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February 1st, 2007 - Mathieu Cailler
A Thursday morning.
My drive from Redondo Beach to Compton, where I work as an elementary-school teacher, is fluid: the 110 North, the 91 East, the 710 North, exit onto Rosecrans.
Tires hum on the asphalt. The yellow marking lines on the road, blend into one long strand. I'm alone, moving at 75—my mind about the same speed. Preset radio buttons are being slammed—sports radio, news, rap music. Super Bowl's around the corner; suspects arrested in the UK accused of plotting the holding and eventual beheading of a serving Muslim solider in Iraq; and the rhymes of Nas.
A stale aroma of drive-thru coffee flirts with my Old Spice. Sports radio: Does Peyton Manning have what it takes? News: What kind of punishment will these suspects receive? Nas: Only if I had one gun, one girl and one crib / One God to show me how to do things his son did.
Inside my Acura, the leather stiff and warm. Dreams navigable as these roads, perhaps. But how to get there—no map, no route, no GPS, no "left turn ahead." Want to write. Write anything—poems, essays, stories, novels. Not worth telling anyone about it, though. If I don't say a word—if the dream never makes contact with the air—then I can't fail. Keep it safe. Yes, safe. Yes, five-star crash rating; yes, seatbelts; yes, airbags; yes, anti-lock brakes.
Slow traffic now, a peek in the rearview. This tie doesn't go with this shirt—too many patterns, optical illusion. What will I do at break today? Did I remember Jim Harrison's book… yes, I think it's in the drawer at school. Maybe not though. But I have some Chinua Achebe in the trunk. And some Wolff, some Dickens, too, a book I actually found on the street. A sign maybe? No, just litter. I think I'll read during the lunch hour; hopefully no meetings; no phone calls; no interruptions. Just savor the prose with my peanut-butter-and-jelly sandwich and the hum of the heating vents and the quietude of rows of desks with no kids behind them.
Have I become one of the students whose favorite "subjects" are recess and lunch? Could I be doing this in ten years? No way.
Maybe instead of reading, I'll write something today—yes, that's it, something short; every day work on something short, watch the pages pile up like unpaid bills. Scrawl some ideas during recess, and then a couple hours later, work on those notes during lunch.
Maybe I'll just tell others to dream; tell my students to dream; maybe that's my destiny: to be a dream cheerleader. There's worth in that, right? Of course there is.
But what if the recess-and-lunch-time writing could be the theme of my day, not just the motif? Is there more than just visiting my ambition like some hospital patient, sitting bedside, and holding its hand, hoping for the best, hearing the beepbeepbeep of the various monitors?
In ten years, when my third graders are seniors in high school and getting ready to graduate, will I be moving forward, too? Or will my visions of writing be tingling with numbness, growing comfortable with discomfort?
Mathieu Cailler is a writer of poetry and prose. His work has been widely featured in national and international publications, including the Los Angeles Times and The Saturday Evening Post. A graduate of the Vermont College of Fine Arts, he is the recipient of a Short Story America Prize for Short Fiction and a Shakespeare Award for Poetry. He is the author of Clotheslines (Red Bird), Shhh (ELJ Publications), and Loss Angeles (Short Story America Press), which has been honored by the Hollywood, New York, Best Book, and International Book Awards.
Mathieu urges you to learn more about Alexandria House, a transitional residence for single women and women with children in the process of moving from emergency shelter to permanent housing. They provide hope and hospitality, and the women and children living in Alexandria House benefit from a supportive community and an encouraging environment. Visit alexandriahouse.org.
Loss Angeles
Mathieu Cailler


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As well as some embellies.
spruced those circles up with some stamping.
it is really tough to get it out of the paper in one piece.
But alas its a cool tree.
journaling, place for embellies or to just be.
The title was die cut from QK Emily font.
Its a beautiful font and I should use it more.
Remember back in the day lower case and caps came separate?
I'll hunt them down on ebay.
The title curtesy of my pal - April.
Some ranger mists going on.
Annie and Owen seem to be having.
Love the tags too!! The green is fabulous :) Great work!!


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Cartan connection
In the mathematical field of differential geometry, a Cartan connection is a flexible generalization of the notion of an affine connection. It may also be regarded as a specialization of the general concept of a principal connection, in which the geometry of the principal bundle is tied to the geometry of the base manifold using a solder form. Cartan connections describe the geometry of manifolds modelled on homogeneous spaces.
The theory of Cartan connections was developed by Élie Cartan, as part of (and a way of formulating) his method of moving frames (repère mobile). [Although Cartan only began formalizing this theory in particular cases in the 1920s Harv|Cartan|1926, he made much use of the general idea much earlier. In particular, the high point of his remarkable 1910 paper on Pfaffian systems in five variables is the construction of a Cartan connection modelled on a 5-dimensional homogeneous space for the exceptional Lie group G2, which he an Engels had discovered independently in 1894.] It operates with differential forms and so is computational in character. The main idea is to develop a suitable notion of the connection forms and curvature using moving frames adapted to the particular geometrical problem at hand. For instance, in relativity or Riemannian geometry, orthonormal frames are used to obtain a description of the Levi-Civita connection as a Cartan connection. For Lie groups, Maurer–Cartan frames are used to view the Maurer–Cartan form of the group as a Cartan connection.
Cartan reformulated the differential geometry of (pseudo) Riemannian geometry, as well as the differential geometry of manifolds equipped with some non-metric structure, including Lie groups and homogeneous spaces. The term Cartan connection most often refers to Cartan's formulation of a (pseudo-)Riemannian, affine, projective, or conformal connection. Although these are the most commonly used Cartan connections, they are special cases of a more general concept.
Cartan's approach seems at first to be coordinate dependent because of the choice of frames it involves. However, it is not, and the notion can be described precisely using the language of principal bundles. Cartan connections induce covariant derivatives and other differential operators on certain associated bundles, hence a notion of parallel transport. They have many applications in geometry and physics: see the method of moving frames, Cartan connection applications and Einstein–Cartan theory for some examples.
At its roots, geometry consists of a notion of "congruence" between different objects in a space. In the late 19th century, notions of congruence were typically supplied by the action of a Lie group on space. Lie groups generally act quite rigidly, and so a Cartan geometry is a generalization of this notion of congruence to allow for curvature to be present. The "flat" Cartan geometries — those with zero curvature — are locally equivalent to homogeneous spaces, hence geometries in the sense of Klein.
A Klein geometry consists of a Lie group "G" together with a Lie subgroup "H" of "G". Together "G" and "H" determine a homogeneous space "G"/"H", on which the group "G" acts by left-translation. Klein's aim was then to study objects living on the homogeneous space which were "congruent" by the action of "G". A Cartan geometry extends the notion of a Klein geometry by attaching to each point of a manifold a copy of a Klein geometry, and to regard this copy as "tangent" to the manifold. Thus the geometry of the manifold is "infinitesimally" identical to that of the Klein geometry, but globally can be quite different. In particular, Cartan geometries no longer have a well-defined action of "G" on them. However, a Cartan connection supplies a way of connecting the infinitesimal model spaces within the manifold by means of parallel transport.
Consider a smooth surface "S" in 3-dimensional Euclidean space R3. Near to any point, "S" can be approximated by its tangent plane at that point, which is an affine subspace of Euclidean space. The affine subspaces are "model" surfaces — they are the simplest surfaces in R3, and are homogeneous under the Euclidean group of the plane, hence they are "Klein geometries" in the sense of Felix Klein's Erlangen programme. Every smooth surface "S" has a unique affine plane tangent to it at each point. The family of all such planes in R3, one attached to each point of "S", is called the congruence of tangent planes. A tangent plane can be "rolled" along "S", and as it does so the point of contact traces out a curve on "S". Conversely, given a curve on "S", the tangent plane can be rolled along that curve. This provides a way to identify the tangent planes at different points along the curve by affine (in fact Euclidean) transformations, and is an example of a Cartan connection called an affine connection.
Another example is obtained by replacing the planes, as model surfaces, by spheres, which are homogeneous under the Möbius group of conformal transformations. There is no longer a unique sphere tangent to a smooth surface "S" at each point, since the radius of the sphere is undetermined. This can be fixed by supposing that the sphere has the same mean curvature as "S" at the point of contact. Such spheres can again be rolled along curves on "S", and this equips "S" with another type of Cartan connection called a conformal connection.
