscopic fibre plug plate is referred as a ``tile'', which has a
circular field of view with a radius of $1^\circ_.49$.). About 30 \%
of the sky is covered in such overlaps. This means that if, for
example, a binary group covered by two ore more tiles, both of the
group members can be assigned fibres. We take this into account by
iteratively repeating the procedure described above, as follows.
\begin{enumerate}
\item First, we determine the number of tiles that cover a given
galaxy and set the quantity $n_{chances}$ equal to this number. For
example, $n_{chances}=2$ for a galaxy covered by two tiles; this
galaxy has two chances to be assigned a fibre.
\item We assign fibres by applying the algorithm described above to
those galaxies with $n_{chances}>0$. If a galaxy obtains a fibre in
this procedure, then the quantity $n_{chances}$ is set to zero. If
not, we set $n_{chances}=n_{chances}-1$.
\item Step (ii) is repeated until $n_{chances}$ reaches zero for all
galaxies. All galaxies that are not assigned fibres are then removed
from our mock catalogue.
\item Finally, we remove a number of galaxies at random so that the
resulting mock sample has the same overall position-dependent
completeness as the real SDSS sample.
\end{enumerate}
\section{Clustering measures}
In order to compute the two-point cross-correlation function (2PCF)
$\xi(r_p,\pi)$ between the AGN host (or matched control) sample and
the reference galaxy sample , we have constructed random samples that
are designed to include all observational selection effects. This is
described in detail in \citet{li06}. $\xi(r_p,\pi)$ is then
calculated using the estimator
\begin{equation}
\xi(r_p,\pi) = \frac{N_R}{N_D} \frac{QD(r_p,\pi)}{QR(r_p,\pi)} -1,
\end{equation}
where $r_p$ and $\pi$ are the separations perpendicular and parallel
to the line of sight; $N_D$ and $N_R$ are the number of galaxies in
the reference sample and in the random sample; $QD(r_p,\pi)$ and
$QR(r_p,\pi)$ are the cross pair counts between AGN (or control) and
the reference sample, and between AGN (or control) and the random
sample, respectively.
In what follows, we focus on the projection of $\xi(r_p,\pi)$ along
the line of sight:
\begin{equation}
w_p(r_p)=\int_{-\infty}^{+\infty}\xi(r_p,\pi)d\pi=
\sum_i\xi(r_p,\pi_i)\Delta\pi_i.
\end{equation}
Here the summation for computing $w_p(r_p)$ runs from $\pi_1 = -39.5 $
h$^{-1}$ Mpc to $\pi_{80} = 39.5$ h$^{-1}$ Mpc, with $\Delta\pi_i = 1$
h$^{-1}$ Mpc.
The errors on the clustering measurements are estimated using the
bootstrap resampling technique \citep{bbs84}. We generate 100
bootstrap samples from the observations and compute the correlation
functions for each sample using the weighting scheme (but not the
approximate formula) given by \citet{mjb92}. The errors are then
given by the scatter of the measurements among these bootstrap
samples. More details about our procedures and tests of our
methodology can be found in \citet{li06}. We also obtain robust
estimates of our uncertainties from the scatter between the results
obtained from disjoint areas of the sky.
We are particularly interested in the amplitude of the AGN-reference
galaxy cross-correlation on small scales ($<100$ kpc), because this
allows us to evaluate whether mergers and interactions play a role in
triggering AGN activity. A careful correction for the effect of fibre
collisions when measuring the clustering is thus very important. As
described in \citet{li06}, we correct for fibre collisions by
comparing the angular 2PCF of the spectroscopic sample with that of
the parent photometric sample. Here we use our mock SDSS catalogues to
test the correction method. We calculate the angular correlation
functions $w_z(\theta)$ and $w_p(\theta)$ using mock catalogues with
and without fibre collisions. The function
\begin{equation}
F(\theta)=\frac{1+w_z(\theta)}{1+w_p(\theta)}
\end{equation}
is then used to correct for collisions by weighting each pair by
$1/F(\theta)$. Figure~\ref{fig:wrp_mock} (the top panel)
shows measurements of
$w_p(r_p)$ for galaxies in one of our mock catalogues. The solid line
is the ``true'' correlation function calculated for the mock
catalogues that do not include fibre collisions. Circles show the
results when fibre collisions are included. Triangles show the
results that are obtained when the 2PCF is corrected for the effect of
fibre collisions using the method described above.
In the bottom panel, we plot the ratios of the uncorrected and
the corrected $w_p(r_p)$ relative to the "true" correlation function.
As can be seen,
our correction procedure works well. The turnover in the amplitude on
small physical scales resulting from the lower sampling of galaxies in
dense regions disappears and the corrected $w_p(r_p)$ is very close to
the real one. It is noticeable that there is still a very small
deficit in the corrected $w_p(r_p)$ on scales between 0.05 and 1 Mpc.
This should not be a significant contribution to the bias between AGN
and normal galaxies (see below), because fibre collisions are expected
to affect the AGN and the reference galaxies in the same way.
\begin{figure}
\centerline{\psfig{figure=f2.ps,width=\hssize}}
\caption{Top: Projected 2PCF $w_p(r_p)$ measured for the mock catalogue
without including fibre collisions (solid line) and for the mock
catalogue with fibre collisions (circles). The filled triangles show
the measured $w_p(r_p)$ for the mock after correcting the effect of
fibre collisions using the method described in the text.
{Bottom: The ratios of the uncorrected and the corrected $w_p(r_p)$ relative
to the "true" $w_p(r_p)$.}}
\label{fig:wrp_mock}
\end{figure}
\section{Observational results}
\subsection{AGN Bias}
We first compute $w_p^{\rm AGN/ref}(r_p)$, the cross-correlation of
the AGN sample with respect to the reference sample. As described in
section 2, we have constructed two sets of 20 control samples. The
first set is constructed by simultaneously matching redshift, stellar
mass, concentration and stellar velocity dispersion, and the second
set by additionally matching the 4000\AA\ break strength. We then
compute $\bar{w}_p^{\rm contr/ref}(r_p)$, the average
cross-correlation of the control samples with respect to the reference
sample. The quantity $w_p^{\rm AGN/ref}(r_p)/\bar{w}_p^{\rm
contr/ref}(r_p)$ then measures the {\em bias} of the AGN sample with
respect to the control sample of non-AGN as a function of projected
radius $r_p$.
The results are shown in Fig. 3. In the top panel, we plot $w_p^{\rm
AGN/ref}(r_p)$ as circles. $\bar{w}_p^{\rm contr/ref}(r_p)$ is
evaluated for the two sets of control samples and the results are
plotted as squares for the first set and triangles for the second set.
The measurement errors are estimated using the bootstrap resampling
technique described in the previous section. In the bottom panel, we
plot the ratio $ w_p^{\rm AGN/ref}(r_p)/\bar{w}_p^{\rm
contr/ref}(r_p)$ for the two control samples, The errors are estimated
in the same manner as in the top panel. For clarity, squares and
triangles in both panels have been slightly shifted along the
$r_p$-axis.
\begin{figure}
\centerline{\psfig{figure=f3.ps,width=\hssize}}
\caption{Top: projected cross-correlation function $w_p^{\rm
AGN/ref}(r_p)$ between AGN and reference galaxies is plotted as
circles. The average cross-correlation between two sets of 20 control
samples of non-AGN and the same reference galaxies is plotted as
squares and triangles (squares: redshift, stellar mass, stellar
velocity dispersion and concentration are matched; triangles: the
control samples are constructed by additionally matching the
4000\AA-break strength). The inset compares the D$_{4000}$
distribution for the two sets of control samples, with red for the
former set and blue for the latter. The histogram shows the
D$_n$(4000) distribution for the AGN. Bottom: ratio of the $w_p(r_p)$
measurement of AGN to that of non-AGN. Symbols are the same as in the
top panel.}
\label{fig:all}
\end{figure}
Figure 3 shows that there exists a {\em scale-dependent bias} in the
distribution of AGN relative to that of normal galaxies. In
particular, the ratio between the two cross-correlations appears to
exhibit a pronounced ``dip'' at scales between 100 kpc and 1 Mpc. We
note that errorbars estimated using the bootstrap resampling technique
do not take into account effects due to cosmic variance. The coherence
length of the large scale structure is large and even in a survey as
big as the SDSS, this can induce significant fluctuations in the
amplitude of the correlation function from one part of the sky to
another. The difference in the clustering amplitude of AGN and
non-AGN shown in Figure 3 is only a 10-30\% effect , so it is
important to test whether the dip seen in Figure 3 is truly robust.
We have thus divided the survey into 6 different areas on the sky.
Each subsample includes $\sim 12,000$ AGN. We recompute the AGN bias
for each of these subsamples and the results are shown in Fig. 4.
Note that in this plot, we only use a single control sample to compute
the bias, not the average of 20 control samples as in Figure 3. The
scatter between the different curves in Figure 4 thus provides an
upper limit to the true error in the measurement of the bias. As can
be seen, on small scales ($< $ 50 kpc) , the different subsamples
scatter in bias above and below unity. On scales between 0.1 and 1
Mpc, however, all 6 subsamples lie systematically below this line. On
scales larger than 1-2 Mpc, five out of six subsamples show bias
values below unity, but the effect is clearly less significant than on
scales between 0.1 and 1 Mpc. In Fig. 5, we examine the dispersion
in the bias measurement for the AGN sample as a whole caused by
differences between the control samples. As can be seen, the scatter
in the measurement of the bias between different control samples is
considerably smaller than the scatter between different survey
regions, showing that that cosmic variance is, in fact, the dominant
source of uncertainty in our results. Once again, there is clear
indication that AGN are antibiased relative to the control galaxies on
scales larger than 100 kpc.
\begin{figure}
\centerline{\psfig{figure=f4.ps,width=\hssize}}
\vspace{-3.5cm}
\caption{ Ratio of the $w_p(r_p)$ measurement of AGN to that of
non-AGN for six disjoint regions of the survey.}
\label{fig:areas}
\end{figure}
We conclude that on scales between 0.1 and 1 Mpc, AGN are
significantly anti-biased relative to non-AGN of the same stellar
mass, concentration and stellar velocity dispersion. Figure 3 shows
that this anti-bias persists even when the mean age of the stellar
population is matched in addition to stellar mass and structural
parameters. We note that these scales are comparable to the
diameters of the dark matter halos that are expected to host galaxies
with stellar masses comparable to the objects in our sample. In
section 6, we construct halo occupation (HOD) models using mock
catalogues constructed from the Millennium Simulation that can
explain the anti-bias on these scales. As we will show, the same
models naturally predict a smaller, but significant antibias on
scales larger than 1 Mpc.
\subsection{Dependence on black hole mass and AGN power }
\begin{figure*}
\centerline{\psfig{figure=f6.ps,width=0.7\hdsize}}
\caption{Top: projected cross-correlation $w_p(r_p)$ in different
$\sigma_\ast$ bins (indicated above each panel), for all AGN (black),
powerful (red) and weak (blue) AGN. The powerful (weak) AGN are
defined as the top (bottom) 25 per cent objects ordered by decreasing
$L$[O {\sc iii}]$/M_\bullet$. The middle row is for control samples of
non-AGN and the bottom row shows the ratio between the results for the
AGN and the control samples. The insets in the bottom panels compare
results for all AGN using different control samples. Black is for
control samples constructed by matching redshift, stellar mass,
stellar velocity dispersion and concentration, while red is for
control samples where the 4000\AA\-break strength is also matched.}
\label{fig:sig}
\end{figure*}
\begin{figure*}
\centerline{\psfig{figure=f7.ps,width=0.7\hdsize}}
\vspace{-6cm}
\caption{$w_p(r_p)$ in different $L$[L {\sc iii}]$/M_\bullet$ bins
(indicated above each panel), for all AGN (solid) and for control
samples of non-AGN (dashed). The small panels give the ratio between
the above two (black). The red lines are results where the
4000\AA-break strength is also matched when constructing control
samples.}
\label{fig:edd}
\end{figure*}
It is interesting to study how AGN clustering depends on black hole
mass and the strength of nuclear activity in the galaxy. As described
above, we use the stellar velocity dispersion as an indicator of the
black hole mass and divide all AGN into three subsamples according to
$\log_{10}\sigma_\ast$. We then use the ratio $L$[O {\sc
iii}]/M$_{BH}$ as a measure of the accretion rate relative to the
Eddington rate. We rank order all the AGN in a given interval of
stellar velocity dispersion according to $L$[O {\sc iii}]/M$_{BH}$ and
we define subsamples of ``powerful'' and ''weak'' AGN as those
contained within the upper and lower 25th percentiles of the
distribution of this quantity.
\begin{figure}
\centerline{\psfig{figure=f5.ps,width=\hssize}}
\vspace{-3.5cm}
\caption{Ratio of the $w_p(r_p)$ measurement of AGN to that of non-AGN
for 20 different non-AGN control samples. The yellow shaded region
shows the ratio of the $w_p(r_p)$ measurements of the different
non-AGN control samples relative to each other.}
\label{fig:ctrl_disp}
\end{figure}
The results are shown in Figure 6. Panels from left to right
correspond to different intervals of $\log_{10}\sigma_\ast$, as
indicated at the top of the figure. The first two rows show the
$w_p(r_p)$ measurements for the AGN and the corresponding control
samples. The third row shows the ratio between the two. Red (blue)
lines correspond to the powerful (weak) subsamples. Black lines show
results for the sample as a whole.
As mentioned previously, there are two sets of control samples: sample
1 is constructed by simultaneously matching redshift, stellar mass,
concentration and stellar velocity dispersion; sample 2 is constructed
by additionally matching the 4000\AA\ break strength. For clarity, the
main panels in in Figure 6 show the results only for sample 1. The
insets in the bottom row compare the ratio $ w_p^{\rm
AGN/ref}(r_p)/\bar{w}_p^{\rm contr/ref}(r_p)$ for the two control
samples (black corresponds to set 1 and red to set 2). The two
different control samples give very similar results on scales less
than a few Mpc, but the large-scale antibias is more pronounced for
sample 2 (note that this is also seen in Figure 2).
As can be seen, the ``dip'' in clustering on scales between 0.1 and 1
Mpc is most pronounced for AGN with the largest central stellar
velocity dispersions and the highest accretion rates. On scales
smaller than 0.1 Mpc, more powerful AGN appear be somewhat more
strongly clustered than weaker AGN and more strongly clustered than
galaxies in the control sample. The error bars on the measurements
are large, however, and effect is not of high significance. In Figure
7 we plot results for AGN of all velocity dispersions, but now in four
different intervals of $L$[O {\sc iii}]/M$_{BH}$, as indicated at the
top of the figure. Once again we see a marginal tendency for AGN with
higher values of $L$[O {\sc iii}]/M$_{BH}$ to be more strongly
clustered on small scales.
\subsection {Close Neighbour Counts}
\begin{figure*}
\centerline{\psfig{figure=f8.ps,width=0.8\hdsize}}
\caption{ Top: Average counts of galaxies in the photometric sample
($r_{lim} < 19$) within a given projected radius $R_p$ from the AGN
(red) and from the control galaxies (blue). Bottom: The difference
between the counts around the AGN and the control galaxies is plotted
as a function of $R_p$. The yellow bands indicate the variance in the
results between the 20 different control samples.}
\label{fig:counts_all}
\end{figure*}
\begin{figure*}
\centerline{\psfig{figure=f9.ps,width=\hdsize}}
\vspace{-12cm}
\caption{Same as the top panel of Fig.~\ref{fig:counts_all}, but for
four subsamples of AGN with different $L$[O {\sc iii}]$/M_\bullet$, as
indicated in each panel.}
\label{fig:counts_edd}
\end{figure*}
As we have discussed, one of the problems with computing the
galaxy-AGN cross- correlation function on very small physical scales
in the SDSS is that corrections for the effect of fibre collisions are
required. These corrections are statistical in nature and even if
they are correct on average, they may still introduce systematic
effects in our analysis. An alternative approach is to count the
number of galaxies in the vicinity of AGN in the photometric sample,
which is not affected by incompleteness. The disadvantage of using the
photometic sample is that many of the close neighbours will not be
truly nearby systems, but rather chance projections of foreground and
background galaxies that lie along the line-of-sight. We can make a
statistical correction for this by evaluating the counts around
randomly placed ``galaxies'' with the same assumed joint distribution
of apparent magnitude and redshift as the AGN (control) samples.
In the upper panel of Figure 8 we plot the average correlated
neighbour count (i.e. after statistical correction for uncorrelated
projected neighbours) within a given value of the projected radius
$R_p$ for the AGN sample (red) and the control samples (blue). The
lower panel and its insets show the difference betweeen the average
correlated counts for the AGN and control samples as a function of
$R_p$. The variance in the counts around the control galaxies
estimated from the 20 different control samples is shown in yellow.
The AGN sample has a $r$-band limiting magnitude of 17.6 and the
photomteric reference sample that we use is limited at $r$=19.0. In
order to ensure that we are counting similar neighbours at all
redshifts, the counts only include those galaxies with $r < r_{\rm
AGN} +1.4$ mag. In this analysis, the control sample is matched in
$r$-band {\em apparent} magnitude as well as redshift, stellar mass,
velocity dispersion and concentration. This ensures that we are
counting galaxies to the same limiting magnitude around both the AGN
and the control galaxies.
Figure 8 shows that the counts around the AGN and the control galaxies
match well on large scales. On small scales, there is a small but
significant excess in the number of neighbours around AGN out to
scales of $\sim 70$ kpc. As may be seen from the bottom panel of
Figure 8,
AGN are appromimately twice as likely to have a near neighbour
as galaxies in the control sample. This does not mean, however,
that every AGN has a close companion. Figure 8 also shows that only one in a
hundred AGN has an additional close ($R_p < 70$ kpc) neighbour as
compared to the control galaxies. On scales larger than 100 kpc, the
pair counts around the AGN dip below the counts around the control
samples, leading to the ``anti-bias'' discussed in the previous
section. This may be compensated on scales larger than several Mpc,
although such compensation is not required with our present statistics.
Figure 9 shows the counts around AGN in four different ranges of
L[OIII]/$M_{BH}$. As can be seen, the excess on small scales increases
as a function of the accretion rate onto the black hole. However, the
excess affects only a few percent of the AGN, even for the objects in
our highest L[OIII]/M$_{BH}$ bin. We note that \citet{serber06}
analyzed galaxy counts around quasars compared to $L_*$ galaxies at
the same redshift and found a clear excess on scales less than 100
kpc, very similar to the $\sim 70$ kpc scales where we see the upturn
in the counts around our sample of narrow-line AGN. Serber et
al also found that the excess was largest for the most luminous
quasars; the excess count reached values $\sim 1$ (i.e. significantly
larger than the excess found for the most powerful narrow-line AGN in
our sample) for quasars with $i$-band magnitudes brighter than $-24$.
If we use the relation between [OIII] line luminosity and quasar
continuum luminosity of \citet{zakamska03} to compare the AGN in our
sample to the quasars studied by Serber et al, we find that the
luminosities where quasars begin to exhibit a significant excess count
lie just beyond those of the AGN that populate our highest
L[OIII]/M$_{BH}$ bin.
Our conclusion, therefore, is that
we do not find strong evidence that interactions and mergers
are playing a significant
role in triggering the activity in typical AGN in the local Universe.
One caveat that should be mentioned is that if the activity is
triggered {\em after} the merger has already taken place,
our pair count statistics would not be a good diagnostic. In order to
assess this, more work is needed to assess whether AGN exhibit any evidence
for disturbed morphologies or stuctural peculiarities.
\section {Interpretion of AGN Clustering using Halo Occupation Models}
In the previous section we showed that the main difference in the
AGN-galaxy cross-correlation function with respect to that of a
closely matched control sample of non-AGN is that AGN are more weakly
clustered on scales between 100 kpc and 1 Mpc. On larger scales, there
is a much smaller difference in the clustering signal of AGN and
non-AGN. The clustering amplitude of AGN on large scales provides a
measure of the mass of the dark matter halos that host these
objects. The fact that there is only a small difference between the
AGN and the control sample tells us that AGN are found in roughly
similar dark matter halos to non-AGN with the same stellar masses and
structural properties.
\begin{figure}
\centerline{\psfig{figure=f10.ps,width=\hssize}}
\caption{ Top: The AGN/reference cross-correlation function calculated
from the mock catalogues is plotted as solid curves, while the
control/reference cross-correlations are plotted as dashed curves.
The different colours indicate models in which a given percentage (as
indicated on the plot) of the AGN are located at the centers of their
own dark matter halos. Bottom: The ratio between the AGN/reference
galaxy cross-correlation functions and the control galaxy/ reference
galaxy correlation functions are plotted for the same set of models.}
\label{fig:model}
\end{figure}
\begin{figure}
\centerline{\psfig{figure=f11.ps,width=\hssize}}
\caption{ Top: The AGN/reference cross-correlation function calculated
from the SDSS is plotted as solid circles. The open circles show the
control galaxy/reference galaxy cross-correlation function from the
SDSS. Results for AGN and control galaxies for our best-fit model are
plotted as solid and dashed red lines. Bottom: Solid circles show the
ratio $w^{\rm AGN/ref}(r_p)/w^{\rm control/ref}(r_p)$ for the SDSS
sample. The solid red curve shows the result for our best-fit
models. The error bars indicate the uncertainty due to cosmic variance
as estimated from 20 different mock catalogues (see text for more
details). The dashed red curves indicate the variance between
different control samples from different mock catalogues (see text).}
\label{fig:model_obs}
\end{figure}
The physical scales of 0.1-1 Mpc where we do see strong differences in
the clustering of AGN and non-AGN are similar to the virial diameters
of the dark matter halos that are expected to host galaxies with
luminosities of $\sim L_*$ \citep{mandelbaum06}. The simplest
interpretation of the AGN anti-bias on these scales, therefore, is
that AGN occupy preferred positions within their dark matter halos
where conditions are more favourable for continued fuelling of the
central black hole. One obvious preferred location would be the halo
centre where gas is expected to be able to reach high enough
overdensities to cool via radiative processes. In the main body of
the more massive dark matter halos, most of the surrounding gas will
have been shock heated to the virial temperature of the halo and will
no longer be able to cool efficiently. In addition, the vast majority
of galaxy-galaxy mergers within a halo will occur with the galaxy that
is located at the halo centre \citep{springel01}.
In this section, we use our mock catalogues to test whether a model in
which AGN are preferentially located at the centres of dark matter
halos can fit our observational results. As mentioned in section 2, we
have used the methodology introduced by \citet{wang06} to assign
stellar masses to the galaxies in the catalogues. These authors
adopted parametrized functions to relate galaxy properties such as
stellar mass to the quantity $M_{infall}$, defined as the mass of the
halo at the epoch where the galaxy was last the central dominant
object in its own halo. It was demonstrated that these parametrized
relations were able to provide an excellent fit to the basic
statistical properties of galaxies in the SDSS, including the stellar
mass function and the shape and amplitude of the two-point correlation
function function evaluated in different stellar mass ranges. We now
introduce a simple model in which $p_{AGN}$, the probability of a
galaxy to be an AGN depends only on whether it is the central galaxy
of its own halo.
In order to create mock AGN and control catalogues that we can compare
directly with the observational data, we follow the following
procedure. For every AGN in our sample, we select galaxies from the
mock catalogue that have the same stellar mass and the same redshift.
We then choose an AGN from among these galaxies based on whether they
are central or satellite systems. The control galaxies are selected
at random from the same set. The AGN and control samples are then
cross-correlated with a reference sample that is drawn from the mock
catalogue in exactly the same way as our real SDSS reference sample.
The top panel in Figure 10 shows how the AGN/reference galaxy
cross-correlation function changes as a function of the fraction of
AGN that are central galaxies. Note that if the probability of being
an AGN is {\em independent} of whether the galaxy is a central or a
satellite system, 73\% of the AGN will be central galaxies. The bottom
panel of Figure 10 shows how the ratio between the AGN and control
galaxy cross-correlation functions varies as this fraction changes.
As the fraction of centrally-located AGN increases, the ``dip'' on
scales smaller than 1 Mpc becomes more and more pronounced. There is
also a small decrease of the ratio $w^{\rm AGN/ref}(r_p)/w^{\rm
control/ref}(r_p)$ on large scales. The latter effect arises because,
as more and more AGN are required to be central galaxies in their own
halos, they also shift into lower mass halos. High mass halos are less
abundant than low mass halos and by definition, each halo can only
contain one central galaxy. As the central galaxy criterion on AGN
becomes more stringent, fewer AGN will reside in halos of
$10^{14}-10^{15} M_{\odot}$ and more in halos with $10^{12} -10^{13}
M_{\odot}$. The biggest effect, however, the dip on scales less than
1 Mpc, results from the fact that central galaxies in lower mass halos
have fewer neighbours than non-central galaxies within rich groups.
In Figure 11, we compare the results of our simple model with the
observational data. In the top panel, the solid and open circles show
the cross-correlation functions of the AGN and the control samples
respectively. The solid and dashed lines show our best-fit models, in
which 84\% of all AGN are located at the centres of their own dark
matter halos. In the bottom panel we compare the ratio of $w(r_p)$
for the observed AGN and control galaxies with that obtained for the
model. The error bars plotted on the model curve provide an estimate
of the uncertainty in the result due to {\em cosmic variance effects}.
In order to estimate these errors, we have created 20 different mock
catalogues by repositioning the virtual observer at random within the
simulation volume. For each mock catalogue, we repeat our
computations of the AGN and control galaxy cross-correlation
functions. The error bars are then calculated by looking at the
variance in the ratio $w^{\rm AGN/ref}(r_p)/w^{\rm control/ref}(r_p)$
for AGN and control galaxies selected from different catalogues. The
errors estimated in this way are similar in size to the errors
estimated by calculating the variance in $w^{\rm control/ref}(r_p)$
from different mock catalogues; these errors are indicated by the
dashed red lines in Figure 11. As can be seen, the model provides a
good fit to the observations from scales of $\sim 30$ kpc out to
scales beyond 10 Mpc. On scales smaller than 30 kpc, the AGN show a
small, but significant excess in clustering with respect to the model.
This is nicely in line with the results presented in the previous
section.
\section {Summary and Conclusions}
In this paper, we have analyzed the clustering of Type 2 narrow-line
AGN in the local Universe using data from the Sloan Digital Sky
Survey. The two physical questions we wish to address are, a) How do
the locations of galaxies within the large-scale distribution of dark
matter influence ongoing accretion onto their central black holes?
b)Is AGN activity triggered by interactions and mergers between
galaxies? To answer these questions, we analyze the scale-dependence
of the AGN/galaxy cross-correlation function relative to control
samples of non-AGN that are closely matched in stellar mass, redshift,
structural properties, and mean stellar age as measured by the 4000
\AA\ break strength. This close matching is important because
previous work has established that the clustering of galaxies depends
strongly on properties such as luminosity, stellar mass, colour,
spectral type, mean stellar age, concentration and stellar surface
mass density \citep{norberg02,zehavi02,zehavi05,li06}. Previous work
has also established that AGN are not a random subsample of the the
underlying galaxy population. Rather, they are found in massive,
bulge-dominated galaxies; powerful AGN tend to occur in galaxies with
smaller black holes and younger-than-average stellar populations for
their mass \citep{kauffmann03,heckman04}. If we wish to understand
whether there is a real physical connection between the location of a
galaxy and the accretion state of its central black hole, it is
important that we normalize out these zero'th order trends with galaxy
mass, structure and mean stellar age.
When we compare the clustering of AGN relative to carefully matched
control samples, and we take the errors due to cosmic variance into
account, we obtain the following results:
\begin {enumerate}
\item On scales larger than a few Mpc, the clustering amplitude of AGN
hosts does not differ significantly from that of similar but
inactive galaxies.
\item On scales between 100 kpc and 1 Mpc, AGN hosts are clustered
more weakly than control samples of similar but inactive
galaxies.
\item On scales less than 70 kpc, AGN cluster more strongly than
inactive galaxies, but the effect is weak. The excess number of
close companions is only one per hundred AGN.
\end {enumerate}
Our clustering results on large scales demonstrate that the host
galaxies of AGN are found in similar dark matter halos to inactive
galaxies with the same structural properties and stellar masses. We
have used mock catalogues constructed from high-resolution N-body
simulations to show that the AGN anti-bias on scales between 0.1 and 1
Mpc can be explained by AGN residing preferentially at the centres of
their dark matter halos. Our result on small scales indicates that
although interactions may be responsible for triggering AGN activity
in a minority of galaxies, an alternative mechanism is required to
explain the nuclear activity in the majority of these systems.
As we have already mentioned, it is easy to understand why dark matter
halo centres may be preferential places for ongoing growth of black
holes. These are the regions where gas would be expected to cool and
settle through radiative processes. In addition, dynamical friction
will erode the orbits of satellite galaxies within a dark matter halo
until they sink to the middle and merge with the central object. Both
these processes may bring fresh gas to the central galaxy and fuel
episodes of nuclear activity and black hole growth. As we have seen,
however, the evidence for an excess number of close neighbours around
AGN is rather weak, perhaps because in most cases the offending
satellite has already been swallowed. We also note that even the most
powerful AGN in our sample are less luminous than the quasars with
$M(i) < -24$ for which \citet{serber06} detected an excess number of
companions on small scales. What about the evidence for cooling?
Direct observational evidence for cooling from hot X-ray emitting gas
at the centers of dark matter halos has also been
elusive. \citet{benson00} used ROSAT PSPC data to seach for extended
X-ray emission from the halos of three nearby, massive spiral
galaxies. Their 95 percent upper limits on the bolometric X-ray
luminosities of the halos show that the present day accretion from any
hot virialized gas surrounding the galaxies is very small. Recently
\citet{pedersen06} detected a gaseous halo aroung the quiescent spiral
NGC 5746 using Chandra observations, but this remains the only spiral
galaxy with evidence for ongoing accretion from an extended reservoir
of hot gas. In clusters, X-ray spectroscopy has shown that most of
the gas gas does not manage to cool below $10^7$ K
\citep[e.g.][]{david01,peterson01}.
Gas accretion in the form of cold HI-emitting clouds is, however, much
less well-constrained. In recent work, \citet{kauffmann06} studied a
volume-limited sample of bulge-dominated galaxies with data both from
the Sloan Digital Sky Survey and from the Galaxy Evolution Explorer
(GALEX) satellite. Almost all galaxies with bluer-than-average
NUV-$r$ colours were found to be AGN. By analyzing GALEX images,
these authors demonstrated that the excess UV light is nearly always
associated with an extended disk. They then went on to study the
relation between the UV-bright outer disk and the nuclear activity in
these galaxies. The data indicate that the presence of the UV-bright
disk is a necessary but not sufficient condition for strong AGN
activity in a galaxy. They suggest that the disk provides a reservoir
of fuel for the black hole. From time to time, some event transports
gas to the nucleus, thereby triggering the observed AGN activity.
The GALEX results indicate that the extended disks of galaxies play an
important role in the fuelling of AGN. The clustering results from the
SDSS indicate that AGN are preferentially located at the centres of
dark matter halos. In theoretical models, rotationally supported
disks are {\em expected} to form at the centers of dark matter halos
\citep{mmw98}. After the galaxy is accreted by more massive halos and
becomes a satellite system, the disks may lose their gas via processes
such as ram-pressure stripping \citep[e.g.][]{cayatte94}. Disks
located at halo centres are likely likely to survive for longer
periods. Dynamical perturbations driven by the dark mattter near the
centres of the halos may result in gas inflows and fuelling of the
central black hole \citep[see][for a recent discussion]{gw06}.
Further progress in understanding the AGN phenomenon in the local
Universe will require detailed modelling of the observable components
of galaxies within evolving dark matter halos, as well as further
investigation of the connection between AGN activity and phenomena
such as bars, warps, lopsided images, and asymmetric rotation curves.
\section*{Acknowledgments}
We thank the referee for helpful comments.
CL acknowledges the financial support by the exchange program between
Chinese Academy of Sciences and the Max Planck Society.
The Millennium Run simulation used in this paper was carried out by the
Virgo Supercomputing Consortium at the Computing Centre of the Max-Planck
Society in Garching. The semi-analytic galaxy catalogue is publicly
available at http://www.mpa-garching.mpg.de/galform/agnpaper
Funding for the SDSS and SDSS-II has been provided by the Alfred P.
Sloan Foundation, the Participating Institutions, the National Science
Foundation, the U.S. Department of Energy, the National Aeronautics
and Space Administration, the Japanese Monbukagakusho, the Max Planck
Society, and the Higher Education Funding Council for England. The
SDSS Web Site is http://www.sdss.org/. The SDSS is managed by the
Astrophysical Research Consortium for the Participating
Institutions. The Participating Institutions are the American Museum
of Natural History, Astrophysical Institute Potsdam, University of
Basel, Cambridge University, Case Western Reserve University,
University of Chicago, Drexel University, Fermilab, the Institute for
Advanced Study, the Japan Participation Group, Johns Hopkins
University, the Joint Institute for Nuclear Astrophysics, the Kavli
Institute for Particle Astrophysics and Cosmology, the Korean
Scientist Group, the Chinese Academy of Sciences (LAMOST), Los Alamos
National Laboratory, the Max-Planck-Institute for Astronomy (MPIA),
the Max-Planck-Institute for Astrophysics (MPA), New Mexico State
University, Ohio State University, University of Pittsburgh,
University of Portsmouth, Princeton University, the United States
Naval Observatory, and the University of Washington.
| {
"redpajama_set_name": "RedPajamaArXiv"
} | 8,215 |
Hieronder een lijst van de stations van de metro van Charkov met lijnkleur, openingsdatum en overstapmogelijkheden. Het metronet van de Oekraïense stad Charkov telt 28 stations, alle ondergronds. De drie overstappunten tussen de verschillende lijnen hebben elk twee namen, aangezien de stationsnaam per lijn verschilt; dit systeem is gebruikelijk in de gehele voormalige Sovjet-Unie.
Deze lijst vermeldt de officiële, Oekraïenstalige namen. Charkov is echter een overwegend Russischtalige stad, waardoor de Russische namen in de praktijk meer gebruikt worden en ook in veel stations (nog) Russischtalige aanduidingen te vinden zijn.
Charkov | {
"redpajama_set_name": "RedPajamaWikipedia"
} | 3,045 |
Here is a copy of the Helmar design team call post. Check out this amazing team that I have had the honor of being a part of for the last 6 months!
*Endorsement fees for published layouts and projects!
*Payment for projects used for trade shows!
The latest & greatest products from our Preferred Vendors (USA)!
Dedication to a minimum of (2) blog posts per month. More are LOVELY!
Dedication to your personal blogs which means keeping them fresh and mentioning Helmar products (we will do our best to promote you personally as well which is a win-win for everyone). Keeping them fresh and new is important.
Involvement with social networking sites such as Facebook and Twitter. Facebook at minimum is required. This is the future for the industry and plays an even bigger part now than publications.
Dedication to our preferred vendors. They treat us great! We work very hard to secure those relationships.
Optional...Teaching experience. We are expanding our marketing efforts and the best way to do this is by demonstration and teaching.
Another great plus is video tutorials.....and step-by-step projects or kits featuring Helmar products.
Members are asked to submit their monthly Helmar projects for possible publication in crafting magazines and idea books.
Members will also complete special projects as requested by Helmar to be used for trade shows, catalogs, promotional items, and various other venues.
Name, address, daytime & evening phone numbers, and email address (USA, Canadian, Australian & New Zealand applicants only, please due to shipping constraints). Current and prior Design Team Members welcome to apply!
Please indicate if you are applying to be a Design Team Member or Educator.
List of other design teams in which you are currently or were previously a member. NOTE: Members are encouraged to be on other design teams (except for competing adhesive companies) and partner their products with Helmar Adhesives & Art Mediums.
A brief paragraph stating why you would like to be a member of our Design Team.
Three example projects (layouts, altered projects paper crafting projects, etc.) no larger than 150k each – Make sure to list any special adhesive techniques used and list the Helmar products. NOTE: You are not required to use Helmar adhesives for your application however, that is preferred so we see how creative you are with our products.
Anything else you want us to know about you…..what sets you apart from the rest? We want to see your enthusiasm!
Optional: Please provide Links to your YouTube or Ustream page including a link to a video showing your demonstration or teaching techniques. Please do not send the video in your email (only a link).
Please submit the above information to info@helmarusa.com by October 26, 2011. No late entries will be accepted. The new Design Team members will be announced on our website.
Tracy WeinzapfelPresident, Helmar USA, Inc."
You can do it!!!! Go for it! I would love to see you on this team!!!!
