Chapter 2 Extremum Principles Predict Equilibria2章极值原理预测平衡

Chapter2Transformations and Vectors2.1Change of BasisLet us reconsider the vectorx=(2,1,3).Fully written out in a given Cartesian frame e i(i=1,2,3),it isx=2e1+e2+3e3.(This is one of the few times we do not use i as the symbol for a Cartesian frame vector.)Suppose we appoint a new frame˜e i(i=1,2,3)such thate1=˜e1+2˜e2+3˜e3,e2=4˜e1+5˜e2+6˜e3,e3=7˜e1+8˜e2+9˜e3.From these expansions we could calculate the˜e i and verify that they are non-coplanar.As x is an objective,frame-independent entity,we can write x=2(˜e1+2˜e2+3˜e3)+(4˜e1+5˜e2+6˜e3)+3(7˜e1+8˜e2+9˜e3)=(2+4+21)˜e1+(4+5+24)˜e2+(6+6+27)˜e3=27˜e1+33˜e2+39˜e3.In these calculations it is unimportant whether the frames are Cartesian; it is important only that we have the table of transformation⎛⎝123 456 789⎞⎠.1112Tensor Analysis with Applications in MechanicsIt is clear that we can repeat the same operation in general form.Let x be of the formx=3i=1x i e i(2.1)with the table of transformation of the frame given ase i=3j=1A ji˜e j.Thenx=3i=1x i3j=1A ji˜e j=3j=1˜e j3i=1A jix i.So in the new basis we havex=3j=1˜x j˜e j where˜x j=3i=1A jix i.Here we have introduced a new notation,placing some indices as subscripts and some as superscripts.Although this practice may seem artificial,there are fairly deep reasons for following it.2.2Dual BasesTo perform operations with a vector x,we must have a straightforward method of calculating its components—ultimately,no matter how ad-vanced we are,we must be able to obtain the x i using simple arithmetic. We prefer formulas that permit us tofind the components of vectors using dot multiplication only;we shall need these when doing frame transfor-mations,etc.In a Cartesian frame the necessary operation is simple dot multiplication by the corresponding basis vector of the frame:we havex k=x·i k(k=1,2,3).This procedure fails in a more general non-Cartesian frame where we do not necessarily have e i·e j=0for all j=i.However,it may still be possible tofind a vector e i such thatx i=x·e i(i=1,2,3)Transformations and Vectors 13in this more general situation.If we set x i =x ·e i =⎛⎝3 j =1x j e j ⎞⎠·e i =3 j =1x j (e j ·e i )and compare the left-and right-hand sides,we see that equality holds whene j ·e i =δi j (2.2)whereδi j = 1,j =i,0,j =i,is the Kronecker delta symbol.In a Cartesian frame we havee k =e k =i kfor each k .Exercise 2.1.Show that e i is determined uniquely by the requirement that x i =x ·e i for every x .Now let us discuss the geometrical nature of the vectors e i .Consider,for example,the equations for e 1:e 1·e 1=1,e 2·e 1=0,e 3·e 1=0.We see that e 1is orthogonal to both e 2and e 3,and its magnitude is such that e 1·e 1=1.Similar properties hold for e 2and e 3.Exercise 2.2.Show that the vectors e i are linearly independent.By Exercise 2.2,the e i constitute a frame or basis.This basis is said to be reciprocal or dual to the basis e i .We can therefore expand an arbitrary vector x asx =3i =1x i e i .(2.3)Note that superscripts and subscripts continue to appear in our notation,but in a way complementary to that used in equation (2.1).If we dot-multiply the representation (2.3)of x by e j and use (2.2)we get x j .This explains why the frames e i and e i are dual:the formulasx ·e i =x i ,x ·e i =x i ,14Tensor Analysis with Applications in Mechanicslook quite similar.So the introduction of a reciprocal basis gives many potential advantages.Let us discuss the reciprocal basis in more detail.Thefirst problem is tofind suitable formulas to define it.We derive these formulas next, butfirst let us note the following.The use of reciprocal vectors may not be practical in those situations where we are working with only two or three vectors.The real advantages come when we are working intensively with many vectors.This is reminiscent of the solution of a set of linear simultaneous equations:it is inefficient tofind the inverse matrix of the system if we have only one forcing vector.But when we must solve such a problem repeatedly for many forcing vectors,the calculation and use of the inverse matrix is reasonable.Writing out x in the e i and e i bases,we used a combination of indices (i.e.,subscripts and superscripts)and summation symbols.From now on we shall omit the symbol of summation when we meet matching subscripts and superscripts:we shall write,say,x i a i.x i a i for the sumiThat is,whenever we see i as a subscript and a superscript,we shall under-stand that a summation is to be carried out over i.This rule shall apply to situations involving vectors as well:we shall understand,for example,x i e i.x i e i to mean the summationiThis rule is called the rule of summation over repeated indices.1Note that a repeated index is a dummy index in the sense that it may be replaced by any other index not already in use:we havex i a i=x1a1+x2a2+x3a3=x k a kfor instance.An index that occurs just once in an expression,for example the index i inA k i x k,is called a free index.In tensor discussions each free index is understood to range independently over a set of values—presently this set is{1,2,3}. 1The rule of summation wasfirst introduced not by mathematicians but by Einstein, and is sometimes referred to as the Einstein summation convention.In a paper where he introduced this rule,Einstein used Cartesian frames and therefore did not distinguish superscripts from subscripts.However,we shall continue to make the distinction so that we can deal with non-Cartesian frames.Transformations and Vectors15 Let us return to the task of deriving formulas for the reciprocal basis vectors e i in terms of the original basis vectors e i.We construct e1first. Since the cross product of two vectors is perpendicular to both,we can satisfy the conditionse2·e1=0,e3·e1=0,by settinge1=c1(e2×e3)where c1is a constant.To determine c1we requiree1·e1=1.We obtainc1[e1·(e2×e3)]=1.The quantity e1·(e2×e3)is a scalar whose absolute value is the volume of the parallelepiped described by the vectors e i.Denoting it by V,we havee1=1V(e2×e3).Similarly,e2=1V(e3×e1),e3=1V(e1×e2).The reader may verify that these expressions satisfy(2.2).Let us mention that if we construct the reciprocal basis to the basis e i we obtain the initial basis e i.Hence we immediately get the dual formulase1=1V(e2×e3),e2=1V(e3×e1),e3=1V(e1×e2),whereV =e1·(e2×e3).Within an algebraic sign,V is the volume of the parallelepiped described by the vectors e i.Exercise2.3.Show that V =1/V.Let us now consider the forms of the dot product between two vectorsa=a i e i=a j e j,b=b p e p=b q e q.16Tensor Analysis with Applications in MechanicsWe havea·b=a i e i·b p e p=a i b p e i·e p.Introducing the notationg ip=e i·e p,(2.4) we havea·b=a i b p g ip.(As a short exercise the reader should write out this expression in full.) Using the reciprocal component representations we geta·b=a j e j·b q e q=a j b q g jqwhereg jq=e j·e q.(2.5) Finally,using a mixed representation we geta·b=a i e i·b q e q=a i b qδq i=a i b iand,similarly,a·b=a j b j.Hencea·b=a i b j g ij=a i b j g ij=a i b i=a i b i.We see that when we use mixed bases to represent a and b we get formulas that resemble the equationa·b=a1b1+a2b2+a3b3from§1.3;otherwise we get more terms and additional multipliers.We will encounter g ij and g ij often.They are the components of a unique tensor known as the metric tensor.In Cartesian frames we obviously haveg ij=δj,g ij=δi j.iTransformations and Vectors17 2.3Transformation to the Reciprocal FrameHow do the components of a vector x transform when we change to the reciprocal frame?We simply setx i e i=x i e iand dot both sides with e j to getx i e i·e j=x i e i·e jorx j=x i g ij.(2.6) In the system of equations⎛⎝x1x2x3⎞⎠=⎛⎝g11g21g31g12g22g32g13g23g33⎞⎠⎛⎝x1x2x3⎞⎠the matrix of the components of the metric tensor g ij is also called the Gram matrix.A theorem in linear algebra states that its determinant is not zero if and only if the vectors e i are linearly independent.Exercise2.4.(a)Show that if the Gram determinant vanishes,then the e i are linearly dependent.(b)Prove that the Gram determinant equals V2.We called the basis e i dual to the basis e i.In e i the metric components are given by g ij,so we can immediately write an expression dual to(2.6):x i=x j g ij.(2.7)We see from(2.6)and(2.7)that,using the components of the metric tensor, we can always change subscripts to superscripts and vice versa.These actions are known as the raising and lowering of indices.Finally,(2.6)and (2.7)together implyx i=g ij g jk x k,henceg ij g jk=δk i.Of course,this means that the matrices of g ij and g ij are mutually inverse.18Tensor Analysis with Applications in MechanicsQuick summaryGiven a basis e i,the vectors e i given by the requirement thate j·e i=δi jare linearly independent and form a basis called the reciprocal or dual basis. The definition of dual basis is motivated by the equation x i=x·e i.The e i can be written ase i=1V(e j×e k)where the ordered triple(i,j,k)equals(1,2,3)or one of the cyclic permu-tations(2,3,1)or(3,1,2),and whereV=e1·(e2×e3).The dual of the basis e k(i.e.,the dual of the dual)is the original basis e k.A given vector x can be expressed asx=x i e i=x i e iwhere the x i are the components of x with respect to the dual basis. Exercise2.5.(a)Let x=x k e k=x k e k.Write out the modulus of x in all possible forms using the metric tensor.(b)Write out all forms of the dot product x·y.2.4Transformation Between General FramesHaving transformed the components x i of a vector x to the corresponding components x i relative to the reciprocal basis,we are now ready to take on the more general task of transforming the x i to the corresponding compo-nents˜x i relative to any other basis˜e i.Let the new basis˜e i be related to the original basis e i bye i=A ji˜e j.(2.8) This is,of course,compact notation for the system of equations⎛⎝e1e2e3⎞⎠=⎛⎝A11A21A31A12A22A32A13A23A33⎞⎠≡A,say⎛⎝˜e1˜e2˜e3⎞⎠.Transformations and Vectors19the subscript indexes Before proceeding,we note that in the symbol A jithe row number in the matrix A,while the superscript indexes the column number.Throughout our development we shall often take the time to write various equations of interest in matrix notation.It follows from(2.8)that=e i·˜e j.A jiExercise2.6.A Cartesian frame is rotated about its third axis to give a new Cartesian frame.Find the matrix of transformation.A vector x can be expressed in the two formsx=x k e k,x=˜x i˜e i.Equating these two expressions for the same vector x,we have˜x i˜e i=x k e k,hence˜e j.(2.9)˜x i˜e i=x k A jkTofind˜x i in terms of x i,we may expand the notation and write(2.9)as ˜x1˜e1+˜x2˜e2+˜x3˜e3=x1A j1˜e j+x2A j2˜e j+x3A j3˜e jwhere,of course,A j1˜e j=A11˜e1+A21˜e2+A31˜e3,A j2˜e j=A12˜e1+A22˜e2+A32˜e3,A j3˜e j=A13˜e1+A23˜e2+A33˜e3.Matching coefficients of the˜e i wefind˜x1=x1A11+x2A12+x3A13=x j A1j,˜x2=x1A21+x2A22+x3A23=x j A2j,˜x3=x1A31+x2A32+x3A33=x j A3j,hence˜x i=x j A i j.