Differential geometers in the late 19th and early 20th century were very interested in using model families such as planes or spheres to describe the geometry of surfaces. A family of model spaces attached to each point of a surface "S" is called a congruence: in the previous examples there is a canonical choice of such a congruence. A Cartan connection provides an identification between the model spaces in the congruence along any curve in "S". An important feature of these identifications is that the point of contact of the model space with "S" "always moves" with the curve. This generic condition is characteristic of Cartan connections.
In the modern treatment of affine connections, the point of contact is viewed as the "origin" in the tangent plane (which is then a vector space), and the movement of the origin is corrected by a translation, and so Cartan connections are not needed. However, there is no canonical way to do this in general: in particular for the conformal connection of a sphere congruence, it is not possible to separate the motion of the point of contact from the rest of the motion in a natural way.
In both of these examples the model space is a homogeneous space "G"/"H".
* In the first case, "G"/"H" is the affine plane, with "G" = Aff(R2) the affine group of the plane, and "H" = GL(2) the corresponding general linear group.
* In the second case, "G"/"H" is the conformal (or celestial) sphere, with "G" = O"+"(3,1) the (orthochronous) Lorentz group, and "H" the stabilizer of a null line in R3,1.The Cartan geometry of "S" consists of a copy of the model space "G"/"H" at each point of "S" (with a marked point of contact) together with a notion of "parallel transport" along curves which identifies these copies using elements of "G". This notion of parallel transport is generic in the intuitive sense that the point of contact always moves along the curve.
In general, let "G" be a group with a subgroup "H", and "M" a manifold of the same dimension as "G"/"H". Then, roughly speaking, a Cartan connection on "M" is a "G"-connection which is generic with respect to a reduction to "H".
Klein geometries as model spaces
Klein's Erlangen programme suggested that geometry could be regarded as a study of homogeneous spaces: in particular, it is the study of the many geometries of interest to geometers of 19th century (and earlier). A Klein geometry consisted of a space, along with a law for motion within the space (analogous to the Euclidean transformations of classical Euclidean geometry) expressed as a Lie group of transformations. These generalized spaces turn out to be homogeneous smooth manifolds diffeomorphic to the quotient space of a Lie group by a Lie subgroup. The extra differential structure that these homogeneous spaces possess allows one to study and generalize their geometry using calculus.
The general approach of Cartan is to begin with such a "smooth Klein geometry", given by a Lie group "G" and a Lie subgroup "H", with associated Lie algebras mathfrak g and mathfrak h, respectively. Let "P" be the underlying principal homogeneous space of "G". A Klein geometry is the homogeneous space given by the quotient "P"/"H" of "P" by the right action of "H". There is a right "H"-action on the fibres of the canonical projection:"π": "P" → "P"/"H"given by "R""h""g" = "gh". Moreover, each fibre of "π" is a copy of "H". "P" has the structure of a principal "H"-bundle over "P"/"H". [Harvnb|Chevalley|1946| p=110.]
A vector field "X" on "P" is "vertical" if d"π"("X") = 0. Any "ξ" ∈ mathfrak h gives rise to a canonical vertical vector field "X""ξ" by taking the derivative of the right action of the 1-parameter subgroup of "H" associated to ξ. The Maurer-Cartan form "η" of "P" is the mathfrak g-valued one-form on "P" which identifies each tangent space with the Lie algebra. It has the following properties:
# Ad("h") "R""h"*"η" = "η" for all "h" in "H"
# "η"("X""ξ") = "ξ" for all "ξ" in mathfrak h
# for all "g"∈"P", "η" restricts a linear isomorphism of T"g""P" with mathfrak g (η is an absolute parallelism on "P").
In addition to these properties, "η" satisfies the structure (or structural) equation: deta+	frac{1}{2} [etawedgeeta] =0.
Conversely, one can show that given a manifold "M" and a principal "H"-bundle "P" over "M", and 1-form "η" with these properties, then "P" is locally isomorphic as an "H"-bundle to the principal homogeneous bundle "G"→"G"/"H". The structure equation is the integrability condition for the existence of such a local isomorphism.
A Cartan geometry is a generalization of a smooth Klein geometry, in which the structure equation is not assumed, but is instead used to define a notion of curvature. Thus the Klein geometries are said to be the flat models for Cartan geometries. [ See R. Hermann (1983), Appendix 1–3 to Harvtxt|Cartan|1951.]
Cartan connections and pseudogroups
Cartan connections are closely related to pseudogroup structures on a manifold. Each is thought of as "modelled on" a Klein geometry "G"/"H", in a manner similar to the way in which Riemannian geometry is modelled on Euclidean space. On a manifold "M", one imagines attaching to each point of "M" a copy of the model space "G"/"H". The symmetry of the model space is then built in to the Cartan geometry or pseudogroup structure by positing that the model spaces of nearby points are related by a transformation in "G". The fundamental difference between a Cartan geometry and pseudogroup geometry is that the symmetry for a Cartan geometry relates "infinitesimally" close points by an "infinitesimal" transformation in "G" (i.e., an element of the Lie algebra of "G") and the analogous notion of symmetry for a pseudogroup structure applies for points that are physically separated within the manifold.
The process of attaching spaces to points, and the attendant symmetries, can be concretely realized by using special coordinate systems. [This appears to be Cartan's way of viewing the connection. Cf. Harvnb|Cartan|1923|p=362; Harvnb|Cartan|1924|p=208 especially "..un repère définissant un système de coordonnées projectives..."; Harvnb|Cartan|1951|p=34. Modern readers can arrive at various interpretations of these statements, cf. Hermann's 1983 notes in Harvnb|Cartan|1951|pp=384–385, 477.] To each point "p" ∈ "M", a neighborhood "U"p of "p" is given along with a mapping φp : "U"p → "G"/"H". In this way, the model space is attached to each point of "M" by realizing "M" locally at each point as an open subset of "G"/"H". We think of this as a family of coordinate systems on "M", parametrized by the points of "M". Two such parametrized coordinate systems φ and φ′ are "H"-related if there is an element "h"p ∈ "H", parametrized by "p", such that: φ′p = "h"p φp. [More precisely, "h"p is required to be in the isotropy group of φp("p"), which is a group in "G" isomorphic to "H".] This freedom corresponds roughly to the physicists' notion of a gauge.
Nearby points are related by joining them with a curve. Suppose that "p" and "p"′ are two points in "M" joined by a curve "p"t. Then "p"t supplies a notion of transport of the model space along the curve. [In general, this is not the rolling map described in the motivation, although it is related.] Let τt : "G"/"H" → "G"/"H" be the (locally defined) composite
t = φpt o φp0-1.Intuitively, τt is the transport map. A pseudogroup structure requires that τt be a "symmetry of the model space" for each "t": τt ∈ "G". A Cartan connection requires only that the derivative of τt be a symmetry of the model space: τ′0 ∈ g, the Lie algebra of "G".
Typical of Cartan, one motivation for introducing the notion of a Cartan connection was to study the properties of pseudogroups from an infinitesimal point of view. A Cartan connection defines a pseudogroup precisely when the derivative of the transport map τ′ can be integrated, thus recovering a true ("G"-valued) transport map between the coordinate systems. There is thus an integrability condition at work, and Cartan's method for realizing integrability conditions was to introduce a differential form.
In this case, τ′0 defines a differential form at the point "p" as follows. For a curve γ("t") = "p"t in "M" starting at "p", we can associate the tangent vector "X", as well as a transport map τtγ. Taking the derivative determines a linear
X mapsto left.frac{d}{dt}	au_t^gamma ight|_{t=0} = heta(X) in mathfrak{g}.So θ defines a g-valued differential 1-form on "M".
This form, however, is dependent on the choice of parametrized coordinate system. If "h" : "U" → "H" is an "H"-relation between two parametrized coordinate systems φ and φ′, then the corresponding values of θ are also related by:	heta^prime_p = Ad(h^{-1}_p)	heta_p + h^*_pomega_H,where ωH is the Maurer-Cartan form of "H".