Ok I am going to give it a shot. | {
"redpajama_set_name": "RedPajamaC4"
} | 9,785 |
#include "EditorEngine.h"
#include <vxEngineLib/Message.h>
#include <vxEngineLib/MessageTypes.h>
#include <vxEngineLib/Locator.h>
#include <vxEngineLib/EditorMeshInstance.h>
#include <vxEngineLib/Ray.h>
#include <vxEngineLib/EditorScene.h>
#include <vxEngineLib/Graphics/Light.h>
#include <vxEngineLib/NavMeshGraph.h>
#include <vxEngineLib/EngineConfig.h>
#include <vxEngineLib/debugPrint.h>
#include "developer.h"
#include <vxEngineLib/FileMessage.h>
#include <vxEngineLib/Reference.h>
#include <vxEngineLib/Material.h>
#include <vxEngineLib/Spawn.h>
#include <vxEngineLib/Actor.h>
#include "EngineGlobals.h"
#include <vxLib/Graphics/Camera.h>
#include <vxEngineLib/MeshFile.h>
#include <vxEngineLib/Joint.h>
#include <vxEngineLib/FileEntry.h>
#include <vxEngineLib/ActorFile.h>
#include <vxEngineLib/Graphics/LightGeometryProxy.h>
#include <Dbghelp.h>
u32 g_editorTypeMesh{ 0xffffffff };
u32 g_editorTypeMaterial{ 0xffffffff };
u32 g_editorTypeScene{ 0xffffffff };
u32 g_editorTypeFbx{ 0xffffffff };
u32 g_editorTypeAnimation{ 0xffffffff };
u32 g_editorTypeActor{ 0xffffffff };
namespace EditorEngineCpp
{
void schedulerThread(vx::TaskManager* scheduler)
{
std::atomic_uint running;
running.store(1);
scheduler->initializeThread(&running);
while (running.load() != 0)
{
scheduler->swapBuffer();
scheduler->update();
}
}
}
EditorEngine::EditorEngine()
:m_msgManager(),
m_physicsAspect(),
m_renderAspect(),
m_resourceAspect(),
m_navmeshGraph(),
m_previousSceneLoaded(false)
{
}
EditorEngine::~EditorEngine()
{
if (m_shutdown == 0)
{
// something bad happened
assert(false);
}
}
bool EditorEngine::initializeImpl(const std::string &dataDir, bool flipTextures)
{
m_memory = Memory(g_totalMemory, 64);
m_allocator = vx::StackAllocator(m_memory.get(), m_memory.size());
m_scratchAllocator = vx::StackAllocator(m_allocator.allocate(1 MBYTE, 64), 1 MBYTE);
m_msgManager.initialize(&m_allocator, 256);
//if (!m_resourceAspect.initialize(&m_allocator, dataDir, &m_msgManager, m_physicsAspect.getCooking()))
if (!m_resourceAspect.initialize(&m_allocator, dataDir, m_physicsAspect.getCooking(), &m_taskManager, &m_msgManager, flipTextures, true))
return false;
Locator::provide(&m_resourceAspect);
return true;
}
bool EditorEngine::createRenderAspectGL(const std::string &dataDir, const RenderAspectDescription &desc, AbortSignalHandlerFun signalHandlerFn)
{
auto handle = LoadLibrary(L"../../../lib/vxRenderAspectGL_d.dll");
if (handle == nullptr)
return false;
auto proc = (CreateEditorRenderAspectFunction)GetProcAddress(handle, "createEditorRenderAspect");
auto procDestroy = (DestroyEditorRenderAspectFunction)GetProcAddress(handle, "destroyEditorRenderAspect");
if (proc == nullptr || procDestroy == nullptr)
return false;
auto renderAspect = proc();
if (renderAspect == nullptr)
return false;
m_renderAspect = renderAspect;
m_renderAspectDll = handle;
m_destroyFn = procDestroy;
return true;
}
bool EditorEngine::initializeEditor(HWND panel, HWND tmp, const vx::uint2 &resolution, AbortSignalHandlerFun signalHandlerFn, Editor::Scene* pScene, Logfile* logfile)
{
vx::activateChannel(vx::debugPrint::Channel_Render);
vx::activateChannel(vx::debugPrint::Channel_Editor);
vx::activateChannel(vx::debugPrint::Channel_FileAspect);
vx::debugPrint::g_verbosity = 1;
const std::string dataDir("../../data/");
m_pEditorScene = pScene;
m_resolution = resolution;
m_panel = panel;
if (!m_physicsAspect.initialize(&m_taskManager))
{
return false;
}
g_engineConfig.m_fovDeg = 66.0f;
g_engineConfig.m_zFar = 250.0f;
g_engineConfig.m_renderDebug = true;
g_engineConfig.m_resolution = resolution;
g_engineConfig.m_vsync = false;
g_engineConfig.m_zNear = 0.1f;
g_engineConfig.m_editor = true;
g_engineConfig.m_rendererSettings.m_renderMode = Graphics::RendererSettings::Mode_GL;
g_engineConfig.m_rendererSettings.m_shadowMode = 0;
g_engineConfig.m_rendererSettings.m_voxelGIMode = 0;
g_engineConfig.m_rendererSettings.m_maxMeshInstances = 150;
g_engineConfig.m_rendererSettings.m_voxelSettings.m_voxelGridDim = 16;
g_engineConfig.m_rendererSettings.m_voxelSettings.m_voxelTextureSize = 128;
bool flipTextures = (g_engineConfig.m_rendererSettings.m_renderMode == Graphics::RendererSettings::Mode_GL);
if (!initializeImpl(dataDir, flipTextures))
return false;
m_taskManager.initialize(2, 10, 30.0f, &m_allocator);
m_taskManagerThread = std::thread(EditorEngineCpp::schedulerThread, &m_taskManager);
RenderAspectDescription renderAspectDesc =
{
dataDir,
panel,
tmp,
&m_allocator,
&g_engineConfig,
logfile,
nullptr,
&m_resourceAspect,
&m_msgManager,
&m_taskManager
};
//renderAspectDesc.hwnd = m_panel;
if (!createRenderAspectGL(dataDir, renderAspectDesc, signalHandlerFn))
{
return false;
}
if (m_renderAspect->initialize(renderAspectDesc, signalHandlerFn) != RenderAspectInitializeError::OK)
{
return false;
}
//dev::g_debugRenderSettings.setVoxelize(0);
//dev::g_debugRenderSettings.setShadingMode(ShadingMode::Albedo);
//m_renderAspect->queueUpdateTask(task);
Locator::provide(&m_physicsAspect);
m_msgManager.initialize(&m_allocator, 255);
m_msgManager.registerListener(m_renderAspect, 1, (u8)vx::MessageType::File | (u8)vx::MessageType::Renderer);
m_msgManager.registerListener(&m_physicsAspect, 1, (u8)vx::MessageType::File);
m_msgManager.registerListener(this, 1, (u8)vx::MessageType::File);
//m_bRun = 1;
m_shutdown = 0;
memset(&m_selected, 0, sizeof(m_selected));
return true;
}
void EditorEngine::shutdownEditor()
{
if (m_taskManagerThread.joinable())
m_taskManagerThread.join();
m_taskManager.shutdown();
m_resourceAspect.shutdown();
m_physicsAspect.shutdown();
if (m_renderAspect)
{
m_renderAspect->shutdown(m_panel);
m_destroyFn(m_renderAspect);
m_renderAspect = nullptr;
}
m_panel = nullptr;
m_shutdown = 1;
m_allocator.release();
}
void EditorEngine::stop()
{
m_taskManager.stop();
}
void EditorEngine::buildNavGraph()
{
auto &navMesh = m_pEditorScene->getNavMesh();
m_influenceMap.initialize(navMesh, m_pEditorScene->getWaypoints(), m_pEditorScene->getWaypointCount());
m_navmeshGraph.initialize(navMesh);
m_renderAspect->updateInfluenceCellBuffer(m_influenceMap);
m_renderAspect->updateNavMeshGraphNodesBuffer(m_navmeshGraph);
}
void EditorEngine::handleMessage(const vx::Message &evt)
{
switch (evt.type)
{
case(vx::MessageType::File) :
handleFileEvent(evt);
break;
default:
break;
}
}
void EditorEngine::handleFileEvent(const vx::Message &evt)
{
auto fe = (vx::FileMessage)evt.code;
switch (fe)
{
case vx::FileMessage::Mesh_Loaded:
{
auto sid = vx::StringID(evt.arg1.u64);
auto pStr = reinterpret_cast<std::string*>(evt.arg2.ptr);
if (call_editorCallback(sid))
{
vx::verboseChannelPrintF(0, vx::debugPrint::Channel_Editor, "Loaded mesh %llu %s", sid.value, pStr->c_str());
auto meshFile = m_resourceAspect.getMesh(sid);
m_pEditorScene->addMesh(sid, pStr->c_str(), meshFile);
}
delete(pStr);
}break;
case vx::FileMessage::Texture_Loaded:
break;
case vx::FileMessage::Material_Loaded:
{
auto sid = vx::StringID(evt.arg1.u64);
auto pStr = reinterpret_cast<std::string*>(evt.arg2.ptr);
if (call_editorCallback(sid))
{
vx::verboseChannelPrintF(0, vx::debugPrint::Channel_Editor, "Loaded material %llu %s", sid.value, pStr->c_str());
Material* material = m_resourceAspect.getMaterial(sid);
m_pEditorScene->addMaterial(sid, pStr->c_str(), material);
}
delete(pStr);
}break;
case vx::FileMessage::EditorScene_Loaded:
{
vx::verboseChannelPrintF(0, vx::debugPrint::Channel_Editor, "Loaded Scene");
call_editorCallback(vx::StringID(evt.arg1.u64));
buildNavGraph();
auto &sortedInstances = m_pEditorScene->getSortedMeshInstances();
m_renderAspect->updateWaypoints(m_pEditorScene->getWaypoints(), m_pEditorScene->getWaypointCount());
m_renderAspect->updateJoints(m_pEditorScene->getJoints(), m_pEditorScene->getJointCount(), sortedInstances);
m_renderAspect->updateSpawns(m_pEditorScene->getSpawns(), m_pEditorScene->getSpawnCount());
m_renderAspect->updateLightGeometryProxies(m_pEditorScene->getLightGeometryProxies(), m_pEditorScene->getLightGeometryProxyCount());
}break;
case vx::FileMessage::Animation_Loaded:
{
auto sid = vx::StringID(evt.arg1.u64);
if (evt.arg2.ptr)
{
auto pStr = reinterpret_cast<std::string*>(evt.arg2.ptr);
vx::verboseChannelPrintF(0, vx::debugPrint::Channel_Editor, "Loaded Animation %llu", sid.value);
call_editorCallback(sid);
m_pEditorScene->addAnimation(sid, std::move(*pStr));
}
else
{
VX_ASSERT(false);
//auto str = m_resourceAspect.getAnimationName(sid);
//if (str)
// m_pEditorScene->addAnimation(sid, std::move(std::string(str)));
}
}break;
case vx::FileMessage::Actor_Loaded:
{
auto sid = vx::StringID(evt.arg1.u64);
auto pStr = reinterpret_cast<std::string*>(evt.arg2.ptr);
call_editorCallback(sid);
delete(pStr);
}break;
default:
{
}break;
}
}
void EditorEngine::requestLoadFile(const vx::FileEntry &fileEntry, vx::Variant arg)
{
m_resourceAspect.requestLoadFile(fileEntry, arg);
}
void EditorEngine::editor_saveScene(const char* name)
{
auto sceneCopy = new Editor::Scene();
m_pEditorScene->copy(sceneCopy);
vx::Variant arg;
arg.ptr = sceneCopy;
m_resourceAspect.requestSaveFile(vx::FileEntry(name, vx::FileType::EditorScene), arg);
}
void EditorEngine::editor_setTypes(u32 mesh, u32 material, u32 scene, u32 fbx, u32 typeAnimation, u32 typeActor)
{
g_editorTypeMesh = mesh;
g_editorTypeMaterial = material;
g_editorTypeScene = scene;
g_editorTypeFbx = fbx;
g_editorTypeAnimation = typeAnimation;
g_editorTypeActor = typeActor;
}
void EditorEngine::update(f32 dt)
{
m_msgManager.update();
//m_physicsAspect.update(1.0f/30.f);
//m_physicsAspect.fetch();
m_resourceAspect.update();
m_renderAspect->update();
m_renderAspect->buildCommands();
m_renderAspect->submitCommands();
m_renderAspect->wait();
m_renderAspect->swapBuffers();
}
void EditorEngine::editor_loadFile(const char *filename, u32 type, Editor::LoadFileCallback f, vx::Variant userArg)
{
vx::Variant arg;
arg.ptr = nullptr;
vx::FileEntry fileEntry;
if (type == g_editorTypeMesh)
{
fileEntry = vx::FileEntry(filename, vx::FileType::Mesh);
arg.ptr = new std::string(filename);
vx::verboseChannelPrintF(0, vx::debugPrint::Channel_Editor, "Trying to load mesh %llu '%s'", fileEntry.getSid().value, filename);
}
else if (type == g_editorTypeMaterial)
{
fileEntry = vx::FileEntry(filename, vx::FileType::Material);
arg.ptr = new std::string(filename);
vx::verboseChannelPrintF(0, vx::debugPrint::Channel_Editor, "Trying to load material %llu '%s'", fileEntry.getSid().value, filename);
}
else if (type == g_editorTypeScene)
{
fileEntry = vx::FileEntry(filename, vx::FileType::EditorScene);
if (m_previousSceneLoaded)
{
VX_ASSERT(false);
}
arg.ptr = m_pEditorScene;
}
else if (type == g_editorTypeFbx)
{
fileEntry = vx::FileEntry(filename, vx::FileType::Fbx);
arg.u32 = 0;
//p = new std::string(filename);
}
else if (type == g_editorTypeAnimation)
{
fileEntry = vx::FileEntry(filename, vx::FileType::Animation);
arg.ptr = new std::string(filename);
}
else if (type == g_editorTypeActor)
{
fileEntry = vx::FileEntry(filename, vx::FileType::Actor);
arg.ptr = new std::string(filename);
}
else
{
vx::verboseChannelPrintF(0, vx::debugPrint::Channel_Editor, "Trying to load unknown file type");
//assert(false);
}
vx::lock_guard<vx::mutex> guard(m_editorMutex);
m_requestedFiles.insert(fileEntry.getSid(), std::make_pair(f, type));
m_resourceAspect.requestLoadFile(fileEntry, arg);
}
void EditorEngine::editor_moveCamera(f32 dirX, f32 dirY, f32 dirZ)
{
m_renderAspect->moveCamera(dirX, dirY, dirZ);
}
void EditorEngine::editor_rotateCamera(f32 dirX, f32 dirY, f32)
{
static f32 x = 0.0f;
static f32 y = 0.0f;
x += dirX * 0.01f;
y += dirY * 0.01f;
vx::float4a rot(y, x, 0, 0);
auto v = vx::quaternionRotationRollPitchYawFromVector(rot);
m_renderAspect->rotateCamera(v);
}
bool EditorEngine::call_editorCallback(const vx::StringID &sid)
{
bool result = false;
vx::lock_guard<vx::mutex> guard(m_editorMutex);
auto it = m_requestedFiles.find(sid);
if (it != m_requestedFiles.end())
{
(*it->first)(sid.value, it->second);
m_requestedFiles.erase(it);
result = true;
}
return result;
}
vx::float4a EditorEngine::getRayDir(s32 mouseX, s32 mouseY) const
{
f32 ndc_x = f32(mouseX) / m_resolution.x;
f32 ndc_y = f32(mouseY) / m_resolution.y;
ndc_x = ndc_x * 2.0f - 1.0f;
ndc_y = 1.0f - ndc_y * 2.0f;
vx::mat4 projMatrix;
m_renderAspect->getProjectionMatrix(&projMatrix);
auto invProjMatrix = vx::MatrixInverse(projMatrix);
vx::float4a ray_clip(ndc_x, ndc_y, -1, 1);
vx::float4a ray_eye = vx::Vector4Transform(invProjMatrix, ray_clip);
ray_eye.z = -1.0f;
ray_eye.w = 0.0f;
vx::mat4 viewMatrix;
m_renderAspect->getViewMatrix(&viewMatrix);
auto inverseViewMatrix = vx::MatrixInverse(viewMatrix);
vx::float4a ray_world = vx::Vector4Transform(inverseViewMatrix, ray_eye);
ray_world = vx::normalize3(ray_world);
return ray_world;
}
vx::StringID EditorEngine::raytraceAgainstStaticMeshes(s32 mouseX, s32 mouseY, vx::float3* hitPosition) const
{
auto ray_world = getRayDir(mouseX, mouseY);
vx::float4a cameraPosition;
m_renderAspect->getCameraPosition(&cameraPosition);
PhysicsHitData hitData;
vx::StringID sid;
if (m_physicsAspect.raycast_staticDynamic(cameraPosition, ray_world, 50.0f, &hitData))
{
*hitPosition = hitData.hitPosition;
sid = hitData.sid;
}
return sid;
}
u32 EditorEngine::getMeshInstanceCount() const
{
u32 result = 0;
if (m_pEditorScene)
{
result = m_pEditorScene->getMeshInstanceCount();
}
return result;
}
const char* EditorEngine::getMeshInstanceName(u32 i) const
{
auto meshInstances = m_pEditorScene->getMeshInstancesEditor();
auto sid = meshInstances[i].getNameSid();
return getMeshInstanceName(sid);
}
const char* EditorEngine::getMeshInstanceName(const vx::StringID &sid) const
{
return m_pEditorScene->getMeshInstanceName(sid);
}
u64 EditorEngine::getMeshInstanceSid(u32 i) const
{
u64 sidValue = 0;
if (m_pEditorScene)
{
auto meshInstances = m_pEditorScene->getMeshInstancesEditor();
sidValue = meshInstances[i].getNameSid().value;
}
return sidValue;
}
u64 EditorEngine::getMeshInstanceSid(s32 mouseX, s32 mouseY) const
{
u64 result = 0;
if (m_pEditorScene)
{
vx::float3 p;
auto sid = raytraceAgainstStaticMeshes(mouseX, mouseY, &p);
result = sid.value;
}
return result;
}
const char* EditorEngine::getSelectedMeshInstanceName() const
{
auto meshInstance = (MeshInstance*)m_selected.m_item;
const char* name = nullptr;
if (meshInstance)
{
name = m_pEditorScene->getMeshInstanceName(meshInstance->getNameSid());
}
return name;
}
void EditorEngine::setSelectedMeshInstance(u64 sid)
{
if (sid != 0)
{
auto instance = m_pEditorScene->getMeshInstance(vx::StringID(sid));
if (instance)
{
m_renderAspect->setSelectedMeshInstance(instance);
m_selected.m_type = SelectedType::MeshInstance;
m_selected.m_item = (void*)instance;
}
}
}
u64 EditorEngine::getSelectedMeshInstanceSid() const
{
u64 sidValue = 0;
auto meshInstance = (MeshInstance*)m_selected.m_item;
if (meshInstance)
{
sidValue = meshInstance->getNameSid().value;
}
return sidValue;
}
u64 EditorEngine::getMeshInstanceMeshSid(u64 instanceSid) const
{
u64 sidValue = 0;
auto meshInstance = m_pEditorScene->getMeshInstance(vx::StringID(instanceSid));
if (meshInstance != nullptr)
{
sidValue = meshInstance->getMeshSid().value;
}
return sidValue;
}
void EditorEngine::setMeshInstanceMeshSid(u64 instanceSid, u64 meshSid)
{
auto meshInstance = m_pEditorScene->getMeshInstance(vx::StringID(instanceSid));
if (meshInstance != nullptr)
{
auto mesh = m_pEditorScene->getMesh(vx::StringID(meshSid));
m_renderAspect->setMeshInstanceMesh(vx::StringID(instanceSid), vx::StringID(meshSid));
meshInstance->setMeshSid(vx::StringID(meshSid));
meshInstance->setBounds(mesh->getMesh());
m_physicsAspect.editorSetStaticMeshInstanceMesh(meshInstance->getMeshInstance());
}
}
u64 EditorEngine::getMeshInstanceMaterialSid(u64 instanceSid) const
{
u64 sidValue = 0;
auto sid = vx::StringID(instanceSid);
auto meshInstance = m_pEditorScene->getMeshInstance(sid);
if (meshInstance)
{
auto material = meshInstance->getMaterial();
sidValue = (*material).getSid().value;
}
return sidValue;
}
void EditorEngine::getMeshInstancePosition(u64 sid, vx::float3* position)
{
auto instance = m_pEditorScene->getMeshInstance(vx::StringID(sid));
auto &transform = instance->getTransform();
*position = transform.m_translation;
}
u64 EditorEngine::deselectMeshInstance()
{
u64 result = 0;
if (m_pEditorScene)
{
auto selectedInstance = (Editor::MeshInstance*)m_selected.m_item;
if (selectedInstance)
{
result = selectedInstance->getNameSid().value;
m_renderAspect->setSelectedMeshInstance(nullptr);
m_selected.m_item = nullptr;
}
}
return result;
}
vx::StringID EditorEngine::createMeshInstance()
{
auto instanceSid = m_pEditorScene->createMeshInstance();
auto instance = m_pEditorScene->getMeshInstance(instanceSid);
m_physicsAspect.addMeshInstance(instance->getMeshInstance());
m_renderAspect->addMeshInstance(*instance);
return instanceSid;
}
void EditorEngine::removeMeshInstance(u64 sid)
{
if (m_pEditorScene)
{
m_pEditorScene->removeMeshInstance(vx::StringID(sid));
m_renderAspect->removeMeshInstance(vx::StringID(sid));
}
}
void EditorEngine::setMeshInstanceMaterial(u64 instanceSid, u64 materialSid)
{
if (m_pEditorScene)
{
auto meshInstance = m_pEditorScene->getMeshInstance(vx::StringID(instanceSid));
auto sceneMaterial = m_pEditorScene->getMaterial(vx::StringID(materialSid));
if (sceneMaterial != nullptr)
{
if (m_renderAspect->setSelectedMeshInstanceMaterial(sceneMaterial))
{
meshInstance->setMaterial(sceneMaterial);
}
}
}
}
void EditorEngine::setMeshInstancePosition(u64 sid, const vx::float3 &p)
{
if (m_pEditorScene)
{
auto instanceSid = vx::StringID(sid);
m_pEditorScene->setMeshInstancePosition(instanceSid, p);
auto instance = m_pEditorScene->getMeshInstance(instanceSid);
auto transform = instance->getTransform();
m_renderAspect->setSelectedMeshInstanceTransform(transform);
m_physicsAspect.editorSetStaticMeshInstanceTransform(instance->getMeshInstance(), instanceSid);
}
}
void EditorEngine::setMeshInstanceRotation(u64 sid, const vx::float3 &rotationDeg)
{
if (m_pEditorScene)
{
auto rotation = vx::degToRad(rotationDeg);
auto r = vx::loadFloat3(&rotation);
auto q = vx::quaternionRotationRollPitchYawFromVector(r);
vx::float4 tmp;
vx::storeFloat4(&tmp, q);
auto instanceSid = vx::StringID(sid);
m_pEditorScene->setMeshInstanceRotation(instanceSid, tmp);
auto instance = m_pEditorScene->getMeshInstance(instanceSid);
auto transform = instance->getTransform();
m_renderAspect->setSelectedMeshInstanceTransform(transform);
m_physicsAspect.editorSetStaticMeshInstanceTransform(instance->getMeshInstance(), instanceSid);
}
}
void EditorEngine::getMeshInstanceRotation(u64 sid, vx::float3* rotationDeg) const
{
if (m_pEditorScene)
{
auto instanceSid = vx::StringID(sid);
auto instance = m_pEditorScene->getMeshInstance(instanceSid);
auto transform = instance->getTransform();
auto q = transform.m_qRotation;
__m128 axis;
f32 angle;
vx::quaternionToAxisAngle(vx::loadFloat4(&q), &axis, &angle);
axis = vx::normalize3(axis);
vx::float4a tmpAxis = axis;
vx::angleAxisToEuler(tmpAxis, angle, rotationDeg);
}
}
bool EditorEngine::setMeshInstanceName(u64 sid, const char* name)
{
bool result = false;
if (m_pEditorScene)
{
auto meshInstance = (MeshInstance*)m_selected.m_item;
result = m_pEditorScene->renameMeshInstance(vx::StringID(sid), name);
}
return result;
}
bool EditorEngine::addNavMeshVertex(s32 mouseX, s32 mouseY, vx::float3* position)
{
vx::float3 hitPos;
auto sid = raytraceAgainstStaticMeshes(mouseX, mouseY, &hitPos);
if (sid.value != 0)
{
auto ptr = m_pEditorScene->getMeshInstance(sid);
auto &navMesh = m_pEditorScene->getNavMesh();
navMesh.addVertex(hitPos);
m_renderAspect->updateNavMeshBuffer(navMesh);
*position = hitPos;
}
return sid.value != 0;
}
void EditorEngine::removeNavMeshVertex(const vx::float3 &position)
{
if (m_pEditorScene)
{
auto &navMesh = m_pEditorScene->getNavMesh();
navMesh.removeVertex(position);
buildNavGraph();
m_renderAspect->updateNavMeshBuffer(navMesh);
}
}
void EditorEngine::removeSelectedNavMeshVertex()
{
if (m_selected.m_navMeshVertices.m_count != 0)
{
auto index = m_selected.m_navMeshVertices.m_vertices[0];
auto &navMesh = m_pEditorScene->getNavMesh();
navMesh.removeVertex(index);
m_renderAspect->updateNavMeshBuffer(navMesh);
}
}
Ray EditorEngine::getRay(s32 mouseX, s32 mouseY)
{
auto rayDir = getRayDir(mouseX, mouseY);
vx::float4a cameraPosition;
m_renderAspect->getCameraPosition(&cameraPosition);
Ray ray;
ray.o.x = static_cast<f32>(cameraPosition.x);
ray.o.y = static_cast<f32>(cameraPosition.y);
ray.o.z = static_cast<f32>(cameraPosition.z);
//vx::storeFloat3(&ray.o, cameraPosition);
vx::storeFloat3(&ray.d, rayDir);
ray.maxt = 50.0f;
return ray;
}
u32 EditorEngine::getSelectedNavMeshVertex(s32 mouseX, s32 mouseY)
{
auto ray = getRay(mouseX, mouseY);
auto &navMesh = m_pEditorScene->getNavMesh();
return navMesh.testRayAgainstVertices(ray);
}
bool EditorEngine::selectNavMeshVertex(s32 mouseX, s32 mouseY)
{
bool result = false;
if (m_pEditorScene)
{
auto selectedIndex = getSelectedNavMeshVertex(mouseX, mouseY);
if (selectedIndex != 0xffffffff)
{
auto &navMesh = m_pEditorScene->getNavMesh();
m_selected.m_navMeshVertices.m_vertices[0] = selectedIndex;
m_selected.m_navMeshVertices.m_count = 1;
m_selected.m_type = SelectedType::NavMeshVertex;
m_renderAspect->updateNavMeshBuffer(navMesh, m_selected.m_navMeshVertices.m_vertices, m_selected.m_navMeshVertices.m_count);
result = true;
}
}
return result;
}
bool EditorEngine::selectNavMeshVertexIndex(u32 index)
{
bool result = false;
if (m_pEditorScene)
{
auto &navMesh = m_pEditorScene->getNavMesh();
m_selected.m_navMeshVertices.m_vertices[0] = index;
m_selected.m_navMeshVertices.m_count = 1;
m_selected.m_type = SelectedType::NavMeshVertex;
m_renderAspect->updateNavMeshBuffer(navMesh, m_selected.m_navMeshVertices.m_vertices, m_selected.m_navMeshVertices.m_count);
result = true;
}
return result;
}
bool EditorEngine::selectNavMeshVertexPosition(const vx::float3 &position)
{
bool result = false;
if (m_pEditorScene)
{
auto &navMesh = m_pEditorScene->getNavMesh();
u32 index = 0;
if (navMesh.getIndex(position, &index))
{
m_selected.m_navMeshVertices.m_vertices[0] = index;
m_selected.m_navMeshVertices.m_count = 1;
m_selected.m_type = SelectedType::NavMeshVertex;
m_renderAspect->updateNavMeshBuffer(navMesh, m_selected.m_navMeshVertices.m_vertices, m_selected.m_navMeshVertices.m_count);
result = true;
}
}
return result;
}
bool EditorEngine::multiSelectNavMeshVertex(s32 mouseX, s32 mouseY)
{
bool result = false;
if (m_pEditorScene)
{
auto selectedIndex = getSelectedNavMeshVertex(mouseX, mouseY);
if (selectedIndex != 0xffffffff)
{
auto &navMesh = m_pEditorScene->getNavMesh();
auto index = m_selected.m_navMeshVertices.m_count;
m_selected.m_navMeshVertices.m_vertices[index] = selectedIndex;
++m_selected.m_navMeshVertices.m_count;
m_selected.m_navMeshVertices.m_count = std::min(m_selected.m_navMeshVertices.m_count, (u8)3u);
m_selected.m_type = SelectedType::NavMeshVertex;
m_renderAspect->updateNavMeshBuffer(navMesh, m_selected.m_navMeshVertices.m_vertices, m_selected.m_navMeshVertices.m_count);
result = true;
}
}
return result;
}
u32 EditorEngine::deselectNavMeshVertex()
{
u32 index = 0;
if (m_pEditorScene)
{
auto &navMesh = m_pEditorScene->getNavMesh();
m_renderAspect->updateNavMeshBuffer(navMesh);
index = m_selected.m_navMeshVertices.m_vertices[0];
m_selected.m_navMeshVertices.m_count = 0;
}
m_selected.m_item = nullptr;
return index;
}
bool EditorEngine::createNavMeshTriangleFromSelectedVertices(vx::uint3* selected)
{
bool result = false;
if (m_selected.m_navMeshVertices.m_count == 3)
{
auto &navMesh = m_pEditorScene->getNavMesh();
navMesh.addTriangle(m_selected.m_navMeshVertices.m_vertices);
buildNavGraph();
m_renderAspect->updateNavMeshBuffer(navMesh, m_selected.m_navMeshVertices.m_vertices, m_selected.m_navMeshVertices.m_count);
selected->x = m_selected.m_navMeshVertices.m_vertices[0];
selected->y = m_selected.m_navMeshVertices.m_vertices[1];
selected->z = m_selected.m_navMeshVertices.m_vertices[2];
result = true;
}
return result;
}
void EditorEngine::createNavMeshTriangleFromIndices(const vx::uint3 &indices)
{
if (m_pEditorScene)
{
m_selected.m_navMeshVertices.m_count = 3;
m_selected.m_navMeshVertices.m_vertices[0] = indices.x;
m_selected.m_navMeshVertices.m_vertices[1] = indices.y;
m_selected.m_navMeshVertices.m_vertices[2] = indices.z;
vx::uint3 tmp;
createNavMeshTriangleFromSelectedVertices(&tmp);
}
}
void EditorEngine::removeNavMeshTriangle()
{
if (m_pEditorScene)
{
auto &navMesh = m_pEditorScene->getNavMesh();
navMesh.removeTriangle();
m_renderAspect->updateNavMeshBuffer(navMesh, m_selected.m_navMeshVertices.m_vertices, m_selected.m_navMeshVertices.m_count);
buildNavGraph();
}
}
u32 EditorEngine::getSelectedNavMeshCount() const
{
return m_selected.m_navMeshVertices.m_count;
}
void EditorEngine::setSelectedNavMeshVertexPosition(const vx::float3 &position)
{
if (m_selected.m_navMeshVertices.m_count != 0)
{
auto &navMesh = m_pEditorScene->getNavMesh();
auto selectedIndex = m_selected.m_navMeshVertices.m_vertices[0];
navMesh.setVertexPosition(selectedIndex, position);
m_renderAspect->updateNavMeshBuffer(navMesh, m_selected.m_navMeshVertices.m_vertices, m_selected.m_navMeshVertices.m_count);
buildNavGraph();
}
}
bool EditorEngine::getSelectedNavMeshVertexPosition(vx::float3* p) const
{
bool result = false;
if (m_selected.m_navMeshVertices.m_count != 0)
{
auto selectedIndex = m_selected.m_navMeshVertices.m_vertices[0];
auto &navMesh = m_pEditorScene->getNavMesh();
auto vertices = navMesh.getVertices();
*p = vertices[selectedIndex];
result = true;
}
return result;
}
u32 EditorEngine::createLight()
{
Graphics::Light light;
light.m_position = vx::float3(0);
light.m_falloff = 5.0f;
light.m_lumen = 100.0f;
auto index = m_pEditorScene->getLightCount();
m_selected.m_item = m_pEditorScene->addLight(light);
m_selected.m_type = SelectedType::Light;
auto lightCount = index+1;
auto lights = m_pEditorScene->getLights();
m_renderAspect->updateLightBuffer(lights, lightCount);
return index;
}
bool EditorEngine::getLightIndex(s32 mouseX, s32 mouseY, u32* index)
{
bool result = false;
if (m_pEditorScene)
{
auto ray = getRay(mouseX, mouseY);
auto light = m_pEditorScene->getLight(ray);
if (light)
{
auto lights = m_pEditorScene->getLights();
*index = light - lights;
}
result = (light != nullptr);
}
return result;
}
void EditorEngine::selectLight(u32 index)
{
m_selected.m_type = SelectedType::Light;
m_selected.m_item = m_pEditorScene->getLight(index);
}
void EditorEngine::deselectLight()
{
if (m_pEditorScene)
{
if (m_selected.m_type == SelectedType::Light)
{
m_selected.m_item = nullptr;
}
}
}
u32 EditorEngine::getLightCount()
{
return m_pEditorScene->getLightCount();
}
f32 EditorEngine::getLightLumen(u32 index)
{
auto light = m_pEditorScene->getLight(index);
return light->m_lumen;
}
void EditorEngine::setLightLumen(u32 index, f32 lumen)
{
auto light = m_pEditorScene->getLight(index);
light->m_lumen = lumen;
//m_renderAspect->updateLightBuffer(m_pEditorScene->getLights(), m_pEditorScene->getLightCount());
}
f32 EditorEngine::getLightFalloff(u32 index)
{
auto light = m_pEditorScene->getLight(index);
return light->m_falloff;
}
void EditorEngine::setLightFalloff(u32 index, f32 falloff)
{
auto light = m_pEditorScene->getLight(index);
light->m_falloff = falloff;
//m_renderAspect->updateLightBuffer(m_pEditorScene->getLights(), m_pEditorScene->getLightCount());
}
void EditorEngine::getLightPosition(u32 index, vx::float3* position)
{
auto light = m_pEditorScene->getLight(index);
*position = light->m_position;
}
void EditorEngine::setLightPosition(u32 index, const vx::float3* position)
{
auto light = m_pEditorScene->getLight(index);
light->m_position = *position;
m_renderAspect->updateLightBuffer(m_pEditorScene->getLights(), m_pEditorScene->getLightCount());
}
SelectedType EditorEngine::getSelectedItemType() const
{
return m_selected.m_type;
}
Editor::Scene* EditorEngine::getEditorScene() const
{
return m_pEditorScene;
}
void EditorEngine::showNavmesh(bool b)
{
if (m_pEditorScene)
{
auto &navMesh = m_pEditorScene->getNavMesh();
m_renderAspect->showNavMesh(b, navMesh, m_navmeshGraph);
}
}
void EditorEngine::showInfluenceMap(bool b)
{
if (m_pEditorScene)
{
m_renderAspect->showInfluenceMap(b, m_influenceMap);
}
}
bool EditorEngine::addWaypoint(s32 mouseX, s32 mouseY, vx::float3* position)
{
bool result = false;
vx::float3 hitPos;
auto sid = raytraceAgainstStaticMeshes(mouseX, mouseY, &hitPos);
if (sid.value != 0)
{
auto &navMesh = m_pEditorScene->getNavMesh();
if (navMesh.contains(hitPos))
{
m_pEditorScene->addWaypoint(hitPos);
m_renderAspect->updateWaypoints(m_pEditorScene->getWaypoints(), m_pEditorScene->getWaypointCount());
*position = hitPos;
result = true;
}
}
return result;
}
void EditorEngine::addWaypoint(const vx::float3 &position)
{
m_pEditorScene->addWaypoint(position);
m_renderAspect->updateWaypoints(m_pEditorScene->getWaypoints(), m_pEditorScene->getWaypointCount());
}
void EditorEngine::removeWaypoint(const vx::float3 &position)
{
m_pEditorScene->removeWaypoint(position);
m_renderAspect->updateWaypoints(m_pEditorScene->getWaypoints(), m_pEditorScene->getWaypointCount());
}
void EditorEngine::addSpawn()
{
if (m_pEditorScene)
{
Spawn spawn;
spawn.type = PlayerType::AI;
spawn.position = {0, 0, 0};
m_pEditorScene->addSpawn(std::move(spawn));
auto count = m_pEditorScene->getSpawnCount();
auto spawns = m_pEditorScene->getSpawns();
m_renderAspect->updateSpawns(spawns, count);
}
}
bool EditorEngine::selectSpawn(s32 mouseX, s32 mouseY, u32* id)
{
bool result = false;
if (m_pEditorScene)
{
auto ray = getRay(mouseX, mouseY);
auto spawnId = m_pEditorScene->getSpawnId(ray);
if (spawnId != 0xffffffff)
{
result = true;
*id = spawnId;
}
}
return result;
}
void EditorEngine::getSpawnPosition(u32 id, vx::float3* position) const
{
auto spawn = m_pEditorScene->getSpawn(id);
if (spawn)
{
*position = spawn->position;
}
}
u32 EditorEngine::getSpawnType(u32 id) const
{
u32 result = 0xffffffff;
auto spawn = m_pEditorScene->getSpawn(id);
if (spawn)
{
result = (u32)spawn->type;
}
return result;
}
void EditorEngine::setSpawnActor(u32 id, u64 actorSid)
{
m_pEditorScene->setSpawnActor(id, vx::StringID(actorSid));
}
u32 EditorEngine::getSpawnCount()
{
return m_pEditorScene->getSpawnCount();
}
u32 EditorEngine::getSpawnId(u32 index)
{
auto spawns = m_pEditorScene->getSpawns();
return spawns[index].id;
}
void EditorEngine::setSpawnPosition(u32 id, const vx::float3 &position)
{
auto spawns = m_pEditorScene->getSpawns();
auto count = m_pEditorScene->getSpawnCount();
m_pEditorScene->setSpawnPosition(id, position);
m_renderAspect->updateSpawns(spawns, count);
}
void EditorEngine::setSpawnType(u32 id, u32 type)
{
m_pEditorScene->setSpawnType(id, type);
}
u64 EditorEngine::getSpawnActor(u32 id)
{
auto spawn = m_pEditorScene->getSpawn(id);
return spawn->actorSid.value;
}
u32 EditorEngine::getMeshCount() const
{
if (m_pEditorScene)
return m_pEditorScene->getMeshes().size();
return 0;
}
const char* EditorEngine::getMeshName(u32 i) const
{
const char* meshName = nullptr;
if (m_pEditorScene)
{
auto &meshes = m_pEditorScene->getMeshes();
auto sid = meshes.keys()[i];
meshName = m_pEditorScene->getMeshName(sid);
}
return meshName;
}
u64 EditorEngine::getMeshSid(u32 i) const
{
u64 sidValue = 0;
if (m_pEditorScene)
{
auto &meshes = m_pEditorScene->getMeshes();
auto sid = meshes.keys()[i];
sidValue = sid.value;
}
return sidValue;
}
u32 EditorEngine::getMaterialCount() const
{
u32 count = 0;
if (m_pEditorScene)
{
count = m_pEditorScene->getMaterialCount();
}
return count;
}
const char* EditorEngine::getMaterialNameIndex(u32 i) const
{
const char* name = nullptr;
if (m_pEditorScene)
{
auto materials = m_pEditorScene->getMaterials();
auto sid = (*materials[i]).getSid();
name = m_pEditorScene->getMaterialName(sid);
}
return name;
}
const char* EditorEngine::getMaterialName(u64 sid) const
{
const char* name = nullptr;
if (m_pEditorScene)
{
name = m_pEditorScene->getMaterialName(vx::StringID(sid));
}
return name;
}
u64 EditorEngine::getMaterialSid(u32 i) const
{
u64 sidValue = 0;
if (m_pEditorScene)
{
auto materials = m_pEditorScene->getMaterials();
auto sid = (*materials[i]).getSid();
sidValue = sid.value;
}
return sidValue;
}
void EditorEngine::setMeshInstanceAnimation(u64 instanceSid, u64 animSid)
{
auto instance = m_pEditorScene->getMeshInstance(vx::StringID(instanceSid));
if (instance)
{
instance->setAnimationSid(vx::StringID(animSid));
}
}
u64 EditorEngine::getMeshInstanceAnimation(u64 instanceSid)
{
u64 result = 0;
auto instance = m_pEditorScene->getMeshInstance(vx::StringID(instanceSid));
if (instance)
{
result = instance->getAnimationSid().value;
}
return result;
}
u32 EditorEngine::getAnimationCount() const
{
return m_pEditorScene->getAnimationCount();
}
const char* EditorEngine::getAnimationNameIndex(u32 i) const
{
return m_pEditorScene->getAnimationNameIndex(i);
}
u64 EditorEngine::getAnimationSidIndex(u32 i) const
{
return m_pEditorScene->getAnimationSidIndex(i);
}
u32 EditorEngine::getMeshPhysxType(u64 sid) const
{
u32 type = 0xffffffff;
auto &meshes = m_pEditorScene->getMeshes();
auto it = meshes.find(vx::StringID(sid));
if (it != meshes.end())
{
type = (u32)(*it)->getPhysxMeshType();
}
return type;
}
void EditorEngine::setMeshPhysxType(u64 sid, u32 type)
{
auto meshSid = vx::StringID(sid);
auto meshFile = m_resourceAspect.getMesh(meshSid);
if (meshFile == nullptr)
{
return;
//VX_ASSERT(false);
/*auto &meshDataAllocator = m_resourceAspect.getMeshDataAllocator();
if (m_physicsAspect.setMeshPhysxType(meshFile, (PhsyxMeshType)type, &meshDataAllocator))
{
auto fileName = m_resourceAspect.getLoadedFileName(vx::StringID(sid));
m_fileAspect.requestSaveFile(vx::FileEntry(fileName, vx::FileType::Mesh), meshFile.get());
}*/
}
auto meshManager = m_resourceAspect.getMeshManager();
auto physxType = (PhsyxMeshType)type;
std::unique_lock<std::mutex> lock;
auto dataAllocator = meshManager->lockDataAllocator(&lock);
if (m_physicsAspect.setMeshPhysxType(meshFile, physxType, dataAllocator))
{
vx::Variant arg;
arg.ptr = meshFile;
auto meshName = meshManager->getName(meshSid);
vx::FileEntry fileEntry(meshName, vx::FileType::Mesh);
m_resourceAspect.requestSaveFile(fileEntry, arg);
}
}
u32 EditorEngine::getMeshInstanceRigidBodyType(u64 sid) const
{
u32 type = 0xffffffff;
auto it = m_pEditorScene->getMeshInstance(vx::StringID(sid));
if (it != nullptr)
{
type = (u32)it->getRigidBodyType();
}
return type;
}
void EditorEngine::setMeshInstanceRigidBodyType(u64 sid, u32 type)
{
auto instanceSid = vx::StringID(sid);
auto editorInstance = m_pEditorScene->getMeshInstance(instanceSid);
if (editorInstance != nullptr)
{
auto rigidBodyType = (PhysxRigidBodyType)type;
if (m_physicsAspect.setMeshInstanceRigidBodyType(instanceSid, editorInstance->getMeshInstance(), rigidBodyType))
{
editorInstance->setRigidBodyType(rigidBodyType);
}
}
}
void EditorEngine::addJoint(const vx::StringID &sid0, const vx::StringID &sid1, const vx::float3 &p0, const vx::float3 &p1)
{
Joint joint;
joint.sid0 = sid0;
joint.sid1 = sid1;
joint.p0 = p0;
joint.q0 = {0, 0, 0, 1};
joint.p1= p1;
joint.q1 = { 0, 0, 0, 1 };
joint.type = JointType::Revolute;
if (sid0.value != 0)
{
joint.p0.x = 0;
joint.p0.y = 0;
joint.p0.z = 0;
}
if (sid1.value != 0)
{
joint.p1.x = 0;
joint.p1.y = 0;
joint.p1.z = 0;
}
if (m_physicsAspect.createJoint(joint))
{
puts("created joint");
m_pEditorScene->addJoint(joint);
auto jointCount = m_pEditorScene->getJointCount();
auto joints = m_pEditorScene->getJoints();
auto &sortedInstances = m_pEditorScene->getSortedMeshInstances();
m_renderAspect->updateJoints(joints, jointCount, sortedInstances);
}
}
void EditorEngine::addJoint(const vx::StringID &sid)
{
auto instance = m_pEditorScene->getMeshInstance(sid);
if (instance)
{
auto &transform = instance->getTransform();
addJoint(sid, vx::StringID(0), transform.m_translation, transform.m_translation);
}
}
void EditorEngine::removeJoint(u32 index)
{
m_pEditorScene->eraseJoint(index);
auto jointCount = m_pEditorScene->getJointCount();
auto joints = m_pEditorScene->getJoints();
auto &sortedInstances = m_pEditorScene->getSortedMeshInstances();
m_renderAspect->updateJoints(joints, jointCount, sortedInstances);
}
u32 EditorEngine::getJointCount() const
{
return m_pEditorScene->getJointCount();
}
#include <DirectXMath.h>
void EditorEngine::getJointData(u32 i, vx::float3* p0, vx::float3* q0, vx::float3* p1, vx::float3* q1, u64* sid0, u64* sid1, u32* limitEnabled, f32* limitMin, f32* limitMax) const
{
auto quaternionToAngles = [](const vx::float4 &q, vx::float3* rotationDeg)
{
if (q.x == 0 && q.y == 0 && q.z == 0)
{
*rotationDeg = {0, 0, 0};
}
else
{
auto qq = vx::loadFloat4(&q);
__m128 axis, axis0;
f32 angle, angle0;
DirectX::XMQuaternionToAxisAngle(&axis0, &angle0, qq);
vx::quaternionToAxisAngle(qq, &axis, &angle);
axis = vx::normalize3(axis);
//auto ttt = _mm_mul_ps(axis, _mm_load1_ps(&angle));
vx::float4a tmpAxis = axis;
vx::angleAxisToEuler(tmpAxis, angle, rotationDeg);
}
};
auto joints = m_pEditorScene->getJoints();
auto &joint = joints[i];
quaternionToAngles(joint.q0, q0);
quaternionToAngles(joint.q1, q1);
*p0 = joint.p0;
*p1 = joint.p1;
*sid0 = joint.sid0.value;
*sid1 = joint.sid1.value;
*limitEnabled = joint.limitEnabled;
*limitMin = joint.limit.x;
*limitMax = joint.limit.y;
}
bool EditorEngine::selectJoint(s32 mouseX, s32 mouseY, u32* index)
{
auto ray = getRay(mouseX, mouseY);
ray.maxt = 10.0f;
auto joint = m_pEditorScene->getJoint(ray, index);
return (joint != nullptr);
}
void EditorEngine::setJointPosition0(u32 index, const vx::float3 &p)
{
m_pEditorScene->setJointPosition0(index, p);
auto &sortedInstances = m_pEditorScene->getSortedMeshInstances();
m_renderAspect->updateJoints(m_pEditorScene->getJoints(), m_pEditorScene->getJointCount(), sortedInstances);
}
void EditorEngine::setJointPosition1(u32 index, const vx::float3 &p)
{
m_pEditorScene->setJointPosition1(index, p);
auto &sortedInstances = m_pEditorScene->getSortedMeshInstances();
m_renderAspect->updateJoints(m_pEditorScene->getJoints(), m_pEditorScene->getJointCount(), sortedInstances);
}
void EditorEngine::setJointBody0(u32 index, u64 sid)
{
m_pEditorScene->setJointBody0(index, sid);
}
void EditorEngine::setJointBody1(u32 index, u64 sid)
{
m_pEditorScene->setJointBody1(index, sid);
}
void EditorEngine::setJointRotation0(u32 index, const vx::float3 &q)
{
auto qq = vx::quaternionRotationRollPitchYawFromVector(vx::degToRad(vx::loadFloat3(&q)));
vx::float4 tmp;
vx::storeFloat4(&tmp, qq);
m_pEditorScene->setJointRotation0(index, tmp);
auto &sortedInstances = m_pEditorScene->getSortedMeshInstances();
m_renderAspect->updateJoints(m_pEditorScene->getJoints(), m_pEditorScene->getJointCount(), sortedInstances);
}
void EditorEngine::setJointRotation1(u32 index, const vx::float3 &q)
{
auto qq = vx::quaternionRotationRollPitchYawFromVector(vx::degToRad(vx::loadFloat3(&q)));
vx::float4 tmp;
vx::storeFloat4(&tmp, qq);
m_pEditorScene->setJointRotation1(index, tmp);
auto &sortedInstances = m_pEditorScene->getSortedMeshInstances();
m_renderAspect->updateJoints(m_pEditorScene->getJoints(), m_pEditorScene->getJointCount(), sortedInstances);
}
void EditorEngine::setJointLimit(u32 index, u32 enabled, f32 limitMin, f32 limitMax)
{
m_pEditorScene->setJointLimit(index, enabled, limitMin, limitMax);
}
u64 EditorEngine::createActor(const char* name, u64 meshSid, u64 materialSid)
{
vx::FileEntry fileEntry(name, vx::FileType::Actor);
auto actorFile = new ActorFile(ActorFile::getGlobalVersion());
auto materialName = m_resourceAspect.getMaterialManager()->getName(vx::StringID(materialSid));
auto meshName = m_resourceAspect.getMeshManager()->getName(vx::StringID(meshSid));
const u32 bufferSize = 31;
auto meshSize = strlen(meshName);
auto materialSize = strlen(materialName);
VX_ASSERT(bufferSize >= meshSize && bufferSize >= materialSize);
char buffer[bufferSize + 1];
memset(buffer, 0, sizeof(buffer));
memcpy(buffer, meshName, meshSize);
actorFile->setMesh(buffer);
memset(buffer, 0, sizeof(buffer));
memcpy(buffer, materialName, materialSize);
actorFile->setMaterial(buffer);
vx::Variant arg;
arg.ptr = actorFile;
m_resourceAspect.requestSaveFile(fileEntry, arg);
Actor actor;
actor.m_mesh = meshSid;
actor.m_material = materialSid;
m_resourceAspect.addActor(fileEntry.getSid(), std::string(name), actor);
return fileEntry.getSid().value;
}
const char* EditorEngine::getActorName(u64 sid) const
{
return m_resourceAspect.getActorManager()->getName(vx::StringID(sid));
}
u32 EditorEngine::getLightGeometryProxyCount() const
{
return m_pEditorScene->getLightGeometryProxyCount();
}
void EditorEngine::createLightGeometryProxy(const vx::float3 ¢er, const vx::float3 &halfDim)
{
AABB bounds;
bounds.min = center - halfDim;
bounds.max = center + halfDim;
m_pEditorScene->addLightGeometryProxy(bounds);
m_renderAspect->updateLightGeometryProxies(m_pEditorScene->getLightGeometryProxies(), m_pEditorScene->getLightGeometryProxyCount());
}
void EditorEngine::setLightGeometryProxyBounds(u32 index, const vx::float3 ¢er, const vx::float3 &halfDim)
{
AABB bounds;
bounds.min = center - halfDim;
bounds.max = center + halfDim;
m_pEditorScene->setLightGeometryProxyBounds(index, bounds);
m_renderAspect->updateLightGeometryProxies(m_pEditorScene->getLightGeometryProxies(), m_pEditorScene->getLightGeometryProxyCount());
}
void EditorEngine::getLightGeometryProxyBounds(u32 index, vx::float3* center, vx::float3* halfDimOut) const
{
auto ptr = m_pEditorScene->getLightGeometryProxies();
auto bounds = ptr[index].m_bounds;
auto halfDim = (bounds.max - bounds.min) * 0.5f;
*center = bounds.min + halfDim;
*halfDimOut = halfDim;
}
u32 EditorEngine::getLightGeometryProxyLightCount(u32 index) const
{
auto ptr = m_pEditorScene->getLightGeometryProxies();
return ptr[index].m_lightCount;
}
void EditorEngine::testLightGeometryProxies()
{
Editor::TestLightGeometryProxiesDesc desc;
desc.lightCount = m_pEditorScene->getLightCount();
desc.lights = m_pEditorScene->getLights();
desc.proxies = m_pEditorScene->getLightGeometryProxies();
desc.proxyCount = m_pEditorScene->getLightGeometryProxyCount();
m_renderAspect->testLightGeometryProxies(desc);
} | {
"redpajama_set_name": "RedPajamaGithub"
} | 9,034 |
{"url":"https:\/\/foyer.mosdef.org\/en\/0.11.3\/topic_guides\/parameter_definitions.html","text":"# Parameter definitions\uf0c1\n\nParameter definitions within force field XMLs follow the same conventions as defined in the OpenMM documentation. Currently, only certain functional forms for molecular forces are supported, while future developments are expected to allow Foyer to support any desired functional form, including reactive and tabulated potentials. The currently supported functional forms for molecular forces are:\n\n\u2022 Nonbonded\n\n\u2022 Bonds\n\n\u2022 Angles\n\n\u2022 Torsions (proper)\n\n\u2022 Torsions (improper)\n\nDefinitions for each molecular force follow the OpenMM standard.\n\nThe harmonic bond potential is defined as\n\n$E = \\frac{1}{2}k(r-r_{0})^{2}$\n\nwhere k is the bond coefficient ($$\\frac{energy}{distance^{2}}$$) and r0 is the equilibrium bond distance. Note the factor of $$\\frac{1}{2}$$.\n\nDihedral potentials reported as a fourier series (e.g., OPLS) can be converted to Ryckaert-Bellemans (RB) torsions as specified in the GROMACS User Manual.\n\n## Classes vs.\u00a0Types\uf0c1\n\nOpenMM allows users to specify either a class or a type (See Atom Types and Atom Classes), to define each particle within the force definition. Here, type refers to a specific atom type (as defined in the <AtomTypes> section), while class refers to a more general description that can apply to multiple atomtypes (i.e.\u00a0multiple atomtypes may share the same class). This aids in limiting the number of force definitions required in a force field XML, as many similar atom types may share force parameters.\n\n## Assigning parameters by specificity\uf0c1\n\nFoyer deviates from OpenMM\u2019s convention when matching force definitions in a force field XML to instances of these forces in a molecular system. In OpenMM, forces are assigned according to the first matching definition in a force field XML, even if multiple matching definitions exist. In contrast, Foyer assigns force parameters based on definition specificity, where definitions containing more type attributes are considered to be more specific.\n\nExample:\n\n<RBTorsionForce>\n<Proper class1=\"CT\" class2=\"CT\" class3=\"CT\" class4=\"CT\" c0=\"2.9288\" c1=\"-1.4644\" c2=\"0.2092\" c3=\"-1.6736\" c4=\"0.0\" c5=\"0.0\"\/>\n<Proper type1=\"opls_961\" type2=\"opls_136\" type3=\"opls_136\" type4=\"opls_136\" c0=\"-0.987424\" c1=\"0.08363\" c2=\"-0.08368\" c3=\"-0.401664\" c4=\"1.389088\" c5=\"0.0\"\/>\n<\/RBTorsionForce>\n\n\nAbove, two proper torsions are defined, both describing a torsional force between four tetrahedral carbons. However, the first definition features four class attributes and zero type attributes, as this describes a general dihedral for all tetrahedral carbons. The second definition features zero class attributes and four type attributes, and describes a more specific dihedral for the case where one end carbon is of type 'opls_961' (a fluorinated carbon) and the remaining three carbons are of type 'opls_136' (alkane carbons). Now consider we want to use a force field containing the above torsion definitions to assign parameters to some molecular system that features partially fluorinated alkanes. When assigning torsion parameters to a quartet of atoms where one end carbon is fluorinated ('opls_961') and the remaining three are hydrogenated ('opls_136'), if using the OpenMM procedure for parameter assignment the more general 'CT-CT-CT-CT' torsion parameters (the first definition above) would be assigned because this would be the first matching definition in the force field XML. However, with Foyer, the second definition will be auto-detected as more specific, due to the greater number of type attributes (4 vs.\u00a00) and those parameters will be assigned instead.\n\nIt should be noted that if two definitions feature the same specificity level (i.e.\u00a0the same number of type definitions) then automatic detection of precedence is not possible and parameter assignment will follow the OpenMM procedure whereby parameters from the first matching force definition in the XML will be assigned.","date":"2022-10-02 23:38:39","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 1, \"mathjax_display_tex\": 1, \"mathjax_asciimath\": 1, \"img_math\": 0, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.7752910852432251, \"perplexity\": 3845.6184719939515}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.3, \"absolute_threshold\": 10, \"end_threshold\": 5, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2022-40\/segments\/1664030337360.41\/warc\/CC-MAIN-20221002212623-20221003002623-00269.warc.gz\"}"} | null | null |
The modular ammunition platoon is a US Army modular sustainment unit responsible for providing munitions support from all echelons of battle minus within a brigade combat team (which is supported by its own Modular Ammunition Transfer Point). The modular ammunition platoon is capable of operating within its parental modular ammunition company in tandem with up to four additional platoons, or it is capable of operating independently on its own. During extended platoon operations, the platoon leader is often given independent command authority. During independent operations, it is not uncommon for the platoon to receive additional support personnel or equipment.