(2.10) It is possible to obtain(2.10)from(2.9)in a succinct manner.On the right-hand side of(2.9)the index j is a dummy index which we can replace with20Tensor Analysis with Applications in Mechanicsi and thereby obtain(2.10)immediately.The matrix notation equivalent of(2.10)is⎛⎝˜x1˜x2˜x3⎞⎠=⎛⎝A11A12A13A21A22A23A31A32A33⎞⎠⎛⎝x1x2x3⎞⎠and thus involves multiplication by A T,the transpose of A.We shall also need the equations of transformation from the frame˜e i back to the frame e i.Since the direct transformation is linear the inverse must be linear as well,so we can write˜e i=˜A jie j(2.11) where˜A ji=˜e i·e j.Let usfind the relation between the matrices of transformation A and˜A. By(2.11)and(2.8)we have˜e i=˜A ji e j=˜A jiA k j˜e k,and since the˜e i form a basis we must have˜A jiA k j=δk i. The relationshipA ji ˜A kj=δk ifollows similarly.The product of the matrices(˜A ji)and(A k j)is the unit matrix and thus these matrices are mutually inverse.Exercise2.7.Show that x i=˜x k˜A ik.Formulas for the relations between reciprocal bases can be obtained as follows.We begin with the obvious identitiese j(e j·x)=x,˜e j(˜e j·x)=x.Putting x=˜e i in thefirst of these gives˜e i=A i j e j,while the second identity with x=e i yieldse i=˜A i j˜e j.From these follow the transformation formulas˜x i=x k˜A k i,x i=˜x k A k i.2.5Covariant and Contravariant ComponentsWe have seen that if the basis vectors transform according to the relatione i=A ji˜e j,then the components x i of a vector x must transform according tox i=A ji˜x j.The similarity in form between these two relations results in the x i being termed the covariant components of the vector x.On the other hand,the transformation lawx i=˜A i j˜x jshows that the x i transform like the e i.For this reason the x i are termed the contravariant components of x.We shallfind a further use for this nomenclature in Chapter3.Quick summaryIf frame transformationse i=A ji˜e j,˜e i=˜A ji e j,e i=˜A i j˜e j,˜e i=A ije j,are considered,then x has the various expressionsx=x i e i=x i e i=˜x i˜e i=˜x i˜e i and the transformation lawsx i=A ji˜x j,˜x i=˜A ji x j,x i=˜A i j˜x j,˜x i=A i j x j,apply.The x i are termed contravariant components of x,while the x i are termed covariant components.The transformation laws are particularly simple when the frame is changed to the dual frame.Thenx i=g ji x j,x i=g ij x j,whereg ij=e i·e j,g ij=e i·e j,are components of the metric tensor.2.6The Cross Product in Index NotationIn mechanics a major role is played by the quantity called torque.This quantity is introduced in elementary physics as the product of a force mag-nitude and a length(“force times moment arm”),along with some rules for algebraic sign to account for the sense of rotation that the force would encourage when applied to a physical body.In more advanced discussions in which three-dimensional problems are considered,torque is regarded as a vectorial quantity.If a force f acts at a point which is located relative to an origin O by position vector r,then the associated torque t about O is normal to the plane of the vectors r and f.Of the two possible unit normals,t is conventionally(but arbitrarily)associated with the vectorˆn given by the familiar right-hand rule:if the forefinger of the right hand is directed along r and the middlefinger is directed along f,then the thumb indicates the direction ofˆn and hence the direction of t.The magnitude of t equals|f||r|sinθ,whereθis the smaller angle between f and r.These rules are all encapsulated in the brief symbolismt=r×f.The definition of torque can be taken as a model for a more general operation between vectors:the cross product.If a and b are any two vectors,we definea×b=ˆn|a||b|sinθwhereˆn andθare defined as in the case of torque above.Like any other vector,c=a×b can be expanded in terms of a basis;we choose the reciprocal basis e i and writec=c i e i.Because the magnitudes of a and b enter into a×b in multiplicative fashion, we are prompted to seek c i in the formc i= ijk a j b k.(2.12) Here the ’s are formal coefficients.Let usfind them.We writea=a j e j,b=b k e k,and employ the well-known distributive property(u+v)×w≡u×w+v×wto obtainc =a j e j ×b k e k =a j b k (e j ×e k ).Thenc ·e i =c m e m ·e i =c i =a j b k [(e j ×e k )·e i ]and comparison with (2.12)shows thatijk =(e j ×e k )·e i .Now the value of (e j ×e k )·e i depends on the values of the indices i,j,k .Here it is convenient to introduce the idea of a permutation of the ordered triple (1,2,3).A permutation of (1,2,3)is called even if it can be brought about by performing any even number of interchanges of pairs of these numbers;a permutation is odd if it results from performing any odd number of interchanges.We saw before that (e j ×e k )·e i equals the volume of the frame parallelepiped if i,j,k are distinct and the ordered triple (i,j,k )is an even permutation of (1,2,3).If i,j,k are distinct and the ordered triple (i,j,k )is an odd permutation of (1,2,3),we obtain minus the volume of the frame parallelepiped.If any two of the numbers i,j,k are equal we obtain zero.Hence ijk =⎧⎪⎪⎨⎪⎪⎩+V,(i,j,k )an even permutation of (1,2,3),−V,(i,j,k )an odd permutation of (1,2,3),0,two or more indices equal.Moreover,it can be shown (Exercise 2.4)thatV 2=gwhere g is the determinant of the matrix formed from the elements g ij =e i ·e j of the metric tensor.Note that |V |=1for a Cartesian frame.The permutation symbol ijk is useful in writing formulas.For example,the determinant of a matrix A =(a ij )can be expressed succinctly asdet A = ijk a 1i a 2j a 3k .Much more than a notational device however, ijk represents a tensor (the so-called Levi–Civita tensor ).We discuss this further in Chapter 3.Exercise 2.8.The contravariant components of a vector c =a ×b can be expressed asc i = ijk a j b kfor suitable coefficients ijk .Use the technique of this section to find the coefficients.Then establish the identity ijk pqr = δp i δq i δr i δp j δq j δr j δp k δq kδr k and use it to show thatijk pqk =δp i δq j −δq i δp j .Use this in turn to prove thata ×(b ×c )=b (a ·c )−c (a ·b )(2.13)for any vectors a ,b ,c .Exercise 2.9.Establish Lagrange’s identity(a ×b )·(c ×d )=(a ·c )(b ·d )−(a ·d )(b ·c ).2.7Norms on the Space of Vectors We often need to characterize the intensity of some vector field locally or globally.For this,the notion of a norm is appropriate.The well-known Euclidean norm of a vector a =a k i k written in a Cartesian frame isa = 3 k =1a 2k1/2.This norm is related to the inner product of two vectors a =a k i k and b =b k i k :we have a ·b =a k b k so thata =(a ·a )1/2.In a non-Cartesian frame,the components of a vector depend on the lengths of the frame vectors and the angles between them.Since the sum of squared components of a vector depends on the frame,we cannot use it to characterize the vector.But the formulas connected with the dot product are invariant under change of frame,so we can use them to characterize the intensity of the vector —its length.Thus for two vectors x =x i e i and y =y j e j written in the arbitrary frame,we can introduce a scalar product (i.e.,a simple dot product)x ·y =x i e i ·y j e j =x i y j g ij =x i y j g ij =x i y i .Note that only in mixed coordinates does this resemble the scalar product in a Cartesian frame.Similarly,the norm of a vector x isx =(x·x)1/2=x i x j g ij1/2=x i x j g ij1/2=x i x i1/2.This dot product and associated norm have all the properties required from objects of this nature in algebra or functional analysis.Indeed,it is neces-sary only to check whether all the axioms of the inner product are satisfied.(i)x·x≥0,and x·x=0if and only if x=0.This property holdsbecause all the quantities involved can be written in a Cartesianframe where it holds trivially.By the same reasoning,we confirmsatisfaction of the property(ii)x·y=y·x.The reader should check that this holds for any representation of the vectors.Finally,(iii)(αx+βy)·z=α(x·z)+β(y·z)whereαandβare arbitrary real numbers and z is a vector.By the general theory then,the expressionx =(x·x)1/2(2.14) satisfies all the axioms of a norm:(i) x ≥0,with x =0if and only if x=0.(ii) αx =|α| x for any realα.(iii) x+y ≤ x + y .In addition we have the Schwarz inequalityx·y ≤ x y ,(2.15) where in the case of nonzero vectors the equality holds if and only if x=λy for some realλ.The set of all three-dimensional vectors constitutes a three-dimensional linear space.A linear space equipped with the norm(2.14)becomes a normed space.In this book,the principal space is R3.Note that we can introduce more than one norm in any normed space,and in practice a variety of norms turn out to be necessary.For example,2 x is also a norm in R3.We can introduce other norms,quite different from the above. One norm can be introduced as follows.Let e k be a basis of R3and letx =x k e k .For p ≥1,we introduce x p =3 k =1|x k |p 1/p.Norm axioms (i)and (ii)obviously hold.Axiom (iii)is a consequence of the classical Minkowski inequality for finite sums.The reader should be aware that this norm is given in a certain basis.If we use it in another basis,the value of the norm of a vector will change in general.An advantage of the norm (2.14)is that it is independent of the basis of the space.Later,when investigating the eigenvalues of a tensor,we will need a space of vectors with complex components.It can be introduced similarly to the space of complex numbers.We start with the space R 3having basis e k ,and introduce multiplication of vectors in R 3by complex numbers.This also yields a linear space,but it is complex and denoted by C 3.An arbitrary vector x in C 3takes the formx =(a k +ib k )e k ,where i is the imaginary unit (i 2=−1).Analogous to the conjugate number is the conjugate vector to x ,defined byx =(a k −ib k )e k .The real and imaginary parts of x are a k e k and b k e k ,respectively.Clearly,a basis in C 3may contain vectors that are not in R 3.As an exercise,the reader should write out the form of the real and imaginary parts of x in such a basis.In C 3,the dot product loses the property that x ·x ≥0.However,we can introduce the inner product of two vectors x and y asx ,y =x ·y .It is easy to see that this inner product has the following properties.Let x ,y ,z be arbitrary vectors of C 3.Then(i)x ·x ≥0,and x ·x =0if and only if x =0.(ii)x ·y =y ·x .(iii)(αx +βy )·z =α(x ·z )+β(y ·z )where αand βare arbitrarycomplex numbers.The reader should verify these properties.Now we can introduce the norm related to the inner product,x = x ,x 1/2,and verify that it satisfies all the axioms of a norm in a complex linear space.As a consequence of the general properties of the inner product, Schwarz’s inequality(2.15)also holds in C3.2.8Closing RemarksWe close by repeating something we said in Chapter1:A vector is an objective entity.In elementary mathematics we learn to think of a vector as an ordered triple of components.There is,of course,no harm in this if we keep in mind a certain Cartesian frame.But if wefix those components then in any other frame the vector is determined uniquely.Absolutely uniquely!So a vector is something objective,but as soon as we specify its components in one frame we canfind them in any other frame by the use of certain rules.We emphasize this because the situation is exactly the same with ten-sors.A tensor is an objective entity,andfixing its components relative to one frame,we determine the tensor uniquely—even though its components relative to other frames will in general be different.2.9Problems2.1Find the dual basis to e i.(a)e1=2i1+i2−i3,e2=2i2+3i3,e3=i1+i3;(b)e1=i1+3i2+2i3,e2=2i1−3i2+2i3,e3=3i1+2i2+3i3;(c)e1=i1+i2,e2=i1−i2,e3=3i3;(d)e1=cosφi1+sinφi2,e2=−sinφi1+cosφi2,e3=i3.2.2Let˜e1=−2i1+3i2+2i3,e1=2i1+i2−i3,˜e2=−2i1+2i2+i3,e2=2i2+3i3,˜e3=−i1+i2+i3,e3=i1+i3.Find the matrix A jof transformation from the basis˜e i to the basis e j.i2.3Let˜e1=i1+2i2,e1=i1−6i3,˜e2=−i2−i3,e2=−3i1−4i2+4i3,˜e3=−i1+2i2−2i3,e3=i1+i2+i3. Find the matrix of transformation of the basis˜e i to e j.2.4Find(a)a jδjk,(b)a i a jδi j,(c)δi i,(d)δijδjk,(e)δijδji,(f)δji δk jδik.2.5Show that ijk ijl=2δlk.2.6Show that ijk ijk=6.2.7Find(a) ijkδjk,(b) ijk mkjδi m,(c) ijkδk mδj n,(d) ijk a i a j,(e) ijk| ijk|,(f) ijk imnδj m.2.8Find(a×b)×c.2.9Show that(a×b)·a=0.2.10Show that a·(b×c)d=(a·d)b×c+(b·d)c×a+(c·d)a×b.2.11Show that(e×a)×e=a if|e|=1and e·a=0.2.12Let e k be a basis of R3,let x=x k e k,and suppose h1,h2,h3arefixed positive numbers.Show that h k|x k|is a norm in R3.。