Formal definition
A Cartan geometry modelled on a homogeneous space "G"/"H" can be viewed as a "deformation" of this geometry which allows for the presence of "curvature". For example:
* a Riemannian manifold can be seen as a deformation of Euclidean space;
* a Lorentzian manifold can be seen as a deformation of Minkowski space;
* a conformal manifold can be seen as a deformation of the conformal sphere;
* a manifold equipped with an affine connection can be seen as a deformation of an affine space.
There are two main approaches to the definition. In both approaches, "M" is a smooth manifold of dimension "n", "H" is a Lie group of dimension "m", with Lie algebra mathfrak h, and "G" is a Lie group "G" of dimension "n"+"m", with Lie algebra mathfrak g, containing "H" as a subgroup.
Definition via gauge transitions
A Cartan connection consists [Harvnb|Sharpe|1997.] [Harvnb|Lumiste|2001a.] of a coordinate atlas of open sets "U" in "M", along with a g-valued 1-form θU defined on each chart such that
# θU : T"U" → g.
# θU mod h : Tu"U" → g/h is a linear isomorphism for every "u" ∈ "U".
#For any pair of charts "U" and "V" in the atlas, there is a smooth mapping "h" : "U" ∩ "V" → "H" such that::	heta_V = Ad(h^{-1})	heta_U + h^*omega_H,,:where ωH is the Maurer-Cartan form of "H".By analogy with the case when the θU came from coordinate systems, condition 3 means that φU is related to φV by "h".
The curvature of a Cartan connection consists of a system of 2-forms defined on the charts, given by:Omega_U = d	heta_U + frac{1}{2} [	heta_U,	heta_U] .ΩU satisfy the compatibility condition::If the forms θU and θV are related by a function "h" : "U" ∩ "V" → "H", as above, then ΩV = Ad("h"-1) ΩU
The definition can be made independent of the coordinate systems by forming the quotient space :P = (coprod_U U	imes H)/simof the disjoint union over all "U" in the atlas. The equivalence relation ~ is defined on pairs ("x","h"1) ∈ "U"1 × "H" and ("x", "h"2) ∈ "U"2 × "H", by:("x","h"1) ~ ("x", "h"2) if and only if "x" ∈ "U"1 ∩ "U"2, θ"U"1 is related to θ"U"2 by "h", and "h"2 = "h"("x")-1 "h"1.Then "P" is a principal "H"-bundle on "M", and the compatibility condition on the connection forms θU implies that they lift to a g-valued 1-form η defined on "P" (see below).
Definition via absolute parallelism
Let "P" be a principal "H" bundle over "M". Then a Cartan connection [This is the standard definition. Cf. Hermann (1983), Appendix 2 to Harvnb|Cartan|1951; Harvnb|Kobayashi|1970| p=127; Harvnb|Sharpe|1997; Harvnb|Slovák|1997.] is a mathfrak g-valued 1-form "η" on "P" such that
# for all "h" in "H", Ad("h")"R""h"*"η" = "η"
# for all "ξ" in mathfrak h, "η"("X""ξ") = "ξ"
# for all "p" in "P", the restriction of "η" defines a linear isomorphism from the tangent space T"p""P" to mathfrak g.
The last condition is sometimes called the Cartan condition: it means that "η" defines an absolute parallelism on "P". The second condition implies that "η" is already injective on vertical vectors and that the 1-form "η" mod mathfrak h, with values in mathfrak g/mathfrak h, is horizontal. The vector space mathfrak g/mathfrak h is a representation of "H" using the adjoint representation of "H" on mathfrak g, and the first condition implies that "η" mod mathfrak h is equivariant. Hence it defines a bundle homomorphism from T"M" to the associated bundle P	imes_H mathfrak g/mathfrak h.The Cartan condition is equivalent to this bundle homomorphism being an isomorphism, so that "η" mod mathfrak h is a solder form.
The curvature of a Cartan connection is the mathfrak g-valued 2-form "Ω" defined by:Omega=deta+	frac{1}{2} [etawedgeeta] .
Note that this definition of a Cartan connection looks very similar to that of a principal connection. There is one important difference however, in 1. above. The g-valued 1-form η is equivariant under the action of "H" (not "G"). Intuitively, this means that η yields information about the behavior of additional directions in the principal bundle (rather than simply being a projection operator onto the vertical space). Concretely, the existence of a solder form binds (or solders) the Cartan connection to the underlying differential topology of the manifold.
An intuitive interpretation of the Cartan connection in this form is that it determines a "fracturing" of the tautological principal bundle associated to a Klein geometry. Thus Cartan geometries are deformed analogues of Klein geometries. This deformation is roughly a prescription for attaching a copy of the model space "G"/"H" to each point of "M" and thinking of that model space as being "tangent" to (and "infinitesimally identical" with) the manifold at a point of contact. The fibre of the tautological bundle "G" → "G"/"H" of the Klein geometry at the point of contact is then identified with the fibre of the bundle "P". Each such fibre (in "G") carries a Maurer-Cartan form for "G", and the Cartan connection is a way of assembling these Maurer-Cartan forms gathered from the points of contact into a coherent 1-form η defined on the whole bundle. The fact that only elements of "H" contribute to the Maurer-Cartan equation Ad("h")"R""h"*"η" = "η" has the intuitive interpretation that any other elements of "G" would move the model space away from the point of contact, and so no longer be tangent to the manifold.
From the Cartan connection, defined in these terms, one can recover a Cartan connection as a system of 1-forms on the manifold (as in the gauge definition) by taking a collection of local trivializations of "P" given as sections "s"U : "U" → "P" and letting θU = "s"*η be the pullbacks of the Cartan connection along the sections.
Cartan connections as principal connections
Another way in which to define a Cartan connection is as a principal connection on a certain principal "G"-bundle. From this perspective, a Cartan connection consists of
* a principal "G"-bundle "Q" over "M"
* a principal "G"-connection "α" on "Q" (the Cartan connection)
* a principal "H"-subbundle "P" of "Q" (i.e., a reduction of structure group)such that the pullback "η" of "α" to "P" satisfies the Cartan condition.
The principal connection "α" on "Q" can recovered from the form "η" by taking "Q" to be the associated bundle "P" ×"H" "G". Conversely, the form η can be recovered from α by pulling back along the inclusion "P" ⊂ "Q".
Since "α" is a principal connection, it induces a connection on any associated bundle to "Q". In particular, the bundle "Q" ×"G" "G"/"H" of homogeneous spaces over "M", whose fibers are copies of the model space "G"/"H", has a connection. The reduction of structure group to "H" is equivalently given by a section "s" of "E" = "Q" ×"G" "G"/"H". The fiber of P	imes_H mathfrak g/mathfrak h over "x" in "M" may be viewed as the tangent space at "s"("x") to the fiber of "Q" ×"G" "G"/"H" over "x". Hence the Cartan condition has the intuitive interpretation that the model spaces are tangent to "M" along the section "s". Since this identification of tangent spaces is induced by the connection, the marked points given by "s" always move under parallel transport.
Definition by an Ehresmann connection
Yet another way to define a Cartan connection is with an Ehresmann connection on the bundle "E" = "Q" ×"G" "G"/"H" of the preceding section. [Harvnb|Ehresmann|1950, Harvnb|Kobayashi|1957, Harvnb|Lumiste|2001b.] A Cartan connection then consists of
*A fibre bundle π : "E" → "M" with fibre "G"/"H" and vertical space V"E" ⊂ T"E".
*A section "s" : "M" → "E".
*A G-connection θ : T"E" → V"E" such that ::"s"*θx : Tx"M" → V"s"("x")"E" is a linear isomorphism of vector spaces for all "x" ∈ "M".This definition makes rigorous the intuitive ideas presented in the introduction. First, the preferred section "s" can be thought of as identifying a point of contact between the manifold and the tangent space. The last condition, in particular, means that the tangent space of "M" at "x" is isomorphic to the tangent space of the model space at the point of contact. So the model spaces are, in this way, tangent to the manifold.