Following a 2016 force design update, the platoon was redesigned into effective teams and squads that provide the required ammunition capability in a more efficient manner. In 2018, the platoon design was applied to the brigade combat team's Ammunition Transfer and Holding Point to create the new Modular Ammunition Transfer Point (MATP).
Sustainment and support units and formations of the United States Army | {
"redpajama_set_name": "RedPajamaWikipedia"
} | 131 |
Q: Error when trying to run spring-boot native with aws credentials I'm trying to migrate a java spring boot application to use spring boot native implementation and I'm facing some problems to realize it. Many of the problems that I've faced I solved just googling, but this one with aws credentials provider I couldn't find any help.
I generate the executable file running: mvn -Pnative -DskipTests clean install. I'm using maven 3.8.6 and sdkman with graalvm 22.2.r17-grl.
The problem occurs when I trying to execute the generated file. This is the error I'm facing: Native reflection configuration for com.amazonaws.auth.AWSStaticCredentialsProvider.<init>(com.amazonaws.auth.AWSCredentials) is missing
This is the main parts of my pom.xml:
...<spring-native.version>0.12.1</spring-native.version>
<native-maven-plugin.version>0.9.13</native-maven-plugin.version>
<springcloud-starter-aws-messaging.version>2.2.6.RELEASE</springcloud-starter-aws-messaging.version>...
...<dependency>
<groupId>org.springframework.cloud</groupId>
<artifactId>spring-cloud-starter-aws-messaging</artifactId>
<version>${springcloud-starter-aws-messaging.version}</version>
</dependency>
<dependency>
<groupId>org.springframework.experimental</groupId>
<artifactId>spring-native</artifactId>
<version>${spring-native.version}</version>
</dependency>
<dependency>
<groupId>org.springframework.experimental</groupId>
<artifactId>spring-aot</artifactId>
<version>${spring-native.version}</version>
</dependency>...
<build>
<plugins>
<plugin>
<groupId>org.springframework.boot</groupId>
<artifactId>spring-boot-maven-plugin</artifactId>
<configuration>
<excludes>
<exclude>
<groupId>org.projectlombok</groupId>
<artifactId>lombok</artifactId>
</exclude>
</excludes>
</configuration>
</plugin>
<plugin>
<groupId>org.springframework.experimental</groupId>
<artifactId>spring-aot-maven-plugin</artifactId>
<version>${spring-native.version}</version>
<executions>
<execution>
<id>test-generate</id>
<goals>
<goal>test-generate</goal>
</goals>
</execution>
<execution>
<id>generate</id>
<goals>
<goal>generate</goal>
</goals>
</execution>
</executions>
</plugin>
</plugins>
</build>
<profiles>
<profile>
<id>native</id>
<dependencies>
<dependency>
<groupId>org.junit.platform</groupId>
<artifactId>junit-platform-launcher</artifactId>
<scope>test</scope>
</dependency>
</dependencies>
<build>
<plugins>
<plugin>
<groupId>org.graalvm.buildtools</groupId>
<artifactId>native-maven-plugin</artifactId>
<version>${native-maven-plugin.version}</version>
<extensions>true</extensions>
<executions>
<execution>
<id>build-native</id>
<goals>
<goal>build</goal>
</goals>
<phase>package</phase>
</execution>
</executions>
<configuration>
<debug>true</debug>
<verbose>true</verbose>
</configuration>
</plugin>
<plugin>
<groupId>org.springframework.boot</groupId>
<artifactId>spring-boot-maven-plugin</artifactId>
<configuration>
<excludes>
<exclude>
<groupId>org.projectlombok</groupId>
<artifactId>lombok</artifactId>
</exclude>
</excludes>
<classifier>exec</classifier>
</configuration>
</plugin>
</plugins>
</build>
</profile>
</profiles>
And this is my java QueueMessagingTemplate configuration:
@Bean
public QueueMessagingTemplate queueMessagingTemplate(AmazonSQSAsync amazonSQSAsync) {
return new QueueMessagingTemplate(amazonSQSAsync);
}
Does anybody have an idea about how to solve it?
| {
"redpajama_set_name": "RedPajamaStackExchange"
} | 3 |
class AvailableAttributesController < ApplicationController
def index
check_access!('admin:attributes:list')
@attributes = AvailableAttribute.all
end
def new
check_access!('admin:attributes:create')
@attribute = AvailableAttribute.new
end
def create
check_access!('admin:attributes:create')
audit_attrs = { audit_comment: 'Created attribute from admin interface' }
@attribute =
AvailableAttribute.new(audit_attrs.merge(available_attribute_params))
unless @attribute.save
return form_error('new', 'Unable to create attribute', @attribute)
end
flash[:success] = "Created attribute with name: #{@attribute.name} and " \
"value #{@attribute.value}"
redirect_to available_attributes_path
end
def edit
check_access!('admin:attributes:update')
@attribute = AvailableAttribute.find(params[:id])
end
def update
check_access!('admin:attributes:update')
@attribute = AvailableAttribute.find(params[:id])
unless update_available_attribute(@attribute)
return form_error('edit', 'Unable to save attribute', @attribute)
end
flash[:success] = "Updated attribute with name: #{@attribute.name} and " \
"value: #{@attribute.value}"
redirect_to(available_attributes_path)
end
def show
check_access!('admin:attributes:read')
@attribute = AvailableAttribute.find(params[:id])
end
def destroy
check_access!('admin:attributes:delete')
@attribute = AvailableAttribute.find(params[:id])
@attribute.audit_comment = 'Deleted attribute from admin interface'
if @attribute.destroy
flash[:success] = "Deleted attribute with name: #{@attribute.name} and " \
"value: #{@attribute.value}"
else
flash[:error] = 'Unable to delete an available attribute while in use'
end
redirect_to available_attributes_path
end
def audits
check_access!('admin:attributes:audit')
if params[:id]
@attribute = AvailableAttribute.find(params[:id])
@audits = @attribute.audits.all
else
@audits = AvailableAttribute.audits.all
end
end
private
def available_attribute_params
params.require(:available_attribute).permit(:name, :value, :description)
end
def update_available_attribute(attribute)
audit_attrs = { audit_comment: 'Edited attribute from admin interface' }
attribute.update_attributes(audit_attrs.merge(available_attribute_params))
end
end
| {
"redpajama_set_name": "RedPajamaGithub"
} | 6,887 |
using Microsoft.Win32;
using System;
using System.Collections.Generic;
using System.Diagnostics;
using System.IO;
using System.Linq;
using System.Runtime.InteropServices;
using System.Text;
using System.Threading.Tasks;
// The Edge entry point.
public class Startup
{
/**
* Promotes all tray items created by the specified EXE from the toolbar customization area
* to the toolbar itself if the user has not explicitly specified that they should never be
* shown in the toolbar.
*
* The function accepts the name of the EXE as argument rather than attempt to determine it itself
* simply because that was easier to determine Node-side.
*
* @param {string} The name of the EXE for which to promote tray items.
*
* @return {null}
*/
public async Task<object> Invoke(string exeToPromote)
{
var trayFixer = new Squirrel.TrayStateChanger();
trayFixer.PromoteTrayItems(exeToPromote);
return null;
}
}
/**
* The below is copied from https://github.com/Squirrel/Squirrel.Windows/blob/a95b9853e650c2bc3e0239c6739d0363f55d20bc/src/Squirrel/TrayHelper.cs
* except for that:
* - it has been pared down to only what was necessary to support `TrayStateChanger.PromoteTrayItem`
* (here renamed to "...Items" to more accurately reflect its effects), and
* - some comments have been added.
*/
namespace Squirrel
{
public class TrayStateChanger
{
public void PromoteTrayItems(string exeToPromote)
{
var instance = new TrayNotify();
try {
var items = default(List<NOTIFYITEM>);
var legacy = useLegacyInterface();
if (legacy) {
items = getTrayItemsWin7(instance);
} else {
items = getTrayItems(instance);
}
exeToPromote = exeToPromote.ToLowerInvariant();
for (int i = 0; i < items.Count; i++) {
var item = items[i];
var exeName = item.exe_name.ToLowerInvariant();
// Ignore items not created by the specified EXE.
if (!exeName.Contains(exeToPromote)) continue;
// Ignore items that are not in the default state. We shouldn't overwrite the
// user's preference if it is to never show an item, and we don't need to overwrite
// the user's preference if it is to always show an item.
if (item.preference != NOTIFYITEM_PREFERENCE.PREFERENCE_SHOW_WHEN_ACTIVE) continue;
item.preference = NOTIFYITEM_PREFERENCE.PREFERENCE_SHOW_ALWAYS;
var writable = NOTIFYITEM_Writable.fromNotifyItem(item);
if (legacy) {
var notifier = (ITrayNotifyWin7)instance;
notifier.SetPreference(ref writable);
} else {
var notifier = (ITrayNotify)instance;
notifier.SetPreference(ref writable);
}
}
} catch (Exception ex) {
Console.WriteLine("Failed to promote Tray icon: " + ex.ToString());
} finally {
Marshal.ReleaseComObject(instance);
}
}
static List<NOTIFYITEM> getTrayItems(TrayNotify instance)
{
var notifier = (ITrayNotify)instance;
var callback = new NotificationCb();
var handle = default(ulong);
notifier.RegisterCallback(callback, out handle);
notifier.UnregisterCallback(handle);
return callback.items;
}
static List<NOTIFYITEM> getTrayItemsWin7(TrayNotify instance)
{
var notifier = (ITrayNotifyWin7)instance;
var callback = new NotificationCb();
notifier.RegisterCallback(callback);
notifier.RegisterCallback(null);
return callback.items;
}
class NotificationCb : INotificationCb
{
public readonly List<NOTIFYITEM> items = new List<NOTIFYITEM>();
public void Notify([In] uint nEvent, [In] ref NOTIFYITEM notifyItem)
{
items.Add(notifyItem);
}
}
static bool useLegacyInterface()
{
var ver = Environment.OSVersion.Version;
if (ver.Major < 6) return true;
if (ver.Major > 6) return false;
// Windows 6.2 and higher use new interface
return ver.Minor <= 1;
}
}
// The known values for NOTIFYITEM's dwPreference member.
public enum NOTIFYITEM_PREFERENCE
{
// In Windows UI: "Only show notifications."
PREFERENCE_SHOW_WHEN_ACTIVE = 0,
// In Windows UI: "Hide icon and notifications."
PREFERENCE_SHOW_NEVER = 1,
// In Windows UI: "Show icon and notifications."
PREFERENCE_SHOW_ALWAYS = 2
};
// NOTIFYITEM describes an entry in Explorer's registry of status icons.
// Explorer keeps entries around for a process even after it exits.
public struct NOTIFYITEM
{
[MarshalAs(UnmanagedType.LPWStr)]
public string exe_name; // The file name of the creating executable.
[MarshalAs(UnmanagedType.LPWStr)]
public string tip; // The last hover-text value associated with this status
// item.
public IntPtr icon; // The icon associated with this status item.
public IntPtr hwnd; // The HWND associated with the status item.
public NOTIFYITEM_PREFERENCE preference; // Determines the behavior of the icon with respect to
// the taskbar
public uint id; // The ID specified by the application. (hWnd, uID) is
// unique.
public Guid guid; // The GUID specified by the application, alternative to
// uID.
};
public struct NOTIFYITEM_Writable
{
public IntPtr exe_name; // The file name of the creating executable.
public IntPtr tip; // The last hover-text value associated with this status
// item.
public IntPtr icon; // The icon associated with this status item.
public IntPtr hwnd; // The HWND associated with the status item.
public NOTIFYITEM_PREFERENCE preference; // Determines the behavior of the icon with respect to
// the taskbar
public uint id; // The ID specified by the application. (hWnd, uID) is
// unique.
public Guid guid; // The GUID specified by the application, alternative to
// uID.
public static NOTIFYITEM_Writable fromNotifyItem(NOTIFYITEM item)
{
return new NOTIFYITEM_Writable {
exe_name = Marshal.StringToCoTaskMemAuto(item.exe_name),
tip = Marshal.StringToCoTaskMemAuto(item.tip),
icon = item.icon,
hwnd = item.hwnd,
preference = item.preference,
id = item.id,
guid = item.guid
};
}
};
[ComImport]
[Guid("D782CCBA-AFB0-43F1-94DB-FDA3779EACCB")]
[InterfaceType(ComInterfaceType.InterfaceIsIUnknown)]
interface INotificationCb
{
void Notify([In]uint nEvent, [In] ref NOTIFYITEM notifyItem);
}
[ComImport]
[Guid("FB852B2C-6BAD-4605-9551-F15F87830935")]
[InterfaceType(ComInterfaceType.InterfaceIsIUnknown)]
interface ITrayNotifyWin7
{
void RegisterCallback([MarshalAs(UnmanagedType.Interface)]INotificationCb callback);
void SetPreference([In] ref NOTIFYITEM_Writable notifyItem);
void EnableAutoTray([In] bool enabled);
}
[ComImport]
[Guid("D133CE13-3537-48BA-93A7-AFCD5D2053B4")]
[InterfaceType(ComInterfaceType.InterfaceIsIUnknown)]
interface ITrayNotify
{
void RegisterCallback([MarshalAs(UnmanagedType.Interface)]INotificationCb callback, [Out] out ulong handle);
void UnregisterCallback([In] ulong handle);
void SetPreference([In] ref NOTIFYITEM_Writable notifyItem);
void EnableAutoTray([In] bool enabled);
void DoAction([In] bool enabled);
}
[ComImport, Guid("25DEAD04-1EAC-4911-9E3A-AD0A4AB560FD")]
class TrayNotify { }
}
| {
"redpajama_set_name": "RedPajamaGithub"
} | 3,284 |
There are ongoing land reclamation projects, which have increased Singapore's land area from 581.5 km2 (224.5 sq mi) in the 1960s to 716.1 km2 (276.5 sq mi) today; it may grow by another 100 km2 (40 sq mi) by 2030. Some projects involve merging smaller islands through land reclamation to form larger, more functional islands, as with Jurong Island. 5% of Singapore's land is set aside as nature reserves. Urbanisation has eliminated most primary rainforest onthe main island, Bukit Timah Nature Reserve being the only significant remaining forest. There are only about 250 acres (101 ha) of farmland remaining in Singapore.
Singapore has a tropical rainforest climate (Köppen: Af ) with no distinctive seasons, uniform temperature and pressure, high humidity, and abundant rainfall. Temperatures usually range from 22 to 35 °C (72 to 95 °F). Relative humidity averages around 79% in the morning and 73% in the afternoon. April and May are the hottest months, with the wetter monsoon season from November to January. From July to October, there is often haze caused by bush fires in neighbouring Indonesia. Although Singapore does not observe daylight saving time, it follows time zone GMT+8, one hour ahead of its geographical location.
Singapore's main territory is a diamond-shaped island, although its territory includes surrounding smaller islands. The farthest outlying island is Pedra Branca. Singapore is slightly more than 3.5 times the size of Washington, D.C. Of Singapore's dozens of smaller islands, Jurong Island, Pulau Tekong, Pulau Ubin and Sentosa are the larger ones. Most of Singapore is no more than 15 meters above sea level.
The highest point of Singapore is Bukit Timah, with a height of 165 m (538 ft) and made up of igneous rock, granite. Hills and valleys of sedimentary rock dominate the northwest, while the eastern region consists of sandy and flatter land. Singapore has no natural lakes, but reservoirs and water catchment areas have been constructed to store fresh water for Singapore's water supply. | {
"redpajama_set_name": "RedPajamaC4"
} | 2,516 |
Q: Will installing new Windows build remove any rootkits and trojans? I have currently installed 2004 version of Windows 10, if i update it to 20H2 version, will i get rid of any trojans or rootkits on my computer? Where are those typically get installed? I don't want to do format on my disk.
A: Updating Windows does not affect any personal files, only system files. As any malicious software would not be a 'system file', there's a reasonable likelihood it would remain untouched.
See How can I remove malicious spyware, malware, adware, viruses, trojans or rootkits from my PC? for further information.
| {
"redpajama_set_name": "RedPajamaStackExchange"
} | 7,798 |
Q: EntityFramework Error about Different Contexts. Looks like the same context to me I'm tryng to run the following LINQ query and getting the indicated error:
var x = (from o in _dataService.Outputs join ov in _dataService.OperandValues on o.OutputID equals ov.OutputID select o).ToList();
The specified LINQ expression contains references to queries that are
associated with different contexts.
I understand that I cannot use two different contexts in the same query, but I'm failing to see how this LINQ query is using multiple contexts. Two different tables in the same context, sure. But I don't understand why I'm getting this error. I would appreciate any insights you have to offer.
Thank you.
Content of the Output class:
//------------------------------------------------------------------------------
// <auto-generated>
// This code was generated from a template.
//
// Manual changes to this file may cause unexpected behavior in your application.
// Manual changes to this file will be overwritten if the code is regenerated.
// </auto-generated>
//------------------------------------------------------------------------------
namespace Dematic.Tools.QMA.DataAccess.QMA
{
using System;
using System.Collections.Generic;
public partial class Output: QmaEntityBase
{
[System.Diagnostics.CodeAnalysis.SuppressMessage("Microsoft.Usage", "CA2214:DoNotCallOverridableMethodsInConstructors")]
public Output()
{
this.OperandValues = new HashSet<OperandValue>();
this.OutputXBrands = new HashSet<OutputXBrand>();
this.OutputCountries = new HashSet<OutputCountry>();
this.HistoryOperandValues = new HashSet<HistoryOperandValue>();
this.HistoryOutputs = new HashSet<HistoryOutput>();
this.ScenarioOptions = new HashSet<ScenarioOption>();
}
public System.Guid OutputID { get; set; }
public string Name { get; set; }
public string Description { get; set; }
public System.Guid RuleSetID { get; set; }
public Nullable<System.Guid> OriginalOutputID { get; set; }
public System.Guid ServiceCatalogID { get; set; }
public System.Guid QuotingOfficeID { get; set; }
public System.Guid StatusID { get; set; }
public int RecipeID { get; set; }
public int SequenceNumber { get; set; }
public bool IsSyncedToOwner { get; set; }
public System.Guid CalculationMethodID { get; set; }
public System.Guid CalculationLevelID { get; set; }
public string ToolTip { get; set; }
public Nullable<bool> IsCtsControlled { get; set; }
public string Notes { get; set; }
public string SourceApplication { get; set; }
public Nullable<System.DateTime> CreateDateTime { get; set; }
public string CreateUser { get; set; }
public Nullable<System.DateTime> ModifyDateTime { get; set; }
public string ModifyUser { get; set; }
public Nullable<System.Guid> LaborLevelID { get; set; }
public System.Guid WBSID { get; set; }
public Nullable<System.Guid> BridgingClassificationTypeID { get; set; }
public Nullable<System.Guid> TradeDisciplineClassificationTypeID { get; set; }
public Nullable<int> ProjectTimelineTypeID { get; set; }
public System.Guid AttributeID { get; set; }
public string PopulatedRecipe { get; set; }
public Nullable<int> OutputCurrencyID { get; set; }
public virtual WBS WBS { get; set; }
public virtual Office Office { get; set; }
public virtual BridgingClassificationType BridgingClassificationType { get; set; }
public virtual CalculationLevel CalculationLevel { get; set; }
public virtual CalculationMethod CalculationMethod { get; set; }
public virtual LaborLevel LaborLevel { get; set; }
[System.Diagnostics.CodeAnalysis.SuppressMessage("Microsoft.Usage", "CA2227:CollectionPropertiesShouldBeReadOnly")]
public virtual ICollection<OperandValue> OperandValues { get; set; }
public virtual Output ParentOutput { get; set; }
public virtual ProjectTimelineType ProjectTimelineType { get; set; }
public virtual Recipe Recipe { get; set; }
public virtual RuleSet RuleSet { get; set; }
public virtual ServiceCatalog ServiceCatalog { get; set; }
public virtual Status Status { get; set; }
public virtual TradeDisciplineClassificationType TradeDisciplineClassificationType { get; set; }
[System.Diagnostics.CodeAnalysis.SuppressMessage("Microsoft.Usage", "CA2227:CollectionPropertiesShouldBeReadOnly")]
public virtual ICollection<OutputXBrand> OutputXBrands { get; set; }
[System.Diagnostics.CodeAnalysis.SuppressMessage("Microsoft.Usage", "CA2227:CollectionPropertiesShouldBeReadOnly")]
public virtual ICollection<OutputCountry> OutputCountries { get; set; }
public virtual Attribute Attribute { get; set; }
[System.Diagnostics.CodeAnalysis.SuppressMessage("Microsoft.Usage", "CA2227:CollectionPropertiesShouldBeReadOnly")]
public virtual ICollection<HistoryOperandValue> HistoryOperandValues { get; set; }
[System.Diagnostics.CodeAnalysis.SuppressMessage("Microsoft.Usage", "CA2227:CollectionPropertiesShouldBeReadOnly")]
public virtual ICollection<HistoryOutput> HistoryOutputs { get; set; }
[System.Diagnostics.CodeAnalysis.SuppressMessage("Microsoft.Usage", "CA2227:CollectionPropertiesShouldBeReadOnly")]
public virtual ICollection<ScenarioOption> ScenarioOptions { get; set; }
public virtual CurrencyType CurrencyType { get; set; }
}
}
Content of the OperandValue class:
//------------------------------------------------------------------------------
// <auto-generated>
// This code was generated from a template.
//
// Manual changes to this file may cause unexpected behavior in your application.
// Manual changes to this file will be overwritten if the code is regenerated.
// </auto-generated>
//------------------------------------------------------------------------------
namespace Dematic.Tools.QMA.DataAccess.QMA
{
using System;
using System.Collections.Generic;
public partial class OperandValue : QmaEntityBase
{
public System.Guid OperandValueID { get; set; }
public System.Guid OutputID { get; set; }
public Nullable<System.Guid> AttributeID { get; set; }
public int SequenceNumber { get; set; }
public string Notes { get; set; }
public string Tag1 { get; set; }
public string Tag2 { get; set; }
public Nullable<decimal> NumericValue { get; set; }
public string TextValue { get; set; }
public string SourceApplication { get; set; }
public Nullable<System.DateTime> CreateDateTime { get; set; }
public string CreateUser { get; set; }
public Nullable<System.DateTime> ModifyDateTime { get; set; }
public string ModifyUser { get; set; }
public decimal InternalValue { get; set; }
public virtual Attribute Attribute { get; set; }
public virtual Output Output { get; set; }
}
}
A: Per the comments on the original question, two different database contexts are indeed being used in the underlying IDataService implementation, related to a UnitOfWork object. To resolve the error, you'll need to figure out how to use a shared database context.
| {
"redpajama_set_name": "RedPajamaStackExchange"
} | 3,768 |
'use strict';
import {IDisposable} from 'vs/base/common/lifecycle';
import URI from 'vs/base/common/uri';
import {IConfigurationService} from 'vs/platform/configuration/common/configuration';
import {ContextMenuService} from 'vs/platform/contextview/browser/contextMenuService';
import {IContextMenuService, IContextViewService} from 'vs/platform/contextview/browser/contextView';
import {ContextViewService} from 'vs/platform/contextview/browser/contextViewService';
import {IEditorService} from 'vs/platform/editor/common/editor';
import {IEventService} from 'vs/platform/event/common/event';
import {EventService} from 'vs/platform/event/common/eventService';
import {IExtensionService} from 'vs/platform/extensions/common/extensions';
import {IInstantiationService} from 'vs/platform/instantiation/common/instantiation';
import {InstantiationService} from 'vs/platform/instantiation/common/instantiationService';
import {ServiceCollection} from 'vs/platform/instantiation/common/serviceCollection';
import {ICommandService} from 'vs/platform/commands/common/commands';
import {CommandService} from 'vs/platform/commands/common/commandService';
import {IOpenerService} from 'vs/platform/opener/common/opener';
import {IKeybindingService} from 'vs/platform/keybinding/common/keybinding';
import {IContextKeyService} from 'vs/platform/contextkey/common/contextkey';
import {MarkerService} from 'vs/platform/markers/common/markerService';
import {IMarkerService} from 'vs/platform/markers/common/markers';
import {IMessageService} from 'vs/platform/message/common/message';
import {IProgressService} from 'vs/platform/progress/common/progress';
import {IStorageService, NullStorageService} from 'vs/platform/storage/common/storage';
import {ITelemetryService, NullTelemetryService} from 'vs/platform/telemetry/common/telemetry';
import {IWorkspaceContextService, WorkspaceContextService} from 'vs/platform/workspace/common/workspace';
import {ICodeEditorService} from 'vs/editor/common/services/codeEditorService';
import {IEditorWorkerService} from 'vs/editor/common/services/editorWorkerService';
import {EditorWorkerServiceImpl} from 'vs/editor/common/services/editorWorkerServiceImpl';
import {IModeService} from 'vs/editor/common/services/modeService';
import {MainThreadModeServiceImpl} from 'vs/editor/common/services/modeServiceImpl';
import {IModelService} from 'vs/editor/common/services/modelService';
import {ModelServiceImpl} from 'vs/editor/common/services/modelServiceImpl';
import {CodeEditorServiceImpl} from 'vs/editor/browser/services/codeEditorServiceImpl';
import {SimpleConfigurationService, SimpleMessageService, SimpleExtensionService, StandaloneKeybindingService} from 'vs/editor/browser/standalone/simpleServices';
import {ContextKeyService} from 'vs/platform/contextkey/browser/contextKeyService';
import {IMenuService} from 'vs/platform/actions/common/actions';
import {MenuService} from 'vs/platform/actions/common/menuService';
import {ICompatWorkerService} from 'vs/editor/common/services/compatWorkerService';
import {MainThreadCompatWorkerService} from 'vs/editor/common/services/compatWorkerServiceMain';
export interface IEditorContextViewService extends IContextViewService {
dispose(): void;
setContainer(domNode:HTMLElement): void;
}
export interface IEditorOverrideServices {
/**
* @internal
*/
compatWorkerService?: ICompatWorkerService;
/**
* @internal
*/
modeService?: IModeService;
/**
* @internal
*/
extensionService?:IExtensionService;
/**
* @internal
*/
instantiationService?:IInstantiationService;
/**
* @internal
*/
messageService?:IMessageService;
/**
* @internal
*/
markerService?:IMarkerService;
/**
* @internal
*/
menuService?:IMenuService;
/**
* @internal
*/
editorService?:IEditorService;
/**
* @internal
*/
commandService?:ICommandService;
/**
* @internal
*/
openerService?:IOpenerService;
/**
* @internal
*/
contextKeyService?:IContextKeyService;
/**
* @internal
*/
keybindingService?:IKeybindingService;
/**
* @internal
*/
contextService?:IWorkspaceContextService;
/**
* @internal
*/
contextViewService?:IEditorContextViewService;
/**
* @internal
*/
contextMenuService?:IContextMenuService;
/**
* @internal
*/
telemetryService?:ITelemetryService;
/**
* @internal
*/
eventService?:IEventService;
/**
* @internal
*/
storageService?:IStorageService;
/**
* @internal
*/
configurationService?:IConfigurationService;
/**
* @internal
*/
progressService?:IProgressService;
/**
* @internal
*/
modelService?: IModelService;
/**
* @internal
*/
codeEditorService?: ICodeEditorService;
/**
* @internal
*/
editorWorkerService?: IEditorWorkerService;
}
export interface IStaticServices {
configurationService: IConfigurationService;
compatWorkerService: ICompatWorkerService;
modeService: IModeService;
extensionService: IExtensionService;
markerService: IMarkerService;
menuService: IMenuService;
contextService: IWorkspaceContextService;
messageService: IMessageService;
telemetryService: ITelemetryService;
modelService: IModelService;
codeEditorService: ICodeEditorService;
editorWorkerService: IEditorWorkerService;
eventService: IEventService;
storageService: IStorageService;
commandService: ICommandService;
instantiationService: IInstantiationService;
}
function shallowClone<T>(obj:T): T {
let r:T = <any>{};
if (obj) {
let keys = Object.keys(obj);
for (let i = 0, len = keys.length; i < len; i++) {
let key = keys[i];
r[key] = obj[key];
}
}
return r;
}
export function ensureStaticPlatformServices(services: IEditorOverrideServices): IEditorOverrideServices {
services = shallowClone(services);
var statics = getOrCreateStaticServices(services);
let keys = Object.keys(statics);
for (let i = 0, len = keys.length; i < len; i++) {
let serviceId = keys[i];
if (!services.hasOwnProperty(serviceId)) {
services[serviceId] = statics[serviceId];
}
}
return services;
}
export function ensureDynamicPlatformServices(domElement:HTMLElement, services: IEditorOverrideServices): IDisposable[] {
let r:IDisposable[] = [];
let contextKeyService:IContextKeyService;
if (typeof services.contextKeyService === 'undefined') {
contextKeyService = new ContextKeyService(services.configurationService);
r.push(contextKeyService);
services.contextKeyService = contextKeyService;
} else {
contextKeyService = services.contextKeyService;
}
if (typeof services.keybindingService === 'undefined') {
let keybindingService = new StandaloneKeybindingService(contextKeyService, services.commandService, services.messageService, domElement);
r.push(keybindingService);
services.keybindingService = keybindingService;
}
let contextViewService:IEditorContextViewService;
if (typeof services.contextViewService === 'undefined') {
contextViewService = new ContextViewService(domElement, services.telemetryService, services.messageService);
r.push(contextViewService);
services.contextViewService = contextViewService;
} else {
contextViewService = services.contextViewService;
}
if (typeof services.contextMenuService === 'undefined') {
let contextMenuService = new ContextMenuService(domElement, services.telemetryService, services.messageService, contextViewService);
r.push(contextMenuService);
services.contextMenuService = contextMenuService;
}
return r;
}
// The static services represents a map of services that once 1 editor has been created must be used for all subsequent editors
var staticServices: IStaticServices = null;
export function getOrCreateStaticServices(services?: IEditorOverrideServices): IStaticServices {
if (staticServices) {
return staticServices;
}
services = services || {};
let serviceCollection = new ServiceCollection();
const instantiationService = new InstantiationService(serviceCollection, true);
let contextService = services.contextService || new WorkspaceContextService({
resource: URI.from({ scheme: 'inmemory', authority: 'model', path: '/' })
});
serviceCollection.set(IWorkspaceContextService, contextService);
let telemetryService = services.telemetryService || NullTelemetryService;
serviceCollection.set(ITelemetryService, telemetryService);
let eventService = services.eventService || new EventService();
serviceCollection.set(IEventService, eventService);
let configurationService = services.configurationService || new SimpleConfigurationService();
serviceCollection.set(IConfigurationService, configurationService);
let messageService = services.messageService || new SimpleMessageService();
serviceCollection.set(IMessageService, messageService);
let extensionService = services.extensionService || new SimpleExtensionService();
serviceCollection.set(IExtensionService, extensionService);
let commandService = services.commandService || new CommandService(instantiationService, extensionService);
serviceCollection.set(ICommandService, commandService);
let markerService = services.markerService || new MarkerService();
serviceCollection.set(IMarkerService, markerService);
let modeService = services.modeService || new MainThreadModeServiceImpl(instantiationService, extensionService, configurationService);
serviceCollection.set(IModeService, modeService);
let modelService = services.modelService || new ModelServiceImpl(markerService, configurationService, messageService);
serviceCollection.set(IModelService, modelService);
let compatWorkerService = services.compatWorkerService || new MainThreadCompatWorkerService(modelService);
serviceCollection.set(ICompatWorkerService, compatWorkerService);
let editorWorkerService = services.editorWorkerService || new EditorWorkerServiceImpl(modelService);
serviceCollection.set(IEditorWorkerService, editorWorkerService);
let codeEditorService = services.codeEditorService || new CodeEditorServiceImpl();
serviceCollection.set(ICodeEditorService, codeEditorService);
let menuService = services.menuService || new MenuService(extensionService, commandService);
serviceCollection.set(IMenuService, menuService);
staticServices = {
configurationService: configurationService,
extensionService: extensionService,
commandService: commandService,
compatWorkerService: compatWorkerService,
modeService: modeService,
markerService: markerService,
menuService: menuService,
contextService: contextService,
telemetryService: telemetryService,
messageService: messageService,
modelService: modelService,
codeEditorService: codeEditorService,
editorWorkerService: editorWorkerService,
eventService: eventService,
storageService: services.storageService || NullStorageService,
instantiationService: instantiationService
};
return staticServices;
}
| {
"redpajama_set_name": "RedPajamaGithub"
} | 1,084 |
\section{Introduction}
\label{sec:intro}
It has long been known that galaxies in cluster environments evolve differently from their counterparts in the field. In particular, the relative number of early-type galaxies in cluster environments is significantly higher than in the field \citep[e.g.][]{Oemler1974,Dressler1980}. In addition, the galaxies that are present in clusters have a smaller atomic gas reservoir than their counterparts in the field \citep{Haynes1984,Cayatte1990,Solanes2001,Gavazzi2005}. The clustering of galaxies generates an extreme environment, that is likely capable of quenching the star formation in galaxies, transforming them from blue, late-type galaxies to red ellipticals.
Over the years, various processes have been proposed as the responsible mechanism for this transformation. Ram pressure stripping (RPS) was first suggested as a candidate by \cite{Gunn1972}, and similarly viscous stripping by \cite{Nulsen1982}, starvation by \cite{Larson1980}, and thermal evaporation by \cite{Cowie1977}. Furthermore there are galaxy-galaxy interactions, such as harassment \citep{Moore1996} and mergers. So called pre-processing, which takes place at higher redshifts when the clusters are first formed and the galaxies' velocities are still relatively low, also plays a role in shaping the galaxies, in the form of minor mergers and tidal interactions (\citealt{Mihos2004,Fujita2004}, see \citealt{Boselli2006} for an extended review). The relative importance of the different mechanisms is still poorly understood. In any case, it is clear that the cluster environment plays a fundamental role in galaxy evolution, especially keeping in mind that $\sim$40\% of galaxies live in groups or clusters \citep[e.g.][]{Robotham2011}, and the majority of the local galaxies live in groups \citep[e.g.][]{Zabludoff1998}.
It is well known that the atomic gas in galaxies is affected by the above-mentioned processes. The situation is more complicated for the molecular gas, because it is more tightly bound to the galaxy and distributed more centrally. The debate about this has therefore been more lively. Early research often concluded that the molecular gas in cluster galaxies is the same as that in field galaxies, and is unaffected by the cluster environment \citep[e.g.][]{Stark1986, Kenney1989, Casoli1991, Boselli1995, Boselli2006}. It was not until more recently that indications of deficiency, i.e. a lower mass than expected based on statistics of similar galaxies in the field, were observed for the molecular gas as well \citep[e.g.][]{Vollmer2008,Fumagalli2009,Boselli2014} and also for dust \citep[e.g.][]{Cortese2010,Cortese2012}. Although, these deficiencies are smaller than for H{\sc i}. On average galaxies which are H{\sc i} deficient by a factor of $\sim$10 are CO deficient by a factor of $\sim$2. \citet{Lee2017} report examples of three galaxies in the Virgo cluster that are ram pressure stripped of their molecular gas as well as their atomic gas. At higher redshifts, evidence of molecular gas stripping and deficiencies in clusters has also recently been observed \citep[e.g.][]{Noble2018,Wang2018,Stach2017}, although cluster galaxies with molecular gas contents similar to \citep[e.g.][]{Rudnick2017} or even higher than \citep[e.g.][]{Hayashi2018} field galaxies are found as well.
Because molecular gas is the direct fuel for star formation, the effects of the cluster environment on this phase of the interstellar medium (ISM) have immediate consequences for the star formation rate of the host galaxy. If it is directly affected by environmental processes, this could have important implications for the quenching of cluster members and therefore for galaxy evolution as a whole.