英语教学法原著选读48：克拉申⼆语习得五假说之⼆——⾃然顺序假说（NaturalOrder）导读：本篇是⼆语习得泰⽃Stephen D. Krashen的著作《⼆语习得原则与实践（Principles andPractice of Second Language Acquisition）》第⼆章“第⼆语⾔习得理论”A节“有关第⼆语⾔习得的五个假说”中的第⼆个假说，探讨的是语⾔习得过程中各学习项⽬的⾃然顺序。

按照这⼀假说，不管教的⼀⽅多么努⼒，学的⼈总是按照⼀定顺序学会语⾔项⽬，从⽐较简单的ing逐步⾛向稍为复杂的s/es、's等。

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祝朋友们学习进步！------------------------原⽂One of the most exciting discoveries in language acquisition research in recent years has beenthe finding that the acquisition of grammatical structures proceeds in a predictable order.Acquirers of a given language tend to acquire certain grammatical structures early, and otherslater. The agreement among individual acquirers is not always 100%, but there are clear,statistically significant, similarities.English is perhaps the most studied language as far as the natural order hypothesis isconcerned, and of all structures of English, morphology is the most studied. Brown (1973)reported that children acquiring English as a first language tended to acquire certaingrammatical morphemes, or functions words, earlier than others. For example, the progressivemarker ing (as in "He is playing baseball".) and the plural marker /s/ ("two dogs") were amongthe first morphemes acquired, while the third person singular marker /s/ (as in "He lives in NewYork") and the possessive /s/ ("John's hat") were typically acquired much later, cominganywhere from six months to one year later. de Villiers and de Villiers (1973) confirmedBrown's longitudinal results cross-sectionally, showing that items that Brown found to beacquired earliest in time were also the ones that children tended to get right more often. In otherwords, for those morphemes studied, the difficulty order was similar to the acquisition order.Shortly after Brown's results were published, Dulay and Burt (1974, 1975) reported thatchildren acquiring English as a second language also show a "natural order" for grammaticalmorphemes, regardless of their first language. The child second language order of acquisitionwas different from the first language order, but different groups of second language acquirersshowed striking similarities. Dulay and Burt's results have been confirmed by a number ofinvestigators (Kessler and Idar, 1977; Fabris, 1978; Makino, 1980). Dulay and Burt used asubset of the 14 morphemes Brown originally investigated. Fathman (1975) confirmed thereality of the natural order in child second language acquisition with her test of oral production,the SLOPE test, which probed 20 different structures.Following Dulay and Burt's work, Bailey, Madden, and Krashen (1974) reported a natural orderfor adult subjects, an order quite similar to that seen in child second language acquisition. Aswe shall see later, this natural order appears only under certain conditions (or rather, itdisappears only under certain conditions!). Some of the studies confirming the natural order inadults for grammatical morphemes include Andersen (1976), who used composition, Krashen,Houck, Giunchi, Bode, Birnbaum, and Strei (1977), using free speech, and Christison (1979),also using free speech. Adult research using the SLOPE test also confirms the natural orderand widens the data base. Krashen, Sferlazza, Feldman, and Fathman (1976) found an ordersimilar to Fathman's (1975) child second language order, and Kayfetz-Fuller (1978) alsoreported a natural order using the SLOPE test.As noted above, the order of acquisition for second language is not the same as the order ofacquisition for first language, but there are some similarities. Table 2.1, from Krashen (1977),presents an average order for second language, and shows how the first language orderdiffers. This average order is the result of a comparison of many empirical studies ofgrammatical morpheme acquisition.TABLE 2.1. "Average" order of acquisition of grammatical morphemes for EnglishWhile English is the best studied language, it is not the only one studied. Research in order of acquisition for other language is beginning to emerge. As yet unpublished papers by Bruce (1979), dealing with Russian as a foreign language, and van Naerssen (1981), for Spanish as a foreign language, confirm the validity of the natural order hypothesis for other languages. We will deal with the pedagogical implications of the natural order hypothesis later, I should point out here, however, that the implication of the natural order hypothesis is not that our syllabi should be based on the order found in the studies discussed here, that is, I do not recommend teaching ing early and the third person singular /s/ late. We will, in fact, find reason to reject grammatical sequencing in all cases where our goal is language acquisition. We will deal with this later, however, after we have finished laying the theoretical groundwork.(a) Transitional formsStudies supporting the natural order hypothesis show only the order in which mature, or well-formed structures emerge. Other studies reveal the path acquirers take en route to mastery. (For a review, see Dulay, Burt, and Krashen, in press. Ravem, 1974; Milon, 1974; Gillis and Weber, 1976; Cancino, Rosansky, and Schumann, 1974; Wode, 1978 and Nelson, 1980 are some second language studies in this area.) There is surprising uniformity here as well--acquirers make very similar errors, termed developmental errors, while they are acquiring. For example, in acquiring English negation, many first and second language acquirers pass through a stage in which they place the negative marker outside the sentence, as in:No Mom sharpen it. (from Klima and Bellugi's (1966)study of child L1 acquisition)and Not like it now. (from Ravem's (1974) study of childL2 acquisition)A typical later stage is to place the negative marker between the subject and the verb, as in:I no like this one. (Cancino et al. (1975) study of childL2 acquisition)and This no have calendar. (from Schumann's (1978a) study of adult L2 acquisition)before reaching the correct form.Predictable stages in the acquisition of wh-questions in English include an early stage in which the wh-word appears before the rest of the sentence, which is otherwise left in its normal uninverted form, as in:How he can be a doctor? (Klima and Bellugi, 1966, child L1acquisition)and What she is doing? (Ravem, 1974, child L2 acquisition)Only later do acquirers begin to invert the subject and verb of the sentence. (A detailed review can be found in Dulay et al., in press.)Transitional forms have been described for other languages and for other structures. The stages for a given target language appear to be strikingly similar despite the first language of the acquirer (although particular first languages may influence the duration of certain stages; see Schumann, 1979). This uniformity is thought to reflect the operation of the natural language acquisition process that is part of all of us. (For a discussion of some of the current issues and controversies concerning the natural order hypothesis, see Krashen, 1981.)------------------------读后感教学者有⾃⼰的⽇程，学习者有⾃⼰的⾃然顺序，克拉申⼜说不⼀定要完全遵循这个⾃然顺序，问题来了：咱们到底该怎么办呢？这让我想起了《西⾏漫记》⾥埃德加·斯诺提到的⼀件趣事：红军招募新战⼠，⼊伍的往往都是中国西部、西北部农村⽬不识丁的青壮年乃⾄少年⼈。

UNIT 2 Economist1.Every field of study has its own language and its own way of thinking. Mathematicians talk about axioms, integrals, and vector spaces. Psychologists talk about ego, id, and cognitive dissonance. Lawyers talk about venue, torts, and promissory estoppel.每个研究领域都有它自己的语言和思考方式。

数学家谈论定理、积分以及向量空间。

心理学家谈论自我、本能、以及认知的不一致性。

律师谈论犯罪地点、侵权行为以及约定的禁止翻供。

2.Economics is no different. Supply, demand, elasticity, comparative advantage, consumer surplus, deadweight loss—these terms are part of the economist’s language. In the co ming chapters, you will encounter many new terms and some familiar words that economists use in specialized ways. At first, this new language may seem needlessly arcane. But, as you will see, its value lies in its ability to provide you a new and useful way of thinking about the world in which you live.经济学家也一样。