This definition also brings prominently into focus the idea of development. If "x"t is a curve in "M", then the Ehresmann connection on "E" supplies an associated parallel transport map τt : "E"xt → "E"x0 from the fibre over the endpoint of the curve to the fibre over the initial point. In particular, since "E" is equipped with a preferred section "s", the points "s"("x"t) transport back to the fibre over "x"0 and trace out a curve in "E"x0. This curve is then called the "development" of the curve "x"t.
To show that this definition is equivalent to the others above, one must introduce a suitable notion of a moving frame for the bundle "E". In general, this is possible for any "G"-connection on a fibre bundle with structure group "G". See Ehresmann connection#Associated bundles for more details.
Special Cartan connections
Reductive Cartan connections
Let "P" be a principal "H"-bundle on "M", equipped with a Cartan connection η : T"P" → g. If g is a reductive module for "H", meaning that g admits an Ad("H")-invariant splitting of vector spaces g=h⊕m, then the m-component of η generalizes the solder form for an affine connection. [For a treatment of affine connections from this point of view, see Harvtxt|Kobayashi|Nomizu|1996|loc= Volume 1.] In detail, η splits into h and m components: :η = ηh + ηm.Note that the 1-form ηh is a principal "H"-connection on the original Cartan bundle "P". Moreover, the 1-form ηm satisfies::ηm("X") = 0 for every vertical vector "X" ∈ T"P". (ηm is "horizontal".):Rh*ηm = Ad("h"-1)ηm for every "h" ∈ "H". (ηm is "equivariant" under the right "H"-action.)In other words, η is a solder form for the bundle "P".
Hence, "P" equipped with the form ηm defines a (first order) "H"-structure on "M". The form ηh defines a connection on the "H"-structure.
Parabolic Cartan connections
If g is a semisimple Lie algebra with parabolic subalgebra p (i.e., p contains a maximal solvable subalgebra of g) and "G" and "P" are associated Lie groups, then a Cartan connection modelled on ("G","P",g,p) is called a parabolic Cartan geometry, or simply a parabolic geometry. A distinguishing feature of parabolic geometries is a Lie algebra structure on its cotangent spaces: this arises because the perpendicular subspace p⊥ of p in g with respect to the Killing form of g is a subalgebra of p, and the Killing form induces a natural duality between p⊥ and g/p. Thus the bundle associated to p⊥ is isomorphic to the cotangent bundle.
Parabolic geometries include many of those of interest in research and applications of Cartan connections, such as the following examples.
* Conformal connections: Here "G" = "SO"("p"+1,"q"+1), and "P" is the stabilizer of a null ray in Rn+2.
* Projective connections: Here "G" = "PGL"(n+1) and "P" is the stabilizer of a point in RPn.
* CR structures: "G" = "PSU"("p"+1,"q"+1), "P" = stabilizer of a point on the projective null hyperquadric.
Associated differential operators
Covariant differentiation
Suppose that "M" is a Cartan geometry modelled on "G"/"H", and let ("Q","α") be the principal "G"-bundle with connection, and ("P","η") the corresponding reduction to "H" with "η" equal to the pullback of "α". Let "V" a representation of "G", and form the vector bundle V = "Q" ×"G" "V" over "M". Then the principal "G"-connection "α" on "Q" induces a covariant derivative on V, which is a first order linear differential operator: ablacolon Omega^0_M(mathbf V)	o Omega^1_M(mathbf V),where Omega^k_M(mathbf V) denotes the space of "k"-forms on "M" with values in V so thatOmega^0_M(mathbf V) is the space of sections of V and Omega^1_M(mathbf V) is the space of sections ofHom(T"M",V). For any section "v" of V, the contraction of the covariant derivative ∇"v" with a vector field "X" on "M" is denoted ∇"X""v" and satisfies the following Leibniz rule:: abla_X(fv)=df(X)v+f abla_X vfor any smooth function "f" on "M".
The covariant derivative can also be constructed from the Cartan connection "η" on "P". In fact, constructing it in this way is slightly more general in that "V" need not be a fully fledged representation of "G". [See, for instance, Harvtxt|Čap|Gover|2002|loc=Definition 2.4.] Suppose instead that that "V" is a (mathfrak g, "H")-module: a representation of the group "H" with a compatible representation of the Lie algebra mathfrak{g}. Recall that a section "v" of the induced vector bundle V over "M" can be thought of as an "H"-equivariant map "P" → "V". This is the point of view we shall adopt. Let "X" be a vector field on "M". Choose any right-invariant lift ar{X} to the tangent bundle of "P". Define: abla_X v=dv(ar{X})+eta(ar{X})cdot v.
In order to show that ∇"v" is well defined, it must:
# be independent of the chosen lift ar{X}
# be equivariant, so that it descends to a section of the bundle V.
For (1), the ambiguity in selecting a right-invariant lift of "X" is a transformation of the form Xmapsto X+X_xi where X_xi is the right-invariant vertical vector field induced from xiinmathfrak h. So, calculating the covariant derivative in terms of the new lift ar{X}+X_xi, one has
: abla_X v=dv(ar{X}+X_xi)+eta(ar{X}+X_xi))cdot v:=dv(ar{X}) +d v(X_xi)+ eta(ar{X})cdot v+ xicdot v:=dv(ar{X})+ eta(ar{X})cdot v
since xicdot v+dv(X_xi)=0 by taking the differential of the equivariance property hcdot R_{h}^*v=v at "h" equal to the identity element.
For (2), observe that since "v" is equivariant and ar{X} is right-invariant, dv(ar{X}) is equivariant. On the other hand, since "η" is also equivariant, it follows that eta(ar{X})cdot v is equivariant as well.
The fundamental or universal derivative
Suppose that "V" is only a representation of the subgroup "H" and not necessarily the larger group "G". Let Omega^k(P,V) be the space of "V"-valued differential "k"-forms on "P". In the presence of a Cartan connection, there is a canonical isomorphism:varphicolon Omega^k(P,V)cong Omega^0(P,Votimesigwedge olimits^kmathfrak g^*)given byvarphi(eta)(xi_1,xi_2,dots,xi_k)=eta(eta^{-1}(xi_1),dots,eta^{-1}(xi_k)) where eta in Omega^k(P,V) and xi_j in mathfrak g.
For each "k", the exterior derivative is a first order operator differential operator:dcolon Omega^k(P,V) ightarrow Omega^{k+1}(P,V),and so, for "k"=0, it defines a differential operator: varphicirc dcolon Omega^0(P,V) ightarrow Omega^0(P,Votimes mathfrak g^*).,Because "η" is equivariant, if "v" is equivariant, so is "Dv" := "φ"(d"v"). It follows that this composite descends to a first order differential operator "D" from sections of V="P"×"H""V" to sections of the bundle P	imes_H (mathbf Votimes mathfrak g^*). This is called the fundamental or universal derivative, or fundamental D-operator.
Example: Affine connections
An affine connection on a manifold "M" is a Cartan connection modelled on the Klein geometry of affine space. [The material in this section is standard, and essentially based on Harvtxt|Kobayashi|Nomizu|1996|loc=Volume 1, with changes made to fit with the general Cartan connection concept. Kobayashi and Nomizu call an affine connection "linear", and its prolongation "affine". We shall not adopt this convention here.]
The affine group "G" = "Aff"("n") consists of all transformations of an "n"-dimensional vector space "V", of the form:φ("x") = "Ax" + "x"0,where "A" is a general linear transformation. The affine group consists then of general linear transformations combined with translations. The stabilizer group of the origin in "V" is a copy "H" = "GL"("n") of the general linear group sitting inside "G". We can also describe "G" and "H" as matrix groups by introducing a basis of "V" to identify it with Rn. First embed Rn in the natural way into Rn+1 as the hyperplane "x"n+1 = 1. With these identifications: G = left{left(egin{matrix}A&x_0\\0&1end{matrix} ight);Ain GL(n), x_0inmathbb{R}^n ight},quad H = left{left(egin{matrix}A&0\\0&1end{matrix} ight);Ain GL(n), x_0inmathbb{R}^n ight}
Likewise, the Lie algebras g = aff("n") and h = gl("n") are given as: mathfrak{g} = left{left(egin{matrix}A&x_0\\0&0end{matrix} ight);Ain mathfrak{gl}(n), x_0inmathbb{R}^n ight},quad mathfrak{h} = left{left(egin{matrix}A&0\\0&0end{matrix} ight);Ain mathfrak{gl}(n), x_0inmathbb{R}^n ight}
Note that g admits an Ad("H")-invariant splitting :g = h ⊕ Rn, (*)and at the group level "G" is a semidirect product of "H" and Rn. [Such geometries are called reductive and play a special role in the differential geometry of Cartan connections.]