The goal of this work is to investigate whether the cluster environment indeed affects the molecular gas in galaxies, and if so, attempt to identify which processes are mainly responsible for this. In order to do this, we focus our attention on the Fornax cluster. Fornax is among the two nearest galaxy clusters, together with the Virgo cluster. They are located at 19.95 \citep{Tonry2001} and 16.8 Mpc (NASA/IPAC Extragalactic Database), respectively. Both clusters are therefore ideal laboratories to study the effects of the cluster environment on galaxies at high resolution. Extensive catalogues exist for both clusters, compiled by \cite{Binggeli1985} for Virgo and by \cite{Ferguson1989} for Fornax. Other, more recent studies of the Virgo cluster include the deep optical Next Generation Virgo Survey (NGVS, \citealt{Ferrarese2012}), the \textit{Herschel} Virgo Cluster Survey (HeViCS, \citealt{Davies2010}) in the far infrared, the GALEX Ultraviolet Virgo Cluster Survey (GUViCS, \citealt{Boselli2011}) in the UV, and the blind narrow-band H$\alpha$ + [NII] imaging survey Virgo Environmental Survey Tracing Ionised Gas Emission (VESTIGE, \citealt{Boselli2018}). Located in the southern hemisphere, Fornax has been studied less than its northern counterpart. However, recently more and more studies of the Fornax cluster have appeared. These include the optical Fornax Deep Survey (FDS, \citealt{Iodice2016,Iodice2017}, Peletier et al., in prep., \citealt{Venhola2017,Venhola2018}), the Herschel Fornax Cluster Survey (HeFoCS, \citealt{Davies2013}) the integral-field spectroscopic survey Fornax3D \citep{Sarzi2018}, the blind H{\sc i} Australia Telescope Compact Array (ATCA) survey \citep{Lee-Waddell2018}, and soon the MeerKAT Fornax HI and radio continuum survey \citep{Serra2016}.
There are some fundamental differences between both clusters that add to the importance of studying the Fornax cluster in addition to the Virgo cluster. First, Fornax is much smaller than Virgo, with Virgo being $\sim$10 times as massive as Fornax \citep{Jordan2007}. It is home to $\sim$2000 galaxies, while Fornax harbours only 350 (detected at the time of the catalogues mentioned above, both complete in magnitudes up to $B_T \approx 18$, and containing members with magnitudes up to $B_T \approx 20$). Despite its smaller size, the Fornax cluster has a number density of roughly three times that of Virgo. Fornax is also more regular and dynamically evolved than Virgo, and has a lower velocity dispersion. Because it is more relaxed, environment and density related effects are easier to identify in Fornax: galaxies in its centre will be more strongly affected by density effects than galaxies in the outskirts. In Virgo these effects are harder to identify, because it is still in the process of assembling. The central hot gas density in Fornax is 4 times lower than in Virgo, and its temperature twice as low \citep{Schindler1999,Paolillo2002,Scharf2005}. These differences suggest that ram pressure stripping plays less of a role in the Fornax cluster, compared to Virgo. According to \cite{Davies2013} ram pressure stripping should be a factor 16 less important in Fornax, based on the equation from \cite{Gunn1972}: $P_r \approx \rho_e v^2$, where $P_r$ is the ram pressure, $\rho_e$ is the intracluster density, and $v$ the velocity of the galaxy. The higher number density in Fornax, on the other hand, suggests that galaxy-galaxy interactions are more important. In this work we turn to a resolved study of the ISM in Fornax galaxies to investigate these processes further.
\cite{Horellou1995} carried out an H{\sc i} and $^{12}$CO(1-0) survey of 21 spirals and lenticulars in the Fornax cluster, using the Nan\c{c}ay radio telescope (France) and the Swedish-ESO Submillimeter Telescope (SEST, \citealt{Booth1989}), respectively. They detected 16 galaxies in HI, and 11 were detected in CO. They found that on average the CO emission of Fornax galaxies is weak: about five times lower than that of spirals in the Virgo cluster. From this it follows that the corresponding molecular gas masses are low as well: they found H$_2$ masses that are about ten times lower than the atomic gas masses. They attribute the decreased molecular gas masses to reduced star-formation activity, and argue that it is in agreement with low far-infrared, radio continuum and H$\alpha$ luminosities. They comment, however, that although the CO emission found for the Fornax galaxies is low compared to that in infrared-selected samples, that may be typical for spirals in optically-selected samples. In this work we revisit the CO($J$=1-0) in the Fornax cluster and investigate whether these observations can be confirmed.
The ALMA Fornax Cluster Survey is a complete survey of the 30 Fornax cluster members that were detected in 3 or more \textit{Herschel} Space Observatory \citep{Pilbratt2010} bands with the \textit{Herschel} Fornax Cluster Survey \citep{Fuller2014} or in H{\sc i} (\citealt{Waugh2002}, Loni et al. in prep. based on ATCA data). The CO(1-0) rotational line (rest frequency: 115.271 GHz) was observed to create spatially resolved maps of the cold molecular gas and its kinematics in these galaxies. The survey covers a range of different galaxy stellar masses and morphologies.
A full description of the sample can be found in \S \ref{sec:sample_selection}. The observations, data reduction, and ancillary data are described in \S \ref{sec:observations}. In \S \ref{sec:results} we present moment maps of the CO emission of the detected galaxies, as well as their position-velocity diagrams (PVDs) and spectra, and a comparison with optical observations. H$_2$ masses are estimated and compared with the expected H$_2$ masses for field galaxies. In \S \ref{sec:discussion} we discuss the results, and the morphologies and kinematics of the galaxies in the sample. Various environmental processes are considered as possible candidates for the irregularities observed, and the surprising detection of several dwarf galaxies is discussed. In \S \ref{sec:conclusions} we summarise the work, and distil conclusions. Although accurate distance measurements are available for some of the AlFoCS galaxies, here we adopt the distance to the Fornax cluster (19.95 Mpc, \citealt{Tonry2001}) as a common distance to all galaxies.
\section{Sample selection}
\label{sec:sample_selection}
\begin{figure}
\centering
\includegraphics[width=0.52\textwidth]{FCC_targets_mono_mirror.pdf}
\caption{Map of the Fornax cluster. The black dots represent Fornax Deep Survey galaxies from \citet[][see \S \ref{sub:optical_data}]{Venhola2018}, the red stars represent the AlFoCS sample. The central galaxy, NGC1399, is indicated with a larger yellow star, and the virial radius (located at 0.7 Mpc, \citealt{Drinkwater2001a}) is shown as a dotted line. AlFoCS targets are distributed evenly over the cluster (except for the infalling subgroup, which was not covered by \textit{Herschel}). NGC1316, the central galaxy of the infalling subgroup, is indicated with a cyan star.}
\label{fig:Fornax}
\end{figure}
\begin{figure}
\centering
\includegraphics[width=0.45\textwidth]{Trumpet.pdf}
\caption{Caustic diagram of the Fornax cluster. The black data points represent the FDS galaxies for which velocity information is available, and the red stars represent the AlFoCS targets. The solid lines represent the escape velocities in the cluster as a function of distance from the cluster centre. The vertical dotted line indicates the virial radius at 0.7 Mpc \citep{Drinkwater2001a}. $\bar{v} = 1493$ km~s$^{-1}$ and $\sigma = 374$ km~s$^{-1}$ \citep{Drinkwater2001a}. The AlFoCS targets are distributed evenly in the caustic space.}
\label{fig:trumpet}
\end{figure}
Our sample is based on the Fornax Cluster Catalogue \citep[FCC,][]{Ferguson1989}. From this catalogue, galaxies with stellar masses $>3 \times 10^8 \text{ M}_\odot$ were selected to ensure high enough metallicity to detect CO. Furthermore, galaxies were selected to contain dust \citep{Fuller2014} or HI down to $\sim3 \times 10^7 M_\odot$ (\citealt{Waugh2002}, Loni et al. in prep. based on ATCA data). This suggests ongoing star formation activity, and therefore the presence of a molecular gas reservoir. Whether a galaxy was selected based on its FIR emission or H{\sc i} content is listed in Table \ref{tab:targets}. The application of these criteria on the FCC leads to a sample of 30 galaxies, spanning a wide range of morphological types, varying from giant ellipticals to irregular dwarfs. A wide range of locations within the cluster is covered by the survey. This is shown in Figure \ref{fig:Fornax}, where we compare the locations of the AlFoCS galaxies with the locations of the galaxies in the Fornax Deep Survey (FDS, \citealt{Iodice2016,Iodice2017}, Peletier et al., in prep., \citealt{Venhola2017,Venhola2018}). The FDS is a recent optical survey of the Fornax cluster, containing 573 galaxies, and is described in more detail in \S \ref{sub:optical_data}. The FDS galaxies are shown as black dots, and the galaxies targeted here are shown as red stars. The brightest cluster galaxy (BCG) NGC1399 is shown as a bigger yellow star, and the dotted line represents the virial radius of the cluster according to \citet{Drinkwater2001a}. The central galaxy of the currently infalling subgroup in the south-east of the figure, NGC1316, is indicated with a cyan star. Aside from a slight ($<$10\%) deficiency of galaxies in the innermost ($\sim$350 kpc or 1 degree) radius of the cluster centre (defined as the location of NGC1399), the AlFoCS targets are spread evenly among the cluster galaxies: they are located at all directions from the cluster centre, and both close to the central galaxy, and outside the virial radius. There are no observations in the infalling subgroup around NGC1316, as this area was not covered by \textit{Herschel}.
\begin{table*}
\centering
\begin{threeparttable}
\caption{Key properties of the galaxies in the sample.}
\label{tab:targets}
\begin{tabular}{lllllll}
\hline
Common name & FCC \# & RA & Dec & $cz$ & $M_\star$ & Selection \\
- & - & (J2000) & (J2000) & (km~s$^{-1}$) & (log($M_{\odot}$)) & - \\
(1) & (2) & (3) & (4) & (5) & (6) & (7) \\
\hline
FCC32 & 32 & 03h24m52.4s & -35d26m08s & 1319 $^\diamond$ & $9.23^{+0.04}_{-0.07}$* & FIR \\
FCC44 & 44 & 03h26m07.4s & -35d07m39s & 1233 $^\diamond$ & $8.50^{+0.07}_{-0.17}$* & FIR \\
NGC1351A & 67 & 03h28m48.7s & -35d10m41s & 1354 & 9.45$^\dagger$ & FIR, H{\sc i} \\
MGC-06-08-024 & 90 & 03h31m08.2s & -36d17m25s & 1814 $^\diamond$ & 8.98$^\dagger$ & FIR, H{\sc i} \\
FCC102 & 102 & 03h32m10.7s & -36d13m15s & 1722 $^\ddagger$ & $8.36^{+0.08}_{-0.10}$* & H{\sc i} \\
ESO358-G015 & 113 & 03h33m06.8s & -34d48m29s & 1389 & 8.88$^\dagger$ & FIR, H{\sc i} \\
ESO358-16 & 115 & 03h33m09.2s & -35d43m07s & 1701 $^\diamond$ & $8.32^{+0.07}_{-0.09}$* & H{\sc i} \\
FCC117 & 117 & 03h33m14.6s & -37d49m11s & - & $7.77^{+0.18}_{-0.20}$* & FIR \\
FCC120 & 120 & 03h33m34.2s & -36d36m21s & 849 $^\ddagger$ & $8.50^{+0.07}_{-0.09}$* & H{\sc i} \\
NGC1365 & 121 & 03h33m36.4s & -36d08m25s & 1638 $^\diamond$ & 11.16$^\dagger$ & FIR, H{\sc i} \\
NGC1380 & 167 & 03h36m27.6s & -34d58m34s & 1878 $^\diamond$ & 10.98$^\dagger$ & FIR \\
FCC177 & 177 & 03h36m47.5s & -34d44m23s & 1562 $^\diamond$ & $10.4^{+0.01}_{-0.02}$* & FIR \\
NGC1386 & 179 & 03h36m46.2s & -35d59m58s & 869 $^\diamond$ & 10.5$^\dagger$ & FIR \\
NGC1387 & 184 & 03h36m57.0s & -35d30m24s & 1303 $^\diamond$ & 10.77$^\dagger$ & FIR \\
FCC198 & 198 & 03h37m42.7s & -37d12m30s & - & $8.09^{+0.05}_{-0.07}$* & FIR \\
FCC206 & 206 & 03h38m13.5s & -37d17m25s & 1403 $^\diamond$ & $9.01^{+0.07}_{-0.10}$* & FIR \\
FCC207 & 207 & 03h38m19.3s & -35d07m45s & 1421 $^\diamond$ & $8.78^{+0.04}_{-0.05}$* & FIR \\
NGC1427A & 235 & 03h40m09.3s & -35d37m28s & 2029 $^\diamond$ & 9.78$^\dagger$ & FIR, H{\sc i} \\
FCC261 & 261 & 03h41m21.5s & -33d46m09s & 1710 $^\ddagger$ & 8.58$^\dagger$ & FIR \\
PGC013571 & 263 & 03h41m32.6s & -34d53m18s & 1725 $^\diamond$ & 9.2$^\dagger$ & FIR, H{\sc i} \\
FCC282 & 282 & 03h42m45.3s & -33d55m14s & 1266 $^\ddagger$ & 9.0$^\dagger$ & FIR \\
NGC1437A & 285 & 03h43m02.2s & -36d16m24s & 891 $^\ddagger$ & 9.38$^\dagger$ & FIR, H{\sc i} \\
NGC1436 & 290 & 03h43m37.1s & -35d51m11s & 1388 $^\diamond$ & 10.1$^\dagger$ & FIR, H{\sc i} \\
FCC302 & 302 & 03h45m12.1s & -35d34m15s & 816 $^\ddagger$ & $8.48^{+0.09}_{-0.07}$* & H{\sc i} \\
FCC306 & 306 & 03h45m45.4s & -36d20m48s & 891 $^\ddagger$ & 8.68$^\dagger$ & FIR, H{\sc i} \\
NGC1437B & 308 & 03h45m54.8s & -36d21m25s & 1515 $^\ddagger$ & 9.39$^\dagger$ & FIR, H{\sc i} \\
ESO358-G063 & 312 & 03h46m19.0s & -34d56m37s & 1920 $^\ddagger$ & 10.04$^\dagger$ & FIR, H{\sc i} \\
FCC316 & 316 & 03h47m01.5s & -36d26m15s & 1547 $^\diamond$ & $8.64^{+0.07}_{-0.12}$* & FIR \\
FCC332 & 332 & 03h49m49.0s & -35d56m44s & 1327 $^\diamond$ & 8.63$^\dagger$ & FIR \\
ESO359-G002 & 335 & 03h50m36.7s & -35d54m34s & 1431 $^\diamond$ & 9.21$^\dagger$ & FIR \\
\hline
\end{tabular}
\textit{Notes:} 1: Common name of the galaxy; 2: Fornax Cluster Catalogue number of the galaxy; 3: Right ascension; 4: Declination; 5: Velocity (defined as the object's redshift times the speed of light); 6: Stellar mass. $^\ddagger$See \S \ref{sub:redshifts}; $^\diamond$Redshifts from NASA/IPAC Extragalactic Database; $^\dagger$Stellar masses from \citet{Fuller2014}; *Stellar masses derived from 3.6 $\mu$m images, (see \S \ref{sub:H2_masses}); 7: Whether the galaxy was selected based on an H{\sc i} (\citealt{Waugh2002}, Loni et al. in prep. based on ATCA data) or a FIR \citep{Fuller2014} detection (or both).
\end{threeparttable}
\end{table*}
To confirm that all targets are indeed cluster members, we create a caustic diagram of all galaxies with known velocities: the (projected) velocities of the galaxies (corrected for the velocity of the cluster and galaxy-to-galaxy velocity dispersion within the cluster) of the cluster as a function of their distance from the cluster centre. This is shown in Figure \ref{fig:trumpet}. The mean velocity and velocity dispersion of the Fornax cluster were taken from \citet{Drinkwater2001a}, and equal 1493 km~s$^{-1}$ and 374 km~s$^{-1}$, respectively. The velocities of the individual galaxies are a combination of velocities from the FCC, the 2dF Galaxy Redshift Survey \citep{Colless2001,Drinkwater1999}, and the 2MASS Redshift Survey \citep{Huchra2012}. Note that velocity information is unavailable for 470 of the 573 FDS galaxies, and these were omitted from the figure. The solid lines represent the escape velocities at each projected distance from the cluster centre, assuming a Navarro-Frenk-White (NFW) density profile for the cluster dark matter distribution \citep{Navarro1997}. They were derived using equation 7 and 16 from \citet{Shull2014}, featuring a dark matter concentration parameter, which was estimated using equation 3 from \citet{Coe2010}. The dotted line again represents the virial radius, and the colours are the same as in Figure \ref{fig:Fornax}. All AlFoCS galaxies shown here have velocities well below the escape velocity at their location, and are distributed evenly in the caustic space.
The locations, velocities, and stellar masses of the galaxies observed are listed in Table \ref{tab:targets}.
\section{Observations and data reduction}
\label{sec:observations}
\subsection{ALMA data}
\label{sub:ALMA_data}
\begin{table*}
\centering
\begin{threeparttable}
\caption{Observational parameters.}
\label{tab:obspars}
\begin{tabular}{cccccccccc}
\hline
SB & Date & \# ants & TOT & Bandpass cal. & Flux cal. & CF spw 3 & CV spw 3 & BW spw 3 & CF spws 0, 1, 2 \\
- & - & - & (mins.) & - & - & (GHz) & (km~s$^{-1}$) & (km~s$^{-1}$) & (GHz, resp.) \\
(1) & (2) & (3) & (4) & (5) & (6) & (7) & (8) & (9) & (10) \\
\hline
Single fields & 07-01-2016 & 42 & 52 & J0336-3616 & J0336-3616 & 114.547 & 1885 & 4898 & 113.001, 100.939, 102.544 \\
Small mosaics & 11-01-2016 & 46 & 125 & Uranus & J0336-3616 & 114.756 & 1340 & 4907 & 112.818, 100.824, 102.713 \\
Dwarfs & 12-01-2016 & 43 & 251 & Uranus & J0336-3616 & 114.716 & 1445 & 4900 & 113.161, 101.089, 102.703 \\
\hline
\end{tabular}
\textit{Notes:} 1: Scheduling Block; 2: Date of the observations; 3: Number of antennas used; 4: Total observation time in minutes; 5: Bandpass calibrator; 6: Flux calibrator; 7: Central frequency of spectral window 3 (centred on the $^{12}$CO(1-0) line); 8: Central velocity of spectral window 3 (centred on the $^{12}$CO(1-0) line); 9: Bandwidth of spectral window 3 (centred on the $^{12}$CO(1-0) line) 10: Central frequencies of the remaining spectral windows.
\end{threeparttable}
\end{table*}
Atacama Large Millimeter/submillimeter Array (ALMA) observations of the $^{12}$CO(1-0) line in 29 AlFoCS targets were carried out under project 2015.1.00497.S (PI: Timothy Davis). ALMA's 12 m configuration was used, which has a primary beam size of $\sim$55'' at $\sim$115 GHz. In cases where the FIR emission of the galaxy extends beyond this scale, multiple pointings are combined into a mosaic to ensure that CO is observed all the way to the outskirts of the galaxy. The largest recoverable scale is 25''. Band 3 observations were performed between the 7th and 12th of January 2016, subdivided in three Scheduling Blocks (SBs) in order to meet the sensitivity requirements of the different targets whilst keeping maximum efficiency: single fields, small mosaics, and dwarfs. The sensitivities achieved are listed in Table \ref{tab:observed_props}. The first Scheduling Block consists of one Execution Block (EB): uid\_\_\_A002\_Xaeaf96\_X515. The small mosaics are divided over two Execution Blocks: uid\_\_\_A002\_Xaec9ef\_X5c0 and uid\_\_\_A002\_Xaec9ef\_X88a. The same is true for the dwarfs, which are divided over Execution Blocks uid\_\_\_A002\_Xaecf7b\_X32d4 and uid\_\_\_A002\_Xaecf7b\_X3943. For each SB one spectral window was centred at 114.756, 114.547, and 114.716 GHz, respectively, to target the $^{12}$CO(1-0) rotational line. The bandwidths are 1.875 GHz, covering 3840 channels. The other spectral windows, covering 128 channels each with total bandwidths of 2 GHz, were used to target the band 3 continuum of the individual galaxies. Their central frequencies, along with other details of the observations, are listed in Table \ref{tab:obspars}. The expected calibration uncertainty of the data is 10\%. Synthesized beam sizes and the sensitivities achieved are listed in Table \ref{tab:observed_props}.
\subsubsection{Data reduction}
\label{subsub:data_reduction}
\indent The data were calibrated manually using the Common Astronomy Software Applications package (CASA, version 5.1.1, \citealt{McMullin2007}), using standard ALMA calibration scripts\footnote{The scripts used can be found on \url{https://github.com/NikkiZabel/AlFoCS_data_reduction_scripts}}. Several antennas were flagged manually, mostly because of high system temperatures or outliers in the data of the flux calibrator. The resulting ``dirty'' images were then ``cleaned'' using the \verb|tCLEAN| algorithm \citep{Hogbom1974} in CASA. In cases where both CO and continuum are detected, a continuum estimate is created using the full line-free bandwidth, and subtracted from the channels containing the CO line using the \verb|uvcontsub| command. Cleaning of the channels containing the CO line was done interactively, using a natural weighting scheme (equivalent to a Briggs weighting scheme \citep{Briggs1995} with a robust parameter of 2). Many of the sources have extended emission, and using natural weighting will help ensure that this is recovered in the data. This choice also maximises the signal-to-noise at the cost of decreased spatial resolution. The channel widths of most final data cubes are 10 km~s$^{-1}$, as is usually chosen for this type of data \citep[e.g.][]{Alatalo2013}, and the pixel sizes 0.5 arcseconds. Exceptions are the dwarf galaxies FCC207 and FCC261, for which channel widths of 2 km~s$^{-1}$ were used, because of their narrow line widths (see Table \ref{tab:observed_props}). The result is a three-dimensional RA-Dec-velocity data cube for each galaxy. Primary beam (PB) corrections are then carried out as a separate step using the \verb|impbcor| command, allowing us to store both PB corrected and non PB corrected data cubes. Beam sizes and sensitivities are listed in Table \ref{tab:observed_props}. Typical rms noise levels are around $\sim$3 mJy/beam. Channel maps of all detected galaxies in the sample can be found in the online data of the journal, or on \url{https://github.com/NikkiZabel/AlFoCS_channel_maps}.
\subsubsection{NGC1365}
\label{subsub:NGC1365}
In order to expand our sample, an already reduced image of NGC1365 was taken from the ALMA archive (project ID: 2015.1.01135.S, PI: Egusa, Fumi). It was observed on 20 March 2016. ALMA's 12m configuration was used, with a primary beam size of $\sim$55'' at $\sim$115 GHz. The mosaic covers an area of $\sim 6.6' \times \sim 4.4'$. The central frequency of spectral window 3 (the window centred on the $^{12}$CO(1-0) line) is 114.848 GHz or 1100 km~s$^{-1}$. The bandwidths are 1.875 GHz, covering 3840 channels. The spectral resolution is 2.55 km~s$^{-1}$. To obtain the final data cube, the \verb|CLEAN| algorithm in CASA version 4.7.0 was used. A continuum estimated and subtracted from the channels containing the CO line as described in \S \ref{subsub:data_reduction}. A briggs weighting scheme was adopted \citep{Briggs1995} with a robust parameter of 0.5. The pixel sizes of the final data cube are 0.3 arcseconds, and the channel width 5 km~s$^{-1}$. The synthesized beam size and the sensitivity achieved are listed in Table \ref{tab:observed_props}.
Aside from the data reduction, this observation is treated the same as the galaxies observed as part of this survey.
\subsection{Mopra data}
\label{sub:Mopra}
Additional single-dish observations of Fornax cluster galaxies from the Mopra Fornax Cluster CO-Line Legacy Survey (PI: M.W.L. Smith) are included, a survey of $^{12}$CO(1-0) in 28 galaxies in the Fornax cluster, carried out between the nights of 08-08-2012 and 17-09-2012. The Mopra Spectrometer (MOPS) was used in Wideband Mode, centred at a rest frequency of 115.500 GHz for all targets. Its coverage is 8.3 GHz (or 30,378 km~s$^{-1}$), and its spectral resolution 0.915 km~s$^{-1}$. The FWHM of the beam is 33 $\pm$ 2'' at 115 GHz \citep{Ladd2005}. The calibration uncertainty is less than 10\% \citep{Ladd2005}, we adopt a conservative value of 10\% here. The data were reduced using the ATNF \verb|LIVEDATA| \citep{Barnes2001} and \verb|GRIDZILLA| \citep{Sault1995} packages. \verb|LIVEDATA| is used to fit baselines and transform the raw datafiles to SDFITS files. We fit linear baselines to all spectra and mask the top and bottom 300 channels. \verb|GRIDZILLA| is then used to combine these files into data cubes. The spatial resolution of these cubes is 0.25' per pixel. We use our own scripts to combine the data from the various pointings into a mosaic. For a few objects only single pointings were required. For these objects the data reduction is done using our own scripts to obtain the quotient spectrum by subtracting and dividing by the obtained reference spectra, perform baseline subtraction, and velocity-bin the data. A ripple in the baseline is present in some of the data. This is a known issue with the Mopra telescope, and attempts to mitigate it here, for example by flagging in Fourier space, were not successful. The noise levels in these data are higher, but the data are still usable for the aims of this work.
\subsection{Optical data}
\label{sub:optical_data}
To allow for a comparison of the distribution of the cold molecular gas with the stellar bodies of the galaxies, and to create three-colour images, \textit{r}-, \textit{g}-, and \textit{u}-band images were obtained from the Fornax Deep Survey (FDS, \citealt{Iodice2016,Iodice2017}, Peletier et al., in prep., \citealt{Venhola2017,Venhola2018}) for all galaxies in which CO(1-0) was detected in AlFoCS. The FDS is a new, deep multi-band optical survey of the Fornax cluster, which covers 26 square degrees around the virial radius, including the SW sub-group centered on NGC1316 \citep{Iodice2017}. It has been obtained with the ESO VLT Survey Telescope (VST), which is a 2.6-meter diameter optical survey telescope located at Cerro Paranal, Chile \citep{Schipani2012}. The imaging is done in the \textit{u}', \textit{g}', \textit{r}' and \textit{i}'-bands using the 1$^o \times 1^o$ field of view OmegaCAM instrument \citep{Kuijken2002} attached to VST. The deep images provide data with excellent resolution with mean seeing of 1 arcsec and pixel size of 0.2 arcsec. The quality of the data and the photometry of the galaxies are described in detail in \citet{Venhola2018}. The survey area is covered with homogeneous depth with the 1$\sigma$ limiting surface brightness over 1 pixel area of 26.6, 26.7, 26.1 and 25.5 mag arcsec$^{-2}$ in \textit{u}', \textit{g}', \textit{r}' and \textit{i}', respectively. When averaged over a 1 arcsec$^2$ area, these numbers correspond to 28.3, 28.4, 27.8, 27.2 mag arcsec$^{-2}$ in \textit{u}', \textit{g}', \textit{r}' and \textit{i}', respectively. The photometric calibration errors of the FDS are 0.04, 0.03, 0.03, and 0.04 mag in \textit{u}', \textit{g}', \textit{r}' and \textit{i}', respectively. \citet{Venhola2018} produced S\'{e}rsic model fits for all the dwarf galaxies within the survey area using GALFIT \citep{Peng2002,Peng2010}. In addition, Iodice et al. (2018) have studied all bright ($m_B<15$ mag) ETGs inside the virial radius of the cluster (some of them are presented in this work). They released the total magnitudes, effective radii and stellar masses and discussed the structure and colors of the galaxy outskirts.
\subsection{Redshift determinations}
\label{sub:redshifts}
A subset of the AlFoCS objects were observed with the 3.9m Anglo-Australian Telescope at the Siding Spring Observatory as part of a larger programme. The AAOmega spectrograph (\citealt{Sharp2006}; \citealt{Saunders2004}) and the Two-degree Field (2dF; \citealt{Lewis2002}) fibre positioner were used, along with the 580V and 385R gratings, providing spectral coverage over 3740--8850\AA. The spectra were reduced using the 2dFDR software package (\citealt{Croom2004}), and spectral classifications and redshifts were determined using MARZ (\citealt{Hinton2016}). Velocities derived from these redshifts are listed in Table \ref{tab:targets}, indicated with a $\ddagger$.
\subsection{Moment maps}
\label{sub:moment_maps}
\indent Cleaned data cubes were used to produce moment maps of the CO(1-0) line emission, using the masked moment method \citep{Dame2011}. While PB corrected images are used in the remainder of this work, for the purpose of clarity uncorrected maps are presented in Figure \ref{fig:moment-maps_reg}, Figure \ref{fig:moment-maps_irreg}, and Appendix \ref{app:moment_maps}. In order to create the mask, a Gaussian smoothing was applied to a copy of the data cube, in both spatial axes as well as the velocity axis, with a full width at half the maximum (FWHM) of 1.5 times the beam's major axis for the spatial axes, and 4 channels (proven to be optimal from previous experience) for the velocity axis. Using this smoothed copy as a mask, the data cubes were then ``clipped'' to the $x\sigma$ level, which means that all spaxels below this value are set to zero, where $x$ is chosen to give the best visual result, and equals 3 or 4.
\begin{figure*}
\centering
\subfloat[]
{\hspace{-5mm}\includegraphics[height=0.35\textwidth \label{subfig:rgb_reg}]{NGC1387/RGB_image.pdf}}
\hspace{5mm}
\subfloat[]
{\includegraphics[height=0.35\textwidth \label{subfig:intens_map_reg}]{NGC1387/zeroth.pdf}}
\subfloat[]
{\hspace{0mm}\includegraphics[height=0.35\textwidth \label{subfig:vel_map_reg}]{NGC1387/first.pdf}}
\hspace{10mm}
\subfloat[]
{\includegraphics[height=0.35\textwidth \label{subfig:vel_disp_map_reg}]{NGC1387/second.pdf}}
\subfloat[]
{\includegraphics[height=0.39\textwidth \label{subfig:PVD_reg}]{NGC1387/PVD.pdf}}
\hspace{6mm}
\subfloat[]
{\includegraphics[height=0.355\textwidth \label{subfig:spectrum_reg}]{NGC1387/spectrum.pdf}}
\caption{a: Three-colour (\textit{r}-\textit{g}-\textit{u}) image of NGC1387. b: Moment zero map: distribution of the cold molecular gas as traced by the ALMA CO data. c: Moment 1 map: velocity map of the cold molecular gas. Each colour represents a 10 km~s$^{-1}$ velocity channel. d: Moment 2 map: linewidth of the CO integrated spectrum. e: Position-velocity diagram or of the cold molecular gas. The uncertainties in the spatial and velocity directions are indicated in the upper right corner. f: the CO(1-0) line. The beam of the observations is shown in the lower left corners of the moment maps, as well as a 1 kpc scale bar in the lower right corners. NGC1387 is a very regular galaxy with symmetric moment maps.}
\label{fig:moment-maps_reg}
\end{figure*}
\begin{figure*}
\subfloat[]
{\hspace{0mm}\includegraphics[height=0.35\textwidth \label{subfig:rgb_irreg}]{MCG-06-08-024/RGB_image.pdf}}
\hspace{0mm}
\subfloat[]
{\includegraphics[height=0.35\textwidth \label{subfig:intens_map_irreg}]{MCG-06-08-024/zeroth.pdf}}
\subfloat[]
{\hspace{-3mm}\includegraphics[height=0.35\textwidth \label{subfig:vel_map_irreg}]{MCG-06-08-024/first.pdf}}
\hspace{3mm}
\subfloat[]
{\includegraphics[height=0.35\textwidth \label{subfig:vel_disp_map_irreg}]{MCG-06-08-024/second.pdf}}
\subfloat[]
{\includegraphics[height=0.39\textwidth \label{subfig:PVD_irreg}]{MCG-06-08-024/PVD.pdf}}
\hspace{6mm}
\subfloat[]
{\includegraphics[height=0.355\textwidth \label{subfig:spectrum_irreg}]{MCG-06-08-024/spectrum.pdf}}
\caption{MGC-06-08-024 (FCC90), similar to Figure \ref{fig:moment-maps_reg}. MGC-06-08-024 is galaxy with irregular CO emission, and therefore has irregular moment maps and an irregular position-velocity diagram.}
\label{fig:moment-maps_irreg}
\end{figure*}
\begin{figure*}
\centering
\subfloat[]
{\includegraphics[height=0.4\textwidth \label{subfig:overplot-MCG}]{MCG-06-08-024/overplot_j2000.pdf}}
\subfloat[]
{\includegraphics[height=0.4\textwidth \label{subfig:overplot-G002}]{ESO359-G002/overplot_j2000.pdf}}
\hspace{1mm}\subfloat[]
{\includegraphics[height=0.4\textwidth \label{subfig:overplot-282}]{FCC282/overplot_j2000.pdf}}
\hspace{2mm}
\subfloat[]
{\includegraphics[height=0.4\textwidth \label{subfig:overplot-332}]{FCC332/overplot_j2000.pdf}}
\caption{CO(1-0) emission overplotted on optical (\textit{g}-band) images from the FDS (\citealt{Iodice2016,Iodice2017}, Peletier et al., in prep., \citealt{Venhola2017,Venhola2018}). The CO emission is shown as 10 coloured contours, the outer contour is set equal to 3 or 4 $\sigma$, while the level of the innermost contour depends on the highest signal measured in the galaxy. The beam is shown in the lower left corners, and a 1 kpc scalebar in the lower right corners. The arrow in the upper right corners indicates the direction towards the cluster centre. The molecular gas in these galaxies is asymmetric with respect to their stellar bodies. In \ref{subfig:overplot-MCG} and \ref{subfig:overplot-G002} it extends beyond the stellar body and forms a tail aligned with the direction of the cluster centre.}
\label{fig:overplots}
\end{figure*}
In Figure \ref{fig:moment-maps_reg} and Figure \ref{fig:moment-maps_irreg} moment maps of NGC1387 and MCG-06-08-024 are shown, serving as examples of the regular and disturbed galaxies, respectively (see \S \ref{sub:morphologies} for more details). The top left panel of each of these figures is a three-colour image, constructed using the \textit{r}-, \textit{g}-, and \textit{u}- band images from the Fornax Deep Survey (\citealt{Iodice2016,Iodice2017}, Peletier et al., in prep., \citealt{Venhola2017,Venhola2018}, see \S\ref{sub:optical_data}).
The top right panels are intensity or moment zero maps of the cold molecular gas as traced by the ALMA CO data, showing its spatial distribution. The black ellipse in the lower left corner shows the beam of the observations, and a 1 kpc scalebar is shown in the lower right corner. This is the same in the other two moment maps.
The middle left panels are velocity or moment one maps of the galaxies. Each of the colours represents a 10 km~s$^{-1}$ (2 km~s$^{-1}$ for FCC207 and FCC261, see \S \ref{subsub:data_reduction}) velocity channel. The warm colours represent the positive, redshifted velocities, and the cold colours represent the negative, blueshifted velocities.
Middle right figures are moment two maps, representing the linewidth.
The bottom left figures are position-velocity diagrams (PVDs), which reveal the motion of gas along the major axes of the galaxies. They are obtained by defining a slit the size of the beam along the major axis of the galaxy in the data cube, and collapsing it along the minor axis. The errorbars in the upper right corner indicate the PSF FWHM (horizontal) and channel width (vertical).
The bottom right figures show the part of the galaxy's spectrum containing the CO(1-0) line. The spectrum was obtained by defining a rectangular aperture around the detected emission in the spatial directions, large enough to contain all its CO emission, and then collapsing the data cube along both spatial axes.
In NGC1387 (Figure \ref{subfig:intens_map_reg}) the gas is distributed as an almost face-on disk, with the projected intensity decreasing radially. Its velocities vary between -80 and +80 km~s$^{-1}$ relative to the systemic velocity, which is determined by taking the mean of the moment one map shown here. The line is widest in a band along the kinematic minor axis, due to beam smeared rotation. The PVD of NGC1387 (Figure \ref{subfig:PVD_reg}) is very regular, showing a smooth and symmetric ``rotation curve'', which reaches its maximum very quickly. The double-peaked line profile, typical for a disk, is clearly visible in its spectrum (Figure \ref{subfig:spectrum_reg}).
In MCG-06-08-024 the molecular gas is distributed irregularly, around three different maxima. The velocities of the gas are between -60 and +60 km~s$^{-1}$ relative to the systemic velocity. The PVD of MCG-06-08-024 has a very irregular shape.%
Similar images of the remaining 14 detected galaxies were created in the same way, and can be found in Appendix \ref{app:moment_maps}.
\subsection{Comparison to optical morphology}
\label{subsub:optical}
Figure \ref{fig:overplots} overplots the CO integrated intensity contours on top of optical images of the galaxies (\textit{g}-band images of the FDS were used, see \S \ref{sub:optical_data}). The CO emission is shown as 10 coloured contours, the outer contour being equal to 3-4$\sigma$, while the innermost contour depends on the highest signal measured in the galaxy in question. The arrows in the upper right corners point towards the cluster centre (here defined as the location of the BCG NGC1399). Similar plots for the remaining galaxies can be found in Appendix \ref{app:overplots}.
The galaxies in Figure \ref{fig:overplots} are all examples of galaxies with irregular CO emission, asymmetric compared to the galaxy's stellar body. In MCG-06-08-024 (Figure \ref{subfig:overplot-MCG}) and ESO359-G002 (Figure \ref{subfig:overplot-G002}) the molecular gas forms a tail that extends beyond the stellar body. These galaxies are discussed further in \S \ref{sub:RPS}. Other examples of galaxies with asymmetric CO emission are FCC207 (Figure \ref{subfig:overplot_FCC207}) and FCC261 (Figure \ref{subfig:overplot_FCC261}). In the cases of the regular galaxies, such as ESO358-G063 (Figure \ref{subfig:overplot_ESO358-G063}), NGC1386 (Figure \ref{subfig:overplot_NGC1386}), NGC1387 (Figure \ref{subfig:overplot_NGC1387}), and NGC1351A (Figure \ref{subfig:overplot_NGC1351A}), the CO emission follows the optical shape of the galaxy. The CO emission in NGC1380 (Figure \ref{subfig:overplot_NGC1380}) is very compact compared to its stellar body in our images, but has been shown to be distributed in a regular disk by \citet{Boizelle2017}.
It would be interesting to compare the CO morphologies to H{\sc i} morphologies, especially for the galaxies that exhibit asymmetric CO emission or gas tails. This would show us whether these galaxies also have H{\sc i} tails, which is expected if ram pressure stripping is at play. The current H{\sc i} observations available are not of sufficient resolution to do this. However, in the future we will be able to use data from the MeerKAT Fornax Survey for this purpose.
\begin{table*}
\centering
\begin{threeparttable}
\caption{Observed and derived properties of the AlFoCS targets.}
\label{tab:observed_props}
\begin{tabular}{llllllllll}
\hline
Common name & FCC \# & Reg./dist. & Gauss/box & $b_{\text{maj}}; b_{\text{min}}; b_{\text{PA}}$ & rms & $\Delta v$ & $\int S_\nu d \nu$ & log$_{10}$($M_{\text{H}_{2}}$) & Deficiency \\
- & - & - & - & (''; ''; $^\text{o}$) & (mJy beam$^{-1}$) & (km~s$^{-1}$) & (Jy km~s$^{-1}$) & ($M_{\odot}$) & (dex) \\
(1) & (2) & (3) & (4) & (5) & (6) & (7) & (8) & (9) & (10) \\
\hline
FCC32 & 32 & - & G & 2.4; 1.8; 84 & 2.6 & 50 & $\leq$ 2.1 & $\leq$ 8.02 & $\leq$ 0.01 \\
FCC44 & 44 & - & G & 2.8; 2.0; 85 & 2.4 & 50 & $\leq$ 1.9 & $\leq$ 8.48 & $\leq$ 1.62 \\
NGC1351A & 67 & R & B & 2.6; 2.0; 61 & 3.6 & 250 $\pm$ 20 & 19.9 $\pm$ 2.0 & 7.83 $\pm$ 0.07 & -0.54 $\mp$ 0.01 \\
MGC-06-08-024 & 90 & D & G & 3.3; 2.4; 71 & 3.0 & 31 $\pm$ 7 & 1.71 $\pm$ 0.22 & 6.97 $\pm$ 0.07 & -1.11 $\mp$ 0.01 \\
FCC102 & 102 & - & G & 2.8; 2.0; 85 & 2.4 & 50 & $\leq$ 1.9 & $\leq$ 8.00 & $\leq$ 0.77 \\
ESO358-G015 & 113 & - & G & 3.1; 2.1; 71 & 3.2 & 50 & $\leq$ 2.5 & $\leq$ 7.61 & $\leq$ -0.36 \\
ESO358-16 & 115 & - & G & 3.3; 2.3; 73 & 3.3 & 50 & $\leq$ 2.6 & $\leq$ 7.66 & $\leq$ 1.36 \\
FCC117 & 117 & - & G & 2.8; 2.0; 84 & 2.4 & 50 & $\leq$ 1.9 & $\leq$ 7.53 & $\leq$ 1.04 \\
FCC120 & 120 & - & G & 2.8; 2.0; 84 & 2.4 & 50 & $\leq$ 1.9 & $\leq$ 8.32 & $\leq$ 0.44 \\
NGC1365 & 121 & R & B & 2.4; 2.0; 12 & 12 & 940 & 1221 $\pm$ 20 & 9.49 $\pm$ 0.04 & 0.53 $\pm$ 0.01 \\
NGC1380 & 167 & R & B & 2.6; 2.0; 80 & 3.6 & 660 $\pm$ 20 & 18.1 $\pm$ 1.8 & 7.67 $\pm$ 0.06 & -1.39 $\mp$ 0.01 \\
FCC177 & 177 & - & G & 3.3; 2.4; 73 & 3.3 & 50 & $\leq$ 2.6 & $\leq$ 8.14 & $\leq$ -0.99 \\
NGC1386 & 179 & R & B & 3.3; 2.4; 72 & 2.9 & 540 $\pm$ 20 & 88.9 $\pm$ 8.9 & 8.37 $\pm$ 0.04 & -0.61 $\mp$ 0.01 \\
NGC1387 & 184 & R & B & 3.3; 2.4; 72 & 3.0 & 200 $\pm$ 20 & 83.3 $\pm$ 8.3 & 8.33 $\pm$ 0.04 & -0.74 $\mp$ 0.01 \\
FCC198 & 198 & - & G & 2.8; 2.0; 84 & 2.4 & 50 & $\leq$ 1.9 & $\leq$ 7.82 & $\leq$ 2.17 \\
FCC206 & 206 & - & G & 2.8; 2.0; 83 & 2.5 & 50 & $\leq$ 2.0 & $\leq$ 7.34 & $\leq$ 0.71 \\
FCC207 & 207 & D & G & 2.8; 2.0; 83 & 2.6 & 11 $\pm$ 3 & 0.6 $\pm$ 0.3 & 6.54 $\pm$ 0.22 & -1.33 $\mp$ 0.01 \\
NGC1427A & 235 & - & G & 2.9; 2.3; 80 & 2.2 & 50 & $\leq$ 1.7 & $\leq$ 7.42 & $\leq$ -1.21 \\
FCC261 & 261 & D & G & 2.9; 2.0; 84 & 2.6 & 9.5 $\pm$ 3.9 & 0.27 $\pm$ 0.55 & 6.27 $\pm$ 0.88 & -1.47 $\mp$ 0.01 \\
PGC013571 & 263 & D & G & 3.3; 2.4; 72 & 3.1 & 54 $\pm$ 10 & 7.0 $\pm$ 0.71 & 7.22 $\pm$ 0.05 & -1.02 $\mp$ 0.01 \\
FCC282 & 282 & D & G & 3.2; 2.4; 70 & 3.1 & 36 $\pm$ 4 & 3.0 $\pm$ 0.34 & 7.15 $\pm$ 0.05 & -0.95 $\mp$ 0.01 \\
NGC1437A & 285 & - & G & 3.0; 2.1; 70 & 3.0 & 50 & $\leq$ 2.3 & $\leq$ 7.83 & $\leq$ -0.85 \\
NGC1436 & 290 & R & B & 2.6; 2.0; 79 & 3.2 & 260 $\pm$ 20 & 97.6 $\pm$ 9.8 & 8.44 $\pm$ 0.05 & -0.44 $\mp$ 0.01 \\
FCC302 & 302 & - & G & 2.8; 2.0; 83 & 2.5 & 50 & $\leq$ 2.0 & $\leq$ 8.82 & $\leq$ 0.78 \\
FCC306 & 306 & - & G & 2.8; 2.0; 84 & 2.4 & 50 & $\leq$ 1.9 & $\leq$ 8.10 & $\leq$ -0.11 \\
NGC1437B & 308 & D & G & 3.2; 2.4; 69 & 3.1 & 91 $\pm$ 14 & 17 $\pm$ 1.67 & 7.76 $\pm$ 0.04 & -0.59 $\mp$ 0.01 \\
ESO358-G063 & 312 & R & B & 2.6; 2.0; 80 & 3.3 & 380 $\pm$ 20 & 131.5 $\pm$ 13.2 & 8.57 $\pm$ 0.05 & -0.34 $\mp$ 0.01 \\
FCC316 & 316 & - & G & 2.8; 2.0; 82 & 2.7 & 50 & $\leq$ 2.1 & $\leq$ 7.31 & $\leq$ 0.53 \\
FCC332 & 332 & D & G & 2.8; 2.0; 84 & 2.3 & 30 $\pm$ 5 & 2.0 $\pm$ 0.25 & 7.18 $\pm$ 0.06 & -0.61 $\mp$ 0.01 \\
ESO359-G002 & 335 & D & G & 3.2; 2.4; 69 & 3.1 & 37 $\pm$ 5 & 2.0 $\pm$ 0.24 & 6.92 $\pm$ 0.05 & -1.33 $\mp$ 0.01 \\
\hline
\end{tabular}
\textit{Notes:} 1: Common name of the galaxy; 2: Fornax Cluster Catalogue number of the galaxy; 3: Whether the morphology and kinematics of the molecular gas in the galaxy are regular (R) or disturbed (D) (see \S \ref{sub:morphologies}); 4: Whether the line profile of the CO(1-0) line is best described by a Gaussian (G) or a boxy (B) profile (see \S \ref{sub:H2_masses}); 4/7: Upper limits were determined assuming a Gaussian line profile with a FWHM of 50 km~s$^{-1}$ (see \S \ref{subsub:upper_limits}); 5: Beam major axis, minor axis and position angle; 6: the typical rms in a single channel in the line-free channels of the data cube; 7: the width of the CO integrated spectrum (see \S \ref{sub:H2_masses}); 8: the total CO emission; 9: total M$_{\text{H}_2}$ mass derived from the CO emission (see \S \ref{sub:H2_masses}); 10: H$_2$ deficiency, defined as $M_{\text{H}_2, \text{observed}} - M_{\text{H}_2, \text{expected}}$ (see \S \ref{sub:H2_masses}).