British Journal of Haematology ,2001,113,369±374Technetium-99m-sestamethoxyisobutylisonitrile scan as a predictor of chemotherapy response in malignant lymphomas compared with P-glycoprotein expression,multidrug resistance-related protein expression and other prognosis factorsChia-Hung Kao,1Shih-Chuan Tsai,2Jhi-Joung Wang,3Yung-Jen Ho,4Shung-Tai Ho 5and Sheng-Ping Changlai 61Department of Nuclear Medicine,Taichung Veterans General Hospital,Taichung,2Department of Nuclear Medicine,Show-Chwan Memorial Hospital,Chunghua,3Department of Medical Research,Chi-Mei Medical Centre,Tainan,4Department of Radiology,Jen-Ai Hospital,Taichung,5School of Medicine,National Defence Medical Centre,Taipei,and 6Department of Nuclear Medicine,Chung-Shan Medical and Dental Hospital,Taichung,TaiwanReceived 13November 2000;accepted for publication 14January 2001Summary .The purpose of the present study was to predict the response of malignant lymphomas (MLs)to chemotherapy usingtechnetium-99m methoxyisobutylisonitrile (Tc-MIBI)scan and to compare it with the predictive ability of P-glycoprotein (P-gp)expression,multidrug resistance-related protein (MRP)expression and other prognosis factors.Twenty-five ML patients were enrolled in this study prior to initiation of chemotherapy .Images were obtained 10min after intravenous injection of Tc-MIBI,interpreted visually and the tumour-to-background (T/B)ratios calculated.Immunohistochemical analyses were performed on sections of the biopsy specimens to determine P-gp and MRP expression.Chemotherapy response was evaluated in the first 1±2years after completion of chemotherapy .The mean T/B ratio of the 15patients with agood response (3´3^0´6)was significantly higher than that of the 10patients with a poor response (1´2^0´1).All 15patients with a good chemotherapy response had positive Tc-MIBI scan results and negative P-gp and MRPexpression.All 10patients with a poor response had negative Tc-MIBI scan results and either positive P-gp or MRP expression.Other prognosis factors showed no significant difference in the incidence of good and poor responses.Tc-MIBI scan results represent P-gp or MRP expression more accurately than other prognosis factors and predict the chemotherapy response in ML patients.Keywords:malignant lymphoma,technetium-99m methoxy-isobutylisonitrile,chemotherapy response,P-glycoprotein expression,multidrugresistance-related protein expression.Chemotherapy is the primary therapeutic modality for many malignant lymphomas (MLs)including all non-Hodgkin's lymphoma (NHL)cases and many cases of Hodgkin's disease (HD)(Barr et al ,1997;Neal &Hoskin,1997;Wilson &Chabner,1998).As resistance to chemotherapeutic agents is a major cause of treatment failure,the goal of chemotherapy for ML is to avoid possible resistance and achieve the highest response.The mechanism of tumour uptake of technetium-99m methoxyisobutylisonitrile (Tc-MIBI)may involve bindingto the cytosol of the tumour cell (Hassan et al ,1989).The cationic charge and lipophilicity of Tc-MIBI,mitochondrial and plasma membrane potentials of tumour cells,and cellular mitochondrial content can all play a significant role in tumour uptake of this agent (Chiu et al ,1990),or the uptake may be caused by indirect phenomena such as increased tumour blood flow and capillary permeability .Tc-MIBI scans have been used to successfully predict the chemotherapy response of MLs (Kapucu et al ,1997;Shih et al ,1998).However,the previous studies have not compared the relationship between Tc-MIBI scan resultsq 2001Blackwell Science Ltd369Correspondence:Chia-HungKao,MD,Department of Nuclear Medicine,TaichungVeterans General Hospital,160Taichung Harbour Road,Section 3,Taichung407,Taiwan.E-mail:kaoch@ .twand P-glycoprotein(P-gp)or multidrug resistance-related protein(MRP)expression in predictingthe chemotherapy response of MLs.Therefore,the aim of this study was to compare Tc-MIBI scan results,immunohistochemical ana-lyses of P-gp and MRP expression,and other prognosis factors as predictors of chemotherapy response in ML patients.PATIENTS AND METHODSPatients.Twenty-five patients(13men,12women;age range25±65years;mean age:46´2^12´3years)with ML(11with HD and14with NHL)were included in the study and underwent Tc-MIBI scans prior to chemotherapy (Table I).The classification of ML followed the Lukes and Butler and updated Kiel systems(Jaffe,1998).After Tc-MIBI scans,the11HD patients received chemotherapy regimens with nitrogen mustard(mechlorethamine),vincristine, procarbazine and prednisone(MOPP),alternatingwith doxorubicin,bleomycin,vinblastine and dacarbazine (ABVD);the14NHL patients received chemotherapy regimens with cyclophosphamide,doxorubicin,vincristine and prednisone(CHOP)protocols(Barr et al,1997;Neal& Hoskin,1997;Wilson&Chabner,1998).Technetium-99m methoxyisobutylisonitrile scan.The ima-ging procedure began30min after oral intake of500mg of perchlorate to prevent any abnormal uptake of free Tc-99m pertechnetate.A commercial MIBI preparation(max. 5´56GBq in approximately1±3ml)was obtained from The Du Pont Merck Pharmaceutical Company(Cardiolite, Billerica,MA,USA).The labellingand quality control procedures were carried out accordingto the manufac-turer's bellingefficiencies were all.95%. Each patient was place in a supine position on the imaging table with the chest strapped to prevent motion. Because of physiological Tc-MIBI accumulation in abdom-inal and pelvic organs,visualization of MLs located in abdominal and pelvic regions is unreliable.In this study, images of supradiaphragmatic MLs were obtained10min after intravenous injection of740MBq Tc-MIBI in the anterior and posterior projection.The equipment consisted of a large field-of-view gamma camera fitted with a low-energy,high-resolution collimator.A single20%energy window was set at140keV and500K counts were obtained for each static image.Tumour-to-background(T/ B)ratios were calculated as the mean counts over the region of interest(ROI)of the tumour outlined in the largest lesion4the mean counts over the ROI ofTable I.Detailed data of patients in this study.Case Tc-MIBI scan results Immunohistochemical stainingAge BChemotherapyresponsenumber Sex T/B ratio Visual interpretation P-gp expression MRP expression(years)Type Stage symptoms results1Female1´0Negative Positive Negative33HD I Yes Poor2Female1´0Negative Negative Positive53NHL III No Poor3Female1´1Negative Positive Negative40HD II Yes Poor4Male1´1Negative Positive Negative51NHL III No Poor5Male1´1Negative Negative Positive62HD IV No Poor6Male1´2Negative Positive Negative35NHL IV No Poor7Male1´2Negative Negative Positive55HD IV Yes Poor8Female1´3Negative Positive Negative27NHL III Yes Poor9Male1´3Negative Negative Positive65NHL III Yes Poor10Male1´4Negative Positive Negative43NHL II Yes Poor11Female2´4Positive Negative Negative43HD II Yes Good12Male2´7Positive Negative Negative56HD IV No Good13Male2´8Positive Negative Negative37NHL III No Good14Male2´9Positive Negative Negative55HD I Yes Good15Male2´9Positive Negative Negative62HD IV No Good16Male3´0Positive Negative Negative61NHL III No Good17Female3´2Positive Negative Negative31NHL III No Good18Male3´2Positive Negative Negative47HD IV No Good19Female3´3Positive Negative Negative60HD III Yes Good20Male3´3Positive Negative Negative25NHL II Yes Good21Female3´6Positive Negative Negative30HD II Yes Good22Female3´6Positive Negative Negative58NHL IV No Good23Male4´0Positive Negative Negative35HD IV No Good24Female4´1Positive Negative Negative50NHL III No Good25Male4´5Positive Negative Negative42NHL II Yes GoodHD,Hodgkin's disease;NHL,non-Hodgkin's lymphoma;P-gp,P-glycoprotein;MRP,multidrug resistance-related protein;Tc-MIBI, technetium-99m methoxyisobutylisonitrile;T/B,tumour-to-background.370 C.-H.Kao et alq2001Blackwell Science Ltd,British Journal of Haematology113:369±374background,defined as the contralateral normal side for the neck and axilia lesions or normal soft tissue of the thorax for mediastinal lesions.Tc-MIBI uptake in the lesions $axillary soft tissue background,based on the visual interpretation of at least two experienced nuclear medicine physicians,was considered a positive Tc-MIBI scan result (Figs 1and 2).Immunohistochemical staining.Formalin-fixed paraffin sections (5m m)were deparaffinized in an oven at 508C for 40min,then hydrated with varyingconcentrations of ethanol±water dilutions.For MRP immunohistochemical staining,antigen retrieval was performed by treatment in citrate buffer in a 700W microwave oven for 5min.Endogenous peroxidase was blocked by 3%hydrogen peroxide for 15min,followed by 5min in phosphate-buffered saline (PBS).The sections were incubated over-night in a moist chamber at 48C with primary antibody MRP QCRL-1(10m g/ml,Signet Laboratories,Dedham,MA,USA)at 1:100concentration.For P-gp immunohis-tochemical staining,endogenous peroxidase was blocked by 3%hydrogen peroxide for 15min.Antigen retrieval was performed by treatment with enzyme digestion in 0´1%trypsin in PBS for 5min at room temperature and inhibited with 10%skimmed milk in PBS for 5min.The sections were incubated for 2h in a moist chamber at 378C with primary antibody JSB-1(50m g/ml,Boehringer Mannheim Biochemica,Germany)at 1:50concentration.After three 5min washes in PBS,detection of the primary antibody was performed with a link antibody accordingto the manufacturer's instructions (DAKO LSAB_2System,Peroxidase,Dako Corporation,Carpinteria,CA,USA)(Niehans et al ,1992;Marie,1995;Yamaguchi et al ,1995;Kostakoglu et al ,1998;Webb et al ,1998).P-gp and MRP expressions were interpreted by an experienced pathologist blind to clinical outcome as follows:negati-ve less than 10%,positive 10%or more stained tumour cells (Figs 3and 4).Chemotherapy response evaluation.In this study ,the chemotherapy response of each patient was evaluated for the first 1±2years after completion of treatment using clinical and radiological methods such as plain chest X-ray ,chest computerized tomography (CT)or magnetic resonance imaging (MRI),as well as head and neck CT or MRI,accordingto the followingscale:(1)Complete response no evidence of disease,(2)Partial respon-se at least 50%decrease in the sum of the products of the maximum perpendicular diameters of all measurable lesions,no evidence of progression in any lesion and no new lesions,(3)No response less than 25%increase in the sum of the products of the maximum perpendicular diameters of all measurable lesions,no evidence of progression in any lesion and no new lesions,and (4)Progressive disease at least 25%increase in the sum of the products of the maximum perpendicular diameters of all measurable lesions and/or the appearance of new lesions.We defined complete and partial responses as good response,while no response and progressive disease were defined as poor response.Statistical analyses.The T/B ratio was expressed as meanT a b l e I I .D i s t r i b u t i o n s o f T c -M I B I s c a n r e s u l t s ,P -g p e x p r e s s i o n ,M R P e x p r e s s i o n ,a g e ,t u m o u r t y p e ,t u m o u r s t a g e a n d B s y m p t o m s r e l a t e d t o c h e m o t h e r a p y r e s p o n s e r e s u l t s .I m m u n o h i s t o c h e m i c a l s t a i n i n gC h e m o t h e r a p y r e s p o n s e T c -M I B I s c a n r e s u l t s P -g p e x p r e s s i o nM R P e x p r e s s i o nA g e T y p e S t a g eB s y m p t o m sr e s u l t s P o s N e g P -v a l u eP o s N e g P -v a l u e P o s N e g P -v a l u e#40y e a r s .40y e a r s P -v a l u e H D N H L P -v a l u e I ±I I I I I ±I V P -v a l u e Y e s N o P -v a l u e G o o d1500150155107851069P o o r 010,0´0164,0´0146,0´01460´73460´74370´86640´33q 2001Blackwell Science Ltd,British Journal of Haematology 113:369±374Tc-MIBI Predicts Chemotherapy Response in HD and NHL371^standard deviation (SD).A Mann±Whitney U -test was used to evaluate the difference in T/B ratios between patients with a good versus a poor response.The difference in incidence of good and poor response was evaluated for eight possible prognosis factors:positive versus negative Tc-MIBI scan results,positive versus negative P-gp expression,positive versus negative MRP expression,HD versus NHL,stage I±II versus stage III±IV ,age .40years versus #40years,and with B symptoms versus without B symptoms (night sweats,fever .388C for three consecutive days and unexplained weight loss of .10%body weight)(Barr et al ,1997;Neal &Hoskin,1997).A Chi-square test was used to determine if the frequency