An affine connection on a manifold "M" consists of a principal "H"-bundle "P", along with a g-valued 1-form ω on "P" such that:# ω is nondegenerate.:# R"h"*ω = Ad("h"-1) ω for all "h" ∈ "H".:# ω("X"ξ) = ξ for all ξ ∈ h, generating the vertical vector field "X"ξ.
To get a clearer picture of these three conditions, we decompose ω using the splitting (*). In this way, write ω = σ + θ, where σ is a 1-form with values in h and θ is a 1-form with values in Rn. Stated in terms of σ and θ, properties 1.–3. can be rewritten
:1σ. σ is a surjective h-valued 1-form:2σ. R"h"*σ = Ad("h"-1) σ for all "h" ∈ "H".:3σ. σ("X"ξ) = ξ for all ξ ∈ h.
:1θ. θ is a surjective Rn-valued 1-form:2θ. ("R"h)*θ("X") = "h"-1θ(X) for any "X" ∈ "TP".:3θ. ("R"h)*θ("X"ξ) = 0 for any vertical vector "X"ξ
Note in particular that properties 1σ.–3σ. correspond precisely to the definition of σ being a principal connection on "P". [This is not, as it happens, a general feature of Cartan connections, but rather a consequence of the reductivity of aff("n").]
Properties 1θ.–3θ. are what "distinguish" affine connections from more general principal connections. They bind the structure of the principal bundle "P" (and the affine connection) to the underlying differentiable structure of "M", and θ is aptly named a solder form.
The key to seeing this is property 3θ. Suppose that "x" ∈ "M" and "u" ∈ "P""x", the fibre over "x". If "X" is a tangent vector to "M" at "X", then we can unambiguously define θu("X"), since θu is insensitive to the addition of vertical vectors. Incorporating now property 1θ::	heta_u: T_xM stackrel{approx}{ ightarrow} mathbb{R}^n defines a linear isomorphism of vector spaces.In other words, for each choice of "u" in the fibre, θ"u" defines a frame of T"x""M".
Finally, property 2θ. ensures that θ has the correct tensorial transformation law to identify the principal bundle "P" with the bundle of linear frames of "M".
Prolongation and development
Associated with an affine connection (or much more generally, any Cartan connection: see below) is a notion of development. Development corresponds to the intuitive idea of "rolling" the tangent copies of the model space along curves in the manifold. Recall the example of the affine tangent plane rolling along a curve in a surface. Here, as the plane moves, the point of contact traces out a curve in the affine plane. So for each curve in the surface, there is a development of that curve into the model affine space. In a general setting, the development of a Cartan connection along a curve is a way of lifting the curve in a natural way to the model space (which may be thought of as the generalization of "rolling" the model space along the curve). [In greater generality, we can also talk about developments of higher dimensional submanifolds or even the whole manifold itself, into the model space. However, such developments will not always exist, and depend on some integrability conditions of the curvature.]
Developments are most naturally conceived using the technique of prolongation of a Cartan geometry. Later in the article, this will be discussed for arbitrary Cartan geometries. The way it works for affine connections is as follows.
From the preceding section, we have seen that once equipped with the data of an affine connection, the bundle "P" → "M" is realized as the bundle of linear frames of "M". The prolongation of this Cartan geometry is a geometric structure defined on the bundle of "affine frames" of "M".
Here we regard the tangent spaces of "M" as "affine spaces" rather than vector spaces. This defines the "affine tangent bundle" A"M". An affine frame of "M" at a point "x" consists of a choice of base point (or origin) "p" ∈ A"x""M" and a choice of linear frame ("X"1, ..., "X"n) attached to the base point "p".
Cartan connections generalize affine connections in two ways.
* The action of "H" on R"n" need not be effective. This allows, for example, the theory to include spin connections, in which "H" is the spin group Spin("n") rather than the orthogonal group O("n").
* The group "G" need not be a semidirect product of "H" with R"n".
* .
*springer|id=a/a010950|title=Affine connection|author=Ü. Lumiste
Metropolitan Borough of Dudley
Captain John Underhill
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redpajama_set_name: RedPajamaCommonCrawl


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After reading the notice in Google groups from Scott Patten about the Leanpub API, my first thought was: I want to use this with perl.
And then I wrote the perl module.
This book may be used as additional documentation to the perl module.
But it's main purpose is to test the Perl binding of the Leanpub API.
So you probably don't want to get noticed about new releases.
Mathias Weidner worked many years as a system and network administrator. Nowadays he configures firewalls for a living.
Besides writing books he sometimes writes Perl modules that can be found on CPAN.
How do I use the Perl module?


Phosphatidylcholine (PC), the major source of dietary choline, has been demonstrated to improve the capability of learning and memory in rodent and the amelioration of long-chain n-3 polyunsaturated fatty acids (PUFA) on anti-aging and anti-oxidation is widely known as well. In this study, three kinds of PC were chose to demonstrate the role of different fatty acids composition on glycerol backbone in improving the brain function of mice induced by scopolamine which was used to impair cholinergic system and cause oxidative stress.
Male BALB/c mice were randomly divided into 5 groups: model (M) group, control (Con) group, egg yolk lecithin (EL) group, squid PC (SQ-PC) group and sea cucumber PC (SC-PC) group. The intraperitoneal injection of scopolamine hydrobromide (5 mg/kg) was carried out on the 8th of group feeding and sustained daily until the end of test. Morris water maze test was used to evaluate the improvement of cognitive decline and the activity of acetylcholinesterase (AchE), superoxide dismutase (SOD) and monoamine oxidase (MAO) and malondialdehyde (MDA) content in brain were measured to assess the physiological changes.
In behavior test, the latency of PC groups was significantly reduced, while number of crossing the platform and time in target quadrant were increased in comparison with M group and the improvements of SQ-PC and SC-PC were better than that of EL (P < 0.05). Similar trend was observed in physiological changes. The AchE activity was effectively decreased and the SOD activity increased in hippocampus, cortex and white matter when comparing PC groups with M group. SQ-PC, SC-PC and EL respectively showed 22.82, 28.80 and 11.81 % decrease in MDA level in brain compared with M group. The MAO activity in white matter of SQ-PC, SC-PC and EL group separately depressed 33.05, 33.64 and 19.73 % in comparison with M group. No significance between SQ-PC and SC-PC was found in these indicators except the SOD activity in hippocampus and white matter. SQ-PC group had a higher SOD activity in hippocampus (103.68U/mg · prot.) and lower in white matter (120.57 U/mg · prot.) than SC-PC group (95.53 U/mg · prot. in hippocampus, 134.49 U/mg · prot. in white matter). PC rich in n-3 PUFA acted more ameliorative effects than that barely contained on the indicators above.
Different fatty acids composition of PC all could diminish the cognitive decline and biological damage and protect the brain. EPA and DHA partly enhaced to the advantageous effects.