\end{threeparttable}
\end{table*}
\section{Results}
\label{sec:results}
\begin{figure*}
\centering
\includegraphics[width=0.8\textwidth]{FCC_targets_mirror.pdf}
\caption{Map of the Fornax cluster, similar to Figure \ref{fig:Fornax}. The coloured symbols represent the AlFoCS targets, their shape and colour indicate whether CO was detected and if so, whether it is morphologically and kinematically disturbed or regular, as indicated in the legend. The central galaxy, NGC1399, is indicated with a yellow star, and the virial radius with a dotted line. The central galaxy of the infalling group in the lower right corner of the figure, NGC1316, is indicated with a cyan star. Non-detections, disturbed galaxies, and regular galaxies are distributed evenly over the cluster.}
\label{fig:Fornax_coloured}
\end{figure*}
CO was detected (at $> 3 \sigma$) in 15 of the 30 galaxies observed. In Figure \ref{fig:Fornax_coloured} the (projected) locations of the detections and non-detections within the cluster are shown, and morphologically and kinematically regular and disturbed galaxies are highlighted. All FDS (see \S \ref{sub:optical_data}) galaxies are shown as black dots, the AlFoCS galaxies are shown in colour. Non-detections are shown as blue plus signs, the pink squares are galaxies in which CO is detected and morphologically and kinematically regular or undisturbed, and the red triangles represent galaxies in which CO is detected and morphologically and kinematically disturbed (see \S \ref{sub:morphologies} for more details). Both detections and non-detections are distributed evenly over the cluster. At first glance it looks like there are slightly more non-detections south of the cluster centre, however this is not statistically significant. Galaxies with disturbed molecular gas reservoirs seem to be mainly located close to or outside the virial radius.
\subsection{Marginal detections}
\label{sub:marginal}
In ESO358-G015, FCC32, and NGC1437A CO is detected, but only marginally. In ESO358-G015 and NGC1437A these are 4 - 5 $\sigma$ detections, but the emission comes from small features away from the galactic centre, and it is not clear whether this emission is related to the galaxy observed. For FCC32 we find a tentative 2 $\sigma$ peak at the centre of the galaxy. These features are likely noise, and for these reasons we do not consider these observations further in this work.
\subsection{Continuum detections}
\label{sub:cont_detections}
Continuum (3 mm) was detected in NGC1380, NGC1386, NGC1387, and NGC1427A. In Figure \ref{fig:continua} the continuum maps of NGC1380, NGC1386, and NGC1387 are shown as coloured contours overplotted on the \textit{g}-band images from the FDS, similar to Figure \ref{fig:overplots}. In all three cases the continuum emission originates from the galactic centre. Two galaxies, NGC1380 and NGC1386, are known to harbour active galactic nuclei (AGN, e.g. \citealt{Boizelle2017,Lena2015,Rodriguez-Ardila2017}). The emission we detect is an unresolved point source at the galactic centre, but has a positive spectral index (see Table \ref{tab:continuum}). It is possible that both thermal and non-thermal emission is contributing the observed emission in these sources.
The 3 mm continuum emission in NGC1387 has a point-like morphology in the lower sideband, but when imaged at the higher frequencies several additional point sources are also detected, in the region where we know dust and molecular gas are present. This additional emission leads to the very large spectral index measured for this source (see Table \ref{tab:continuum}).
Given this, the detected 3 mm emission is again likely due to a mix of AGN activity and thermal emission from dust.
In the case of NGC1427A the emission originates from a small source at the edge of the galaxy. This is shown and discussed separately in \S \ref{subsub:NGC1427A}.
\subsection{H$_2$ masses}
\label{sub:H2_masses}
H$_2$ masses for all detected galaxies were estimated using the following equation:
\begin{equation}
\label{eq:H2mass}
M_{\text{H}_2} = 2m_\text{H} \ D^2 \ X_{\text{CO}} \ \frac{\lambda^2}{2\ k_\text{B}} \int S_\nu\ d \nu\ ,
\end{equation}
where $m_\text{H}$ is the mass of a hydrogen atom, $D$ is the distance to the galaxy, $X_{\text{CO}}$ is the CO-to-H$_2$ mass conversion factor, $\lambda$ is the rest wavelength of the line observed, $k_\text{B}$ is the Boltzmann constant, and $\int S_\nu\ d\nu$ the total flux of the line observed.
\begin{figure*}
\centering
\subfloat[NGC1380]
{\includegraphics[height=0.29\textwidth]{NGC1380/ContNGC1380.pdf}}
\subfloat[NGC1386]
{\includegraphics[height=0.28\textwidth]{NGC1386/ContNGC1386.pdf}}
\subfloat[NGC1387]
{\includegraphics[height=0.28\textwidth]{NGC1387/ContNGC1387.pdf}}
\caption{3 mm continuum emission overplotted on optical (\textit{g}-band) images from the FDS (see \S \ref{sub:optical_data}), similar to Figure \ref{fig:overplots}. The emission is shown as 10 coloured contours; the lower (outer) contour level equals 5$\sigma$. The emission originates from the galaxies' centres, and is likely due to a combination of AGN activity and thermal emission from dust.}
\label{fig:continua}
\end{figure*}
We use the metallicity-dependent mass conversion factor derived from \citet[eqn. 25]{Accurso2017}:
\begin{multline}
\text{log}\ \alpha_{\text{CO}} = 14.752 - 1.623 \left[ 12 + \text{log} \left( \text{O/H} \right) \right] \\
+ 0.062\ \text{log}\ \Delta \left( \text{MS} \right),
\label{eq:accurso}
\end{multline}
where $12 + \text{log} \left( \text{O/H} \right)$ is the metallicity and $\text{log}\ \Delta \left( \text{MS} \right)$ the distance from the main sequence, discussed below. The $1 \sigma$ spread in $\text{log}\ \alpha_{\text{CO}}$ from this relation is 0.165 dex. It is multiplied by $2.14 \times 10^{20}$ to obtain X$_\text{CO}$ \citep{Bolatto2013}. For reference, this equation gives a conversion factor of $2.08 \pm 0.02 \times 10^{20}$ for solar metallicity ($12 + \text{log} \left( \text{O/H} \right)$ = 8.69, \citealt{Asplund2009}). Since we do not have independent metallicity measurements for each object, metallicities were derived directly from the stellar masses of the galaxies, using the mass-metallicity relation from \citet{Sanchez2017}, which uses the calibration from \citet{Pettini2004}. Stellar masses ($M_\star$) are listed in Table \ref{tab:targets}. They were taken from \cite{Fuller2014} where possible (see Table \ref{tab:targets}). Alternatively, they were obtained from aperture photometry on archival Wide-field Infrared Survey Explorer (WISE, \citealt{Wright2010}) band 1 (3.6 $\mu$m) images, assuming a mass-to-light ratio of 1 (see Table \ref{tab:targets}). Apertures were chosen using the effective radii determined by \citet[][see \S \ref{sub:optical_data}]{Venhola2018} if available, and alternatively chosen by eye. Uncertainties on the stellar mass in these cases are a combination of the uncertainty in the effective radius and the rms in the image.
\begin{table*}
\begin{threeparttable}
\centering
\caption{Properties of the detected 3mm continuum emission.}
\label{tab:continuum}
\begin{tabular}{llllllll}
\hline
Galaxy & Frequency & Flux density & Frequency USB & Flux density USB & Frequency LSB & Flux density LSB & Spectral index \\
- & (GHz) & (mJy) & (GHz) & (mJy) & (GHz) & (mJy) & - \\
(1) & (2) & (3) & (4) & (5) & (6) & (7) & (8) \\
\hline
NGC1380 & 107.765 & 4.18 $\pm$ 0.04 & 113.763 & 4.65 $\pm 0.08$ & 101.775 & 4.12 $\pm 0.04$ & 1.1 $\pm$ 0.2 \\
NGC1386 & 107.718 & 3.69 $\pm$ 0.05 & 113.750 & 3.99 $\pm 0.07$ & 101.748 & 3.64 $\pm 0.07$ & 0.8 $\pm$ 0.2 \\
NGC1387 & 107.718 & 1.85 $\pm$ 0.06 & 113.750 & 4.3 $\pm 0.1$ & 101.748 & 1.04 $\pm$ 0.06 & 12.7$^{+0.6}_{-0.5}$ \\
NGC1427A & 107.765 & 0.16 $\pm$ 0.03 & 113.763 & 0.20 $\pm 0.06$ & 101.775 & 0.16 $\pm 0.03$ & 2.0$^{+3.0}_{-3.5}$ \\
\hline
\end{tabular}
\textit{Notes:} 1: Name of the galaxy; 2: Central frequency of the 3 mm continuum; 3: Flux density of the 3 mm continuum emission; 4: Central frequency of the upper sideband; 5: Flux density of the continuum in the upper sideband; 6: Central frequency of the lower sideband; 7: Flux density of the continuum in the lower sideband; 8: Spectral index of the continuum emission.
\end{threeparttable}
\end{table*}
The $X_{\text{CO}}$ calibration from \cite{Accurso2017} requires a distance from the main sequence \citep[e.g.][]{Brinchmann2004,Noeske2007,Elbaz2007}. Here we assume a distance from the main sequence $\Delta$MS = 0 for all galaxies. It is a second order parameter, so varying this does not strongly affect our results. Equation \ref{eq:accurso} is valid for values of -0.8 $<$ $\Delta$MS $<$ 1.3. Varying $\Delta$MS over this range results in a maximum error of 0.08 in $\alpha_{\text{CO}}$, which is indeed small compared to the other errors.
To make sure we include all the CO emission, while minimising the inclusion of noise, galaxies were subdivided into two groups: a group whose line profiles are best described by a Gaussian profile (mostly dwarf galaxies with narrow CO lines), and another group whose line profiles are best described by a box profile (mostly larger galaxies). Which profile best describes a galaxy is listed in Table \ref{tab:observed_props}. The widths of the CO integrated spectra are given. For boxy line profiles an uncertainty of 20 km~s$^{-1}$ (the equivalent of two channels) is adopted, for Gaussian profiles the formal fitting errors on the linewidth are quoted. For the first group we fit a Gaussian to the CO(1-0) line and integrate this fit to obtain the total line flux. For the second group, we integrate directly under the line observed. In this case the boundaries of the line are determined using the PVDs. Uncertainties are a combination of the error on the total integrated line emission $\int S_\nu d\nu$ and an adopted 10\% calibration error, and are often dominated by the latter. For galaxies with a boxy profile, the error in the integrated line emission is estimated according to the following equation, adapted from equation 1 from \citet{Young2011}:
\begin{equation}
\sigma_I^2 = \left( \Delta v \right) ^2 \sigma ^ 2 N_l,
\end{equation}
where $N_l$ is the number of channels that is summed over, $\Delta v$ the width of each channel, and $\sigma$ the rms noise level in the line free part of the spectrum. For galaxies with an approximately Gaussian line profile, the error on the total integrated line emission is estimated by combining the formal fitting errors on the parameters of the fit. The resulting molecular gas masses are listed in Table \ref{tab:observed_props}.
\begin{table*}
\begin{threeparttable}
\caption{Key properties and derived quantities of the Mopra targets included in this work.}
\label{tab:mopra}
\centering
\begin{tabular}{lllllll}
\hline
Name & RA & Dec & Stellar mass & rms & log$_{10}(M_{\text{H}_2}$) & Deficiency \\
- & (J2000) & (J2000) & (log($M_{\odot}$)) & (mJy km~s$^{-1}$) & ($M_\odot$) & (dex) \\
(1) & (2) & (3) & (4) & (5) & (6) & (7) \\
\hline
NGC1316 & 03h22m41.718s & -37d12m29.62s & 10.0$^\dagger$ & 273 & $\leq$ 8.27 & $\leq$ -0.52 \\
NGC1317 & 03h22m44.286s & -37d06m13.28s & 9.98$^\dagger$ & 192 & 8.69 $\pm$ 0.04 & -0.08 $\pm$ 0.01 \\
NGC1350 & 03h31m08.12s & -33d37m43.1s & 10.71$^\dagger$ & 602 & $\leq$ 8.61 & $\leq$ -0.38 \\
ESO359 G3 & 03h52m00.92s & -33d28m03.5s & $10.11^{+0.01\ \ddagger}_{-0.02}$ & 130 & $\leq$ 7.95 & $\leq$ 0.05 \\
FCCB857/858* & 03h33m19.49s & -35d20m41.4s & $9.31^{+0.01\ \ddagger}_{-0.04}$ & 34 & $\leq$ 7.36 & $\leq$ -0.07 \\
FCCB950 & 03h34m31.65s & -36d52m20.7s & $9.47^{+0.02\ \ddagger}_{-0.04}$ & 31 & $\leq$ 7.32 & $\leq$ -0.64 \\
FCCB990 & 03h35m11.38s & -33d22m25.6s & $9.39^{+0.02\ \ddagger}_{-0.04}$ & 97 & $\leq$ 7.82 & $\leq$ 0.04\\
FCCB713** & 03h31m20.94s & -35d29m29.9s & - & 55 & $\leq$ 7.57 & $\leq$ -0.59 \\
FCCB792** & 03h32m25.95s & -38d05m33.8s & - & 21 & $\leq$ 7.16 & $\leq$ -0.48 \\
FCCB1317** & 03h39m11.70s & -33d31m56.0s & - & 97 & $\leq$ 7.81 & $\leq$ 0.10 \\
\hline
\end{tabular}
\textit{Notes:} 1: Name of the galaxy observed; 2: Right ascension; 3: Declination; 4: Stellar mass (see \S \ref{sub:H2_masses}); 5: rms in the spectrum; 6: Derived molecular gas mass (see \S \ref{sub:H2_masses}); 7: H$_2$ deficiency (see \S \ref{sub:gas_fractions}); *FCCB857 and FCCB858 are close to each other on the sky and were therefore contained within one beam. The stellar mass quoted here is the addition of the stellar masses of both galaxies. The coordinates of FCCB858 are quoted here. **These galaxies were observed but later found to be background objects. They are therefore omitted in Figures \ref{fig:gas_fraction} and \ref{fig:mass_distance}, and stellar masses were therefore not determined for them; $^\dagger$Stellar masses from \citet{Fuller2014}; $^\dagger$Stellar masses derived from 3.6 $\mu$m images, (see \S \ref{sub:H2_masses}).
\end{threeparttable}
\end{table*}
\subsubsection{Upper limits}
\label{subsub:upper_limits}
For non-detections, 3$\sigma$ upper limits were determined using the rms in the (spatial) inner area of the PB corrected data cubes. Since all non-detections can be considered dwarf galaxies, we assume Gaussian line profiles with FWHM of 50 km s$^{-1}$. This is slightly broader than the profiles of the dwarf galaxies detected here, and therefore a conservative assumption. The maximum of the assumed line profile was set to 3 times the rms in the corresponding data cube. We use stellar mass dependent CO-to-H$_2$ conversion factors, as described above in \S \ref{sub:H2_masses}. We then use Equation \ref{eq:H2mass} to obtain the upper limits for the H$_2$ mass listed in Table \ref{tab:observed_props}.
\subsubsection{Mopra}
\label{subsub:Mopra}
Of the 28 galaxies observed with Mopra, CO was detected in one additional galaxy which was not observed with ALMA; NGC1317. After removing data affected by bad weather, we were able to obtain this one additional H$_2$ mass measurement and 8 additional upper limits. Due to a problem with the observations, we only have single, central pointing observations of NGC1317. Since the molecular gas is usually centrally located, however, we expect this to cover most if not all of its CO emission. Upper limits are 3$\sigma$ upper limits, estimated as described above. Despite the rather prominent baseline ripple in some of the observations, a known issue with the Mopra Telescope (see \S \ref{sec:observations}), these upper limits provide reasonably good constraints. The resulting upper limits, as well as the estimated H$_2$ mass of NGC1317, are listed in Table \ref{tab:mopra}.
\subsection{Gas fractions \& deficiencies}
\label{sub:gas_fractions}
In Figure \ref{fig:gas_fraction} the galaxies' molecular-to-stellar mass ratios are shown as a function of their stellar mass (see \S \ref{sub:H2_masses} for more details about the stellar masses used here), and compared with those of field control galaxies with the same stellar masses. The molecular gas fraction is given by $\left( \frac{M_{\text{H}_2}}{M_{\text{total}}} \right)$. Since $M_{\text{H{\sc i}}}$ and $M_{\text{H}_2}$ are relatively small contributions to the total mass of the galaxy compared to the stellar mass, for convenience and consistency with the definition in \citet{Saintonge2017} (see below), we define the gas fraction here as $\left( \frac{M_{\text{H}_2}}{M_\star} \right)$. We use the extended CO Legacy Database for \textit{GALEX} Arecibo SDSS Survey (xCOLD GASS, \citealt{Saintonge2017}) as a field galaxy control sample. xCOLD GASS is a survey of molecular gas in the local universe, built upon its predecessor COLD GASS \citep{Saintonge2011}. It is a mass-selected ($M_\star > 10^9 M_\odot$) survey of galaxies in the redshift interval 0.01 $< z < 0.05$ from the SDSS, and is therefore representative of the local galaxy population within this mass range. We use the relation based on the median values that they obtained by subdividing the sample in bins based on their stellar mass \citep[see][their Figure 10]{Saintonge2017}, and interpolate linearly (in log space) to obtain the relation represented by the dashed line. Since xCOLD GASS galaxies were selected to have stellar masses $M_\star > 10^9 M_\odot$, the first stellar mass bin is located at $M_\star = 9.388 M_\odot$. Below this stellar mass, the dashed line is obtained using linear extrapolation (in log space). Expected mass fractions for galaxies in this mass range, 5 detections and 11 upper limits, should be treated with caution. The shaded areas represent the 1, 2, and 3 sigma levels in the xCOLD GASS data, from dark to lighter. Galaxies with disturbed molecular gas are shown in red, and galaxies with regular, undisturbed molecular gas are shown in black (see \S \ref{sub:morphologies} for the definitions). Galaxies that have clear gas tails that extend beyond their optical emission, or otherwise asymmetric CO emission, are indicated with red triangles. ALMA upper limits for the H$_2$ mass are shown as magenta open triangles, and Mopra upper limits as cyan open triangles. NGC1317, the only Mopra detection included here, is shown as a cyan dot. There is a systematic offset between the xCOLD GASS H$_2$ mass fractions for field galaxies and our values of up to about $\sim$1 dex. This offset is not very significant at an individual level for regular galaxies, whose offset is mostly within or close to the 1$\sigma$ scatter in the xCOLD GASS data. With exception of NGC1437B and FCC332, all disturbed galaxies lie below 3$\sigma$ (for FCC261 and FCC207 we cannot be certain because they lie below the mass range of the xCOLD GASS data, but based on this figure it seems plausible to assume they would fall below 3$\sigma$ as well). In particular the galaxies with asymmetric CO emission have low gas fractions.
We define H$_2$ deficiencies here as log($M_{H_{2}, \text{observed}}$) - log($ M_{H_{2}, \text{expected}}$). Estimates of the H$_2$ deficiency for each galaxy are listed in Table \ref{tab:observed_props}. Galaxies with regular CO emission have an average H$_2$ deficiency of -0.50 dex, and galaxies with disturbed CO emission have an average H$_2$ deficiency of -1.1 dex. In Figure \ref{fig:mass_distance} H$_2$ deficiencies are plotted as a function of the (projected) distance between the galaxy and the cluster centre. Markers and colours are the same as in Figure \ref{fig:gas_fraction}. It seems like galaxies within a (projected) radius of 0.4 Mpc from the cluster centre are slightly more deficient than galaxies outside this radius. However, Kolmogorov-Smirnov and Mann-Whitney \textit{U} tests are unable to reject the null hypothesis that both groups of galaxies are drawn from the same distribution at more than $\sim$2$\sigma$. Possible explanations for this and a further discussion of this figure can be found in \S \ref{sub:RPS}.
\begin{figure*}
\hspace{3mm}
\centering
\includegraphics[width=0.8\textwidth]{gas_fraction.pdf}
\caption{Molecular gas fraction, as a function of stellar mass. Black dots are regular galaxies, red markers are disturbed galaxies. The shape of the marker indicates whether the galaxy may be undergoing ram pressure stripping, based on visual inspection. ALMA upper limits are shown as magenta open triangles, and Mopra upper limits as cyan open triangles. The Mopra detection of NGC1317 is shown as a cyan dot. Within the shaded area, the dashed line represents the expected gas fraction based on \citet{Saintonge2017}. The three shades of grey indicate the 1, 2, and 3 $\sigma$ levels (from the inside out) of the xCOLD GASS data. Outside the shaded area the dashed line is based on linear extrapolation (in log space). Galaxies with high deficiencies and the galaxies that were classified as disturbed are labelled. There is a discrepancy between the expected gas fractions and the gas fractions observed, especially the disturbed galaxies are H$_2$ deficient compared to field galaxies.}
\label{fig:gas_fraction}
\end{figure*}
\section{Discussion}
\label{sec:discussion}
\subsection{Gas morphologies \& kinematics}
\label{sub:morphologies}
The galaxies detected here can be divided into two categories: galaxies with disturbed molecular gas morphologies and regular systems. Whether a galaxy is morphologically disturbed or regular is determined by visual inspection of the moment 0 and 1 maps (see Figures \ref{fig:moment-maps_reg}, \ref{fig:moment-maps_irreg}, Appendix \ref{app:moment_maps}, and Table \ref{tab:observed_props}). Non-disturbed galaxies have molecular gas that is concentrated symmetrically around the galactic centre, whereas galaxies with disturbed morphologies contain molecular gas that is asymmetric with respect to the (optical) centre of the galaxy. It sometimes has a very irregular shape, and, in some cases, even extends beyond the galaxy's stellar body (see \S \ref{subsub:rps_gals}). Of the galaxies detected here, eight are classified as disturbed galaxies, and seven have regular molecular gas morphologies.
The galaxies with morphologically disturbed molecular gas reservoirs also have disturbed molecular gas kinematics. Looking at the velocity maps in Figure \ref{fig:moment-maps_reg} and the regular galaxies in Appendix \ref{app:moment_maps}, regular galaxies follow a standard ``spider diagram'' shape, indicative of a regular rotation. Disturbed galaxies, on the other hand, have irregular velocity maps, indicating the presence of non-circular motions. In some cases rotation is still present (in NGC1437B and PGC013571, for example, Figures \ref{fig:NGC1437B} and \ref{fig:PGC013571}, respectively), in other cases no rotation can be identified (for example, ESO359-G002 and FCC332, Figures \ref{fig:ESO359-G002} and \ref{fig:FCC332}, respectively). This is also reflected in the PVDs, which look like smooth rotation curves for the regular galaxies, but have very asymmetric and irregular shapes for the disturbed galaxies. Maps of the CO(1-0) linewidth of the regular galaxies often reveal symmetric structures such as rings or spiral arms (see, for example, Figures \ref{fig:ESO358-G063}). For disturbed galaxies this is, again, much more irregular (for example, Figure \ref{fig:NGC1437B}). A further discussion of each galaxy in detail can be found in Appendix \ref{sub:individual}.
\subsection{Stripping and gas stirring in Fornax in comparison with the field}
\label{sub:things}
There is a clear mass split between galaxies with regular and disturbed molecular gas morphologies, where all galaxies with stellar masses below $3 \times 10^9 M_\odot$ have disturbed molecular gas (see Figure \ref{fig:gas_fraction}). In the absence of a comparable field sample tracing molecular gas at these stellar masses, we compare this result to the Local Irregulars That Trace Luminosity Extremes, The H{\sc i} Nearby Galaxy Survey (LITTLE THINGS, \citealt{Hunter2012}). LITTLE THINGS is a multi-wavelength survey of 37 dwarf irregular and 4 blue compact nearby ($\leq$ 10.3 Mpc) (field) dwarf galaxies that is centred around H{\sc i}-line data, obtained with the National Radio Astronomy Observatory (NRAO) Very Large Array (VLA). It has high sensitivity ($\leq$1.1 mJy beam$^{-1}$ per channel), high spectral resolution ($\leq$2.6 km~s$^{-1}$), and high angular resolution ($\sim$6''), resulting in detailed intensity and velocity maps. If the molecular gas in a galaxy is disturbed, we expect their atomic gas to be disturbed as well. Therefore this comparison, although not ideal, is still meaningful. Categorising the LITTLE THINGS dwarfs in the same way as the AlFoCS galaxies (see above, \S \ref{sub:morphologies}), only about half of these dwarf galaxies show disturbed H{\sc i} kinematics and morphologies. Since all AlFoCS galaxies with stellar masses lower than $3 \times 10^9 M_\odot$ have disturbed morphologies and kinematics, this indicates that these low mass galaxies are more disturbed than their counterparts in the field. This suggests that Fornax is still a very active environment, having significant effects on its members. Furthermore, it implies that less massive galaxies are more susceptible to the effects of the cluster environment, likely because of their shallower potential wells. This difference in gas deficiency between massive and less massive galaxies is also seen in simulations \citep[e.g.][]{Voort2017}, and is likely driven by their shallower potential wells.
\begin{figure}
\centering
\includegraphics[width=0.48\textwidth]{DistanceDeficiency.pdf}
\caption{Molecular gas mass deficiencies (see \S \ref{sub:gas_fractions}) as a function of the (projected) distance to the cluster centre (defined as the location of NGC1399). Marker shapes and colours are the same as in Figure \ref{fig:gas_fraction}. There is no clear correlation between a galaxy's H$_2$ deficiency and its distance from the cluster centre.}
\label{fig:mass_distance}
\end{figure}
\subsection{Ram pressure stripping or galaxy-galaxy interactions?}
\label{sub:RPS}
The AlFoCS galaxies with disturbed molecular gas reservoirs are H$_2$ deficient compared to field galaxies (see Figure \ref{fig:gas_fraction} and \S \ref{sub:gas_fractions}). This confirms the result from \citet{Horellou1995}, who find that the CO emission in Fornax cluster galaxies is relatively weak, and the H$_2$ masses relatively low. AlFoCS galaxies have deficiencies up to -1.1 dex (see \S \ref{sub:gas_fractions}). These deficiences are higher than those found in \citet{Boselli2014}, who find H$_2$ deficiencies of a factor $\sim$2 for the most H{\sc i} deficient galaxies in the Virgo cluster. The molecular gas in the most deficient AlFoCS galaxies is centrally located and asymmetric. Mechanisms that are possibly responsible for this include ram pressure stripping and galaxy-galaxy interactions.
Two of the irregular galaxies, MCG-06-08-024 and ESO359-G002, show molecular gas tails that extend well beyond the brightest parts of the galaxy's stellar body (see \S \ref{subsub:rps_gals}). Together with the dwarfs FCC207 and FCC261, they have the lowest gas fractions of the disturbed galaxies (see Figure \ref{fig:gas_fraction} and Table \ref{tab:observed_props}). In both cases, this tail is aligned with the direction of the cluster centre (see \S \ref{subsub:rps_gals}). This, in combination with their low gas fractions, can be interpreted as a sign of ongoing ram pressure stripping. This is striking, since RPS is not thought to affect the molecular gas much, as it is bound much more tightly to the galaxy than the atomic gas. Moreover, RPS is thought to be less important in the Fornax cluster than in, for example, the Virgo cluster, given its relatively small size and large density of galaxies (see \S \ref{sec:intro}).
The fact that the gas tails align with the direction of the cluster centre is, however, not necessarily proof that ram pressure stripping is in play. There are confirmed RPS tails pointing in all directions, even nearly perpendicular to the direction of the cluster centre \cite[e.g.][]{Kenney2014}. This is also seen in simulations \citep[e.g.][]{Yun2018}. Moreover, the kinematics of these galaxies are more irregular than expected based on RPS alone, which suggests that a past galaxy-galaxy interaction may be (co-)responsible for this. In deep FDS images (Iodice et al. 2018, submitted to A\&A), MCG-06-08-024 shows a very disturbed morphology in the outskirts, which could indicate a past galaxy-galaxy interaction. Furthermore, these RPS candidates are not necessarily close to the cluster centre, nor do they have particularly high velocities, as one might expect for galaxies that are undergoing RPS. However, \cite{Jaffe2018}, recently found galaxies undergoing RPS all over the cluster, and also in a wide variety of locations in the velocity phase-space. Simulations by \citet{Yun2018} show that ram pressure stripped galaxies are more common beyond half the virial radius, where most of the AlFoCS galaxies with disturbed molecular gas are located. Both galaxies discussed here have relatively low masses and shallow potential wells, so they are expected to be susceptible to ram pressure stripping. \citet{Yun2018} also find that galaxies with shallow potential wells can experience extended stripping due to weak ram pressure.
Based on these data alone, it is difficult to say whether it is ram pressure affecting these galaxies. The combination with additional data, for example a study of the stellar kinematics of these galaxies, would allow us to distinguish between galaxy-galaxy interactions and ram pressure stripping with more certainty.
Several other galaxies, such as FCC282 and FCC332, also show asymmetric molecular gas reservoirs, and were therefore labelled as possible RPS candidates. Asymmetric molecular gas distributions and molecular gas tails can, however, also be the result of galaxy-galaxy interactions. Other galaxies, such as NGC1437B and FCC261, have relatively massive neighbours that are close to them on the sky, which could mean that they are experiencing tidal forces. NGC1437B is the least H$_2$ deficient of the disturbed galaxies (see Figure \ref{fig:gas_fraction}). If we look at its velocity map and PVD (see Figure \ref{fig:NGC1437B}), we can see that it has maintained its rotation and still shows a coherent structure, but it appears to be influenced by a pull on its south side. Although a second tail at the north side is missing, this could be an indication of an ongoing tidal interaction. Although the extension of the molecular gas on the south side of the galaxy does not align with the direction of the cluster centre, it is also possible that this asymmetry is caused by RPS, depending on the galaxy's orbit through the cluster (see above). It is currently still relatively far out, located approximately at the virial radius on the sky.
In Figure \ref{fig:mass_distance}, there appears to be no correlation between a galaxy's H$_2$ mass deficiency and its distance from the cluster centre. Although we suffer from small number statistics, there are a few other possible explanations for this:
\begin{itemize}
\item We are looking at a 2D projection of the cluster, the positions of the galaxies along the line of sight are not taken into account.
\item Lower mass galaxies end up more H$_2$ deficient than their higher mass counterparts, because of their shallower potential wells. The total H$_2$ mass per galaxy is therefore more a function of their intrinsic mass than of their location in the cluster.
\item The responsible mechanism is galaxy-galaxy interactions. While RPS is much more effective in the cluster centre, depending quadratically on the density of the hot halo, galaxy-galaxy interactions are, relatively, more common at the outskirts of the cluster. If the latter play a role, we would expect less of a trend in the gas deficiencies as we move away from the cluster centre.
\item The galaxies are moving through the cluster, so if they experienced RPS when they were near its centre, they can have moved to the outskirts of the cluster since then.
\item The galaxies were selected to have FIR emission, and therefore galaxies that lost all their gas are excluded from the sample.
\end{itemize}
\subsection{Dwarfs}
\label{sub:dwarfs}
Among the detections are several galaxies with low stellar masses, that can be classified as early-type dwarfs. Four of these have stellar masses $M_\star \leq 1.0 \times 10^9 M_\odot$. It was long thought that early-type dwarf galaxies in cluster environments would not have a molecular ISM, due to their expected short stripping timescales and shallow potentials.
The currently accepted theory is that these galaxies are the remnants of low mass late-type galaxies that have fallen into the cluster. This hypothesis is supported by the presence of visible structures such as spiral arms, bars, disks, and nuclei and cores \citep{Lisker2006a,Lisker2006b,Jerjen2000,Barazza2002,DeRijcke2003}, the rotational support of their stellar kinematics \citep{Pedraz2002,Rys2013}, and the detection of significant amounts of gas and dust in some of them \citep{Conselice2002,Serego2007,DeLooze2010,DeLooze2013,Serego2013}.
It is also possible that they were already early-type dwarf galaxies to begin with, but re-accreted material through tidal interactions either with the intracluster medium or with another galaxy, which could also trigger new star formation. Inconsistencies in the observations supporting the infalling-spiral scenario \citep{Miller1998,Sanchez2012} may add to the favourability of this idea. However, the limited spatial resolution of most of these studies to date make it hard to draw strong conclusions.
\citet{DeLooze2013} observed ``transition-type dwarf galaxies'' (TTDs) in the Virgo cluster. These galaxies are dwarfs that have an apparent early-type morphology, but still show dust emission and thus evidence of a cold ISM and star formation. They posit that TTDs are in the process of having their ISM removed by the cluster environment, transforming them from late-type dwarfs to quiescent ones (see \citealt{Boselli2008, Koleva2013} for a more detailed description of the definition and identification of TTDs). They find that many of the dust properties of these objects lie in between what is expected for early-type galaxies and for late-type galaxies, supporting the hypothesis that they are infalling low mass spirals that are in the process of being quenched. The presence of central cores and dust concentrations are additional evidence in favour of this outside-in gas removal theory.
We suspect that the dwarf galaxies we observe here are TTDs moving through the cluster and being stripped of their gas and thus in the process of being quenched. Each dwarf galaxy observed has a very disturbed and irregular molecular ISM, both morphologically and kinematically, suggesting that they are being stripped by the hot intracluster gas (for example MCG-06-08-024 and ESO359-G002, see Figures \ref{fig:moment-maps_irreg} and \ref{fig:ESO359-G002}), or being torn apart by tidal forces. This is in favour of the hypothesis that they are the remnants of infalling gas-rich galaxies. The observation that galaxies with disturbed molecular gas reservoirs seem to favour locations around the virial radius (see \S \ref{sec:results}) supports the idea that these dwarfs are starting their first passage through the cluster, or have just crossed it for the first time.
\subsection{NGC1427A}
\label{subsub:NGC1427A}
\begin{figure}
\centering
\begin{tikzpicture}
\node[anchor=south west] (image) at (0,0) {\includegraphics[width=0.48\textwidth]{NGC1427A/ContNGC1427A.pdf}};
\begin{scope}[x={(image.south east)},y={(image.north west)}]
\draw[blue,very thick] (0.601,0.541) rectangle (0.665,0.607);
\end{scope}
\begin{scope}[x={(image.south east)},y={(image.north west)}]
\draw[blue,very thick] (0.601,0.607) -- (0.731,0.896);
\draw[blue,very thick] (0.665,0.540) -- (0.923,0.681);
\end{scope}
\node[anchor=south west] (image) at (6.26,5.3) {\includegraphics[width=0.095\textwidth]{NGC1427A/ContNGC1427A_zoom.png}};
\end{tikzpicture}
\caption{3 mm continuum emission in the observation of NGC1427A, overplotted on an optical (\textit{g}-band) image from the FDS (see \S \ref{sub:optical_data}). The emission is shown as 10 coloured contours; the lower (outer) contour level equals 4$\sigma$, the inner one 5.6$\sigma$. The emission likely originates from a background source.}
\label{fig:NGC1427A}
\end{figure}
NGC1427A has been proposed to be undergoing ram pressure stripping \citep{Chaname2000,Mora2015}, although recent H{\sc i} observations by \citet{Lee-Waddell2018} suggest that previous tidal interactions are responsible for the galaxy's irregular shape, and for star formation triggering in the disk. It was detected in all five \textit{Herschel} bands \citep{Fuller2014}. Based on the above observations, the expectation was to detect CO in this galaxy. However, none was detected.
NGC1427A is vigorously star forming. It is expected to have approximately solar metallicity, based on both its stellar mass and analysis of the colours of its star clusters \citep{Mora2015}. Its atomic hydrogen mass is $M_{\text{H{\sc i} }} = 2.1 \times 10^9 M_\odot$ \citep{Lee-Waddell2018}, we find an upper limit on its molecular hydrogen mass of $M_{\text{H}_2} = 2.63 \times 10^7$, and its SFR is 0.05 $\pm$ 0.03 \citep{Mora2015}. This leads to the surprisingly high atomic-to-molecular gas ratio $\frac{M_{\text{H{\sc i} }}}{M_{\text{H}_2}} > 79$ and short depletion time $\frac{M_{\text{H}_2}}{\text{SFR}} <$1.3 Gyr.
It is possible that the flux is resolved out, since the galaxy extends well beyond the largest recoverable scale of 25'' (see Figure \ref{fig:NGC1427A}). However, as CO emission is broken between velocity channels due to its motion within the galaxy, in our mosaic we would still expect to see some emission.
If the CO emission has not been resolved out, this makes the non-detection of CO surprising. A natural explanation for this would be if the galaxy underwent a merger or other event which has diluted its gas phase metallicity. We test this by deriving the gas-phase metallicity from the measured gas-to-dust ratio. This is done using the empirical relation between the gas-to-dust ratio and metallicity from \citet[][Figure 4 and Table 1]{RemyRuyer2014} for galaxies in the low metallicity regime, where we expect the galaxy to be. Using the relation for the higher metallicity regime instead would result in an even lower metallicity, thus only amplifying the analysis below. We use the relation for a metallicity-dependent X$_\text{CO}$ . Rewriting for the metallicity gives:
\begin{equation}
12 + \text{log}(\text{O/H}) = \frac{- \left( \text{log} \left( \frac{\text{G}}{\text{D}} \right) - b \right)}{\alpha_\text{L}} + x_\odot
\end{equation}
where $b$ = 0.96, $\alpha_\text{L} = 3.10 \pm 1.33$, and $x_\odot$ = 8.69 the solar metallicity \citep{Asplund2009}. The gas-to-dust ratio is derived using the H{\sc i} and H$_2$ masses stated above, and a dust mass of $4.2 \times 10^{6} M_\odot$ from \citet{Fuller2014}. Since our upper limit on the H$_2$ mass depends on X$_\text{CO}$, we combine the relation above and that between X$_\text{CO}$ and metallicity (Equation \ref{eq:accurso}) to estimate the metallicity (and thus the resulting X$_\text{CO}$) in this object. The resulting metallicity, assuming these relations hold, is $12 + \text{log}(\text{O/H})$ = 8.12 (or 0.27 $Z_\odot$). This is significantly lower than the metallicity derived from the stellar mass ($12 + \text{log}(\text{O/H})$ = 8.71; 1.05 $Z_\odot$, see \S \ref{sub:H2_masses}), and that found for young star clusters by \citet{Mora2015}, who find values of $\sim$0.4-1 $Z_\odot$. It implies an X$_\text{CO}$ of $\sim18 \times 10^{20}$ cm$^{-2}$ (K km~s$^{-1}$)$^{-1}$ (see \S \ref{sub:H2_masses}), in which case the H$_2$ mass limit we can set in this object increases to $\sim 2.1 \times 10^{8}$ $M_\odot$. This revised values for the atomic-to-molecular gas ratio and the molecular gas depletion time yield $>$10 and $<$4.2 Gyr respectively, much more consistent with canonical values.
We do detect a 3 mm continuum source in our NGC1427A observations. This is shown in Figure \ref{fig:NGC1427A}, where the continuum is overplotted as coloured contours on a \textit{g}-band image from the FDS, similar to Figure \ref{fig:continua}. The emission originates from a source towards the north of NGC1427A, slightly to the east side relative to its centre. There are two possible candidates for its origin: either the emission comes from a background source, or from an AGN associated with NGC1427A, that has been moved off-centre as a result of a galaxy-galaxy interaction. The latter interpretation seems quite speculative. However based on the information currently available and the galaxy's turbulent history, it is a possibility. In case the continuum originates from a background source, we would expect to see an optical counterpart in the optical FDS image. These images are quite deep, and can detect point sources down to $\sim$25-26 mag. However, no optical counterpart is detected. Moreover, no emission lines are detected in archival MUSE observations of this area. Thus, if it is indeed a background object, it must be heavily obscured by dust.