of good and poor response was the same for each pair.If the P -value was ,0´05,the difference was considered significant.RESULTSDetailed patient data are shown in Table I.The mean T/B ratio of the 15patients with a good response (3´3^0´6)was significantly (P ,0´01)higher than that of the 10patients with a poor response (1´2^0´1).All 15(100%)patients with a good response had positive Tc-MIBI scan results and negative P-gp and MRP expression.All 10(100%)patients with a poor response had negativeTc-MIBI scan results,six (60%)of whom had positive P-gp expression while the other four (40%)had positive MRP expression.Tc-MIBI scan results,P-gp expression and MRP expression all showed significant differences in the rate of good and poor responses.However,no significant difference in the incidences of good and poor responses was found for lymphoma type,stage,age or B symptoms (Table II).DISCUSSIONOur review of previous literature found only one paper that reported that 17ML children with positive Tc-MIBI scan results and a higher mean T/B ratio had a better response to chemotherapy than seven ML children with negative Tc-MIBI scan results and a lower mean T/B ratio (Kapucu et al ,1997).Our results support their findings.However,their study did not examine the relationship between other prognosis factors,P-gp or MRP expression,and chemo-therapy response.The mechanism of chemotherapy resistance in ML is thought to involve expression of P-gp and MRP (Niehans et al ,1992;Yamaguchi et al ,1995;Zhan et al ,1997;Webb et al ,1998).The retention of Tc-MIBI in tumour cells depends on P-gp and MRP expression and they function as ATP-dependent efflux pumps for manychemotherapyFig 1.Case no.25had a goodchemotherapy response result.(A)Tc-MIBI scan reveals significant tracer uptake in the right neck and the result is positive (T/B ratio 4´5)(arrow).(B)Neck computerized tomography shows a mass in the same area(arrow).Fig 2.Case no.4had a poorchemotherapy response result.(A)Tc-MIBI scan reveals no definitely abnormal tracer MIBI uptake in the chest and neck and the result is negative (T/B ratio 1´1).(B)Gallium-67citrate scan shows multiple abnormal tracer uptake in the chest and neck (arrows).372 C.-H.Kao et alq 2001Blackwell Science Ltd,British Journal of Haematology 113:369±374agents (Hendrikse et al ,1998,1999;Vergote et al ,1998;Sun et al ,2000).Therefore,in this study we used the Tc-MIBI scan to predict the response of MLs to chemother-apy .We found that positive Tc-MIBI scan results accurately predicted all good chemotherapy results,which were also related to negative P-gp and MRP expression.Moreover,negative Tc-MIBI scan results accurately predicted poor chemotherapy results in all patients with positive P-gp or MRP expression (Table I).In our previous studies,only early chest images performed 10min after intravenous injection of Tc-MIBI proved to be accurate enough to predict chemotherapy response in lung and breast cancer (Kao et al ,1998,2000;Vergote et al ,1998).Therefore,in this study ,we did not consider it necessary to perform delayed chest imaging to calculate the tumour washout rate or retention index of Tc-MIBI to predict the chemotherapy response.mRNA expression is not fully corrected with P-gp or MRP expression in the tumour cell membrane,Tc-MIBI tumour uptake is directly based onthe P-gp or MRP expression in the tumour cell membrane,and it was impossible to extract mRNA from the formalin-fixed paraffin sections of biopsy specimens (Wang et al ,1997;Dexter et al ,1998;Yokogami et al ,1998).Therefore,we directly detected P-gp or MRP expression using immunostainingto correct with Tc-MIBI tumour uptake (T/B ratio)in our study .Based on our findings,we conclude that Tc-MIBI scan results can represent P-gp and MRP expression for predict-ingthe chemotherapy response in ML patients.However,further studies includinglarg er case numbers and patients who have relapsed followingchemotherapy are necessary to confirm our findings.ACKNOWLEDGMENTSThis work was supported in part by grants from Taichung Veterans General Hospital (TCVGH-896708D)andNationalFig 3.Immunohistochemistry performed on sections of malignant lymphomaspecimens from two different groups reveals (A)negative and (B)positive P-gp expression (Â500).Fig 4.Immunohistochemistry performed on sections of malignant lymphomaspecimens from two different groups reveals (A)negative and (B)positive MRP expression (Â1000).q 2001Blackwell Science Ltd,British Journal of Haematology 113:369±374Tc-MIBI Predicts Chemotherapy Response in HD and NHL 373Science Council(NSC89±2314-B-075A-015,89±2320-B-075A-001,88±2314-B-075A-006),Taiwan.REFERENCESBarr,L.,Cowan,R.&Nicolson,M.(1997)Haematological Malignancies.In:Oncology(ed.by L.Barr,R.Cowan&M. Nicolson),p.150.Churchill Livingstone,New York.Chiu,M.L.,Kronauge,J.F.&Piwnica-Worms,D.(1990)Effect of mitochondrial and plasma membrane potentials on accumula-tion of hexakis(2-methoxyisobutylisonitrile)technetium(I)in cultured mouse fibroblast.Journal of Nuclear Medicine,31,1646±1653.Dexter,D.W.,Reddy,R.K.,Geles,K.G.,Bansal,S.,Myint,M.A., Rogakto,A.,Leighton,J.C.&Goldstein,L.J.(1998)Quantitative reverse transcriptase-polymerase chain reaction measured expression of MDR1and MRP in primary breast carcinoma. Clinical Cancer Research,4,1533±1542.Hassan,I.M.,Sahweil,A.,Constantinides,C.,Mahmoud,A.,Nair, M.,Omar,Y.T.&Abdel-Dayem,H.M.(1989)Uptake and kinetics of Tc-99m hexakis2-methoxy isobutyl isonitrile in benign and malignant lesions in the lungs.Clinical Nuclear Medicine,14, 333±340.Hendrikse,N.H.,Franssen,E.J.,van-der-Graaf,W.T.,Meijer,C., Piers, D.A.,Vaalburg,W.&de-Vries, E.G.(1998)99mTc-sestamibi is a substrate for P-glycoprotein and the multidrug resistance-associated protein.British Journal of Cancer,77,353±358.Hendrikse,N.H.,Franssen,E.J.,van-der-Graaf,W.T.,Vaalburg,W.& de-Vries,E.G.(1999)Visualization of multidrugresistance in vivo.European Journal of Nuclear Medicine,26,283±293. Jaffe,E.S.(1998)Histopathology of the non-Hodgkin's lymphomas and Hodgkin's disease.In:The Lymphomas(ed.by G.P.Canellos, T.A.Lister&J.L.Sklar),p.77.Saunders,Philadelphia.Kao, C.H.,ChangLai,S.P.,Chieng,P.U.&Yen,T.C.(1998) Technetium-99m methoxyisobutylisonitrile chest imaging of small cell lungcarcinoma.Relationship to patient prog nosis and chemotherapy response±a preliminary report.Cancer,83, 64±68.Kao,C.H.,Hsieh,J.F.,Tsai,S.C.,Ho,Y.J.&Lee,J.K.(2000)Quickly predictingchemotherapy response to paclitaxel-based therapy in non-small cell lungcancer by early technetium-99m methox-yisobutylisonitrile chest single-photon-emission computed tomo-graphy.Clinical Cancer Research,6,820±824.Kapucu,L.O.,Akyuz, C.,Vural,G.,Oguz, A.,Atasever,T., Buyukpamukcu,M.&Unlu,M.(1997)Evaluation of therapy response in children with untreated malignant lymphomas using technetium-99m-sestamibi.Journal of Nuclear Medicine,38,243±247.Kostakoglu,L.,Guc,D.,Canpinar,H.,Kars,A.,Alper,E.,Kiratli,P., Hayran,M.,Gunduz,U.&Kansu,E.(1998)P-glycoproteinexpression by technetium-99m-MIBI scintigraphy in hematologic malignancy.Journal of Nuclear Medicine,39,1191±1197. Marie,J.P.(1995)P-glycoprotien in adult hematologic malignan-cies.Hematology Oncology Clinics of North America,9,239±249. Neal,A.J.&Hoskin,P.J.(1997)Lymphoma.In:Clinical Oncology: Basic Principle and Practice(ed.by A.J.Neal&P.J.Hoskin),p.162. Arnold,London.Niehans,G.A.,Jaszca,W.,Brunetto,V.,Perri,R.T.,Gajl-Peczalska, K.,Wick,M.R.,Tsuruo,T.&Bloomfield,C.D.(1992)Immuno-histochemical identification of P-glycoprotein in previously untreated,diffuse large cell in immunoblastic lymphomas.Cancer Research,52,3768±3775.Shih,W.J.,Rastogi,A.,Stipp,V.,Magoun,S.&Coupal,J.(1998) Functional retention of Tc-99m MIBI in mediastinal lymphomas as a predictor of chemotherapeutic response demonstrated by consecutive thoracic SPECT imaging.Clinical Nuclear Medicine, 23,505±508.Sun,S.S.,Hsieh,J.F.,Tsai,S.C.,Ho,Y.J.,Lee,J.K.&Kao,C.H.(2000) Expression of mediated p-glycoprotein multidrug resistance related to Tc-99m MIBI scintimamography results.Cancer Letters, 153,95±100.Vergote,J.,Moretti,J.L.,de-Vries,E.G.&Garnier-Suillerot,A.(1998) Comparison of the kinetics of active efflux of99mTc-MIBI in cells with P-glycoprotein-mediated and multidrug-resistance protein-associated multidrug-resistance phenotypes.European Journal of Biochemistry,252,140±146.Wang,C.S.,LaRue,H.,Fortin,A.,Gariepy,G.&Tetu,B.(1997) mdr1mRNA expression by RT-PCR in patients with primary breast cancer submitted to neoadjuvant therapy.Breast Cancer Research and Treatment,45,63±74.Webb,M.,Brun,M.,McNiven,M.,Le-Couteur,D.&Craft,P.(1998) MDR1and MRP expression in chronic B-cell lymphoproliferative disorders.British Journal of Haematology,102,710±717. Wilson,W.H.&Chabner,B.A.(1998)Principles of chemotherapy for lymphomas.In:The Lymphomas(ed.by G.P.Canellos,T.A. Lister&J.L.Sklar),p.235.Saunders,Philadelphia. Yamaguchi,M.,Kita,K.,Miwa,H.,Nishii,K.,Oka,K.,Ohno,T., Shirakawa,S.&Fukumoto,M.(1995)Frequent expression of P-glycoprotein/MDR1by nasal T-cell lymphoma cells.Cancer,76, 2351±2356.Yokogami,K.,Kawano,H.,Moriyama,T.,Uehara,H.,Sameshima,T., Oku,T.,Goya,T.,Wakisaka,S.,Nagamachi,S.,Jinnouchi,S.& Tamura,S.(1998)Application of SPET usingtechnetium-99m sestamibi in brain tumours and comparison with expression of the MDR-1gene:is it possible to predict the response to chemotherapy in patients with gliomas by means of99mTc-sestamibi SPET? European Journal of Nuclear Medicine,25,401±409.Zhan,Z.,Sandor,V.A.,Gamelin,E.,Regis,J.,Dickstein,B.,Wilson, W.,Fojo,A.T.&Bates,S.E.(1997)Expression of the multidrug resistance-associated protein gene in refractory lymphoma: quantitation by a validated polymerase chain reaction assay. Blood,89,3795±3800.374 C.-H.Kao et alq2001Blackwell Science Ltd,British Journal of Haematology113:369±374。