Alzheimer's disease (AD) is characterized by the progressive decline in memory and cognitive function . It is also one of the most important forms of dementia and has become into an enormous financial burden on society with the rapid growth of elderly population in the worldwide . The most disappointing and hopeless thing is that we have not found an effective treatment to cure or just suspend the disease. AD causes substantial changes in brain including synaptic and neuronal loss, Aβ deposition, hyperphosphorylation of Tau and neurobrillary tangles [3, 4]. There are many hypothesis reported about the pathogenesis of AD, in which oxidative stress and cholinergic damage are highly acceptable [5, 6]. It is a critical element that the level of brain acetylcholine (Ach) was persistently decreasing in the process of AD. The drugs that increase the content of the neurotransmitter Ach by inhibiting acetylcholine esterase for treating the AD patients are approved by U.S. Food and Drug Administration (FDA) currently . However, most of these drugs should be used for a long-term condition on account of their transiently curative effect, which resulted in a series of adverse effects and suffering such as headache, insomnia and emesis . The developments of preventing and curing AD through diet therapy are pregnant and necessary. It is a very appropriate way to enhance nutraceuticals in daily diet. It provides plenty of medical or health benefits such as improving the metabolism of glucose and lipid , changing the lipid composition of brain , antioxidation and anti-aging . Escalating reports give us a common sense that diet supplementation with phospholipids (especially functional type) plays a positive role in protecting the nervous system and improving memory [12–14]. Meanwhile, the effect of long-chain n-3 polyunsaturated fatty acids (PUFA) of aquatic product on anti-oxidative damage is generally recognized . Docosahexaenoic acid (DHA) and eicosapentaenoic acid (EPA), the main PUFA in fish oil, make the greatest contribution to the biological activities such as promoting the growth of cerebral cells and improving memory . DHA is the main composition of member lipid in the nerve cells and the priority resource of fatty acid in brain cells. As an effective anti-inflammatory bioactivator, EPA has been increasingly reported to own the capability of preventing the inflammation in neurodegenerative disease [17, 18]. It is widely acknowledged that egg yolk lecithin has a good effect on mopping up free radicals and anti-aging . Meanwhile phosphatidylcholine (PC) is the major source of dietary choline and it has been demonstrated that intake of PC can improve the capability of learning and memory in rats to some extent . As the main component of lipid bilayer structure of cell membrane, PC acts a vital part in membrane fusion and transport , endocytosis and the catalytic activity of enzymes  and the function of lowering blood lipid and cholesterol levels, preventing cardiovascular disease and inhibiting obesity have been illuminated as well . However, it is rarely illustrated whether the difference of fatty acids composition on glycerol backbone of PC molecule has influence on the improvements.
As a muscarinic anti-cholinergic drug, Scopolamine (SCO) can block the combination of neural acetyl choline (Ach) and its receptor, disrupt the transmission of cholinergic signal and lead to clinical manifestations of dementia . Simultaneously, it is able to decrease the anti-oxidative enzyme activity and increase the level of radical . Therefore, it becomes a widely used drug to induce dementia models by impairing short-term learning and memory . SCO induces cognitive impairment with an attenuation of cholinergic neurotransmission and increase of oxidative stress . Thus, nutraceuticals which can significantly improve cholinergic system and/or oxidative stress might reverse this damage. In this study, we chose three kinds of PC: egg yolk lecithin (coventional type PC), sea cucumber PC (rich in EPA) and squid PC (rich in DHA) to investigate the effect of different fatty acids composition of PC on the brain function of dementia BALB/c mice induced by intraperitoneal injection of scopolamine hydrobromide in 2-week short term test.
As the intraperitoneal injection of Scopolamine hydrobromide was daily kept during the entire test, the time used to find the platform was becoming significant longer in M group than that in Con group during the 6-day's training (Fig. 1). Compared to the Model group, the latency of SQ-PC group and SC-PC group mice was continuous and notablely decreased and the significance of EL group emerged on the 4th (P < 0.05), 5th (P < 0.01) and 6th (P < 0.01) day of the test. In the meantime, we found a significance arose between EL group and SC-PC group as well as that between EL group and SQ-PC group and was persistent until the end of the test. Nonetheless, the difference between SQ-PC group and SC-PC group was not distinct (Fig. 1a).
No significance was found in total distance traveled of all groups mice, however the number of crossing the platform and the time in target quadrant (quadrant I) had a remarkable difference after the platform was removed from the pool (Fig. 1b). Numbers of M (P < 0.01) group mice crossing the platform was significantly less than that of the Con group and SQ-PC group (P < 0.01) and SC-PC (P < 0.01) group mice showed a great improvements and EL group (P < 0.05) also achieved partially better when compared with M group. The result of the contrast among three PC groups showed the ameliorative effect of SQ-PC group and SC-PC group was better than EL group (Fig. 1c). According to the comparison between Con group and M group mice, time in the quadrant I notly decreased from 38.39 s to 10.89 s.SQ-PC group and SC-PC group mice remained in quadrant I for respectively 32.24 s and 29.40s which meant obvious increase in contrast to M group, meanwhile EL group mice improved the time to 24.30s and also showed significance. In consistent with the performance of number of crossing the platform, SQ-PC group and SC-PC group had also achieved a better result than EL group in the time in quadrant I (Fig. 1d).
Since acetylcholin esterase was one of the most relevant enzyme to acetyl choline (Ach), which was the important neurotransmitter in central cholinergic system and played a vital role in learning and memory, we investigated the AchE activity in hippocampus (Fig. 2a), cortex (Fig. 2b) and white matter (Fig. 2c). Generally, SCO-administration severely increased the AchE activity of M group (P < 0.01) in the areas of mice brain when compared to Con group. Contrasting the PC groups with M group, we could conclude that the PC groups all decreased the AchE activity effectively and SQ-PC group (P < 0.01) and SC-PC group (P < 0.01) showed more significant than EL group (P < 0.05). Similar trend of difference was observed in hippocampus, cortex and white matter with the comparison among the PC groups, that SQ-PC group and SC-PC group had a remarkable effect on decreasing the AchE activity by contrast with EL group and no significance was presented when comparing SQ-PC group and SC-PC group.
Superoxide dismutase (SOD) activity and malondialdehyde (MDA) level, two representative oxidative stress indicators, were measured. The results showed that the administration of Scopolamine hydrobromide significantly increased the oxidative stress in M group mice as the SOD activity in cortex (P < 0.01), hippocampus (P < 0.01) and white matter (P < 0.01) of M group mice were markedly lower and the MDA level in brain (P < 0.01) was higher in comparison with Con group (Fig. 3). Compared to M group, the three kinds of PC effectively improved the SOD activity in hippocampus (Fig. 3a), cortex (Fig. 3b) and white matter (Fig. 3c).
Similar results were presented in the comparison of the effect on decreasing the MDA level (Fig. 3d) in mice brain between the PC groups and M group. Furthermore, SQ-PC group and SC-PC group showed more effective results than EL group while comparing with the PC groups. The difference between SQ-PC group and SC-PC group was not as same as that in the test above. SQ-PC group mice had a higher SOD activity in hippocampus and lower in white matter than SC-PC group. However, no significance was showed in SOD activity in cortex and MDA level in brain between the two groups.
The result of MAO activity in white matter was shown in Fig. 4. M group displayed a significant increase of MAO activity in white matter when compared with Con group. EL group, SQ-PC group and SC-PC group decreased the MAO activity by 19.7 % (P < 0.05), 34.0 % (P < 0.01) and 34.6 % (P < 0.01) respectively in contrast to M group. No significance was found between SQ-PC group and SC-PC group and each of the two groups performed better than EL group in improving the MAO activity in white matter with the comparison between the PC groups.
Recently, increasing interest in improving the clinical symptoms of AD patients and enhancing their self-care ability of daily living has generated [26, 27]. It is an appropriate strategy to add some effective compounds derived from plants and animals into the diets so that this fragile population will be able to keep away from the painful side effects which most of drugs have in common. It has been thousands of years since sea cucumbers became a traditional tonic food in China and their medical value has already been acknowledged widely . A. molpadioides, material of SC-PC used in this study, is low-value and high yielding with an extensive distribution around the coastal regions of China . Squid (Sthenoteuthis oualaniensis) roe, used to extract SQ-PC, is the wastes of processing and so that it is a kind of deep processing to extract phospholipid from this byproduct . Here we investigated three different kinds of phosphatidylcholine (PC) respectively from egg yolk, squid roe and sea cucumber and comparatively studied the effects of different fatty acid composition of PC on brain function. Scopolamine, a traditional anti-cholinergic drugs, is reported to have the capability of impairing spatial learning and memory and influencing the formation of short term memory . In addition, 7 days of SCO-administration has been found to elevate oxidative stress level in rat brain and also increased the neuroinflammatory in the hippocamous .