\section{Conclusions / summary}
\label{sec:conclusions}
We have presented the first results from the ALMA Fornax Cluster Survey (AlFoCS), a complete survey of the CO(1-0) in all Fornax cluster galaxies above $>3 \times 10^8 \text{ M}_\odot$ that contain dust \citep{Fuller2014} and/or HI (\citealt{Waugh2002}, Loni et al. in prep. based on ATCA data). The goal of this survey is to study the effects of the cluster environment on the cold molecular gas inside galaxies. We present moment zero, one, and two maps, as well as position-velocity diagrams, spectra, and comparisons with optical images for all galaxies detected. Furthermore we estimate H$_2$ masses and derive the corresponding H$_2$ deficiencies compared to field galaxies. The main conclusions from this initial analysis are:
\begin{itemize}
\item The cold molecular gas in galaxies is indeed affected by the cluster environment. All galaxies with stellar masses below $3 \times 10^9 M_\odot$ (8 out of 15 detected galaxies) have morphologically and kinematically disturbed gas reservoirs. ``Disturbed'' means that their molecular gas is distributed asymmetrically with respect to the optical centre of the galaxy, sometimes with irregular shapes or large tails. The moment one maps and PVDs show irregular motions, and in most cases no rotation can be identified. This suggests that Fornax is still a very active environment, having a significant impact on its members. More massive galaxies are probably experiencing the same interactions, however the molecular gas may not be affected in the same way, because of their deeper potential wells. \\
\item Continuum was detected in four of the galaxies observed. In three of them it is likely associated with AGN activity. In one case (NGC1427A) the emission does not originate from the centre of the galaxy, but rather from the galaxy's edge. It is unclear whether the source of this emission is a background object or an AGN that was moved off-centre due to a recent galaxy-galaxy interaction. \\
\item Galaxies with regular CO emission have an average H$_2$ deficiency of -0.50 dex, and galaxies with disturbed CO emission have an average H$_2$ deficiency of -1.1 dex. AlFoCS galaxies with disturbed molecular gas reservoirs are therefore, with few exceptions, significantly deficient in H$_2$ compared to their counterparts in the field (as probed by the xCOLD GASS sample). \\
\item Whether a galaxy has a molecular gas reservoir, and whether that reservoir is disturbed or regular, appears to be independent of the galaxy's location within the cluster. However, the sample size is small. \\
\item Two molecular gas tails were detected, that extend beyond the galaxy's stellar body and align with the direction of the cluster centre. These galaxies are possibly undergoing ram pressure stripping. Relatively high H$_2$ deficiencies support this explanation. Several other galaxies have molecular gas reservoirs that are asymmetric with respect to their stellar bodies as well, and are therefore possible RPS candidates, however it is difficult to draw definite conclusions from these data alone. \\
\end{itemize}
To be able to really distinguish between ram pressure stripping and galaxy-galaxy interactions, we need to compare the stellar kinematics (derived from e.g. MUSE observations: \citealt{Sarzi2018}) of the galaxies in question with the kinematics of their disturbed molecular gas. If both the molecular gas and stars show similar kinematics, ram pressure stripping can be ruled out. If only the molecular gas kinematics are disturbed, on the other hand, we can confirm that ram pressure stripping plays a role. This will be the aim of a future work. Similarly, we will compare our data with those of the \textit{Herschel} Fornax Cluster Survey \citep{Fuller2014} to compare the molecular gas and dust distributions, and derive gas-to-dust ratios for the galaxies in our sample. \\
In conclusion, the detection of a relatively high number of galaxies with disturbed molecular gas reservoirs and H$_2$ deficiencies of sometimes more than an order of magnitude reveal the importance of the cluster environment for even the tightly bound molecular gas phase, and motivate further study of environmental effects on molecular gas in nearby clusters.
\section*{Acknowledgements}
This publication has received funding from the European Union's Horizon 2020 research and innovation programme under grant agreement No 730562 [RadioNet].
This project has received funding from the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation programme (grant agreement no. 679627; project name FORNAX).
NZ acknowledges support from the European Research Council (ERC) in the form of Consolidator Grant CosmicDust (ERC-2014-CoG-647939)
TAD acknowledges support from a Science and Technology Facilities Council Ernest Rutherford Fellowship.
FvdV is supported by the Klaus Tschira Foundation.
R.F.P. acknowledges financial support from the European Union's Horizon 2020 research and innovation program under the Marie Skłodowska-Curie grant agreement No. 721463 to the SUNDIAL ITN network.
This paper makes use of the following ALMA data: ADS/JAO.ALMA\#2015.1.01135.S. ALMA is a partnership of ESO (representing its member states), NSF (USA) and NINS (Japan), together with NRC (Canada) and NSC and ASIAA (Taiwan) and KASI (Republic of Korea), in cooperation with the Republic of Chile. The Joint ALMA Observatory is operated by ESO, AUI/NRAO and NAOJ.
The Mopra radio telescope is part of the Australia Telescope National Facility which is funded by the Australian Government for operation as a National Facility managed by CSIRO.
This publication makes use of data products from the Wide-field Infrared Survey Explorer, which is a joint project of the University of California, Los Angeles, and the Jet Propulsion Laboratory/California Institute of Technology, funded by the National Aeronautics and Space Administration.
This research has made use of the NASA/IPAC Extragalactic Database (NED), which is operated by the Jet Propulsion Laboratory, California Institute of Technology, under contract with the National Aeronautics and Space Administration.
\bibliographystyle{mnras}
| {
"redpajama_set_name": "RedPajamaArXiv"
} | 7,262 |
<?php
/**
* Created by PhpStorm.
* User: Kurraz
*/
namespace app\modules\game\models\game_data\family_origins;
use app\modules\game\helpers\ArrayHelper;
use app\modules\game\models\game_data\base\IFamilyOrigin;
class ChurchFamily implements IFamilyOrigin
{
public function getId()
{
return 'church';
}
public function getName()
{
return 'Воспитанница церковного приюта';
}
public function getNameAuc()
{
return 'воспитанница церковного приюта';
}
public function affectJsonData($data)
{
return ArrayHelper::sumArrays($data, [
'seed_temper' => -1,
'seed_ego' => -1,
'seed_intellect' => 1,
'seed_custom' => 1,
]);
}
public function getDescriptions()
{
return [
'Еще во младенчестве я осталась сиротой, но мне повезло попасть в церковный приют. Монахи приучали нас правильно себя вести, помогать по хозяйству и чтить Бога. Самые способные обучались грамоте. Конечно, мы иногда шалили, и за это меня не раз пороли или запирали в келье.'
];
}
public function getAvailableOccupations()
{
return [
'beggar',
'nun',
'valertry',
'nun',
'nun',
];
}
} | {
"redpajama_set_name": "RedPajamaGithub"
} | 7,108 |
Q: How to estimate the upper bound of y in this situation? How to estimate the upper bound of y in this situation?
Given
1. a function y=f(x_1,x_2,x_3,x_4,x_5) with 5 parameters (y=f(...) can be any function).
2. for each x_i there are k_i possible values.
I want to estimate the upper bound of y but I don't want to try all combinations of input, which has size k_1*k_2*k_3*k_4*k_5.
Any idea or direction?
A: There is no practical upper bound possible without bounding f(...) to a particular type of function. Suppose y=f(x1,x2,x3,...)=C for some constant C. There is then no way to put any bound on f(...) based on inputs x1,x2,... since C has no connection to any of them.
Alternatively, suppose f(x1,x2,...)=x1^(x2^(...)) and compare with f(x1,x2,...)=x1+x2+... Both of these functions are possible to place a bound on, although the bound on the first function may be exceptionally large (in absolute value).
| {
"redpajama_set_name": "RedPajamaStackExchange"
} | 3,529 |
Q: c# - how to show result of a query within the same web page in MVC I have an MVC app in which after I chose the value from dropdown menu the function is executed in which sql is handled. The dropdown is at:
http://localhost:9030/Courses/Index
And after I make a selection the result is at:
http://localhost:9030/Courses/getCoursesByTeachers?Teacher=(here is an ID of the element)
getCoursesByTeachers is the function in my controller which takes the ID as the parameter.
Here is the function:
public string getCoursesByTeachers(int Teacher)
{
string sql = "SELECT * FROM Course WHERE teacher_Id = @Teacher";
string connectionString = "Data Source=TSSKKEWKS0619;Initial Catalog=T-Timetable;Integrated Security=True;MultipleActiveResultSets=True;Application Name=EntityFramework";
//string course = "No courses are being taught by this teacher";
List<string> list = new List<string>();
using (SqlConnection connection = new SqlConnection(connectionString))
{
SqlCommand command = new SqlCommand(sql, connection);
command.Parameters.AddWithValue("Teacher", Teacher);
connection.Open();
SqlDataReader reader = command.ExecuteReader();
try
{
while (reader.Read())
{
list.Add(reader["name"].ToString());
}
}
finally
{
reader.Close();
}
}
if (list.Count==0)
{
list.Add("There are no courses being taught by this teacher.");
}
return string.Join(System.Environment.NewLine, list);
}
And here is how I call it in my cshtml:
<h2>Courses taught by:</h2>
@using (Html.BeginForm("getCoursesByTeachers", "Courses", FormMethod.Get))
{
@Html.DropDownList("Teacher", (SelectList)ViewBag.Teacher, "Select teacher", new { onchange = @"form.submit()" }); // form.action('getCoursesByTeacher')
}
Is there a way of modifiying it so the result is not shown at the redirected page but within the same one in the url at: http://localhost:9030/Courses/Index. (maybe like underneath it or so, I am guessing I have to change it somehow in the cshtml right? I cant figure out how and I don't want to screw it up when it works :D so I figured I ask you guys)
Hope the question was clear enough. Thank you for any help.
A: Use AJAX to retrieve the result, then insert it into the current DOM. You can drop the <form> tag if it has only been used to send the dropdown data.
I am using jQuery in the following example.
<div id="teacherResultDisplay">@*result will be inserted here*@</div>
// load on dropdown change
$('#Teacher').change(function () {
var selected = $(this).val(); // assume the <option value="..."/> is the teacher id
$.ajax({
type: 'GET',
cache: false, /* to prevent problems with dynamic data that gets cached */
url: '@Url.Action("getCoursesByTeachers", "Courses")',
data: {
Teacher: selected
},
success: function (stringResult) {
$('#teacherResultDisplay').html(stringResult);
}
});
});
A: Does your function need to be called getCoursesByTeachers and not index?
If you cannot change where your form action. You could rename getCoursesByTeachers to index and have the following
public string getCoursesByTeachers(int Teacher)
{
return RedirectToAction("index", new { Teacher= Teacher });
}
| {
"redpajama_set_name": "RedPajamaStackExchange"
} | 4,484 |
Publicly funded applied research pays off: The effects of the Fraunhofer-Gesellschaft on firm performance
Diego Comin, Georg Licht, Maikel Pellens, Torben Schubert 08 March 2018
Governments invest in public applied research institutions in the hope of transferring scientific knowledge to industry and thus boost private innovation. But do these investments actually pay off? This column presents results from the Horizon 2020 FRAME project, in which the activities of Germany's leading applied research organisation, the Fraunhofer-Gesellschaft, were analysed. When firms collaborate on research projects with Fraunhofer, they do significantly better in terms of growth, productivity, as well as innovation. Furthermore, the macroeconomic benefits of Fraunhofer appear to outweigh its costs.
The importance of frontier knowledge for the generation of ideas
Alessandro Iaria, Carlo Schwarz, Fabian Waldinger
Why poor countries invest too little in R&D
Xavi Cirera, Edwin A. Goñi Pacchioni, William Maloney
Government financing of R&D
Saul Lach, Zvika Neeman, Mark Schankerman
New indicators of the science intensity of industry
Kenta Ikeuchi, Kazuyuki Motohashi, Ryuichi Tamura, Naotoshi Tsukada
Scientists and policymakers agree that innovation is the most important driver of sustainable growth, welfare creation, and high employment rates. In the Lisbon Strategy, the European Commission announced its main goal of turning the EU into the most competitive knowledge-based economy in the world. In order to achieve this goal, the Commission makes significant investments in R&D and innovation through its Framework Programmes.
But is this enough? The EU is lagging behind the US not only in productivity and R&D spending, but also in its ability to transform the latter into the former (Ortega-Argilés et al. 2014), an issue which is particularly pronounced in many south-eastern European countries. Furthermore, this gap seems to have widened further both during and after the crisis (Castellani et al. 2016).
The EU's more limited ability to profit from R&D has led several authors to propose that innovation policies should not only focus on increasing R&D investment, but should also become more learning oriented. That is to say, policies should improve firms' ability to turn R&D into growth and productivity gains (Castellani et al. 2016). This approach can already be observed in the encouragement of collaborations between firms and public research organisations through formal requirements in EU-funded projects.
The vast majority of studies analysing the effects of private-public research collaborations have focused on universities as the primary providers of basic scientific knowledge (compare Robin and Schubert 2013). While in most countries, universities are indeed the dominant actors in the public research landscape, a number of countries possess quite sizeable public research organisations which explicitly focus on helping private firms to derive industrial applications and innovation from scientific knowledge – examples include TNO in the Netherlands, the RISE institutes in Sweden, VTT in Finland, and the Fraunhofer-Gesellschaft in Germany. The fact that these countries arguably also rank among the innovation leaders in Europe begs the question of the extent to which their success is to the result of investment in public applied research. To date, however, the effects of collaborating with applied public research organisations on the firms involved have not been sufficiently studied.
The FRAME project
In a study which forms part of the project Horizon 2020 project FRAME funded by the European Commission, we provide the first empirical evidence on how the Fraunhofer-Gesellschaft, the world's largest applied research organisation, affects the performance of collaborating firms (Comin et al. 2018). Founded in 1949, Fraunhofer today employs approximately 24,500 employees who conduct applied research in all fields of science, producing around 500 patents per year (Comin et al. 2015). Fraunhofer scientists also participate in research contracts in which they solve specific technological problems facing individual firms. Fraunhofer's revenue stemming from projects for and with private firms exceeds €600 million per annum and thus represents a third of its total budget of €2 billion.
To test the effect of these projects on firm performance, we combined a confidential dataset of Fraunhofer research contracts signed with German firms between 1997 and 2014 with information from the German contribution to the Community Innovation Survey, which contains information on the performance and innovation activities of a large panel of companies. In order to establish whether collaborating with Fraunhofer actually improves performance, we had to eliminate problems associated with selection bias (i.e. the possibility that better performing firms are more likely to enter into a research contract with Fraunhofer than worse performing ones). To that end, we made use of recently developed heteroscedasticity-based IV estimators (Lewbel 2012). Using these IV methods, we analyse how collaborating with Fraunhofer affects various dimensions of firm performance.
Core results
Our key empirical findings suggest that Fraunhofer contracts have a strong effect on firm performance – a 1% increase in Fraunhofer expenditure made by a firm generates an increase in turnover growth of 1.4 percentage points and a 0.7 percentage point rise in productivity growth. These increases amount to 21% and 11% of average turnover and productivity growth, respectively.
We also find that these effects are at least partially driven by a shift in the firm's innovation strategy, which suggests that Fraunhofer is generally successful in its mission to disseminate and apply scientific knowledge. An initial piece of evidence for this is that interacting with Fraunhofer changes firms' hiring behaviour, with a 1% increase in Fraunhofer expenditure leading to a 0.2 percentage point increase in the share of employees with a tertiary education background. Second, Fraunhofer expenditure also leads to a more successful innovation strategy, with a 1% increase in Fraunhofer expenditure translating to a 0.7 percentage point increase in the share of sales drawn from new products and services.
Based on certain assumptions, we can use the firm-level results to infer the macroeconomic effects of these projects in Germany. Our results indicate that Fraunhofer induces a total increase in value added of €2.2 billion.1 Since Fraunhofer's total annual budget is about €2.1 billion, the overall benefits in terms of increased value added exceed the total 'costs' of Fraunhofer. Compared to total expenditure of €682 million incurred by German industry, the benefits appear even more pronounced.
Policy implications
Public R&D policy largely focuses on R&D tax credits to private R&D and for financing of basic research typically conducted in universities. Our research illustrates that a fruitful strategy to foster innovation capacity and productivity growth is to strengthen organisations that transfer technological knowledge to companies.
Applied research organisations such as Fraunhofer-Gesellschaft2 are capable of bridging the gap between basic scientific knowledge (falling into the domain of universities) and the development of new commercial applications (falling into the domain of firms). By bridging this gap, companies can have access to state-of-the-art technological knowledge that enables a knowledge-intensive/innovation strategy which leads to faster sales and productivity growth, as well as to more jobs for skilled workers. The establishment of, and investment in, applied research organisations could therefore form a central pillar of national and European innovation policy.
Editors' note: This research is part of the FRAME project. This project has received funding from the European Union's Horizon 2020 research and innovation programme under grant agreement No #727073
Castellani, D, M Piva, T Schubert and M Vivarelli (2016), "R&D and Productivity in the US and the EU: Sectoral Specificities and Differences in the Crisis", Papers in Innovation Studies No. 2016/15, Lund University, CIRCLE-Center for Innovation, Research and Competences in the Learning Economy.
Comin, D (2014), Malaysia Beyond 2020, UTM Press.
Comin, D, G Trumbull and K Yang (2015), "Fraunhofer: Innovation in Germany", in Drivers of Competitiveness, World Scientific Publishing: 409-444.
Comin, D, G Licht, M Pellens and T Schubert (2018), "Do Companies Benefit from Public Research Organizations? The Impact of the Fraunhofer Society in Germany", Papers in Innovation Studies No. 2018/7, Lund University, CIRCLE - Center for Innovation, Research and Competences in the Learning Economy.
Frietsch, R, C Rammer and T Schubert (2015), "Heterogeneity of Innovation Systems in Europe and Horizon 2020", Intereconomics 50(1): 9-13.
Lewbel, A (2012), "Using heteroscedasticity to identify and estimate mismeasured and endogenous regressor models", Journal of Business & Economic Statistics 30(1): 67-80.
Ortega-Argilés, R, M Piva and M Vivarelli (2014), "The transatlantic productivity gap: Is R&D the main culprit?", Canadian Journal of Economics 47(4): 1342-1371.
Robin, S and T Schubert (2013), "Cooperation with public research institutions and success in innovation: Evidence from France and Germany", Research Policy 42(1): 149-166.
[1] Further regression in levels show that the multiplier of Fraunhofer expenditures with respect to turnover is 13.18. Total project revenue with private firms in 2016 was €0.68 billion, leading to an increase in turnover of €8.99 billion. In Germany, the ratio of value added to turnover is stable and approximately 24% corresponding to an estimated increase in value added of €2.2 billion.
[2] See Comin (2014) for another example of such an organisation and a discussion on why the market does not provide these kind of services.
Topics: Frontiers of economic research Productivity and Innovation
Tags: undefined
Diego Comin
Professor of Economics, Dartmouth, and CEPR
Georg Licht
Head of the Research Department of Economics of Innovation and Industrial Dynamics, Centre for European Economic Research (ZEW)
Maikel Pellens
Senior Researcher, ZEW
Torben Schubert
Associate Professor, CIRCLE, Lund University; Senior Researcher, Fraunhofer ISI | {
"redpajama_set_name": "RedPajamaCommonCrawl"
} | 683 |
Q: How to get system configuration settings Magento 2 i need to retrieve my configuration settings i setup in the system.xml file of my Magento plugin.
i have setup the plugin fields in my config file and trying to retrieve them in the javscript file.is this possible?
<config xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xsi:noNamespaceSchemaLocation="urn:magento:module:Magento_Config:etc/system_file.xsd">
<system>
<section id="payment">
<group id="custompayment" translate="label" sortOrder="2" showInDefault="1" showInWebsite="1" showInStore="1">
<label>Emipro Payment</label>
<field id="active" translate="label comment" sortOrder="1" type="select" showInDefault="1" showInWebsite="1" showInStore="0">
<label>Enable</label>
<source_model>Magento\Config\Model\Config\Source\Yesno</source_model>
</field>
<field id="title" translate="label" type="text" sortOrder="30" showInDefault="1" showInWebsite="1" showInStore="1">
<label>Title</label>
</field>
<field id="businessID" translate="label" type="text" sortOrder="65" showInDefault="1" showInWebsite="1" showInStore="0">
<label>Business ID</label>
</field>
<field id="password" translate="label" type="text" sortOrder="66" showInDefault="1" showInWebsite="1" showInStore="0">
<label>Password</label>
</field>
</group>
</section>
</system>
</config>
Below is what i've tried in my javascript file
define(
[
'Magento_Checkout/js/view/payment/default',
'jquery',
'jquery/ui',
],
function (Component,$) {
'use strict';
return Component.extend({
defaults: {
template: 'Emipro_Custompayment/payment/custompayment'
},
initialize: function () {
self = this;
this._super();
},
getConfigPassword: function () {
return checkoutConfig.payment.custompayment.password;
},
| {
"redpajama_set_name": "RedPajamaStackExchange"
} | 8,541 |
El alacrán de manos negras (Centruroides nigrimanus) es miembro de la familia Buthidae del orden Scorpiones. Esta especie fue descrita por Pocock en 1898.
Clasificación y descripción
El nombre del género Centruroides proviene de las palabras griegas kentron- que significa "espina" y "oura" que significa "cola", es decir, Centruroides podría traducirse como cola en forma de espina. El género originalmente se llamaba Centrurus pero tuvo que cambiarse a Centruroides debido a que Centrurus ya había sido usado para otro animal. La terminación -oides significa "semejanza" o "proveniente de". El origen del nombre específico proviene del latín niger que significa negro y -manus que significa "mano".
Descripción: El mesosoma está toscamente granulado por arriba, la patela y fémur del pedipalpo son de color amarillento claro, la mano y dedos son claramente más obscuros que el resto del pedipalpo; segmento caudal V y a veces la vesícula de color más obscuro que el resto del metasoma; el quinto segmento caudal tiene sus crestas granuladas y también las superficies lateral e inferior; la vesícula por otro lado en lugar de ser granular, es lisa por debajo y el diente está mucho más cerca del aculeus; las crestas inferio-laterales del tercer segmento caudal están provistas con aproximadamente 30 gránulos. Son alacranes grandes entre 8-10 cm; pines con 35-36 dientes en los machos y 29-33 en las hembras.
Distribución
Esta especie es endémica de México, se encuentra en el estado de Oaxaca y se debe confirmar su presencia en Guerrero.
Hábitat terrestre
Todas las especies del género Centruroides son nocturnas y permanecen ocultos y en reposo durante el día. Son animales que en zonas desérticas sobreviven con muy poca agua (incluso sólo la que toman de su alimento); pero en otras áreas, requieren beber agua de vez en cuando, para complementar sus requerimientos metabólicos, además de la que toman de su alimento, lo que hace que busquen áreas húmedas durante la noche y sea común verlos en zonas cercanas a fuentes de agua, naturales o artificiales, áreas que desgraciadamente, también son preferidas por los humanos para establecerse.
Estado de conservación
Esta especie de escorpión no se encuentra dentro de ninguna categoría de riesgo en las normas nacionales o internacionales.
Referencias
Enlaces externos
Enciclovida tiene un artículo sobre la especie Centruroides nigrimanus
Naturalista tiene un artículo sobre la especie Centruroides nigrimanus
Arácnidos de México
Arácnidos de América
Arácnidos de América del Norte
nigrimanus | {
"redpajama_set_name": "RedPajamaWikipedia"
} | 4,299 |
\section{Top quark production at the Tevatron}
The properties of the top quark, in particular its mass
and production cross section, are subjects of intense study at
the Tevatron \cite{CDF,D0}.
The most accurate theoretical prediction \cite{NKRV} for top quark pair
production at the Tevatron includes soft-gluon corrections
\cite{KS,NKhq,NKuni}
through next-to-next-to-next-to-leading logarithmic (NNNLL)
accuracy at next-to-next-to-leading order (NNLO), denoted
as NNLO-NNNLL \cite{NKRV}.
These corrections are sizable and provide a dramatic decrease
in the scale dependence of the cross section. Results have been
derived in both single-particle-inclusive (1PI) kinematics and
pair-invariant-mass (PIM) kinematics. There are differences in the
results in the two kinematics due to subleading terms, and the best
estimate is given by the average of the two kinematics.
For a top quark mass $m_t=175$ GeV the theoretical value of the
cross section is \cite{NKRV}
\newline
$\sigma_{t \bar t}^{NNLO-NNNLL}$($\sqrt{S}=1.8$ TeV, $m_t$=175 GeV)
$=5.24 \pm 0.31$ pb \hspace{3mm} and
\newline
$\sigma_{t \bar t}^{NNLO-NNNLL}$($\sqrt{S}=1.96$ TeV, $m_t$=175 GeV)
$=6.77 \pm 0.42$ pb
\newline
\noindent at Run I and Run II, respectively.
The uncertainty indicated is due to the kinematics ambiguity;
the scale uncertainty is much smaller.
Some recent data from the Tevatron suggest a value for the top quark mass
around $m_t=178$ GeV. For that value of top mass the theoretical
cross sections become
\newline
$\sigma_{t \bar t}^{NNLO-NNNLL}$($\sqrt{S}=1.8$ TeV, $m_t$=178 GeV)
$=4.76 \pm 0.28$ pb \hspace{3mm} and
\newline
$\sigma_{t \bar t}^{NNLO-NNNLL}$($\sqrt{S}=1.96$ TeV, $m_t$=178 GeV)
$=6.15 \pm 0.38$ pb.
\newline
Results for the top quark transverse momentum distributions
at NNLO-NNNLL are also available \cite{NKRV}.
\section{Charged Higgs production via $bg \rightarrow t H^-$}
A future discovery of a charged Higgs boson would be an
umistakable sign of new physics beyond the Standard Model \cite{HiggsLH}.
The LHC has good potential for such a discovery through the
partonic process $bg \rightarrow t H^-$.
The Born cross section is proportional to $\alpha \alpha_s
(m_b^2\tan^2 \beta+m_t^2 \cot^2 \beta)$, where
$\tan \beta=v_2/v_1$ is the
ratio of the vacuum expectation values (vev's) of two Higgs doublets in
the MSSM.
Full NLO calculations have recently become available \cite{Zhu,Plehn},
and they show that
the NLO corrections are big. Since charged Higgs production will
be a near-threshold process at the LHC, given the expected large
mass of this particle (hundreds of GeV), threshold soft-gluon
corrections can provide significant enhancements of the cross section.
A next-to-leading logarithm (NLL) calculation of these corrections
at NNLO, denoted as NNLO-NLL \cite{NKch}, showed that indeed the
soft-gluon corrections are substantial and they decrease the scale
dependence of the cross section, thus providing a better theoretical
prediction.
For the process
$b(p_b) + g(p_g) \longrightarrow t(p_t)+H^-(p_{H^-})$ we
define $s=(p_b+p_g)^2$, $t=(p_b-p_t)^2$, $u=(p_g-p_t)^2$,
and $s_4=s+t+u-m_t^2-{m_{H^-}}^2$.
At threshold $s_4 \rightarrow 0$.
The soft-gluon corrections take the form
{$[(\ln^l(s_4/m_{H^-}^2))/s_4]_+$}.
For the order $\alpha_s^n$ corrections, $l \le 2n-1$. The
leading logarithms (LL) are those with
$l=2n-1$, while for the NLL $l=2n-2$.
We calculate NLO and NNLO corrections at NLL accuracy.
\begin{figure}
\begin{center}
\includegraphics[width=10cm]{higgsmhplot.eps}
\caption{The total cross section for charged Higgs production at the LHC.}
\end{center}
\end{figure}
In Figure 1 we plot the cross section versus
charged Higgs mass for $pp$ collisions at the LHC with $\sqrt{S}=14$ TeV.
We use the MRST2002 approximate
NNLO parton distributions functions (PDF) \cite{mrst2002}
with the respective three-loop evaluation of $\alpha_s$.
We set the factorization scale equal to the renormalization scale
and denote this common scale by $\mu$.
We show results for the Born, NLO-NLL, and NNLO-NLL
cross sections, all with a choice of scale $\mu=m_{H^-}$.
In our calculations we use $\tan \beta=30$.
The NLO and NNLO threshold corrections are positive and provide a significant
enhancement to the lowest-order result.
We note that the cross sections for the related process
${\bar b} g \rightarrow {\bar t} H^+$ are exactly the same.
\begin{figure}
\begin{center}
\includegraphics[width=6.5cm]{Khiggsmhplot.eps}
\hspace{1mm}
\includegraphics[width=6.5cm]{higgsNLOcomparplot.eps}
\caption{$K$-factors for charged Higgs production at the LHC.}
\end{center}
\end{figure}
In Figure 2 we plot $K$-factors, i.e. ratios of cross
sections at various orders.
On the left-hand side, the NLO-NLL / Born curve shows that the
NLO threshold corrections enhance the Born cross section by approximately
25\% to 50\% depending on the mass of the charged Higgs.
The NNLO-NLL / Born curve shows that if we include the NNLO threshold
corrections we get an enhancement over the Born result of approximately
35\% to 70\% in the range of masses shown.
Finally, the NNLO-NLL / NLO-NLL curve shows clearly the further enhancement
over NLO that the NNLO threshold corrections provide, between 7\% and
14\%.
On the right-hand side we compare our NLO-NLL results with the exact results
that have been derived in \cite{Zhu}.
To make the comparison with \cite{Zhu}, the NLO-NLL result is calculated
here for $\mu=m_{H^-}+m_t$, the choice of scale used in that reference,
and also using a two-loop $\alpha_s$. Also the use of $K$-factors removes
any discrepancies
arising from different choices of parton distribution functions.
The NLO-NLL / NLO-exact curve
is very close to 1 (only a few percent difference), and this shows
that the NLO-NLL cross section is a
remarkably good approximation to the exact NLO result. As noted before,
we might have expected this on theoretical grounds since this is
near-threshold production, and also from prior experience with many
other near-threshold hard-scattering cross sections
\cite{NKRV,NKhq,HSvar}.
\begin{figure}
\begin{center}
\includegraphics[width=10cm]{higgsmuextraplot.eps}
\caption{The scale dependence of the charged Higgs cross section.}
\end{center}
\end{figure}
In Figure 3, we plot the scale dependence of the
cross section for a fixed charged Higgs mass $m_{H^-}=500$ GeV.
We plot a large range in scale, $0.1 \le \mu/m_{H^-} \le 10$, and see indeed
that the threshold corrections greatly decrease the scale dependence
of the cross section. The NNLO-NLL curve is relatively flat.
For comparison we also plot the results using only a leading logarithm (LL)
approximation.
We see that the LL results
display a large scale dependence at both NLO and NNLO,
and are not an improvement over the Born result. The NLL terms are
essential in diminishing the scale dependence.
The difference between the LL and NLL results at both NLO
and NNLO can be very substantial. Thus having a complete NLL calculation,
as provided here, is crucial in providing stable theoretical
predictions.
Finally, we note that even higher-order corrections may provide
sizable contributions to hard-scattering cross sections. In particular
current calculations of next-to-next-to-next-to-leading order
(NNNLO) soft-gluon corrections indicate a non-negligible enhancement
of the cross section for charged Higgs production.
| {
"redpajama_set_name": "RedPajamaArXiv"
} | 291 |
\section{Introduction} \label{sec: Introd}
Multi-agent systems involve interacting elements with computing capabilities, also called agents or nodes, who communicate with each other to achieve a collective control task that is \jmh{more} difficult or \jmh{sometimes even} impossible to be performed by an individual agent. This configuration of multi-agent systems has a great benefit to model and solve many problems in different fields of applications including sensor networks \cite{Olfati-ACC08-Distributed, Shi-IET10-Resource, Demigha-CST12-On}, computer networks \cite{Cerf-TC74-protocol, Muthuk-TCS98-First} and social science \cite{Hegs-JASSS02-opinion, Blondel-SIAM10-continuous, Liu-CDC12-Dynamic}. One of the common problems that has been studied in these applications is the consensus of multi-agent systems on aggregate functions such as, e.g., MIN, MAX, SUM and AVERAGE. For instance, in a group of distributed sensors, it can be required to compute the average temperature of a specific region or to elect the sensor with maximum power resource to preserve the communication over a costly link or to reduce energy for a wireless sensor network, see, e.g., \cite{Boyed-TAC06-Randomized, Iutz-IEEETSP12-max-xonsensus, Giannini-TCS16-Asynch}.
Most existing results of the literature rely on the assumption that the system composition is static, i.e., the set of agents present in the system does not change after the initial time, see, e.g., \cite{Olfati-IEEE07-Consensus, Iutz-IEEETSP12-max-xonsensus, Hendrickx-TAC11-Distributed, Ren-ACC05-Survey} and the references therein. However, this requirement can be difficult to satisfy in some implementation scenarios where new agents can join and/or existing agents can leave the network at any time instant. This phenomenon is known in the literature as ``\textit{network churn}" \cite{Stutz-ACM06-Understanding, Kuhn-DistComp10-Towards}, ``\textit{dynamic network}" \cite{Jelas-ACM05-Gossip, Kuhn-ACM10-Distributed, Dutta-ACM13-On} or ``\textit{open multi-agent systems}" \cite{Hendrickx-AAC16-Open, Huynh-AAMAS06-An, Pinyol-AIR13-Computational}. In this case, the consensus problem on aggregate estimates becomes more challenging to handle compared to the case of static networks. For instance, consider the paradigmatic problem of MAX-consensus with distributed communications and assume that the agent with the largest state value has left the network after all the agents have converged to its state value. In this case, all the existing nodes in the network will then hold outdated information.
This scenario cannot occur in static networks, which highlights one of the inherent challenges of open multi-agent systems.
In this paper, we investigate the problem of MAX-consensus in open multi-agent systems with distributed communications. The agents are assumed to be anonymous, do not have global identifiers, and all run the same algorithm.
We further assume that interactions only occur via pairwise \quotes{gossip} exchanges between randomly selected agents in the sense that, at any (discrete) time instant, (only) two agents are selected randomly to exchange their information, update their MAX estimates and possibly other variables. To cope with the dynamic nature of the network, two different solutions are proposed depending on whether or not it is possible for the leaving agents to announce their departures.
\jmh{In the case in which announcements are made, our algorithm relies on a variable that describes how \quotes{up-to-date} agents are with respect to recent departures, and priority is given to information coming from the most \quotes{up-to-date} agents. In the case where agents disappear without sending a last message, our algorithm maintains an estimate of the age of the information, and estimates corresponding to information deemed too old are discarded.}
We will show that our two approaches ensure that outdated information can be forgotten, and that the consensus on the MAX value can be achieved (with high probability) if the system composition stops evolving.
The problem of MAX-consensus in multi-agent systems has been studied in, e.g., \cite{Nejad-ISICAT09-MAx, Iutz-IEEETSP12-max-xonsensus, Zhang-IEEESJ16-MAX, Giannini-TCS16-Asynch}. Among existing techniques, the work of \cite{Iutz-IEEETSP12-max-xonsensus} has considered MAX-consensus with random gossip interactions between agents, \jmh{on a \textit{static} network.}
\MA{Compared to existing works of the literature, our result is adapted to the problem of MAX-consensus in multi-agent systems when the network is \emph{open}, which has not been considered in the previously mentioned works. Our proposed approach encompasses the result of pairwise gossip interaction in static networks in \cite{Iutz-IEEETSP12-max-xonsensus} as a particular case.}
The remainder of the paper is organized as follows. Notations are given in Section \ref{sec: notation}. The problem is formulated in Section \ref{sec: problem-formulation}. In Section \ref{sec: counters}, we treat the case where leaving agents send a last message, and in Section \ref{sec: timeout}, we treat the case where they do not.
Numerical simulations are given in Section \ref{sec: example}. Conclusions \jmh{and discussions} are provided in Section \ref{sec: conclusion}.
\section{Notation} \label{sec: notation}
Let $\R{}{} := (-\infty,\infty)$, $\R{}{\geqslant 0} := [0,\infty)$, $\ensuremath{\mathbb{N}} := \{ 0, 1, 2, \ldots \}$, $\ensuremath{\mathbb{N}_{\geqslant 1}} := \{ 1, 2, \ldots \}$ and $\ensuremath{\mathbb{N}_{\geqslant T}} := \{ T, T+1, \ldots \}$ for $T\in\ensuremath{\mathbb{N}}$. We denote by $\boldsymbol 0_n$ and $\boldsymbol 1_n$ the vectors in $\R{n}{}$ whose all elements are 0 or 1, respectively. We write $A^{T}$ to denote the transpose of $A$, and $(x,y)\in\R{n_x+n_y}{}$ to represent the vector $[x^{T}, y^{T}]^{T}$ for $x \in \R{n_x}{}$ and $y \in \R{n_y}{}$. The symbol $\mathbb{I}_{n}$ stands for the identity matrix of dimension $n$. For a random variable $R$, the symbol $\mathbb{E}(R)$ denotes the expectation of $R$.
\section{Problem statement} \label{sec: problem-formulation}
Consider a connected time-varying graph $\mathcal{G}(t)=(\mathcal{V}(t), \mathcal{E}(t))$, where $\mathcal{V}(t)$ and $\mathcal{E}(t)$ denote, respectively, the set of existing agents and the set of edges in the graph at time $t\in\ensuremath{\mathbb{N}}$. The graph $\mathcal{G}(t)$ is dynamic in the sense that new agents can join and/or existing agents can leave at any time $t$. Hence, the cardinality of $\mathcal{V}(t)$, denoted by $\mathcal{N}(t)$, is not necessarily constant for all $t\in\ensuremath{\mathbb{N}}$. The agents communicate with each other in a \textit{pairwise} randomized gossip fashion \cite{Boyed-TAC06-Randomized}. \jmh{In other words, at any time instant $t\in\ensuremath{\mathbb{N}}$, there are three possibilities: (i) an agent joins the system and $\mathcal{N}(t+1)= \mathcal{N}(t)+1$, (ii) an agent leaves the system and $\mathcal{N}(t+1)= \mathcal{N}(t)-1$, or (iii) two randomly selected agents $i,j\in\mathcal{V}(t), i\neq j$ communicate with each other (Note that these discrete-time instants may be interpreted as the sampling of an asynchronous process at those times where an event occurs). Joining agents are assumed to know that they join the system. Leaving agents may or may not be able to send one last message (to one other agent) before leaving, which are two cases of interest, which will be discussed in Section \ref{sec: counters} and \ref{sec: timeout}}, respectively.
Every agent $i$ has \jmh{two special states: $x_i\in \R{}{}$ is its intrinsic value, which is constant and determined arbitrarily when joining the system, and $y_i(t)$ is its estimated answer at time $t\in\ensuremath{\mathbb{N}}$ for the MAX value. Our goal is to estimate the maximum intrinsic value of all the agents present in the system,} \MA{so we would ideally want, when no more agents are joining or leaving the network after time $T\in\ensuremath{\mathbb{N}}$, that there is a time $T^*\in\ensuremath{\mathbb{N}}\geqslant T$ such that $y_i(t) = \ensuremath{\textnormal{MAX}}(t) := \max_{j\in \mathcal{V}(t)} x_j$, for all $i\in \mathcal{V}(t)$ and for $t\in\ensuremath{\mathbb{N}}\geqslant T^*$.} Agents may then have other states that they use to reach this goal.
If the network would be static, i.e., $\mathcal{G}(t)$ is time-invariant, the estimation of the maximum could be achieved in finite time by starting from $y_i(0)=x_i(0)$ for every agent, and setting $y_i(t+1)=y_j(t+1)=\max(y_i(t),y_j(t))$ whenever agents $i$ and $j$ interact at time $t\in\ensuremath{\mathbb{N}}$, see, e.g., \cite{Iutz-IEEETSP12-max-xonsensus}. The main challenge in a dynamic or open network lies with the need for the algorithm to take new agents into account and to eventually discard information related to agents no longer present in the system to ensure that $\max_jx_j$ is eventually recovered once the system composition stops evolving. \MA{Classical algorithms such as that in \cite{Iutz-IEEETSP12-max-xonsensus} do not guarantee this: outdated values from agents no longer in the system may never be discarded.}
\jmh{Note that an alternative and maybe more natural goal would be to have the $y_i(t), i\in\mathcal{V}(t)$ track $\ensuremath{\textnormal{MAX}}(t) = \max_{j\in \mathcal{V}(t)} x_j$ sufficiently accurately. This more ambitious goal is left for future studies, see Section \ref{sec: conclusion} for further discussions on this issue.}
Finally, we chose to make the following assumption for the sake of simplicity of exposition.
\MA{
\begin{assmp} \label{assmp:graph-complete}
The graph $\mathcal{G}(t)=(\mathcal{V}(t), \mathcal{E}(t))$ is complete for all $t\in\ensuremath{\mathbb{N}}$. \hspace*{\fill} $\Box$
\end{assmp}}
This means that every pair of distinct agents in the network can communicate directly with each other. The algorithms we develop would actually also work on general dynamic graphs under suitable connectivity assumptions, but the analysis would be more complex.
\section{Departures are announced} \label{sec: counters}
\subsection{Algorithm description}
If leaving agents announce their departure (to one other agent), then we can benefit from this knowledge to correct the outdated information. For that purpose, we introduce an auxiliary variable $\kappa_i(t)\in\ensuremath{\mathbb{N}}$ at each agent, meant to represent the \quotes{level of information} available to $i$ about the departures up to time $t\in \ensuremath{\mathbb{N}}$. It will in general \emph{not be equal to the actual number of departures, nor converge to it}. The algorithm is designed to ensure that those with the largest value $\kappa_i$ have valid estimates, i.e. their $y_i(t)$ correspond to the $x_j$ of agents present in the system. For this purpose, information coming from agents with higher $\kappa_i$ will be given priority over information coming from agents with lower values, and it will be made sure that agents with a lower value of $\kappa_i$ will never have influenced those with a higher value.
The algorithm is summarized as follows. Initially, every existing agent at $t=0$ sets $y_i(0) = x_i$ and $\kappa_i=0, i\in \mathcal{V}(0)$, as shown in Algorithm \ref{Intialization algorithm}.
\begin{algorithm}[h]
\caption{Intialization algorithm}
\label{Intialization algorithm}
At time $t=0$, every existing node $i\in\mathcal{V}(0)$ initializes its state as
\begin{algorithmic}[1]
\State $y_i(0) = x_i$
\State $\kappa_i(0) = 0$
\end{algorithmic}
\end{algorithm}
When a new agent $n$ joins the group at time $t\in\ensuremath{\mathbb{N}}$, it initializes its counter $\kappa_n(t)$ and its estimate $y_n(t)$ according to Algorithm \ref{Joining algorithm}.
\begin{algorithm}[h]
\caption{Joining algorithm}
\label{Joining algorithm}
Assume at any time $t\in\ensuremath{\mathbb{N}_{\geqslant 1}}$, a new agent $n$ wants to join, i.e., $\mathcal{V}(t+1) = \mathcal{V}(t)\cup\{n\}$. Agent $n$ initializes its state as
\begin{algorithmic}[1]
\State $y_n(t) = x_n$
\State $\kappa_n(t) = 0$
\end{algorithmic}
\end{algorithm}
If an agent $\ell$ leaves the system, it sends a last message containing its counter value $\kappa_\ell$ to a randomly selected agent $m$. The reaction of $m$ is governed
by Algorithm \ref{Departure algorithm}, which can be interpreted as follows: If the counter $\kappa_\ell(t)$ of the leaving agent $\ell$ is less than $\kappa_m(t)$, then agent $m$ ignores this departure since the information of $\ell$ is deemed less up-to-date than its own and has not influenced it.