AbstractThe importance of an accurate branch prediction mechanism has been well documented. Since the introduction of gshare [1] and the observation that aliasing in the PHT is a major factor in reducing prediction accuracy [2,3,4,5], several schemes have been proposed to reduce aliasing in the PHT [6, 7, 8, 9]. All these schemes are aimed at maximizing the prediction accuracy with the fewest resources. In this paper we introduce Yet Another Global Scheme (YAGS) — a new scheme to reduce the aliasing in the PHT — that combines the strong points of several previous schemes. YAGS introduces tags into the PHT that allows it to be reduced without sacrificing key branch outcome information. The size reduction more than offsets the cost of the tags. Our experimental results show that YAGS gives better prediction accuracy for the SPEC95 benchmark suite than several leading prediction schemes, for the same cost. It also performs better than the other schemes in the presence of a context switch. Finally, YAGS displays good results for the go benchmark, which is of special interest since it has a large number of static branches and reflects situations where aliasing in the PHT can be a problem.1.IntroductionTo realize the performance potential of today’s widely-issued, deeply pipelined superscalar processors, a good branch prediction mechanism is essential. The introduction of two level adaptive schemes was an important step in this direction [10]. They are able to achieve predicted levels of 90% or more. Of the two level schemes, global history schemes appear to work best for integer code [11]. This, in part, is due to the large number of if-else instructions in integer programs. Sequences of if-else are often highly correlated.The main problem which reduces the prediction rate in the global schemes is aliasing between two indices (an index is typically formed from history and address bits) that map to the same entry in the Pattern History Table (PHT). Since the information stored in the PHT entries is either “taken”or “not taken,” two aliased whose corresponding information is the same will not result in mispredictions. We define this situation as neutral aliasing. On the other hand, two aliased indices with different information might interfere with each other and result in a misprediction. We define this situation as destructive aliasing. This paper is organized as follows: the next section looks at previous schemes to reduce aliasing and highlights their strong and weak points. In the third section we introduce Yet Another Global Scheme (YAGS), which combines the strengths of the previous schemes to eliminate aliasing. The fourth section presents the results of our performance studies. The fifth section offers concluding remarks and proposes future directions for this research.2.Previous WorkGshare. The first scheme to address the aliasing problem in two level adaptive branch predictors was gshare [1] (figure 1). The observation that the usage of the PHT entries is not uniform when indexed by concatenations of the global history and the branch address, led to idea of using the “exclusive or” function instead of concatenation to more evenly use the entries in the PHT. Detailed studies have shown it yields little, if any, advantage [4].The Agree Predictor. The agree predictor (figure 2) assigns a biasing bit to each branch in the Branch Target Buffer (BTB) according to the branch direction just before it is written into the BTB [7]. The PHT information is then changed from “taken” or “not taken” to “agree” or “disagree” with the prediction of the biasing bit. The idea behind the agree predictor is that most branches are highly biased to be either taken or not taken and the hope is that the first time a branch is introduced into the BTB it will exhibit its biased behavior. If this is the case, most entries in the PHT will be “agreeing,” so if aliasing does occur it will more likely be neutral aliasing, which will not result in a misprediction.It is one of the first two level scheme to take advantage branches’ biased behavior to reduce destructive aliasing by replacing it with neutral aliasing. It considerably reduces destructive aliasing. However, there is no guarantee that the first time a branch is introduced to the BTB its behaviorThe Y AGS Branch Prediction Scheme A. N. Eden and T. Mudge, {ane, tnm}@Dept. EECS, University of Michigan, Ann ArborFigure 1. GshareFigure 4.SkewFigure 2.AgreeFigure 3.Bi-ModeFigure 6.YAGS Figure 5. Filterwill correspond to its bias. When such cases occur, the biasing bit will stay the same until the branch is replaced in the BTB by a different branch. Meanwhile, it will pollute the PHT with “disagree” information. There is still aliasing between instances of a branch which do not comply with the bias and instances which do comply with the bias. Furthermore, when a branch is not in the BTB, no prediction is available.The Bi-Mode Predictor. The bi-mode predictor (figure 3) tries to replace destructive aliasing with neutral aliasing in a different manner [8]. It splits the PHT table into even parts. One of the parts is the choice PHT, which is just a bimodal predictor (an array of two bit saturating counters) with a slight change in the updating procedure. The other two parts are direction PHTs; one is a “taken” direction PHT and the other is a “not taken” direction PHT. The direction PHTs are indexed by the branch address xored with the global history. When a branch is present, its address points to the choice PHT entry which in turn chooses between the “taken” direction PHT and the “not taken” direction PHT. The prediction of the direction PHT chosen by the choice PHT serves as the prediction. Only the direction PHT chosen by the choice PHT is updated. The choice PHT is normally updated too, but not if it gives a prediction contradicting the branch outcome and the direction PHT chosen gives the correct prediction.As a result of this scheme, branches which are biased to be taken will have their predictions in the “taken” direction PHT, and branches which are biased not to be taken will have their predictions in the “not taken” direction PHT. So at any given time most of the information stored in the “taken” direction PHT entries is “taken” and any aliasing is more likely not to be destructive. The same phenomenon happens in the “not taken” direction PHT. The choice PHT serves to dynamically choose the branches’ biases.In contrast to the agree predictor, if the bias is incorrectly chosen the first time the branch is introduced to the BTB, it is not bound to stay that way while the branch is in the BTB and as a result pollute the direction PHTs. However, the choice PHT takes a third of all PHT resources just to dynamically determine the bias. It also does not solve the aliasing problem between instances of a branch which do not agree with the bias and instances which do.The Skewed Branch Predictor. The skewed branch predictor (figure 4) is based on the observation that most aliasing occurs not because the size of the PHT is too small, but because of a lack of associativity in the PHT (the major contributor to aliasing is conflict aliasing and not capacity aliasing). The best way to deal with conflict aliasing is to make the PHT set-associative, but this requires tags and is not cost-effective. Instead, the skewed predictor emulates associativity using a special skewing function [6].The skewed branch predictor splits the PHT into three even banks and hashes each index to a 2-bit saturating counter in each bank using a unique hashing function per bank (f1, f2 and f3). The prediction is made according to a majority vote among the three banks. If the prediction is wrong all three banks are updated. If the prediction is correct, only the banks that made a correct prediction will be updated (partial updating).The skewing function should have inter-bank dispersion. This is needed to make sure that if a branch is aliased in one bank it will not be aliased in the other two banks, so the majority vote will produce an unaliased prediction. The reasoning behind partial updating is that if a bank gives a misprediction while the other two give correct predictions, the bank with the misprediction probably holds information which belongs to a different branch. In order to maintain the accuracy of the other branch, this bank is not updated.The skewed branch predictor tries to eliminate all aliasing instances and therefore all destructive aliasing. Unlike the other methods, it tries to eliminate destructive aliasing between branch instances which obey the bias and those which do not. However, to achieve this, the skewed predictor stores each branch outcome in two or three banks. This redundancy of 1/3 to 2/3 of the PHT size creates capacity aliasing but eliminates much more conflict aliasing, resulting in a lower misprediction rate. However, it is slow to warm-up on context switches.The Filter Mechanism. Reducing the amount of redundant information stored in the PHT is the main point of this scheme [9]. The idea is that highly biased branches can be predicted with high accuracy with just one bit. The filtering of such branches out of the PHT is done by a bias bit and a saturating counter (figure 5) for each BTB entry. When a branch is introduced to the BTB the bias bit is set to the direction of the branch when it is resolved and the counter is initialized. When every branch instance is resolved, if the direction of the branch is the same as the bias bit the counter is incremented. If not, the counter is zeroed and the bias bit is toggled. A branch is predicted using the PHT if the counter is not saturated. If the counter is saturated, it means that the branch is highly biased in the direction indicated by the bias bit, and therefore the bias bit is used as a prediction. In this case, when the counter is saturated, the PHT is not updated with the branch outcome— the saturated counter filters this information from the PHT.The size of the counter has to be tuned to the size of the PHT. If the PHT size is large, the amount of filtering needed is small, and therefore the size of the counters should be large.When a branch is first introduced in the BTB, the counter is initialized. It was found that it is best to initialize the counter to its maximum value so the filtering mechanism will start working immediately. If the branch is not highly biased, the bias bit will flip fairly quickly and the counter will be zeroed. On the other hand, if the counter is initialized to zero and the branch is highly biased, it will take time for the filtering mechanism to start working and the PHT will be polluted in the meantime.The filter mechanism tries to eliminate all aliasing instances, neutral and destructive, by considerably reducing the amount of information stored in the PHT. However, it mispredicts instances of highly biased branches which do not comply with the bias.3.YAGSThe brief overview above, of earlier proposals to reduce aliasing in global schemes, suggests that splitting the PHT into two branch streams corresponding to biases of “taken”and “not taken,” as is done in the agree and bi-mode predictors, is a good idea. However, as in the skewed branch predictor, we do not want to neglect aliasing between biased branches and their instances which do not comply with the bias. Finally, it will be beneficial if we can reduce the amount of unnecessary information in the PHT, as in the filter mechanism, but not at the expense of mispredicting some of the branch instances.The motivation behind YAGS is the observation that for each branch we need to store its bias and the instances when it does not agree with it (figure 6). If we employ a bimodal predictor to store the bias, as the choice predictor does in the bi-mode scheme, than all we need to store in the direction PHTs are the instances when the branch does not comply with its bias. This reduces the amount of information stored in the direction PHTs, and therefore the direction PHTs can be smaller than the choice PHT. To identify those instances in the direction PHTs we add small tags (6-8 