In water maze test, the result of latency showed that egg yolk lecithin (EL), squid PC (SQ-PC) and sea cucumber PC (SC-PC) all can prevent the damage of SCO-administration in mice brain. Otherwise, SQ-PC and SC-PC performed better than EL. Numbers of crossing the platform and time in the target quadrant was used to measure the short term memory of mice. Results revealed that PC improved the decline of memory and in consistent with the place navigation test, SQ-PC and SC-PC with massive n-3 PUFA have more effective functions. According to the behavior test, SQ-PC rich in DHA and SC-PC rich in EPA have a better protection of brain from being damaged in spatial learning and memory by SCO-administration than EL (which barely contained EPA or DHA). Dietary supplement of PC helps slow the aging process and enhance intelligence [33, 34]. As one of the main cerebral material and possessed a high ratio in cerebral fat, it is widely accepted that DHA plays a vital part on maintaining the fluency of cytomembrane and has a relationship with the transmission of nerve signals [34, 35]. The enhanced function of cytomembrane produces amelioration of cell information conducting and leads to raise the activity of brain and nervous system. Recent studied has demonstrated that dietary intake of EPA can be converted into DHA rapidly in brain . EPA and DHA probably adopt some common pathways to prevent cognitive decline. Thus, different fatty composition of PC molecule showed different degree of improvement on behavior test and the species that contained abundant DHA or EPA acted even better.
Ach, a major neurotransmitter in the central cholinergic system, is known to be closely associated with learning and memory. AchE, the hydrolase of Ach, is investigated to evaluate the influence on nerve conduction . There are G1 and G4 isoforms of the enzyme in the brain, both of which were abundant in different brain areas . It has been reported that the G1 isoform of AChE was observed in the brain of AD patients . Several studies suggest that human AChE promotes the fibrilization and deposition of Aβ in pathological aggregates [39, 40]. Decrease of choline acetyltransferase (ChAT) activity, increase of acetylcholin esterase (AchE) activity, low acetyl choline (Ach) content and dysfunction of central nerve system are important pathologies of AD patients . As the result shown, the PC groups displayed significance of reducing the AchE activity in hippocampus, cortex and white matter. Choline, obtained from PC, combines with acetyl-CoA and generates Ach in brain tissues. Supplemental PC in diet could rise the content of choline in brain, and the shrinkage of AchE suppressed the decomposition of Ach, then increased the level of Ach and gained a better effect on cognitive behavior. In addition, it has been reported that n-3 PUFA may have an influence on signal recognition and transduction which was related to the transmission of cholinergic pathways . According to our data, the depression of AchE activity in hippocampus, cortex and white matter was executed better by PC which had high n-3 PUFA content in fatty acids than that with EPA or DHA scarcely included.
Oxidative stress has been one of the primary factors of cognitive decline in neurodegenerative disease for many years. Superoxide anion radicals is the inevitable by-product of the mitochondrial respiration . On the basis of free-radical theory, the reactive oxygen species (ROS) induce the oxidative stress, leading to the damage of protein and DNA, lipid peroxidation and the toxicity against mitochondrial structures. It is so susceptible to oxidation for the long polyunsaturated fatty acid chains of mitochondrial membranes that may lead to the depolarization of membrane and consecutively to mitochondrial impairments [44, 45]. SOD, a momentous antioxidative enzyme, is able to prevent the free radicals from disrupting cells by translating superoxide radical into hydrogen peroxide . As a molecule of cytotoxicity, MDA indicates the degree of membrane lipid peroxidation. The mice with intake of PC acquired better amelioration of oxidative stress (Fig. 3). Interestingly, we found that PC with a mass of DHA was more effective than that with abundant EPA on enhancing the SOD activity in hippocampus and the situation was reverse in cortex. Because of containing EPA and DHA, it was reasonable and turned out that PC with the composition of n-3 PUFA gained more powerful strength of antioxidation than ordinary forms . Nonetheless, there is rarely reported that the distinction of the oxidative function between DHA and EPA is significant in specific tissues and moreover, depending on the result we obtained, the tendency of significance in hippocampus was not as same as that in cortex. There are probably potential mechanisms on the novel phenomenon we can hardly express now. More investigation should be developed to demonstrate the mechanisms. Generally, n-3 PUFA in PC notablely strengthened the anti-oxidative function on the basis of the better performance acted by SQ-PC and SC-PC which were rich in DHA and EPA separately.
MAO, the main enzyme involved in the metabolism of amine such as serotonin, monoamine and catecholamine, has two subunits, MAO-A and MAO-B. Both forms are found with high level in the brain . MAO-B which is the major form in serotonergic neurons and astrocytes has been discovered to closely relate to the impairment of neural functions in central nervous system . The hydrogen peroxide, generated by the reactions of MAO and neural transmitter, could combine with Fe2+ and then free radicals were created which promotes the damage of neurone . An increase of MAO activity were detected in the brains of patients with AD . MAO has the ability of increasing the expression of β-secretase and γ-secretase and improving Aβ generation  and could be also related to the formation of neurofibrillary tangles  when be activated. The alteration of MAO activity in white matter indicated that the supplemental PC had effectively decreased the neural lesions. It is recently reported that 4-weeks' intragastric administration of fish oil can significantly decline the 5-hydroxyindole acetic acid content and MAO activity and increase serotonin level . In consistent with the present study, SC-PC and SQ-PC, both rich in n-3 PUFA, performed better than EL which mainly had no EPA or DHA on reversing the high MAO activity induced by SCO-administration.
In summary, intraperitoneal injection of scopolamine hydrobromide impaired the brain function seriously in mice and intake of PC could improve the damage effectively. It is widely known that dietary supplement of phospholipid can facilitate the growth and development of infant brain . Intragastric administration of DHA-PC liposome increase the content of unsaturated fatty acid and depressed the TchE activity in mice brain which was accordant in this study . Soybean lecithin and egg yolk lecithin had been reported to improve the PUFA (especially AA and DHA) content and reduce the saturated fatty acid content in rat brain by dietary intake . Boudrault et.al had proved that DHA played a good effect on preventing dementia in four kinds of AD mouse models . Fish oil rich in DHA and EPA was discovered to be capable to decrease anger and anxiety and had been used as hygienical product of brain health for several years .
Different fatty acids composition of PC all could diminish the cognitive decline and biological damage and protect the brain. As PC rich in EPA or DHA showed better improvement than that barely contained, n-3 PUFA partly contributed to the advantageous effects of PC on brain function of demented mice induced by SCO-administration.
The preparation of Squid (Sthenoteuthis oualaniensis, provided by Weihai Boyu Food Company, Shandong Province, China) PC and sea cucumber (A. molpadioides, obtained from Nanshan Aquatic Products Market, Shandong Province, China) PC referenced to the Folch Method. Dried powder of squid roes and sea cucumber was extracted with 20-fold volume of the solution of CHCl3/MeOH (2:1) for 24 h respectively. Then the resultant filtrate was combined with the 0.88 % (mass fraction) KCl solution into an aqueous condition. The chloroform layer was collected after stratification and used to obtain total lipids by vacuum concentration. Insoluble part of total lipid was dissolved in chloroform at the end of two times of acetone washing. The solution was finally separated on a silica-gel column chromatography to acquire PC component. The purity of PC extracted from squid roe and sea cucumber determined respectively by high performance liquid chromatography (Waters 2695, Milford, MA) were all greater than 95 %. Egg yolk lecithin (EL), obtained from Beijing Aobox Biotechnology co., LTD (Beijing, China), was washed with cold acetone for three times before utilization. According to the fatty acids composition of EL, SQ-PC and SC-PC (Table 1), there was barely DHA and EPA in EL and the content of DHA and EPA were significantly different between SQ-PC and SC-PC. Scopolamine hydrobromide were supplied by Shanghai Harvest Pharmaceutical co., LTD (Shanghai, China). The kits used in the experiments were purchased from Nanjing Jiancheng Bioengineering Institute (Jiangsu Province, China).