On the other hand, if $\kappa_\ell(t) \geqslant\kappa_m(t)$, then $\ell$ may have influenced $m$ and possibly agents $i$ with values $\kappa_i$ higher than $\kappa_m$, but no larger than $\kappa_{\ell}$. To ensure that none of the agents with the highest values $\kappa$ hold the now outdated value $x_l$,
$m$ will reset its $y_m$ to $x_m$, which is by definition a valid value, and set its $\kappa_m$ to $\kappa_{\ell}+1$, a value above that of all those who could have been influenced by $\ell$.
\begin{algorithm}[h]
\caption{Departure algorithm}
\label{Departure algorithm}
Assume at time $t\in\ensuremath{\mathbb{N}}$, agent $\ell$ leaves, i.e., $\mathcal{V}(t+1) = \mathcal{V}(t)\setminus\{\ell\}$.\\
Agent $\ell$ picks a random agent $m$ to inform, and agent $m$ updates its state as follows
\begin{algorithmic}[1]
\If{$\kappa_\ell(t) < \kappa_m(t)$}
\State $y_m(t+1) = y_m(t)$
\State $\kappa_m(t+1) = \kappa_m(t)$
\ElsIf{$\kappa_\ell(t) \geqslant \kappa_m(t)$}
\State $y_m(t+1) = x_m$
\State $\kappa_m(t+1) = \kappa_\ell(t) + 1$
\EndIf
\end{algorithmic}
\end{algorithm}
The gossip communication between agents is performed via Algorithm \ref{Modified random gossip} (values not explicitly updated remain constant between $t$ and $t+1$). When $\kappa_i(t) = \kappa_j(t)$, this implies that agents $i$ and $j$ either have not been informed about any departure from the group, i.e., $\kappa_i(t) = \kappa_j(t) = 0$, or have equal information level about the departure of one or more agents. In either case, agents $i$ and $j$ can exchange their information to update their estimate for the MAX value. When $\kappa_i(t) > \kappa_j(t)$, agent $i$'s information about past departures is deemed more up to date. Agent $j$ is then not allowed to transfer its estimate $y_j$ to avoid infecting $i$ with possibly outdated information (unless its estimate is actually its own value, which is by definition valid). Therefore, agent $j$ restarts to $\max(y_i(t), x_j)$ and increments its counter to $\kappa_j(t+1) = \kappa_i(t)$ in order to alert other future agents who have not been informed yet to restart. The case when $\kappa_j(t) > \kappa_i(t)$ is completely symmetric.
\begin{algorithm}[h]
\caption{Gossip algorithm}
\label{Modified random gossip}
At each time step $t\in\ensuremath{\mathbb{N}}$, two agents $i,j\in\mathcal{V}(t)$ are picked randomly (with possibly $i=j$)
\begin{algorithmic}[1]
\If{$\kappa_i(t) = \kappa_j(t)$}
\State $y_i(t+1) = y_j(t+1) = \max(y_i(t), y_j(t))$
\ElsIf{$\kappa_i(t) > \kappa_j(t)$}
\State $y_i(t+1) = y_j(t+1) = \max(y_i(t), x_j)$
\State $\kappa_j(t+1) = \kappa_i(t)$
\Else
\State $y_i(t+1) = y_j(t+1) = \max(x_i, y_j(t))$
\State $\kappa_i(t+1) = \kappa_j(t)$
\EndIf
\end{algorithmic}
\end{algorithm}
\subsection{Eventual Correctness} \label{sec:correct_with_messages}
\jmh{We now show that the algorithm described in the previous subsection is correct in the sense that, with high probability (and even almost surely), it eventually settles on the correct value if arrivals and departures stop.}
Remember that $\mathcal{V}(t):=\{1,\ldots,\mathcal{N}(t)\}$ denotes the group of agents \jmh{present at time $t$, and let $X:=\{x_1,\ldots,x_{\mathcal{N}(t)}\}$ be the set } of intrinsic values of nodes in $\mathcal{V}(t)$. Assume that after some time $T\in\ensuremath{\mathbb{N}}$ no agent leaves and no new agent joins the system, so that $\mathcal{V}(t) = \mathcal{V}(T)=\overline{\mathcal{V}}$, $\mathcal{E}(t) = \mathcal{E}(T)=\overline{\mathcal{E}}$ and $\mathcal{N}(t)= \mathcal{N}(T)=\overline{\mathcal{N}}$ for all $t\in\ensuremath{\mathbb{N}_{\geqslant T}}$. Then, we need to show that all the currently existing agents $\mathcal{V}(T)$ in the network will successfully reach the correct maximum value. For that purpose, we define the following property.
\MA{
\begin{defn}\label{def: eventual-correctness}
We say that an algorithm is eventually correct if for any $T\in\ensuremath{\mathbb{N}}$ with $\mathcal{G}(t)=(\overline{\mathcal{V}}, \overline{\mathcal{E}})$ for all $t\in \ensuremath{\mathbb{N}}_{T}$, there exists a $T^* \in\ensuremath{\mathbb{N}_{\geqslant T}}$ such that $y_i(t) = \max_{j\in \overline{\mathcal{V}}}x_j$ for all $i\in\overline{\mathcal{V}}$ and all $t\in\ensuremath{\mathbb{N}}_{T^*}$.
\end{defn}
}
Denote $K(t):=\underset{i\in\mathcal{V}(t)}{\max}\kappa_i(t)$, MAX$(t)=\underset{i\in\mathcal{V}(t)}{\max}x_i$ and $X_{K}(t):=\{x_i: i\in\mathcal{V}(t) \wedge \kappa_i(t)=K(t)\}$. We state the following result.
\begin{lma} \label{lma: max-kappa}
For all $t\in\ensuremath{\mathbb{N}}$ and any $j\in\mathcal{V}(t)$, if $\kappa_j(t)=K(t)$ then $y_j(t)\in X_{K}(t) \subseteq X(t)$.
\end{lma}
\noindent Lemma \ref{lma: max-kappa} states that, at any time $t\in \ensuremath{\mathbb{N}}$, if the counter value of an agent $j\in\mathcal{V}(t)$ is equal to the maximum value $K(t)$, then its estimate $y_j(t)$ is equal to an intrinsic value $x_i\in X_{K}(t)$ of one of the agents present in the system at this time $t$ and whose value $\kappa_i$ is $K(t)$.
\vspace{0.5cm}
\noindent \textbf{Proof.} Consider any agent $j\in \mathcal{V}(t)$ with $\kappa_j(t)=K(t)$. We have three scenarios:
\noindent (a) Agent $j$ has just joined the \jmh{system} at time $t$. Hence, $\kappa_j(t)=0$ and $y_j(t)=x_j$ according to Algorithm \ref{Joining algorithm}. Since $\kappa_j(t)= K(t)$, this implies that $K(t)=0$. Hence, $K_i(t)=0$ for all $i\in\mathcal{V}(t)$. Consequently, it holds that $y_j(t)\in X_{K}(t) = X(t)$. ~\\[-2pt]
\noindent (b) $K(t)>K(t-1)$ \jmh{(and $j$ is not a new agent)}. In this case, since at most one agent can change its counter at any time, there is exactly one agent $j$ with $\kappa_j(t) = K(t)$. This implies that an agent $\ell\in\mathcal{V}(t-1)$ with $\kappa_\ell(t-1)=K(t-1)$ has left at time $t$ and informed agent $j$ about its departure, otherwise $\kappa_j(t)\neq K(t)$ or $K(t)\ngtr K(t-1)$. Consequently, agent $j$ restarts according to lines 7-9 in Algorithm \ref{Departure algorithm} and we have that $\kappa_j(t)=K(t-1)+1=K(t)$ and $y_j(t)=x_j\in X_{K}(t)$. ~\\[-2pt]
\noindent (c) $K(t)=K(t-1)$ \jmh{(and $j$ is not a new agent)}. We have two possibilities:
\noindent c1)
$\kappa_j(t)>\kappa_j(t-1)$, i.e., agent $j$ has increased its counter value at time $t$ such that $\kappa_j(t)=K(t)=K(t-1)$, which can happen by one of the following actions:
\begin{itemize}
\item [-] an agent $i\in\mathcal{V}(t-1)$ with $\kappa_i(t-1) = K(t-1)-1\geqslant \kappa_j(t-1)$ has left the group and informed agent $j$ about its departure. Consequently, in view of lines 4-6 in Algorithm \ref{Departure algorithm}, agent $j$ has incremented its counter to $\kappa_j(t)=\kappa_i(t-1)+1=K(t-1)=K(t)$, otherwise $\kappa_j(t)\neq K(t-1)$ and $y_j(t)=x_j\in X_K(t)$.
\item [-] no departure occurred but agent $j$ has interacted with an agent $i\in\mathcal{V}(t-1)$ with $\kappa_i(t-1)=K(t-1)$. Consequently, in view of lines 4-6 in Algorithm \ref{Modified random gossip}, we obtain $\kappa_j(t)=\kappa_i(t-1)=K(t-1)=K(t)$ and $y_j(t)=\max(x_j, y_i(t-1))\in X_{K}(t)$.
\end{itemize}~\\[-2pt]
\noindent c2) $\kappa_j(t)=\kappa_j(t-1)$, i.e., agent $j$ did not increase its counter value at time $t$. Then, since $K(t)=K(t-1)$, it holds that $\kappa_j(t-1)=K(t-1)$ and we know that $y_j(t-1)=x_i$ for some $x_i\in X(t-1)$. There are two different possibilities:
\begin{itemize}
\item [-] $y_j(t)\neq y_j(t-1)$, which can only happen if agent $j$ has interacted via algorithm \ref{Modified random gossip} with an agent $h$ with $\kappa_h(t-1)= K(t-1)$. Hence, in view of line 3 in algorithm \ref{Modified random gossip}, it holds that $y_j(t)=y_h(t-1)\in X_{K}(t)$.
\item [-] $y_j(t) = y_j(t-1) = x_i$. We know that agent $i$ did not leave because otherwise it would have been true that agent $i$ has informed some neighbour $m$ about its departure and resulted in $\kappa_m(t)=\kappa_i(t-1)+1 = K(t-1)+1$, which leads to case (b) not case (c). Hence, since $i\in\mathcal{V}(t)$, it holds that $y_j(t)\in X_{K}(t)$.
\end{itemize}
This completes the proof of Lemma \ref{lma: max-kappa}. \hspace*{\fill} $\Box$
\MA{
\begin{thm} \label{thm: convergence}
Suppose that Assumption \ref{assmp:graph-complete} holds. Then, Algorithm \ref{Intialization algorithm}-\ref{Modified random gossip} is eventually correct.
\end{thm}
}
\vspace{0.5cm}
\noindent \textbf{Proof.}
The proof of Theorem \ref{thm: convergence} relies on Lemma \ref{lma: max-kappa} and the result developed in \cite{Iutz-IEEETSP12-max-xonsensus}. Note that an essential difference between our problem and the setup in \cite{Iutz-IEEETSP12-max-xonsensus} is that the gossip interaction between agents (as in Algorithm \ref{Modified random gossip}) depends considerably on their counter values, which is not the case in static networks as in \cite{Iutz-IEEETSP12-max-xonsensus}. Therefore, we will invoke their result twice, once on the counter values $\kappa_i$ to show that all agents eventually have the maximal counter value $K(T)$, and once on the actual estimate $y_i(t)$ to show that they eventually reach $\ensuremath{\textnormal{MAX}}(T)$.
\jmh{After time $T$, only Algorithm \ref{Modified random gossip} is applied. Ignoring for the moment its effect on the $y_i(t)$, observe that it performs a classical gossip operation on the $\kappa_i(t)$, in the sense that an interaction between $i$ and $j$ results in $\kappa_i(t+1) = \kappa_j(t+1) = \max(\kappa_i(t),\kappa_j(t))$.} Theorem 4, 5 in \cite{Iutz-IEEETSP12-max-xonsensus}, applied to complete graphs following Assumption \ref{assmp:graph-complete}, allows us then to guarantee that the counters of all agents converge to the maximum counter value $K(T)$ in a finite time $T^*_1$ with the following properties
\begin{equation}\label{T1star-expect}
\mathbb{E}(T^*_1-T) \leqslant (\overline{\mathcal{N}} -1)h_{\overline{\mathcal{N}}-1},
\end{equation}
where $h_n$ denotes the $n$th harmonic number, i.e., $h_n:=\sum_{k=1}^{n}\frac{1}{k}$. Moreover, we have, with probability $1-\epsilon$ that $T^*_1-T$ is bounded by
\begin{equation}\label{T1star-bound}
(\overline{\mathcal{N}} -1)h_{\overline{\mathcal{N}}-1}
\left(1 \!+\! \log\left(\frac{\overline{\mathcal{N}}}{\epsilon}\right)\left(1 \!+\! \sqrt{1 \!+\! \frac{1}{\log\frac{\overline{\mathcal{N}}}{\epsilon}}}\right)\right).
\end{equation}
\jmh{After $T$, since $\kappa_i(t)=K(t)$ for all $i$, it follows from Lemma \ref{lma: max-kappa} that all $y_i(t)$ correspond to actual values $x_j, j\in \overline{\mathcal{V}}$. Moreover, since one can easily verify that $y_i(t)\geqslant x_i$ at all times, there holds $\max_{i\in \overline{\mathcal{V}}}y_i(t) = \max_{i\in \overline{\mathcal{V}}}x_i= \ensuremath{\textnormal{MAX}}(t)=\ensuremath{\textnormal{MAX}}(T)$. It is therefore sufficient to show that all $y_i(t)$ eventually settle on the same value.}
For this purpose, observe that when all agents have the same $\kappa_i(t) = K(t)$, Algorithm \ref{Modified random gossip} reduces to its line 2, $y_i(t+1)=y_j(t+1) = \max(y_i(t),y_j(t))$, which is again a classical pairwise gossip. We can then re-invoke Theorem 4, 5 in \cite{Iutz-IEEETSP12-max-xonsensus} to show the existence of a $T^*$ after which
$y_i(t) = \max_{i\in \overline{\mathcal{V}}} y_i(T^*) = \max_{i\in barV} x_i=\ensuremath{\textnormal{MAX}}$, with the same bounds on $T^*-T^*_1$ as on $T^*_1-T$. In particular,
$\mathbb{E}(T^*-T)\leqslant2(\overline{\mathcal{N}} -1)h_{\overline{\mathcal{N}}-1}$, and there is a probability
$1-\epsilon$ that $T^*-T$ is at most twice the expression in \eqref{T1star-bound}. This achieves the proof of Theorem \ref{thm: convergence}. \hspace*{\fill} $\Box$
\begin{rmrk}
Note that, since we apply the result of \cite{Iutz-IEEETSP12-max-xonsensus} \emph{twice} to prove that Algorithm \ref{Intialization algorithm}-\ref{Modified random gossip} is eventually correct, the upper bound that we obtain on the time needed to achieve this property is conservative. This comes from the fact that, in Algorithm \ref{Intialization algorithm}-\ref{Modified random gossip}, the agents update their counters and their estimates simultaneously and not sequentially. \hspace*{\fill} $\Box$
\end{rmrk}
\section{Departures are not announced} \label{sec: timeout}
\subsection{Algorithm description}
Leaving agents may not always be able to announce their departure, such as in case of unforeseen failures or disconnections.
The algorithms in Section \ref{sec: counters} can no longer be applied in such a more challenging setting. Therefore, we now propose an alternative algorithm that does not use messages from departing agents.
The idea is to have each agent maintain a variable $\mathcal{T}_i$ representing the \quotes{age} of its information. This age $\mathcal{T}_i$ is kept at 0 when the agent's estimate $y_i(t)$ of $\ensuremath{\textnormal{MAX}}(t)$ corresponds to (only) its own value $x_i$, as the validity of its information is then guaranteed. Otherwise $\mathcal{T}_i$ is increased by 1 every time agent $i$ interacts with another agent, as the information gets \quotes{older}. When an agent $i$ changes its estimate $y_i(t)$ by adopting the estimate $y_j(t)$ of an agent $j$, it also sets $\mathcal{T}_i(t)$ to the value $\mathcal{T}_j(t)$, which corresponds to the age of the new information it now holds. Finally, when $\mathcal{T}_i(t)$ reaches a threshold $\mathcal{T}^*$, the information $y_i(t)$ is considered too old to be reliable and is discarded; $y_i(t)$ is reset to $x_i$ and $\mathcal{T}_i(t)$ to 0. We defer the discussion on the value of $\mathcal{T}^*$ to Section \ref{sec: conclusion}, but already note that it should depend on (bounds of) the system size, or (possibly) change with time.
Formally, the behavior of an agent joining the system is governed by Algorithm \ref{Joining algorithm_timeout}, while the update of $\mathcal{T}_i(t)$ and the gossip interactions are governed by Algorithms \ref{update_timer} and \ref{Modified_random_gossip_timeout_sep_from_update} (where we use $y_i(t^+),\mathcal{T}_i(t^+)$ to denote intermediate values the variables $y_i,\mathcal{T}_i$ may take during the computation leading to their values at $t+1$). Observe that when $i$ and $j$ have the same estimate $y_i(t)=y_j(t)$ they update the age of information to the smallest among $\mathcal{T}_i(t)$ and $\mathcal{T}_j(t)$. Observe also that the algorithms guarantee that $y_i(t)\geqslant x_i$ for every $i$ at all times, since $y_i(t)$ can never decrease except when it is re-initialized at $x_i$.
Finally, there is no algorithm for the departure, since agents are not assumed to be able to take any action when other agents leave as this is not announced.
\begin{algorithm}[H]
\caption{Joining algorithm}
\label{Joining algorithm_timeout}
Assume at time $t\in\ensuremath{\mathbb{N}_{\geqslant 1}}$, a new agent $n$ wants to join. Agent $n$ initializes its state as follows
\begin{algorithmic}[1]
\State $y_n(t) = x_n$
\State $\mathcal{T}_n(t) = 0$
\end{algorithmic}
\end{algorithm}
\begin{algorithm}[H]
\caption{UpdateTimer}
\label{update_timer}
When agent $i$ calls this procedure\footnote{T}:
\begin{algorithmic}[1]
\If{$y_i(t) = x_i$} \Comment{guaranteed validity of estimate}
\State{$\mathcal{T}_i(t^+) = 0$}
\State{$y_i(t^+) = x_i$}
\Else\Comment{estimate gets one period older}
\State $\mathcal{T}_i(t^+)=\mathcal{T}_i(t)+1$
\State{$y_i(t^+) = y_i(t)$}
\EndIf
\If{$\mathcal{T}_i(t) = \mathcal{T}^*$} \Comment{Reset if threshold reached}
\State{$y_i(t^+) = x_i$}
\State{$\mathcal{T}_i(t^+)=0$}
\EndIf
\end{algorithmic}
\end{algorithm}
\begin{algorithm}[H]
\caption{Gossip algorithm}
\label{Modified_random_gossip_timeout_sep_from_update}
At each time step $t$, two agents $i,j$ are picked randomly
\begin{algorithmic}[1]
\State UpdateTimer(i), UpdateTimer(j)
\If{$y_i(t^+) > y_j(t^+)$}
\State $y_j(t+1) = y_i(t^+)$
\State $\mathcal{T}_j(t+1) = \mathcal{T}_i(t^+)$
\ElsIf{$y_j(t^+)<y_i(t^+)$}
\State $y_i(t+1)=y_j(t^+)$
\State $\mathcal{T}_i(t+1)=\mathcal{T}_j(t^+)$
\ElsIf{$y_j(t^+)=y_i(t^+)}$
\State $\mathcal{T}_i(t+1),\mathcal{T}_j(t+1) := \min(\mathcal{T}_i(t^+),\mathcal{T}_j(t^+))$
\EndIf
\end{algorithmic}
\end{algorithm}
\subsection{Eventual Correctness}
We now discuss the eventual correctness of the algorithm described above. For space reasons, only sketches of proofs will be presented. We use the same conventions as in Section \ref{sec:correct_with_messages}. We first prove that outdated values are eventually discarded if agents stop leaving or arriving.
\begin{lma}\label{lma:discard_time_out}
If no arrival or departure takes place after time $T\in\ensuremath{\mathbb{N}}$, then almost surely there exists a time $T'\in\ensuremath{\mathbb{N}}$ after which every estimate $y_i$ corresponds to the value of an agent present in the system, i.e., for $t\in\ensuremath{\mathbb{N}}\geqslant T'$, for all $i$ there exists a $j\in \mathcal{V}(t)=\overline{\mathcal{V}}$ such that $y_i(t) = x_j$. As a consequence, $y_i(t) \leqslant\ensuremath{\textnormal{MAX}}(T) = \max_{j\in \overline {\mathcal{V}}} x_j$ for every $i\in \mathcal{V}(t)=\overline{\mathcal{V}}$ and $t\in\ensuremath{\mathbb{N}}\geqslant T'$.
\end{lma}
\noindent \textbf{Proof.}
Observe first that agents can only set their $y_i$ to their own $x_i$ or to the value $y_j$ of some other agent. Hence, since the set of values $x_i$ remains unchanged after $T$, values $y_i(t)$ for times $t\geqslant T$ that are not equal to some $x_j, j\in \overline{\mathcal{V}}$, must be equal to some $y_j(T)$, i.e., must have been held as estimated at time $T$. We show that these outdated values are eventually discarded.
Let $z\in \R{}{}$ be such an outdated value, that is, $y_i(T) = z$ for some $i\in \overline{\mathcal{V}}$ but $z= x_j$ for no $j\in \overline{\mathcal{V}}$. Let then $D(t)=\{i\in \overline{\mathcal{V}}: y_i(t)=z\}$ be the set of agents holding $z$ as estimate at time $t$, and $\tau(t) = \min\{\mathcal{T}_i(t):i\in D(t)\}$ be the minimal age of information at $t$ for those holding this outdated value as estimate. As long as $D(t)$ is non-empty, there must hold $\tau(t) \leqslant\mathcal{T}^*$ due to the reset in Algorithm \ref{update_timer}. We will show that $\tau(t)$ must keep increasing if $D(t)$ remains non-empty, leading to a contradiction.
Every time an agent $i\in D(t)$ for which $\mathcal{T}_i(t) = \tau(t)$ interacts with some other agent, It follows from Algorithm \ref{Modified_random_gossip_timeout_sep_from_update} and the timer update in Algorithm \ref{update_timer} that it must increase its counter $\mathcal{T}_i$ by 1, unless it changes its value $y_i$ and no longer belongs to $D(t+1)$. In both cases the set of agents in $D(t)$ with this $\mathcal{T}_i$ taking this value has decreased by 1.
Besides, since $z$ is equal to no $x_i$, the only way an agent $i$ can join $D(t+1)$ if it was not in $D(t)$ is by interacting with an agent $j\in D(t)$, and the rules of the algorithm imply then that $\mathcal{T}_i(t+1)= \mathcal{T}_j(t) +1 \geqslant \tau(t) +1$.
Hence $\tau(t)= \min_{i\in D(t)} T_i(t)$ never decreases, and when it is not increasing, the number of agents in $D(t)$ for which $\mathcal{T}_i(t) = \tau(t)$ either remains constant, or decreases as soon as one of them is involved in an interaction (once it reaches 0, $\tau(t)$ automatically increases). Since all agents are almost surely repeatedly involved in interactions, this means $\tau(t)$ will almost surely eventually increase as long as $D(t)$ is nonempty, in contradiction with the fact that it cannot exceed $\mathcal{T}^*$. $D(t)$ must thus almost surely eventually be empty, which means that any outdated value is thus almost surely eventually discarded, so that after some time $T'$ every estimate $y_i(t)$ corresponds to a $x_j$ for $j\in \overline{\mathcal{V}}$. \hspace*{\fill} $\Box$
Let us now prove that the agents' estimates $y_i$ eventually take the correct value $\ensuremath{\textnormal{MAX}}$ with a high probability.
\begin{thm}\label{thm:correctness_time_out}
For all $\epsilon>0$, there exists a (sufficiently large) $\mathcal{T}^*\in\ensuremath{\mathbb{N}}$ such that, if no arrival or departure takes place after time $T\in\ensuremath{\mathbb{N}}$, then there exists a time $T''\in\ensuremath{\mathbb{N}}\geqslant T$ after which $y_i(t) =\ensuremath{\textnormal{MAX}}(T) = \max_{j\in \overline {\mathcal{V}}}x_j$ holds for every $i\in \overline {\mathcal{V}}$ with a probability at least $1-\epsilon$.
\end{thm}
\noindent \textbf{Proof.}
Let $m$ be an agent holding the maximal value after time $T$: $x_m = \ensuremath{\textnormal{MAX}} = \max_{i\in \mathcal{V}}x_i$. It follows from Lemma \ref{lma:discard_time_out} that $y_m(t)\leqslant\ensuremath{\textnormal{MAX}}$ holds after some $T'$, which implies $y_m(t) = \ensuremath{\textnormal{MAX}}= x_m$, since one can verify that $y_i(t) \geqslant x_i$ holds for all agents at all times. The timer update Algorithm \ref{update_timer} implies then that $\mathcal{T}_m(t)=0$ at all times after $T'$.
Let us now fix some arbitrary time $t_0\geqslant T'$ and let $C(t)\subseteq \overline{\mathcal{V}}$ be the set of agents $i$ such that (i) $y_i(t) = \ensuremath{\textnormal{MAX}}$, and (ii) $\mathcal{T}_i \leqslant t - t_0$. The set $C(t_0)$ contains at least agent $m$. Moreover, for $t\in [t_0,t_0+\mathcal{T}^*-1]$, there holds $C(t) \subseteq C(t+1)$.
Indeed, observe first that no agent of $C(t)$ \quotes{resets} because the $\mathcal{T}_i$ of agents in $C(t)$ are by definition smaller than $\mathcal{T}^*$. Moreover, agents in $C(t)$ do not change their value $y_i$ either because it follows from Lemma \ref{lma:discard_time_out} that no agent $j$ has a value $y_j\geqslant y_i= \ensuremath{\textnormal{MAX}}$, so condition (i) still holds.
Besides, the timer $\mathcal{T}_i$ increase by at most 1 at each iteration so condition (ii) also holds.
Observe now that whenever an agent $i\in C(t)$ interacts with an agent $j\not\in C(t)$ at a time $t\in [t_0,t_0+\mathcal{T}^*-1]$, agent $j$ will set $y_j(t+1)$ to $y_i(t) = \ensuremath{\textnormal{MAX}} $ and join $C(t+1)$. A reasoning similar to that the analysis of classical pairwise gossip algorithm in \cite{Iutz-IEEETSP12-max-xonsensus} shows then that, for every $\epsilon$, there exists of a $\tau$ given by \eqref{T1star-bound} such that with probability at least $1-\epsilon$, all agents will be in $C(t)$ after $t_0+\tau$ and at least until $t_0+\mathcal{T}$ (provided $\mathcal{T} \geqslant \tau$).
There would thus hold $y_i=\ensuremath{\textnormal{MAX}}$ for all $i$.
Since this holds true for any arbitrary $t_0\geqslant T'$, it follows that for every $i$ and $t\geqslant T'+\tau$, $y_i(t)= \ensuremath{\textnormal{MAX}}$ holds with probability at least $1-\epsilon$. \hspace*{\fill} $\Box$
The proofs of eventual correctness show that the value of the threshold $\mathcal{T}^*$ is subject to a trade-off:
We see from the proof of Lemma \ref{lma:discard_time_out} that the time needed to discard outdated values increases when $\mathcal{T}^*$ is increased. On the other hand, a sufficiently large threshold is needed in Theorem \ref{thm:correctness_time_out}. In its proof, we see that larger thresholds allow larger $\tau$, which imply smaller probabilities $\epsilon$ of some agent not having the correct value.
Besides, we see in Theorem \ref{thm:correctness_time_out} that $\mathcal{T}^*$ must be sufficiently larger than the expression \eqref{T1star-bound}, \emph{which depends on $\overline{\mathcal{N}}$}, the eventual size of the system. This implies that agent must know at least a bound on this size, unlike in the algorithm developed in Section \ref{sec: counters} when leaving agents could send a last message. One theoretical solution to avoid this problem would be to let $\mathcal{T}^*$ slowly grow with time, so that it would eventually always be sufficiently large if the system composition stops changing (This growth should be sufficiently slow for the argument of Lemma \ref{lma:discard_time_out} still to be valid).
However, the system would also become slower and slower in discarding outdated information.
\section{Simulations} \label{sec: example}
We demonstrate the application of our algorithms on a group of 25 agents: Initially, the intrinsic states $x_i$ of all agents were assigned to random integer values between 0 and 1000. The largest two values of $x_i$ are found to be $x_{9} = 936$ and $x_{13} = 815$. The estimates $y_i(0)$ for all agents are initialized to $x_i$ and all the counters $\kappa_i(0)$ and ages $\mathcal{T}_i(0)$ are initialized to 0. Agent $9$ with the highest value, $x_9=936$ leaves at $t=200$. Pairwise interactions between two randomly selected agents take place at every other time.
\begin{figure}
\centering
\begin{tabular}{c}
\includegraphics[scale=.4]{consensus_counters}\\
(a)\\
\includegraphics[scale=.4]{consensus_timeout_T40}\\
(b)\\
\includegraphics[scale=.42]{consensus_timeout_T200}\\
\\
(c)
\end{tabular}
\caption{Evolution with time of the agent estimates $y_i(t)$ for the algorithm of Section \ref{sec: counters} where departures can be announced (a), and of Section \ref{sec: timeout} where departures are not announced, for tresholds $\mathcal{T}^*=40$ (b) and $\mathcal{T}^*=200$ (c). (The scale is different in (a)). Departure of the agent with highest value is represented by a dashed line. }
\label{fig:simulations}
\end{figure}
We have simulated the two algorithms, with two thresholds $\mathcal{T}^*$ for that of Section \ref{sec: timeout}, and the results are represented in Fig. \ref{fig:simulations}. We note that in the three cases, all the agents first converge to the MAX value of $x_{9} = 936$ in a bit more than 100 time steps, before agent 9 leaves the network. After the departure of agent $9$ at $t=200$, we see that the algorithm of Section \ref{sec: counters} that uses messages from departing agents reconverges to the new maximal value $x_{13} = 815$ in 137 time steps. The performance of the algorithm of Section \ref{sec: timeout} without messages from leaving agents are significantly worse. For a threshold $\mathcal{T}^*=40$, we see that it takes 506 time steps to reconverge to the new maximal value, but the system later suffers from several spurious resets. These are caused by agents reaching the threshold by chance. The probability of this occurring can be significantly reduced by taking a higher threshold, but this results in an even longer time to react to the departure of $9$, as seen in Fig. \ref{fig:simulations}(c) with $\mathcal{T}=200$. 2439 time-steps are indeed needed to re-obtain the correct value, mostly because it takes very long before the agents abandon their former estimate. This clearly illustrates the trade-off on the threshold value $\mathcal{T}^*$: a too small value will result in spurious resets as soon as some agents \quotes{have not heard} about the agent with the highest value for too long. But a too large threshold will result in a significant delay before agents decide that an agent has probably left the system.
We also performed comparisons between the two approaches on the convergence time to reach consensus after the agent with MAX has left the group for other numbers of nodes. The results are summarized in Table \ref{tble: comparison-number-nodes}. We take $\mathcal{T}^* = 1.1 \mathcal{N}(0)$ with the algorithm of Section \ref{sec: timeout}. We observe that when the number of agents increases, the algorithm of Section \ref{sec: counters} requires proportionally much fewer iterations to reach consensus, as expected and already observed in Fig. \ref{fig:simulations}. Moreover, it also achieves a stronger version of the property of eventual correctness than the algorithm of Section \ref{sec: timeout}, as it avoids spurious resets, as discussed above. It does however require the possibility of sending messages when leaving.
\begin{table}[H]
\centering
\begin{tabular}{c|cc}
\toprule
\multirow{2}{*}{Number of nodes} & \multicolumn{2}{c}{Iterations to reach MAX-consensus} \\
\cmidrule(r){2-3}
& Algorithm \ref{Intialization algorithm}-\ref{Modified random gossip} & Algorithm \ref{Intialization algorithm}, \ref{Joining algorithm_timeout}-\ref{Modified_random_gossip_timeout_sep_from_update} \\
\midrule
10 & 21 & 64 \\
20 & 129 & 162 \\
30 & 194 & 599 \\
50 & 246 & 1885\\
100 & 628 & 6580\\
\bottomrule
\end{tabular}
\vspace{0.3cm}\caption{Comparison between the two techniques with different number of nodes.}
\label{tble: comparison-number-nodes}
\end{table}
\section{Discussion and Conclusion}\label{sec: conclusion}
We have investigated the distributed MAX-consensus problem for \textit{open} multi-agent systems. Two algorithms have been proposed depending on whether the agents who leave the network can inform another existing agent about their departure or cannot. The eventual correctness has been proven for both.
Taking a step back, we see two main challenges in the design of algorithms for open multi-agent systems, as also briefly noted in \cite{Hendrickx-AAC16-Open}:
\emph{Robustness and dynamic information treatment:} The algorithms should be robust to departures and arrivals, in the sense that they should \MA{keep updating their estimates to discard outdated information.} Moreover, novel information held by arriving agents should be taken into account, and outdated information, for example, related to agents no longer in the system, should eventually be discarded.
\emph{Performance in open context:} The performance of classical multi-agents algorithms is often measured by the rate at which they converge to an exact solution or a desired situation (or the time to reach such a situation). This approach is no longer relevant in a context where agents' departures and arrivals keep \quotes{perturbing} the system, and possibly the algorithm goal (as is the case here). Rather, efficient algorithms would be those for which the estimated answer remains \quotes{close} to some \quotes{instantaneous exact solution}, according to a suitable metric.
The algorithms we have developed here do answer the first issue of robustness and information treatment for the problem of distributed maximum computation.
The characterization and optimization of their performance in an open context, however, remains unanswered at present and could be the topic of further works. We note that the behavior of a gossip averaging algorithm in an open multi-agent system was characterized in \cite{Hendrickx-AAC16-Open}, but this algorithm was not designed to compute a specific value, as is the case here.
In particular, we observe that both algorithms would suffer from occasional apparently unnecessary resets. This may happen after the departure of an agent that did not have the largest value in the algorithm of Section \ref{sec: counters}, or when an agent has been isolated for too long from that with the highest value in the algorithm of Section \ref{sec: timeout}. We do not know at this stage if these spurious resets can be entirely avoided, especially when leaving agents cannot send a final message. In this case, it is indeed impossible to know for sure whether the agent with the highest value has left or has just not communicated for a while. There are, however, several possibilities to mitigate the damage of these spurious resets and to play on the trade-off between the effect of these perturbation and the speed at which the system reacts. A simple solution could be for example to apply an additional filtering layer when the algorithm requires an important decrease of $y_i$. In this case, a new estimate $\tilde y_i$ would follow $y_i$ except that sharp decrease would be replaced by gradual ones.
We also observe that our second algorithm will either only work when the system size is not too large with respect to $\mathcal{T}^*$ (case of a fixed threshold) or eventually work for all size but gradually become slower and slower to react (case of a growing $\mathcal{T}^*$). Whether this can be avoided in a context when leaving agents do not warn others about their departure also remains an open interesting question.
\bibliographystyle{IEEEtran}
| {
"redpajama_set_name": "RedPajamaArXiv"
} | 3,286 |
\section{Introduction}
More than two decades ago, Nambu [1] proposed a generalization
to classical Hamiltonian mechanics.
In his formalism, he replaced the usual pair of canonical variables found
in Hamiltonian mechanics with a triplet of coordinates in
an odd dimensional phase space.
Furthermore, he formulated his dynamics via a
ternary operation, the Nambu bracket, as opposed to the
usual binary Poisson bracket.
Yet, the fundamental principles of a canonical form
of Nambu's generalized mechanics, similar to the invariant geometrical
form of Hamiltonian mechanics, has only recently been given [2].
The re-emergence of this little known theory is possibly due to its
relevence to the recent mathematical structures having their
basis in Hamiltonian mechanics such as the Poisson-Lie group,
quantum groups, and the Yang-Baxter equation. Since the basic idea
of Nambu mechanics is to extend the usual binary operation on phase space
to multiple operations of higher order, this theory may also give
some insights into the theory of higher order algebraic structures
and their possible physical significance.
The fact that the development of Nambu mechanics is still at the
preliminary stages can be seen by the relatively few known examples
of dynamical systems which admit a Nambu-type formulation.
Nambu himself came up with only one example; the Euler equations
for the angular momentum of a rigid body in three dimensions [1].
Another (somewhat exotic) example is that of Nahm's system of equations
in the theory of static SU(2)-monopoles [3], [4]. A third example
was found in [2].
Here, we
present four new examples of systems taking on the Nambu form. These
systems share the common property of possessing dynamical or hidden
symmetries resulting in extra integrals of motion beyond those
needed for complete integrability. It is felt that these new examples
may help in further understanding the elements of Nambu's theory
such as its algebraic structure and its (possible)
quantization. We begin by stating the basic facts of Nambu
mechanics leaving all details to the recent comprehensive study
by Takhtajan [2].
\vspace{1.0cm}
\section {Nambu Mechanics}
For comparisons sake, let us first review certain fundamental definitions
and results of Hamiltonian mechanics (see [5]). Let $M$ denote
a smooth manifold of finite dimension and $C^{\infty }(M)$ the
algebra of smooth real-valued functions on $M$. A {\em Poisson
Bracket} on $M$ is a ${\rm I\kern-.20em R}$-bilinear map
\begin{equation}
\{ ~, ~ \} ~:~ C^{\infty }(M) \times C^{\infty }(M) \rightarrow
C^{\infty }(M),
\end{equation}
such that $\forall ~f_1, f_2,$ and $f_3 \in C^{\infty }(M)$,
\begin{equation}
\{ f_1 , f_2 \} = -\{ f_2 , f_1 \} ~~~~(skew-symmetry),
\end{equation}
\begin{equation}
\{ f_1 f_2 , f_3 \} = f_1 \{ f_2 , f_3 \} + \{ f_1 , f_3 \} f_2
~~~~(Leibniz ~rule),
\end{equation}
\begin{equation}
\{ f_1 , \{ f_2 , f_3 \} \} + \{ f_2 , \{ f_3 , f_1 \} \}
+ \{ f_3 , \{ f_1 , f_2 \} \} = 0 ~~~~(Jacobi ~identity).
\end{equation}
By property (3), it is clear that $\forall ~h \in C^{\infty }(M)$,
the map $ f \rightarrow \{ f , h \} $ is a derivation of $C^{\infty }(M)$.
Thus, one may define a vector field $X_h $ such that $X_h (f) = \{ f , h \}$,
$\forall ~f \in C^{\infty }(M)$. In Hamilton's formulation of
dynamics, one defines a very special vector field $X_H $ on the phase
space $M$ via a Hamiltonian function $H \in C^{\infty }(M)$ such that
\begin{equation}
X_H (f) = \{ f , H \} = \frac{df}{dt} , ~~\forall ~f \in C^{\infty }(M).
\end{equation}
This, of course, produces Hamiltons' equations of motion.
The Poisson bracket given above is explicitly defined
by a $C^{\infty }$ tensor field
$\omega \in \wedge ^2 TM$, an element of the square of the tangent
bundle $TM$ of the phase space $M$, such that
\begin{equation}
\{ f , g \} = \omega (df,dg) = \omega ^{ij} \frac {\partial{f}}
{\partial{x^i}} \frac {\partial{g}}{\partial{x^j}},
\end{equation}
where $(x^i)$ are some local coordinates on $M$ and we use the Einstein
summation convention. For the purposes of regular
Hamiltonian dynamics, $\omega ^{ij}$ is a constant antisymmetric
two-tensor. Outside of Hamiltonian mechanics, there exists
linear Poisson structures such that if $(x_1 , x_2 , ... , x_n )$
is a basis for a Lie algebra, the Poisson bracket is given by
\begin{equation}
\{ f , g \} = [x_i , x_j ]_{Lie} ~ \frac {\partial{f}}{\partial{x^i}}
\frac {\partial{g}}{\partial{x^j}},
\end{equation}
$[~,~]_{Lie} $ denoting the Lie algebra bracket. A more modern example
is that of a {\em Poisson-Lie group} where the phase space $M$ is some
Lie group $G$ such that the group multiplication of $G$ is compatible,
in some sense, with the Poisson-structure on $G$ (for a precise definition,
see [6]). A complete description of such structures (Poisson-Lie Manifolds)
may be found in the monograph [7].
Finally, the dynamical picture resulting from a solution to (5)
produces a phase space (time) flow
\begin{equation}
x \longmapsto T_t (x), ~~x \in M
\end{equation}
and an evolution operator
\begin{eqnarray}
U_t : C^{\infty }(M) & \rightarrow & C^{\infty }(M), \nonumber \\
U_t (f)(x) & = & f(T_t (x)),
\end{eqnarray}
where $x \in M,~f \in C^{\infty }(M)$.
For consistency, $U_t$ must preserve the two algebraic operations defined
on $C^{\infty }(M)$, the usual multiplication of functions and the
Poisson bracket. This requirement of $U_t$ to be an algebra isomorphism
($U_t (f_1 f_2 ) = U_t (f_1) U_t (f_2)$ and $U_t (\{ f_1 , f_2 \} ) =
\{ U_t (f_1 ) , U_t (f_2 ) \} $) is equivalent to the properties
(3) and (4) of the Poisson bracket. A similar requirement will lead
to a certain fundamental identity in Nambu mechanics.
Nambu's generalization of mechanics is based upon a higher order
($n~>~2$) algebraic structure defined on a (possibly odd
dimensional) phase space $M$. A {\em Nambu
Bracket} of order $n$ on a manifold $M$ is an ${\rm I\kern-.20em R}$
-multilinear map
\begin{equation}
\{ ~,~\ldots ~,~ \}~:~[C^{\infty }(M)]^{\otimes n} \rightarrow C^{\infty }(M)
\end{equation}
such that $\forall f_1 , f_2 , \ldots , f_{2n-1} \in C^{\infty }(M)$,
\begin{equation}
\{ f_1, \ldots ,f_n \}=(-1)^{P(\sigma)}\{ f_{\sigma(1)}, \ldots ,
f_{\sigma(n)} \},
\end{equation}
\begin{equation}
\{ f_1 f_2, f_3, \ldots ,f_{n+1} \}=
f_1 \{f_2, f_3, \ldots , f_{n+1} \} +
\{ f_1, f_3, \ldots, f_{n+1} \} f_2,
\end{equation}
and
\begin{eqnarray}
\{ \{ f_1, \ldots , f_{n-1}, f_n \}, f_{n+1}, \ldots, f_{2n-1} \} +
\{ f_n, \{ f_1, \ldots, f_{n-1}, f_{n+1} \}, f_{n+2}, \ldots , f_{2n-1} \} \\
+ \ldots + \{ f_n, \ldots ,f_{2n-2}, \{ f_1, \ldots , f_{n-1}, f_{2n-1} \}\}
= \{ f_1, \ldots , f_{n-1}, \{ f_n, \ldots , f_{2n-1} \}\}, \nonumber
\end{eqnarray}
where $\sigma \in S_n$ (the permutation group) and $P$ is the parity
of the permutation $\sigma $.