bits) to each entry, referring to them now as direction caches. These tags store the least significant bits of the branch address and they virtually eliminate aliasing between two consecutive branches.When a branch occurs in the instruction stream, the choice PHT is accessed. If the choice PHT indicated “taken,” the “not taken” cache is accessed to check if it is a special case where the prediction does not agree with the bias. If there is a miss in the “not taken” cache, the choice PHT is used as a prediction. If there is a hit in the “not taken” cache it supplies the prediction. A similar set of actions is taken if the choice PHT indicates “not taken,” but this time the check is done in the “taken” cache. The choice PHT is addressed and updated as in the bi-mode choice PHT. The “not taken” cache is updated if a prediction from it was used. It is also updated if the choice PHT is indicating “taken” and the branch outcome was “not taken.” The same happens with the “taken” cache.We still need to take care of aliasing for instances of a branch which do not agree with the branch’s bias. After making the introduction of tags cost-effective, the natural solution for the aliasing problem is to add associativity (in [6] it was showed that the vast majority of aliasing in the PHT is conflict aliasing).When making the direction caches set-associative, there is some extra cost for keeping a correct replacement policy. For example, in a two-way set-associative cache, one bit for every two entries will suffice to keep track of which entry was replaced last. We use an LRU replacement policy with one exception: an entry in the “taken” cache which indicates “not taken” will be replaced first to avoid redundant information. If an entry in the “taken” cache indicates “not taken,” this information is already in the choice PHT and therefore is redundant and can be replaced.4.Performance Studies4.1MethodologyThe experimental data presented in this paper were collected using SPEC95 benchmark traces. The benchmarks were compiled on the SunOS operating system using the gcc compiler. The traces were run to completion. In order to simulate a context switch for the context switch study only, a new trace file was created by interleaving all eight SPEC95 benchmarks every 60,000 instructions until one of the files runs out of instructions The number was chosen not to reflect a real context switching interval, which would be much less frequent, but to emphasize the effect of context switching on the various predictors. The size of the YAGS predictors includes the tags of the direction caches. In the case where YAGS is set-associative the LRU and history bits are also added.4.2ResultsFigure 7 shows the misprediction rate for gshare, theskewed predictor, the bi-mode predictor and YAGS with direct mapped direction caches. As can be seen, YAGS performs better than the other schemes, particularly for small sizes. However, as the size of the PHT increases,YAGS’s advantage over the other schemes decreases. This is to be expected, because, the aliasing problem in the PHT decreases with size and therefore the performance of all the schemes converges.One of the pitfalls of the SPEC95 benchmark suite is that most traces have a small static branch signature [8]. For example, the compress benchmark has only 482 static branches. These branches are executed over and over again throughout the course of the program. However, the small static branch signature implies each branch is more likely to have a unique entry in the PHT for each history instance,resulting in a very small amount of aliasing in the PHT.This yields optimistic figures for many branch predictions schemes.The gcc and go benchmarks are thus of special interest because of their large static and dynamic branch signatures.As can be seen in figures 8 and 9, YAGS also outperforms the other schemes for the go and gcc benchmarks. The go benchmark is particularly interesting because it suffers the most from destructive aliasing. The gshare scheme for small predictors achieves a 69% correct prediction rate for go. For about the same amount of resources (0.5KB)YAGS achieves a 77% correct prediction rate. The bi-mode, which is designed to reduce destructive aliasing,achieves only 73% correct prediction rate.4.3Set Associativity in the Direction Caches When increasing the size of the PHT, we increase the size of the history register to better exploit correlation between branches. However, if the direction caches are made two way set-associative, not all the bits in the history register are used to index into the direction caches. In fact, one less bit is used than if the direction caches were direct-mapped.This loss of correlation has a negative effect on the prediction rate. In the present YAGS scheme, the amount0.860.880.900.920.940.960.1110100predictor size in K-bytesprediction rateyags6bimode skew gshareFigure 7.Prediction rates for four schemes including YAGS6 (6 bits in the tags).Figure 8. Predicting GO.0.600.650.700.750.800.850.900.950.1110100predictor size in K-bytesprediction rateyags6bimode gshare0.600.650.700.750.800.850.900.951.000.1110100predictor size in K-bytesp r e d i c t i o n r a t eyags6bimode gshareFigure 9. Predicting GCC.of remaining aliasing is so little that the advantage gained by making the direction PHT set-associative is offset by the loss of correlation. In order to maintain the same level of correlation, one bit of history is used as a tag in addition to the usual tag.Figure 10 shows the prediction rate of a 6 bit tag YAGS vs.the same predictor with a 2 way set associative cache. The extra bits that are used by the two way set-associative are the LRU bits and the extra tag bit which is taken from the history register. As expected, the two way set-associative version is able to reduce the aliasing in the direction caches. The small difference between the schemes is due to lack of aliasing in the direction caches.4.4 Context SwitchingFuture high-performance microprocessors will use larger branch prediction schemes — a trend that is very likely to continue in the near future. Ideally, the prediction rate should improve in proportion to the amount of hardware put into the scheme. However, a pitfall of large predictors is the time it takes them to reach peak performance from a cold start. In the presence of intensive context switching the warm-up time of the branch prediction scheme can have a significant influence on the misprediction rate.Furthermore, some complex schemes might end up achieving less accurate predictions than a less sophisticated scheme, due to long warm-up times. It was shown that a hybrid predictor (first proposed in [1]) composed of gshare and the bimodal predictor has good performance in thepresence of a context switch [9]. This is due to a short warm up time of the bimodal component. Each branch is mapped to only one entry in the PHT of the bimodal scheme. Therefore, it takes only few executions of a branch for its respective entry to reflect the information stored the branch. On the other hand, the gshare scheme has to execute a branch several times for each history instance for it to warm up. The potentially large number of history instances (i.e., 2history length ) will result in a very long warm-up time and that in turn will cause a degradation in performance in the presence of context switches. The same phenomenon is observed in the skewed predictor.However, one would expect the bi-mode predictor and YAGS to be more tolerant of context switches. Most of the information in the “not taken” direction PHT of the bi-mode predictor is “not taken.” Once the choice PHT points to the “not taken” direction PHT the probability of a “taken” prediction is very small. Thus only a few executions of each branch are needed to warm up the choice PHT (it is essentially the bimodal predictor). After that, it will take more executions to warm up the branch’s history instances which do not comply with the branch bias. But for the most part, the predictor will perform as well as the bimodal. The same phenomenon occurs in YAGS. This time it is due to the tags. There is a low probability that the tags will match after a context switch.Therefore, until some tags match, the choice PHT (which is, in fact, the bimodal) will serve as the predictor. In a sense, YAGS and the bi-mode predictors are hybrid predictors which combine the gshare scheme with the simple bimodal predictor. In the presence of a context switch, they should exhibit the short warm up time of the bimodal predictor. (Similar behavior is seen in the agree predictor.)Figure 11 shows the performance of the schemes tested in the presence of context switches. As expected, YAGS and the bi-mode predictor perform much better than gshare and the skew predictor because of their short warm-up times.The differences between the performance of the different methods is much more pronounced in the presence of context switches. The gshare scheme would converge with the others only if the PHT were large enough to accommodate most of the branch instances from all the SPEC95 benchmarks. Without context switches, the schemes would converge if the gshare PHT were big enough to accommodate the benchmark with the largest branch signature.The gshare scheme does not perform as well as the others.This is because of its long warm-up time, as discussed above.0.900.910.920.930.940.950.960.1110100predictor size in K-bytesprediction rateyags6-2way yags6Figure 10. 