Conditions (11) and (12) are the familiar skew-symmetric and derivation
properties found for the Poisson Bracket. On the other hand,
(13) is a generalized Jacobi identity
called the Fundamental Identity (FI). The FI was first introduced by
Takhtajan [2] and by M. Flato and C. Fronsdal. It was also independently
found by Sahoo and Valsakumar [8], [9].
Now, analagous to (5), Nambu dynamics is determined by a special
Nambu-Hamiltonian vector field $X_{NH}$ given by
\begin{equation}
X_{NH}(f) = \{ f ,~ H_1 ,~ \ldots ~,~H_{n-1} \} = \frac {df}{dt},
\end{equation}
$\forall ~f \in C^{\infty }(M)$ where $H_1 ,~ \ldots ,~H_{n-1}$ are the
generalized Hamiltonians of the system. A solution to the above equations
of motion produces an evolution operator $U_t$ as described
earlier by (8) and (9). As is the case in Hamiltonian mechanics, Nambu
dynamics is consistent if and only if $U_t$ is an isomorphism of the
above defined algebraic structure on $C^{\infty }(M)$. It can be shown
that the corresponding isomorphism requirement of
\begin{equation}
U_t ( \{ f_1 ~,~\ldots ~,f_n \}) = \{ U_t (f_1 ),~\ldots ,~
U_t ( f_n ) \}
\end{equation}
is equivalent to the FI (13) for the Nambu bracket. Furthermore,
the FI provides a very important dynamical result. First of all,
a function $I \in C^{\infty }(M)$ is an {\em integral of motion}
if $\{ I,~H_1 ,~ \ldots ,~H_{n-1} \}=0$. Then, using the FI, one can
prove that the Nambu bracket of $n$ integrals of motion is also
an integral of motion (analogous to {\em Poisson's Theorem} in
Hamiltonian mechanics). Consequently, one can define the concept of
integrability in Nambu mechanics.
The Nambu bracket is explicitly generated by a {\em Nambu tensor field}
$\eta \in \wedge ^{n} TM$ such that
\begin{equation}
\{ f_1, \ldots , f_n \} = \eta(df_1, \ldots, df_n) =
\eta_{i_1...i_n}(x) \frac{\partial}{\partial x_{i_1}} \wedge \ldots
\wedge \frac{\partial}{\partial x_{i_n}},
\end{equation}
where $(x_1 , x_2 , \ldots )$ are some local coordinates on $M$
and repeated indices are summed. The FI imposes
serious constraints on the Nambu tensor field $\eta $. Yet, for our
purposes, we only need to define the simplest type of Nambu bracket.
Let $M={\rm I\kern-.20em R}^{n}$ be our phase space with coordinates
$x_1,\ldots ,x_n$. Then the so-called `canonical' Nambu bracket is
\begin{equation}
\{ f_1, \ldots , f_n \} = C~\frac {\partial (f_1, \ldots , f_n )}
{\partial (x_1,\ldots ,x_n )}
\end{equation}
where the right hand side is the Jacobian of the mapping
$(f_1, \ldots , f_n )~:~{\rm I\kern-.20em R}^{n} \rightarrow
{\rm I\kern-.20em R}^{n}$ and $C$ is a constant factor. This
bracket will be used throughout the rest of the paper.
\section {The SU(n)-Isotropic Harmonic Oscillator}
It is well known that the Hamiltonian for the n-dimensional simple
harmonic oscillator where all the frequencies have been set to one,
\begin{equation}
H= \sum_{i=1}^{n}(p_{i}^2 + q_{i}^2)
\end{equation}
is invariant under the symmetry group SU(n) and has the
following integrals of motion,
\begin{equation}
L_{ij} = q_i p_j - q_j p_i ,
\end{equation}
and
\begin{equation}
A_{ij} = p_i p_j + q_i q_j ,
\end{equation}
where $i,j=1, \ldots ,n$.
Obviously, the $L_{ij}$'s are the angular momenta of the system
whereas the diagonal components of $A_{ij}$ are the individual
energies associated with the separate one-dimensional oscillations.
It is the off-diagonal components of $A_{ij}$ which provide the
hidden integrals of motion thus forcing all the trajectories
in phase space to lie on curves. That is, the $L_{ij}$'s
and the $A_{ij}$'s provide $(2n-1)$ independent integrals
of motion within the $2n$ dimensional phase space, and therfore all orbits
lie on one-dimensional manifolds. By Bertrand's theorem (see [10]),
these orbits are closed implying that the extra dynamical
integrals of motion are simple functions of the phase space coordinates.
Beginning with the two-dimensional case, if one defines the following
functions
\begin{eqnarray}
S_1 &=& (A_{12}+A_{21})/2, \nonumber \\
S_2 &=& (A_{22}-A_{11})/2, \\
S_3 &=& \frac{L_{12}}{2}, \nonumber
\end{eqnarray}
it is easy to verify that
\begin{equation}
\{ S_i , S_j \} = \epsilon _{ijk} S_k
\end{equation}
which are simply the commutation relations for the Lie algebra
su(2). Furthermore, the Casimir function is related to the Hamiltonian
since
\begin{equation}
S_{1}^2 + S_{2}^2 + S_{3}^2 = S^2 = \frac {H^2}{4}.
\end{equation}
The integrals of motion for this system are,
\begin{eqnarray}
I_1 &=& p_{1}^2 + q_{1}^2 = C_1 , \nonumber \\
I_2 &=& p_{2}^2 + q_{2}^2 = C_2 , \\
I_3 &=& q_1 p_2 - q_2 p_1 = C_3 , \nonumber \\
I_4 &=& p_1 p_2 + q_1 q_2 = C_4 , \nonumber
\end{eqnarray}
where the $C_i$'s are the constant values taken by the $I_i$'s.
Using these $I_i$'s as the generalized Hamiltonians, we can describe the
corresponding Nambu dynamics as follows. Consider the following Nambu
bracket,
\begin{equation}
\{ f , I_1 , I_2 , I_3 \} = \left( \frac {-1}{2C_4} \right)
\frac {\partial (f , I_1 , I_2 , I_3 )}
{\partial (p_1 , p_2 , q_1 , q_2)},
\end{equation}
where, as before, the right hand side symbolizes the Jacobian
operation and $f$ is some function of the phase space coordinates.
Straightforward calculations will show that
this bracket in fact produces all the correct equations
of motion, i.e. ${dp_1 }/{dt} = \{ p_1 , I_1 , I_2 , I_3 \} = -2q_1$, etc.
Note that since only three generalized Hamiltonians were needed,
$I_4$ was not used at all. Another definition, using $I_4$, and
giving the correct equations of motion is
\begin{equation}
\{ f , I_1 , I_2 , I_4 \} = \left( \frac {1}{2C_3} \right)
\frac {\partial (f , I_1 , I_2 , I_4 )}
{\partial (p_1 , p_2 , q_1 , q_2)}.
\end{equation}
Even products of $I_i$'s can be used as generalized Hamiltonians.
For instance, the bracket
\begin{equation}
\{ f , I_1 , I_2 , I_3 I_4 \} =
\frac {1}{2(C_{3}^{~2} - C_{4}^{~2})}
\frac {\partial (f , I_1 , I_2 , I_3 I_4 )}
{\partial (p_1 , p_2 , q_1 , q_2)}
\end{equation}
also works. By the derivation property (12) for Nambu brackets, it can be
checked that the alternate definitions (25)-(27) are consistant with
each other. For example, let $f=p_1 $ in (27) and add to the brackets
in (25), (26), and (27) the extra subscripts $I_3$, $I_4$, and $I_{34}$
respectively to distinguish them. Then
$$ \{ p_1 , I_1 , I_2 , I_3 I_4 \} _{I_{34}} = I_3 \{ p_1 , I_1 ,
I_2 , I_4 \} _{I_{34}} + \{ p_1 , I_1 , I_2 , I_3 \} _{I_{34}} I_4 $$
$$ = \frac{I_3 }{ 2(C_{3}^{~2} - C_{4}^{~2}) }
\frac{ \partial (p_1 , I_1 , I_2 , I_4 ) }
{ \partial (p_1 , p_2 , q_1 , q_2) } +
\frac{I_4 }{ 2(C_{3}^{~2}- C_{4}^{~2}) }
\frac{ \partial (p_1 , I_1 , I_2 , I_3 ) }
{ \partial (p_1 , p_2 , q_1 , q_2) } $$
$$ = \frac{2C_{3}^{~2} }{ 2(C_{3}^{~2} - C_{4}^{~2}) }
\{ p_1 , I_1 , I_2 , I_4 \} _{I_4 }
- \frac{2C_{4}^{~2} }{ 2(C_{3}^{~2} - C_{4}^{~2}) }
\{ p_1 , I_1 , I_2 , I_3 \} _{I_3 } $$
$$ = \frac{2C_{3}^{~2} }{ 2(C_{3}^{~2} - C_{4}^{~2}) } (-2q_1)
- \frac{2C_{4}^{~2} }{2(C_{3}^{~2} - C_{4}^{~2})} (-2q_1)
= ~-2q_1 $$
as needed. It is a staightforward exercise to verify that the above
calculation also holds for the remaining phase space variables.
By the above arguments and the fact that
$$ \frac{ \partial (I_1 , I_2 , I_3 , I_4 ) }
{ \partial (p_1 , p_2 , q_1 , q_2) } = 0, $$
it is clear that one may choose any three of the four integrals
of motion (24) as the generalized Hamiltonians. One must simply
find the correct factors in front of the common Jacobian
term. Once these basic brackets have been established,
linear combinations such as $\{ f , I_1 , I_2 + I_3 , I_4 \} $ and
those of the type similar to that of (27) can easily be found
using the linearity and derivation properties of the Nambu
bracket. This extra flexibility not found in Hamiltonian mechanics
is obviously due to the multiple Hamiltonian structure of Nambu mechanics.
Finally, it is relatively straightforward to extend the above
arguments to higher dimensional systems. One simply uses the
integrals of motion given by (19) and (20) as the generalized
Hamiltonians and finds the correct constants related to these
integrals to multiply the Jacobian term in the definition
of the Nambu bracket.
Thus, the SU(n)-isotropic harmonic oscillator
is realizable as an $n^{th}$ order Nambu mechanical system.
\section {The SO(4)-Kepler Problem}
The well known Kepler Hamiltonian is
\begin{equation}
H= \frac{\vec{p}^{~2}}{2} - \frac{1}{r},
\end{equation}
where $r=\sqrt{(x^2 + y^2 + z^2 )}$. Because $H$ possesses rotational
symmetry, the orbital angular momentum $\vec{L} = \vec{r} \times \vec{p}$
is an integral of motion. This rotational symmetry implies that the orbit
lies in some two dimensional plane, though it is not enough to ensure that
the orbit is closed. An extra dynamical symmetry must exist for a closed
orbit since the integrals of motion $H$ and $\vec{L}$ only reduce
the phase space to a two dimensional (as opposed to a one dimensional)
manifold. Such an integral was first discovered by Laplace
(but is called the Runge-Lenz vector in classical mechanics
or the Lenz-Pauli vector in quantum mechanics) and is given by
\begin{equation}
\vec{A}=\vec{p} \times \vec{L} - \frac{\vec{r}}{r}.
\end{equation}
One can easily check that
$$ \{ A_i , L_j \} = \epsilon _{ijk} A_k $$
and
$$ \{ A_i , A_j \} = -\epsilon _{ijk} \left( \vec{p}^{~2} - \frac{2}{r}
\right) L_k = -2HL_k = -2EL_k , $$
where $E$ is the constant value taken by $H$. For bound state
problems ($E < 0$), one can define a new conserved vector $\vec{D}$
as
$$ \vec{D} = \frac{\vec{A}}{\sqrt{-2E}}. $$
Then one finds that the commutation relations reduce to
\begin{eqnarray*}
\{ L_i , L_j \} &=& \epsilon _{ijk} L_k, \\
\{ D_i , L_j \} &=& \epsilon _{ijk} D_k, \\
\{ D_i , D_j \} &=& \epsilon _{ijk} L_k,
\end{eqnarray*}
which is the Lie algebra so(4).
(Note that for scattering problems where $E > 0 $,
one instead finds the Lie algebra so(3,1)).
Explicitly, we have
\begin{equation}
H=\frac{p_1 ^2 + p_2 ^2 + p_3 ^2}{2} - \frac{1}{(q_1 ^2 +
q_2 ^2 + q_3 ^2)^{1/2}},
\end{equation}
and,
\begin{eqnarray}
I_1 &=& p_2 ( q_1 p_2 - q_2 p_1 ) - p_3 ( q_3 p_1 - q_1 p_3 ) -
\frac{q_1 }{(q_1 ^2 + q_2 ^2 + q_3 ^2)^{1/2}} = C_1,
\nonumber \\
I_2 &=& p_3 ( q_2 p_3 - q_3 p_2 ) - p_1 ( q_1 p_2 - q_2 p_1 ) -
\frac{q_2 }{(q_1 ^2 + q_2 ^2 + q_3 ^2)^{1/2}} = C_2,
\nonumber \\
I_3 &=& p_1 ( q_3 p_1 - q_1 p_3 ) - p_2 ( q_2 p_3 - q_3 p_2 ) -
\frac{q_3 }{(q_1 ^2 + q_2 ^2 + q_3 ^2)^{1/2}} = C_3,
\nonumber \\
I_4 &=& ( q_2 p_3 - q_3 p_2 ) = C_4, \\
I_5 &=& ( q_3 p_1 - q_1 p_3 ) = C_5, \nonumber \\
I_6 &=& ( q_1 p_2 - q_2 p_1 ) = C_6, \nonumber
\end{eqnarray}
with the relations
\begin{eqnarray}
I_1 ^{~2} + I_2 ^{~2} + I_3 ^{~2} &=& 1 + 2 H ( I_4 ^{~2}
+ I_5 ^{~2} + I_6 ^{~2} ), \nonumber \\
I_1 I_4 + I_2 I_5 + I_3 I_6 &=& 0,
\end{eqnarray}
where, as before, the $ C_i $'s are the constant values taken
by the $ I_i $'s.
Therefore, there exists only five independent constants of motion
as expected. As was the case for the harmonic oscillator, one
may choose any five of the above six
$ I_i $'s (or products thereof)
as the generalized Hamiltonians.
For example, one may define the
Nambu bracket for this system as
$$
\{ f , I_2 , I_3 , I_4 , I_5 , I_6 \} = \left( \frac {1}{C_4
(C_4 ^2 + C_5 ^2 + C_6 ^2 )} \right)
\frac {\partial (f , I_2 , I_3 , I_4 , I_5 , I_6 )}
{\partial (p_1 , p_2 , p_3 , q_1 , q_2 , q_3 )},
$$
or,
\begin{equation}
\{ f , I_1 , I_3 , I_4 , I_5 , I_6 \} = \left( \frac {-1}{C_5
(C_4 ^2 + C_5 ^2 + C_6 ^2 )} \right)
\frac {\partial (f , I_1 , I_3 , I_4 , I_5 , I_6 )}
{\partial (p_1 , p_2 , p_3 , q_1 , q_2 , q_3 )},
\end{equation}
or,
$$
\{ f , I_1 , I_2 , I_3 , I_4 , I_5 \} = \left( \frac {-1}{C_3
(C_4 ^2 + C_5 ^2 + C_6 ^2 )} \right)
\frac {\partial (f , I_1 , I_2 , I_3 , I_4 , I_5 )}
{\partial (p_1 , p_2 , p_3 , q_1 , q_2 , q_3 )},
$$
etc. An interesting fact to note here is that we were unable
to (directly) incorporate the original Hamiltonian $H$ into
a form of the Nambu bracket.
\section{Two More Examples}
First of all, let us analyse a Hamiltonian related to the motion
of two vortices in an ideal incompressible fluid. A physical
description of this system may be found in the monograph [10].
The Hamiltonian and the corresponding integrals of motion are
\begin{equation}
H=\ln {[(q_1 - q_2 )^2 + (p_1 - p_2 )^2 ]} = E,
\end{equation}
and,
\begin{eqnarray}
I_1 &=& q_1 + q_2 = C_1 , \nonumber \\
I_2 &=& p_1 + p_2 = C_2 ,\\
I_3 &=& p_1 ^2 + p_2 ^2 + q_1 ^2 + q_2 ^2 = C_3 . \nonumber
\end{eqnarray}
Since we have three independent integrals of motion
and a four dimensional phase space, (35) incorporates a dynamical
symmetry reducing the flow in phase space to a (not necessarily closed)
curve. This system, like the previous examples, has several
different Nambu brackets all producing the correct equations of motion.
Below, we simply list the basic choices.
\begin{equation}
\{ f , I_1 , I_2 , I_3 \} = \left( \frac {-1}{\exp{(E)} } \right)
\frac {\partial (f , I_1 , I_2 , I_3 )}
{\partial (p_1 , p_2 , q_1 , q_2)}
\end{equation}
\begin{equation}
\{ f , H , I_1 , I_2 \} = \left( \frac {-1}{2} \right)
\frac {\partial (f , H , I_1 , I_2 )}
{\partial (p_1 , p_2 , q_1 , q_2)}
\end{equation}
\begin{equation}
\{ f , H , I_1 , I_3 \} = \left( \frac {-1}{2C_2 } \right)
\frac {\partial (f , H , I_1 , I_3 )}
{\partial (p_1 , p_2 , q_1 , q_2)}
\end{equation}
\begin{equation}
\{ f , H , I_2 , I_3 \} = \left( \frac {1}{2C_1 } \right)
\frac {\partial (f , H , I_2 , I_3 )}
{\partial (p_1 , p_2 , q_1 , q_2)}
\end{equation}
Note that the constant factor in the above examples is usually
related to the integral of motion {\em not} chosen to be one
of the Hamiltonians (as was the case in the oscillator example
of Section 3). One can use the derivation property of the Nambu
bracket to find other brackets from the four listed above. For instance,
one can show that (37) and (38) are consistant with
\begin{equation}
\{ f , H , I_1 , I_2 I_3 \} = \left (\frac {-1}{2(C_3 + C_2 ^{~2})} \right)
\frac {\partial (f , H , I_1 , I_2 I_3 )}
{\partial (p_1 , p_2 , q_1 , q_2)},
\end{equation}
and so on.
Finally, consider the (unphysical) Hamiltonian
\begin{equation}
H = q_1 (p_1 - q_1 ) - q_2 ( p_2 - q_2 ),
\end{equation}
and its integrals of motion
\begin{eqnarray}
I_1 &=& q_1 (p_1 - q_1 ) = C_1 , \nonumber \\
I_2 &=& q_2 (p_2 - q_2 ) = C_2 , \\
I_3 &=& q_1 q_2 = C_3 . \nonumber
\end{eqnarray}
Since $ H=I_1 -I_2 $, there exists only the following basic Nambu bracket,
\begin{equation}
\{ f , I_1 , I_2 ,I_3 \} = \left( \frac {1}{C_3 } \right)
\frac {\partial (f , I_1 , I_2 , I_3 )}
{\partial (p_1 , p_2 , q_1 , q_2)}.
\end{equation}
This two dimensional system can be extended to higher dimensions
by simply adding the appropriate terms to the Hamiltonian (41)
(such as $q_3 (p_3 - q_3 )$) and finding the extra integrals
of motion (i.e. $q_1 q_3 $ or $q_2 q_3 $).
\section {Conclusion}
We have demonstrated that several Hamiltonian systems possessing
dynamical symmetries can be realized in the Nambu formalism
of generalized mechanics. For all but one of these systems, an
extra freedom was found in the choice of the generalized
Hamiltonians needed for their Nambu construction. Finally, one
may speculate that since the harmonic oscillator is a very
important example in quantum mechanics, its Nambu formulation
may lead to a better understanding of the yet unsolved problem
of the quantization of Nambu mechanics.
\vspace{1cm}
{\bf Acknowledgements} \\
The author is grateful to L.A.Takhtajan for suggesting this
problem and for many helpful discussions. Thanks also go to
M.Flato for suggesting improvements in Section 4 of this
paper.\\
\section{References}
1. Nambu, Y., {\em Phys.~Rev.~D. } {\bf 7}, 2405 (1973).\\
2. Takhtajan, L.A., {\em Comm.~Math.~Phys. } {\bf 160}, 295 (1994). \\
3. Chakravarty, S., and Clarkson, P., {\em Phys.~Rev.~Lett. }
{\bf 65}, 1085 (1990). \\
4. Takhtajan, L.A., preprint PAM no.{\bf 121}, University
of Colorado (1991). \\
5. Arnold, V.I., {\em Mathematical Methods Of Classical Mechanics},
Springer-Verlag, Berlin, (1978). \\
6. Takhtajan, L.A., in Mo-Lin Ge and Bao-Heng Hao (eds), {\em
Introduction To Quantum Groups and Integrable Massive Models
of Quantum Field Theory }, World Scientific, Singapore, (1990). \\
7. Vaisman, I., {\em Lectures on the Geometry of Poisson
Manifolds}, Birkhauser, Berlin, (1994). \\
8. Sahoo, D., and Valsakumar, M.C., {\em Mod.~Phys.~Lett.~A.} {\bf 9},
2727, (1994). \\
9. Sahoo, D., and Valsakumar, M.C., {\em Phys.~Rev.~A. } {\bf 46},
4410 (1992). \\
10. Arnold, V.I., {\em Dynamical Systems 3 }, Springer-Verlag,
Berlin, (1988).
\end{document}
| {
"redpajama_set_name": "RedPajamaArXiv"
} | 9,006 |
Eaglecrest's 2018-19 winter season is coming to an end. After two weeks of sustained warm temperatures, the snowpack is thinning rapidly and we're forced to adjust the operating schedule.
Sunday, March 31st will be the last day of chairlifts on the main mountain. The Porcupine Learning Area will be open to the public and for scheduled school groups Thursday, April 4 and Friday, April 5.
This season has been a real treat! We've enjoyed powder days, storm days, bluebird skies, and some truly awesome spring conditions.
Join us in celebrating this wonderful season's end at Slush Fest 2019. We'll have live music, BBQ, and a beer garden at the base of Ptarmigan Chairlift (beer garden pending permit approval). The lift will run for an extra hour until 5:00 PM.
In total, Eaglecrest's 2018-19 season will amount to 85 operating days, including 78 with Ptarmigan, Black Bear, and/or Hooter Chairlifts.
As always, our goal is to provide consistent and dependable winter operations to the people of Juneau & Southeast Alaska. We are excited to learn, improve, and grow in the years to come!
Thank you for a great season! See you on the slopes! | {
"redpajama_set_name": "RedPajamaC4"
} | 2,922 |
{"url":"https:\/\/www.lukethorburn.com\/blog\/probability\/","text":"Index\n\nJan 10, 2018\nWhat is a probability?\nEssay\nEpistemic Status Mostly confident, but please don't place much stock in my summary of quantum mechanics.\n\nI have a friend who maintains that probabilities are a Stoppardian conspiracy of mathematicians. The chance that any given event will occur, she says, is fifty-fifty. Lottery victories? Asteroid impacts? Spontaneous combustion? All (apparently) decided on a metaphorical coin toss.\n\nThis line of reasoning doesn\u2019t mesh with any of the common conceptions of probability, but that doesn\u2019t immediately render it flawed, and I can sympathise with the joke\u2019s premise. There is something deeply unintuitive and forced about thinking probabilistically: trying to quantify the instantaneous implosion of numerous possibilities into singular fact. When learning the maths behind statistics or random processes, we are more-or-less cornered into accepting a pragmatic definition. So long as the methods are useful in making predictions or understanding data, it\u2019s best not to worry too much about whether they correspond to how uncertainty works in the real world.\n\nMathematics may be defined as the subject in which we never know what we are talking about, nor whether what we are saying is true. \u2014 Bertrand Russell\n\nDoes it really matter how uncertainty works in the real world? Not really. A remarkable feature of the maths of probability is that it is apathetic to your definition thereof: it is useful despite us not really knowing what we are talking about. But the mechanics of uncertainty do matter if we care about sating metaphysical curiosity which I, for one, do.\n\nSet aside for a moment the vast philosophical literature on conceptions of probability, and even the notion of numerical probabilities altogether. Probabilities are stand-ins for the more nebulous concept of uncertainty which, as I see it, can have two components.\n\nThe first component is uncertainty arising in human minds due to a lack of knowledge about the state of the reality. This locates uncertainty \u2018in our heads\u2019 or\u2014more precisely\u2014in the discrepancy between reality and our brains\u2019 mental model thereof.\n\nThe second component is fundamental, real indeterminism. It is debatable whether or not this component exists. If not, then reality is a clockwork, with the current positions and momenta of subatomic particles fully determining the future. If it does exist then there are random number generators built into the fabric of the universe, with the future to be determined by the randomness spat out along the way. A prima facie reading of modern quantum mechanics suggests that this is the case. Some uncertainty would thus originate \u2018in the real world\u2019, in the laws of nature.\n\nI am not the first to find this dichotomy natural. The two components are less-colloquially known as \u2018epistemic\u2019 uncertainty and \u2019ontic\u2019 uncertainty, respectively. Characteristics, proponents and detractors are summarised in the following table.\n\nThis two-way classification deals with a different aspect of the topic than the standard roll-call of probability interpretations2. The Classical, Logical, Subjective, Frequency, Propensity & Best-System conceptions all dance around the issue of where the uncertainty comes from, instead trying to articulate an interpretation of what numerical probabilities (eg. $$30\\%$$ chance of rain in Coburg on Thursday) mean in a manner that will work for all probabilistic statements. This is an unattainable goal because\u2014while superficially similar\u2014numerical probabilities are used in fundamentally different ways in different contexts. Casinos will do fine with a mostly classical interpretation, pundits use subjective probabilities, and statistians aim to find best-system models. All interpretations (particularly frequency and propensity) gloss over the underlying source of the uncertainty, which numerical probability can only ever quantify imperfectly.\n\nIn this essay I argue that epistemic uncertainty is unavoidable, contemplate the existence of ontic uncertainty, and discuss some limitations of numerical probability.\n\n#### Epistemic Uncertainty\n\nThat humans (both individually and collectively) can never have perfect knowledge of the world may seem patently true, but there is value in documenting the reasons why this is the case. The first is that there are regions of spacetime about which it is impossible to know anything, either due to the laws of physics or the limits of human observation and communication capabilities. Consider the following diagram.\n\nThis is a stylised map of everything and everywhere3. You are at the origin, with the past on the left, the future on the right and physical distance on the vertical axis. The slope of the diagonal boundaries is the speed of information transition throughout the universe. (Simplistically drawn here as if it were constant, but of course reality is more complex.) This speed can be no larger than the speed of light, and in reality is much slower due to difficulties in the logistics of communication and data-collection.\n\nThe future cannot be known with certainty, but the consequence of the upper limit is that some of the past (the parts that fall in regions Y and Z) also cannot be known with certainty; the information originating there has not yet had time to reach us. This is most blatant in the domain of astrophysics, where the time taken for light to travel between points of interest is non-negligble, but the concept is applicable to all information. Supernovae, political misappropriation, and hiking-sock leeches share the property that we find out about them after the fact. When we get to f it will become possible to know what happened in the chevron Y, but there will be a new set of historical unknowables.\n\nYou might argue that we can, in principle, extrapolate our current, local models of reality into unknown regions of spacetime. Even if we ignore Hume\u2019s problem of induction, we run up against computational intractability fairly quickly when trying to do this. Many of the domains we are interested in are chaotic systems, so small errors in our specification of the initial conditions would cause large flaws in our predictions. It is for this reason that we cannot predict weather more than a few weeks in advance, or human behaviour with any meaningful detail. One needs a universe to compute a universe.\n\nAnd even for events that are theoretically knowable, there are fundamental limits to our knowledge of them, because the data upon which we are basing our inference will be unavoidably incomplete. All measuring equipment, including biological sensory perception, has upper limits on the precision it is capable of. The human eye, for example, is known to be limited in its ability to distinguish in colour, position and simultaneity. Similarly, digital detectors can record only discrete approximations of continuous phenomena. The precision of devices can be increased through improved design, but there will always be some margin of error.\n\nAll these arguments point to a universal insufficiency of human knowledge. When you get down in the weeds, we can\u2019t be completely, epistemically certain of anything.\n\n#### Ontic Uncertainty\n\nAssume, temporarily, that quantum mechanics describes reality accurately, and that when not being measured particles are not particles but probability density functions describing their likely physical properties (position, momentum etcetera). The Heisenburg Uncertainty Principle states that the uncertainty in these physical properties cannot all be negligible at the same time. When the most likely superimposed positions of a particle converge, the spread of likely superimposed momenta diverges; there is a fundamental limit to how precisely position and momentum can be specified at the same time. When we measure a property of the particle, we get a single observation from the current probability distribution of that property.\n\nIs it possible for randomness in the position and momentum of particles to \u2018trickle up\u2019 into randomness in macroscopic, everyday phenomena that humans are interested in? I asked someone who\u2019d know, and\n\nThe short answer is no. Quantum effects such as superposition and indeterminacy wash away as the size of the system increases, from atoms to molecules to footballs; it also is compromised by the interactions of the system with the environment. \u2014 Marcelo Gleiser\n\nThis phenomena is known as decoherence. When you interact with a system, your perception of its macroscopic properties constrains the set of microscopic configurations that are possible. This amounts to an indirect observation of the particles involved, collapsing their probabilistic wavefunction. Somewhere between micro and macro there is a soft threshold where quantum indeterminacy goes from playing a role, to not.\n\nAre there any ways in which microscopic ontic uncertainty could survive or bypass decoherence and be magnified into macroscopic indeterminism? One possible magnifier might be human brains, which at least one scientist-of-repute4 has conjectured to rely on quantum effects. Others5 have countered that the timescale over which particles would decohere in the brain ($$10^{-13}\\sim 10^{-20}$$ seconds) is much shorter than the timescales at which known neuronal processes operate ($$10^{-3}\\sim 10^{-1}$$ seconds), and so is unlikely to impact upon them.\n\nEfforts to use quantum mechanics and its weirdness to explain consciousness or even lower brain functions must deal with the fact that the brain is a warm and wet environment, and thus a hard place to maintain any kind of quantum entanglement. \u2014 Marcelo Gleiser1\n\nAt present, neither view is conclusive. But there exists another possible means of magnification, because the fact that we know about quantum indeterminacy demonstrates that the phenomenon has in some way influenced the human-scale world. At some point, truly random numbers popped up on a physicist\u2019s screen, representing a measurement of a particle. In a chaotic system such as the human mind\u2014even if it is completely deterministic\u2014a small change in visual perception (a different number) might cause a significant change in behaviour down the track. In this way, randomness might be introduced into the course of history. That said, I find it hard to believe the universe stopped being deterministic when humans conducted the first double-slit experiment.\n\nOf course, to take a step back, quantum mechanics is just a model that describes our observations to date, and our ability to observe elementary particles is imperfect. If you squint at any system from far enough away, its behaviour may appear random, because the few observable features might be determined by some as-yet unobservable mechanism6. This point is not an emphatic denial of quantum mechanics, \u00e0 la Einstein\u2019s quip that \u201cGod does not play dice with the universe\"7. Rather it is a plea to not let quantum theory\u2019s coziness with uncertainty discourage the search for unseen causes.\n\nQuantum physicists have only probability laws because for two generations we have been indoctrinated not to believe in causes \u2013 and so we have stopped looking for them. Indeed, any attempt to search for the causes of microphenomena is met with scorn and a charge of professional incompetence and \u2019obsolete mechanistic materialism\u2019. Therefore, to explain the indeterminacy in current quantum theory we need not suppose there is any indeterminacy in Nature; the mental attitude of quantum physicists is already sufficient to guarantee it. \u2026 [Present quantum theory] cannot, as a matter of principle, answer any question of the form: \u2018What is really happening when \u2026?\u2019 [This mathematical formalism], like Orwellian newspeak, does not even provide the vocabulary in which one could ask such a question. \u2014 Edwin Thompson Jaynes\n\nFurther, it is possible to view the probabilistic laws of quantum mechanics as simply encapsulating our current epistemic uncertainty.\n\nIn current quantum theory, probabilities express our own ignorance due to our failure to search for the real causes of physical phenomena; and, worse, our failure even to think seriously about the problem. This ignorance may be unavoidable in practice, but in our present state of knowledge we do not know whether it is unavoidable in principle; the \u2018central dogma\u2019 simply asserts this, and draws the conclusion that belief in causes, and searching for them, is philosophically na\u00efve. If everybody accepted this and abided by it, no further advances in understanding physical law would ever be made. \u2014 Edwin Thompson Jaynes\n\nIn short, if you accept that epistemic uncertainty is unavoidable, then we can never have certainty about the existence of ontic uncertainty. There is a strange interplay between the two:\n\nEpistemic is the gap between knowledge and reality\nBut Ontic says reality is not well-defined\nSo neither is the gap, or Ontic. Oh, [profanity]!\nWhether the gap\u2019s defined or not is uncertain, in kind.\n\nThis leads us to the limitations of numerical probabilities. If the gap between knowledge and reality might not be well-defined, how can we quantify it? The standard approach is to simply assume that reality is accurately described by a model we define in the mathematics of probability. While often useful, this is merely an assumption, a point clearly demonstrated by the Bertrand Paradox8. Consider a circle containing an equilateral triangle.\n\nChoose a chord at random. What is the probability that the chord is longer than the sides of the triangle?\n\nMany possible answers can be justified, depending on the method by which you formalise the random chord-choice. Here are three possible methods, each giving a different solution.\n\n1. Pick two points on the circumference of the circle uniformly at random, and join them to create a chord. Align one of the triangle\u2019s vertices with the first point chosen. For the chord to be longer than a triangle side, the second point chosen needs to be between the opposite two vertices, on a segment of the circumference that is one-third of the total. The point is chosen uniformly, so the probability in this case is $$1\/3$$.\n2. Pick a radius uniformly at random, then pick a midpoint for a chord uniformly at random along that radius. (A chord is uniquely specified by its midpoint.) Midpoints on the peripheral half of the radius will produce a chord shorter than the triangle side; those on the central half of the radius will produce a chord longer than the triangle side. Thus, the probability in this case is $$1\/2$$.\n3. Pick a midpoint uniformly at random. Chords will be longer than the side of the triangle if their midpoint falls within a circle with half the radius of the original circle. The area of this circle is one-quarter the area of the original circle, so the probability in this case is $$1\/4$$.\n\nThe paradox only exists if you think there is a single true, numerical value for the probability, independent of the mechanism by which the chord is generated. In practice, we always need to impose a mathematical model of some form or another on the randomness we observe in order to quantify it in a well-defined way. We can choose models that seem to fit better than others, but can never claim our chosen model to be true, as that would contradict the ever-presence of epistemic uncertainty. The map is not the territory, and all that.\n\nThe choice of model, then, is necessarily subjective. This subjectivity is compounded by the \u2018soft\u2019 nature of probabilistic predictions, which (unless $$0$$ or $$1$$) leave room for any outcome to occur. In practice, this makes it impossible to categorically rule out models that do a poor job of explaining reality, preventing us from narrowing the pool of candidates. A contrived example: consider the following three probabilistic predictions for a set of six events.\n\nModel AModel BModel COutcome\n$$1\/2$$ $$1\/3$$ $$0$$\n$$1\/2$$ $$1\/3$$ $$1$$\n$$1\/2$$ $$1\/3$$ $$0$$\n$$1\/2$$ $$2\/3$$ $$1$$\n$$1\/2$$ $$2\/3$$ $$0$$\n$$1\/2$$ $$2\/3$$ $$1$$\n\nThe observed outcomes were possible under\u2014and so are compatible with\u2014all three probability assignments. There are thus multiple models that could describe the phenomena in question9. To distinguish between them we might consider additional criteria, such as how likely the model makes the observed outcomes, or how well the model generalises to new data. But we cannot definitively say which model is the best description of reality, without making further normative choices about how to define \u201cbest\u201d. Though this point holds for any finite set of probabilities10, it is most commonly known as the \u2018problem of the single case\u2019. When an event only happens once, whose to say that it happened with probability $$1$$ or probability $$1\/1000$$? Improbable events happen all the time.\n\nSo what is a probability? A subjective, imperfect quantification of uncertainty, which is predominantly epistemic and a little bit ontic. But don\u2019t take my word for it, I\u2019m probably wrong.\n\n1. I highly recommend Marcelo Gleiser\u2019s book The Island of Knowledge: The Limits of Science and the Search for Meaning, from which this quote was taken. In particular, there is a very helpful Socratic dialogue on the fundamentals of quantum mechanics in Chapter 23.\n\n2. H\u00e1jek, Alan, \u201cInterpretations of Probability\u201d, The Stanford Encyclopedia of Philosophy (Winter 2012 Edition), Edward N. Zalta (ed.), URL = <https:\/\/plato.stanford.edu\/archives\/win2012\/entries\/probability-interpret\/>.\n\n3. Inspired by a similar diagram that appears in the final quarter of A Curious Incident of the Dog in the Nighttime by Mark Haddon.\n\n4. Sir Roger Penrose, a collaborator of Stephen Hawking, is the one I have in mind. A good summary of his quantum consciousness theory, and the reception to it, is given in this Nautilus article\n\n5. See Max Tegmark\u2019s paper The Importance of Quantum Decoherence in Brain Processes\n\n6. More spritually: particles are to humans as zero is to infinity. See Ouspensky, 1949\n\n7. See Wikiquote\n\n8. The Wikipedia article explains things further.\n\n9. Sometimes referred to as the Rashomon Effect, because the film entitled Rashomon presents the same event from different perspectives.\n\n10. One definition for the true probability of an event is the limit of the proportion of times the event occurs as the number of \u2018trials\u2019 approaches infinity. But all the events to which we assign probabilities only occur a finite number of times \u2013 or if they occur infinitely often, can only be observed finitely many times. (If we describe an event well enough, such the \u2018Australian federal election, 1972\u2019, it only occurs once.) So we can never be certain of the veracity of probabilistic models; there will always be multiple candidates that are compatible with reality.\n\nThank you to Marcelo Gleiser, Harry Power, Nic Roumeliotis, Edmund Lau Tiew Hong & Yao-ban Chan for their correspondence and conversations on this topic.","date":"2018-09-23 14:41:56","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 0, \"mathjax_display_tex\": 1, \"mathjax_asciimath\": 0, \"img_math\": 0, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.5890924334526062, \"perplexity\": 735.5433789871022}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2018-39\/segments\/1537267159470.54\/warc\/CC-MAIN-20180923134314-20180923154714-00219.warc.gz\"}"} | null | null |
Mad Dogs Series 2 Confirmed For Early 2012
Sky1 HD
The Gang is Back
Mad Dogs 2 is set for early 2012 – the boys are back.
Mad Dog fans – the wait is finally over. Mad Dogs 2 has been confirmed for early 2012 and Max Beesley, Philip Glenister, John Simm and Marc Warren will all reprise their roles.
Leftbank Pictures are once more behind the second series, filming this summer in Majorca and Ibiza, and will once again comprise 4 hour-long episodes for transmission in early 2012 with all cast optioned for a potential third series too.
The story picks up where series one ended with Woody, Baxter and Rick driving away from the villa as Quinn has chosen to stay and make a new life in Majorca. In the opening scenes viewers will see Woody, Baxter and Rick have a change of heart and turn back.
So there's more of this…
However, it isn't long before they realise they've made the wrong move, setting themselves on an even more misguided course. In the series two opener viewers will see another killing and an escape with the drug money but can they really make a getaway when there are people who want their money back? The complicated situation the friends have found themselves in continues to spin wildly out of control and surely it can only be a matter of time before they face their day of reckoning…
Series one proved a big success with viewers earlier this year gaining a loyal weekly audience to become the eleventh most watched programme in Sky 1's history. And the programme has also received a BAFTA nomination for Drama Serial.
Stuart Murphy, Director of Programmes, Sky 1 HD, Sky 1, 2 & Pick TV and Director of Commissioning, Sky Entertainment commented: "Customers loved this show so it's great to commit to more. At Sky we work hard to bring our viewers high quality original entertainment made by the very best production companies with fantastic talent so I'm delighted we can confirm Mad Dogs' return just a few weeks after the first series has finished its run. This also marks a growing investment in British scripted content, to sit alongside our great American shows."
And a little more of this…
Andy Harries and Suzanne Mackie return to executive produce for Leftbank Productions with James Hawes (Merlin, Doctor Who) directing scripts written again by Cris Cole.
Andy Harries commented: "Mad Dogs had such an impact that it was as obvious as a dead goat that we had to do more and all the our amazing cast felt the same."
Suzanne Mackie said: "Before we had finished the first series of Mad Dogs we felt that there was so much more to do with these characters. I have been working with Cris Cole on the scripts ever since we finished shooting series one and the ideas for series two and three are every bit as explosive and inventive as they were at the beginning."
Excited? Can't wait to see the boys back in action? Let us know and join the conversation on our Facebook page and Twitter stream.
With thanks to The Railway Arms for the News Link!
Tags: actor, john, mad dogs, marc warren, max beesley, philip glenister, series 2, simm, sky 1, sky1. Bookmark the permalink.
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Q: make center aligned content stay justified to the left in bootsrap 4 I have text in a card center but i want to make the text remain in the middle but along a straight on the left.
Here is the image of what i have.Below is what i want
I have text center class on the column containing the card that centers the text,But the are not on the same line.
here is the code.
<div class="container">
<p>Discover</p>
<hr >
<div class="row">
<div class="col-sm-4 text-center" >
<div class="card ">
<div class="card-block ">
<div class="row">
<div class="col-5">
<img class="thumbnail" src="./assets/images/foodposter.jpg">
</div>
<div class="col-7">
<p style="font-weight: bold;">Snail master</p>
<!-- <p><i class="material-icons" style="font-size: 0.8em;">info_outline</i>In Food and Drink</p> -->
<p class="cardfont p-2">
<i class="material-icons" style="font-size: 1em;">today</i> 12 sept 2017</p>
<p class="cardfont p-2">
<i class="material-icons" style="font-size: 1em;">location_on</i>TRM,Thika Road</p>
<p class="cardfont p-2">
<i class="material-icons" style="font-size: 1em;">today</i> KSH.1200</p>
<p class="cardfont p-2">_</p>
<button type="button" class="btn btn-outline-primary btn-2 " style="font-size: 0.8em;line-height: 80%;">Get Tickets</button>
</div>
</div>
</div>
</div>
</div>
<div class="col-sm-4" >
<div class="card">
<div class="card-block">
<div class="row">
<div class="col-5">
<img class="thumbnail" src="./assets/images/comedyposter.jpg">
</div>
<div class="col-7">mate</div>
</div>
</div>
</div>
</div>
<div class="col-sm-4" >
<div class="card">
<div class="card-block">
<div class="row">
<div class="col-5">
<img class="thumbnail" src="./assets/images/midnightposter.jpg">
</div>
<div class="col-7">mate</div>
</div>
</div>
</div>
</div>
</div>
A: easiest ways is to use text-left instead of text-center
and give it a new class and margin it left and right equally to make it in centre
<div class="row">
<div class="col-4">
Image here
</div>
<div class="col-8 text-left">
<div class="xyz">
Snail master<br>
aaaaaa<br>
aaaaaaa
</div>
</div>
.xyz{
margin:0px 30px; as per your wish to make class in centre.
}
or you can use offset
| {
"redpajama_set_name": "RedPajamaStackExchange"
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