6 bit tags vs. 2-way set associative.The difference between the performance of YAGS and that of the bi-mode scheme is very small. Only for very small predictor size is the difference significant. It might be that YAGS would do better in the presence of a context switch if a larger tag size were used. 4.5Design SpaceThe YAGS version shown so far has a 6 bit tag and the direction caches are each half the size of the choice PHT.This is somewhat arbitrary. How big do the tags need to be to identify the branch in most cases? Figure 12 shows the prediction rate as a function of the tag size for SPEC95.The size of the choice PHT is 0.25KB (1024 entries), each direction cache has 512 entries and its size varies according to the size of the tag. According to figure 12, there is no reason to increase the size of the tag beyond 8 bits —prediction improvement is almost zero. There may be no reason to increase the size of the tag from 6 to 8 bits since the prediction improvement is very small and may not justify the increase in the predictor size. Figure 13 shows the prediction rate as a function of tag size for the go benchmark only. The difference between the prediction rate for a 6 bit tag and 8 bit tag is more noticeable for the go benchmark than for SPEC95 in general. As mentioned before, the go benchmark has a large branch signature and can benefit from an increase in tag size.Figures 14 and 15 shown the prediction rate vs. predictor size for the SPEC95 and go benchmark respectively. On average for SPEC95, increasing the tag from 6 bits to 8 bitsdoes not result in better predictions (figure 14). On the other hand, it does improve the prediction rate for the go benchmark (figure 15). The prediction rate improvement is minimal and almost negligible. Even increasing the size of the tag to 32 bits does not result in a better prediction rate,but it increases the size of the predictor considerably. By reducing the amount of unnecessary information stored in the direction caches, we are able to reduce the number of entries in the direction caches and to make the introduction of tags cost-effective. Figure 16 gives some insight as to0.880.890.900.910.920.930.940.950.1110100predictor size in K-bytesprediction rateyags6bimode skew gshareFigure 11. Predicting in the presenceof context switches.0.9370.9380.9390.9400.9410.9420.9430.94451015tag size in bitsprediction rateFigure 12. Tag sizes for SPEC95.0.90820.90840.90860.90880.90900.90920.90940.90960.9098051015tag size in bitsprediction rateFigure 13. Tag sizes for GO.how small the direction caches can be with respect to the choice PHT. Figure 16 shows the prediction rate vs.predictor size for three versions of YAGS. The direction caches in the first version are each half the size of the choice PHT. In the second version, they are one quarter the size of the choice PHT, and in the third are one eighth of the size. All versions use a six bit tagFigure 16 shows that for small predictor sizes the 0.125version is best, while for large predictor sizes, the 0.5version is best. For small predictor sizes, most of the resources should be allocated to the choice PHT, ensuring that the predictor will predict at least as well as a simplebimodal predictor. When the amount of resources increases, there is much less aliasing in the choice PHT and resources can be freed to handle the cases where a branch does not agree with its bias (i.e. larger direction caches).Thus the size of the direction caches should be tuned according to the overall size of the predictor.5. SummaryWe introduced YAGS, a two level global branch prediction scheme which tries to eliminate aliasing in the PHT by combining the advantages of previous schemes. YAGS performs as well as all other schemes tested. In many cases it was considerably better. YAGS and the bi-mode predictors perform well in context switches.Some work was done to investigate the design space.Increasing the size of the tags only improves performance up to a point. After that, increasing the tag size will degrade performance, and the marginally better prediction rate does not justify the resources taken up by the larger tag. We have found that the size of the direction caches should be tuned to the size of the predictor.We believe the potential of YAGS is greater than what we were able to demonstrate in this paper. In all experiments conducted for this paper, the size of the history register was dictated by the amount of resources allocated for the predictor. For example, in a 1KB gshare, there are 4KB entries and therefore the size the history register was forced to be 12 bits. The closest bi-mode predictor in size which was tested is a 0.75KB predictor, from which only 0.25KB (1K entries) were dedicated to each direction PHT. This forced this instance of the bi-mode predictor to use only a 10 bit history register. As a result, the bi-mode although reducing the aliasing in the PHT, has reduced correlation0.890.900.910.920.930.940.950.960.1110100predictor size in K-bytesprediction rateyags8yags6Figure 14. Predictor size for SPEC95.0.700.750.800.850.900.1110100predictor size in K-bytesprediction rateyags8yags6Figure 15. Predictor size for GO.0.890.900.910.920.930.940.950.960.1110100predictor size in K-bytesprediction rate0.50.250.125Figure 16. Direction cache size.information for use in the prediction, compared to a similar sized gshare. This phenomena holds true for the YAGS predictor as well, since the size of the direction caches is reduced even further than in the bi-mode predictor and as a result the size the history register (and therefore the correlation information) was reduced. An example is the 1.25KB YAGS where 0.25KB are dedicated to the choice PHT. Each direction cache takes 0.5KB and has 64 entries, i.e., the history register is only 6 bits.In figure 16, whenever the size of the direction caches was decreased by half, the size of the history register was decreased by one bit and therefore correlation information was lost. A better experiment would decrease the relative size of the direction caches while adding history bits as tags. Making the direction caches 2 way set associative hardly improved the prediction. This led us to believe that the aliasing problem in the direction PHT was almost completely solved. Therefore, decreasing the size of the direction caches degraded the performance because of the reduction in correlation information, and not necessarily because of increased aliasing.We hypothesize that an improved YAGS would have much smaller direction caches with more history bits in the tags to preserve or increase the correlation information for use in prediction. Of course history bits can be tagged in every predictor scheme but the overhead in YAGS would be significantly smaller than all the other schemes. Finally, the basic idea behind YAGS could be combined with other of the schemes, particularly the filter mechanism. An enhancement that might be tried is add a small cache to capture the instances filtered out of the PHT which do not agree with the bias bit. Acknowledgments. This work was supported in part by DAPRA contract DABT63-97-C-0047. The authors would also like to thank Elly Z. Winner and C.-C. Lee for their help.References[1]S. McFarling. Combining Branch Predictors.Technical Report TN-36, Digital Western Research Laboratory, June 1993.[2] A. Talcott, M. Nemirovsky, and R. Wodd. The Influence ofBranch Prediction Table Interference on Branch Prediction Scheme Performance. Proc. 3rd Ann. Int. Conf. on Parallel Architectures and Compilation Techniques, 1995.[3] C. Young, N. Gloy, and M. Smith. A comparative Analysisof Schemes for Correlated Branch Prediction. Proc. 22nd Ann. Int. Symp. on Computer Architecture, June 1995[4]S. Sechrest, C.-C. Lee, and T. Mudge. Correlation andAliasing in Dynamic Branch Predictors. Proc. 23rd Ann. Int.Symp. on Computer Architecture, May 1996.[5] C. Young, N. Gloy, B. Chen, and M. Smith. An Analysis ofDynamic Branch Prediction Schemes on System Workloads.Proc. 23rd Ann. Int. Symp. on Computer Architecture, May 1996.[6]P. Michaud, A. Seznec, and R. Uhlig. Trading Conflict andCapacity Aliasing in Conditional Branch Predictors. Proc.24th Ann. Int. Symp. on Computer Architecture, May 1997.[7] E. Sprangle, R. Chappell, M. Alsup, and Y. Patt, The AgreePredictor: A Mechanism for Reducing Negative Branch History Interference. Proc. 24th Ann. Int. Symp. on Computer Architecture, May 1997.[8] C.-C. Lee, I.-C. Chen, and T. Mudge. The Bi-Mode BranchPredictor. Proc. MICRO 30, Dec. 1997.[9]P.-Y. Chang, M. Evers, and Y. Patt. Improving BranchPrediction Accuracy by Reducing Pattern History Table Interference. Proc. Int. Conf. on Parallel Architectures and Compilation Techniques, Oct. 1996.[10]T.-Y. Yeh and Y. Patt. Two-level Adaptive BranchPrediction. Proc 24th ACM/IEEE Int. Symp. on Microarchitecture, Nov. 1991.[11]T.-Y. Yeh and Y. Patt. A Comparison of Dynamic BranchPredictors that us Two Level of Branch History. Proc. 20th Ann. Int. Symp. on Computer Architecture, May 1993.。

一．概论Chapter 1. Introducing SLA1.Second language acquisition (SLA)2.Second language (L2)（也可能是第三四五外语） also commonly called a target language (TL)3.Basic questions:1). What exactly does the L2 learner come to know?2). How does the learner acquire this knowledge?3). Why are some learners more successful than others?4.linguistic; psychological; social.Only one (x) Combine (√)Chapter 2. Foundations of SLAⅠ. The world of second languages1.Multi-; bi-; mono- lingualism1)Multilingualism: the ability to use 2 or more languages.(bilingualism: 2 languages; multilingualism: >2)2)Monolingualism: the ability to use only one language.3)Multilingual competence (Vivian Cook, Multicompetence)Refers to: the compound state of a mind with 2 or more grammars.4)Monolingual competence (Vivian Cook, Monocompetence)Refers to: knowledge of only one language.2.People with multicompetence (a unique combination) ≠ 2 monolingualsWorld demographic shows:3.Acquisition4.The number of L1 and L2 speakers of different languages can only beestimated.1)Linguistic information is often not officially collected.2)Answers to questions seeking linguistic information may not bereliable.3) A lack of agreement on definition of terms and on criteria foridentification.Ⅱ. The nature of language learning1.L1 acquisition1). L1 acquisition was completed before you came to school and thedevelopment normally takes place without any conscious effort.2). Complex grammatical patterns continue to develop through the1) Refers to: Humans are born with an innate capacity to learnlanguage.2) Reasons:♦Children began to learn L1 at the same age and in much the same way.♦…master the basic phonological and grammatical operations in L1 at 5/ 6.♦…can understand and create novel utterances; and are not limited to repeating what they have heard; the utterances they produce are often systematically different from those of the adults around them.♦There is a cut-off age for L1 acquisition.♦L1 acquisition is not simply a facet of general intelligence.3)The natural ability, in terms of innate capacity, is that part oflanguage structure is genetically “given” to every human child.3. The role of social experience1) A necessary condition for acquisition: appropriate socialexperience (including L1 input and interaction) is2) Intentional L1 teaching to children is not necessary and may havelittle effect.3) Sources of L1 input and interaction vary for cultural and socialfactors.4) Children get adequate L1 input and interaction→sources has littleeffect on the rate and sequence of phonological and grammatical development.The regional and social varieties (sources) of the input→pronunciationⅢ. L1 vs. L2 learningⅣ. The logical problem of language learning1.Noam Chomsky:1)innate linguistic knowledge must underlie language acquisition2)Universal Grammar2.The theory of Universal Grammar:Reasons:1)Children’s knowledge of language > what could be learned from theinput.2)Constraints and principles cannot be learned.3)Universal patterns of development cannot be explained bylanguage-specific input.Children often say things that adults do not.♦Children use language in accordance with general universal rules of language though they have not developed the cognitive ability to understand these rules. Not learned from deduction or imitation.♦Patterns of children’s language development are not directly determined by the input they receive.。