Male BALB/c mice (20 ± 2 g, procured from Beijing Vital River Experiment Animal Technology co., LTD.) were housed under temperature (20 ± 2 °C) and relative humidity (50–60 %) with a 12/12 h light/dark cycle (light starting at 8 a.m.).After 1-week adaptation, mice were randomly divided into 5 groups (8 animals per group): model (M) group, control (Con) group, egg yolk lecithin (EL) group, squid PC (SQ-PC) group and sea cucumber PC (SC-PC) group. A modified 93-G Diet was used to feed the mice of Con group and M group. Mice in PC groups were respectively fed with modified 93 M + 0.5 % EL (m/m) diet, modified 93 M + 0.5 % SQ-PC diet and modified 93 M + 0.5 % SC-PC diet. Experimental diets were prepared in accord with recommendations of the American Institute of Nutrition. The ingredients of the experimental diets was displayed in Table 2.
The schedule of animal experiments is shown in Fig. 5. The intraperitoneal injection of scopolamine hydrobromide (5 mg/kg) of all mice except Con group initiated on the 8th day of grouped feeding, while Con group mice were injected with the same volume of saline. The injection was daily sustained until the end of test and water maze test started at 1 h after SCO administration.
Morris Water Maze was made up of a trajectory recording device and a circular pool with a platform. The pool (1.3 m in diameter and 0.5 m in height) was divided into four quadrants and named respectively: I, III, II, IV. With the water (0.3 m in depth) temperature controlled at 21–23 °C, the platform (9 cm in diameter) was submerged 1.5 cm under the water level in the center of quadrant I. A camera linked to a computer was located 2 m above the center of the pool and the movement of the mice trajectory was automatically recorded and analyzed by ANY-maze behavior tracking software (Stoelting Co., Wood Dale, USA). The test included place navigation test and spatial probe test. In place navigation test, each mouse received four trails to be trained to find the platform when being put into the pool respectively from four different quadrants and the sequence was changed every day during the whole training. The time of finding the platform was recorded as latency. If the animal was unable to arrive the hidden platform within 60s test, the latency was recorded as 60s and mouse was placed on the platform for 10s by hand. There was a 20s interval between each trail. The spatial probe test was carried out on the 7th day while the platform was removed and the animals were placed into the pool from quadrant III (opposite to quadrant I) and allowed to search the whole area until the termination. Swim path, time in target quadrant (quadrant I) and numbers of crossing the platform were measured and analyzed.
One day after the behavior test, mice were sacrificed and their brains were rapidly separated and divided into cortex, hippocampus and white matter. The intact brain tissue was dissected into left and right brain after cerebellum was removed. With the hemisphere being unfolded from the gap of ventricle, the Crescent-shaped hippocampus was drawn out gently. The metathalamus under the gap should be infibulated so that the lamellar white matter attached above the ventricle could be avulsed lightly. The part connected to the white matter was discard to ensure the purity of the cortex.
Brain tissues were respectively extracted with saline at the mass-liquid ratio of 1:9, then the tissue homogenate was centrifuged at 3500 r/min for 10 min. The supernate fluid was applied to measure enzymes activity through the related kits including Acetylcholinesterase (AchE) and superoxide dismutase (SOD) activity in cortex, white matter and hippocampus, monoamine oxidase (MAO) in white matter and malondialdehyde (MDA) content of right brain.
All experiment data were analyzed by SPSS 19.0 and presented as means ± standard errors. Student's t test was used to determine the difference between Con group and M group as well as that between the PC groups and M group, the difference between the PC groups were evaluated by One-way ANOVA with Tukey's post hoc test. Differences were considered significant at P < 0.05.
This project was supported by grants from State Key Program of National Natural Science of China (No. 31330060), National Natural Science Foundation of China (No. 31371757) and Program for New Century Excellent Talents in University (NCET-13-0534).
Author MMZ wrote a first draft of the paper. YX performed the data analysis and created the tables and figures. YMW and CHX substantially contributed to the study design, literature search and manuscript preparation. MW, MMZ and SHS carried out all the experiments. ZJL, JX and JFW refined the manuscript for publication. TY helped the design of the study and reviewed the manuscript. All authors read and approved the final manuscript for publication.


So far, three of the four main themes for 2018 that we shared in January's report – more aggressive Fed rate hikes, mean reversion of low vol, and geopolitical risks from Trump's foreign and trade policy – appear on track and our Q1 positioning was accretive. On our fourth theme, U.S. dollar strengthening, we remain confident, although it did not materialize during Q1.
This quarter's report contains our current country and sector positions in detail, as well as a special section on FM, "Frontier Outlook & Index Updates".
Global risk assets spared no time ringing in the new year, surging 7.3% (10% for emerging markets) in the opening weeks of January. But a cocktail of fears including are pricing of the pace of rate tightening in the U.S. and an unwinding of short vol positions cascaded through global markets, wiping out most of the year's gains in a brief two-week period (see Chart 1). Since then, markets have been contained in a range-bound trend, that many observers are hailing as a return to normalcy in the markets. Part of this boundedness is surely over fears of a trade war as the Trump Administration has finally launched their long promised salvo of trade measures against China. We profile this conflagration in further detail in our recent FIS Foresights piece, The Real Target is "Made In China 2025"; Not the US-China Trade Deficit. Over the past five quarters, Japan has modestly outperformed Europe, which has in turn modestly outperformed the U.S., though all developed markets have been dwarfed by emerging and to a lesser extent frontier markets (see Chart 1).
So far our four main themes for 2018 – more aggressive Fed rate hikes, U.S. dollar strengthening, mean reversion of low vol, and geopolitical risks from Trump's foreign and trade policy – appear on track, other than of course the U.S. dollar, which slumped again in Q1 against major global currencies (see Chart 2). Although the US dollar's long-term structural downtrend from a slower underlying pace of U.S. productivity growth relative to the rest of the world and a persistent external deficit, over the 6 to 12 month investment horizon, the US dollar could be buoyed by cyclical factors. For example, U.S. fiscal stimulus is initially bullish for the dollar, despite the fact that this will worsen the current account balance. Additional protectionist measures should also support the dollar as long as retaliation is muted. Already in early Q2 the USD has begun to retrace some of its earlier losses and we think the positioning of the markets in long EUR remains particularly crowded.
Most of our positioning from Q1 was accretive, as we remained overweight Japan and Emerging Markets (EM) relative to the U.S. and the UK. Within EM, Korea and Poland underperformed, but our favor to Brazil, Russia, Taiwan, Nigeria, Pakistan, Colombia, and Chile relative to EM all proved accretive, as did our tactical underweight to India despite our longer-term bullish outlook on the market. During Q1 we exited our position in Nigeria for a handsome gain and switched into Egypt, which has since also outperformed.
Looking towards Q2, on the surface we have made few changes, remaining constructive on Core Europe and Japan, neutral to the U.S. and UK while eschewing Australia. Within Europe and Japan we have tilted more heavily towards financials in particular, as we believe that rate normalization in both markets will accrue disproportionately towards banks, which remain at depressed valuations, especially in Japan.
For this next quarter, we are neutral overall on emerging markets, as our longer-term constructive view is tempered by some expectation for U.S. dollar strengthening and potential weakness in the Chinese credit cycle in the near term. We have reversed our bullish position in Taiwan and are now underweight the market as it is perhaps the most susceptible to Sino-American trade tensions. We are similarly a little more cautious on Korea, though tactically positioned to benefit from what we believe could be some positive news flow coming out of the summit meetings with North Korea. In Russia we are bucking the market consensus and staying overweight, having even added slightly to the position on price weakness following the most recent round of sanctions over Russia's support for Syria. While Russian geopolitics remain deplorable, (particularly their brazen assassination of a British national on British soil), Russian economics continue to improve. We believe that a stable to positive outlook for oil prices will ultimately prove more important for Russian risk assets than current geopolitics; while we are being paid to ride out the storm with a 5.3% dividend yield on the market (for the ETF). Moreover, Russian equities, which should trade at a discount to their peers, remain too cheap for the improving economic fundamentals and in an environment which remains supportive of oil prices. As noted in the Table outlining our sector positioning, both supply-demand dynamics and geopolitics (particularly with the Trump Administration threatening to withdraw from the Iran Agreement) should continue to support oil prices for at least the next few quarters (if not higher or for longer). This quarter, we added Thailand to our EM portfolio. Despite multiple delays in holding a civilian election, Thailand's military junta has brought relatively competent and stable economic management. Moreover, Thailand's relatively low external debt and foreign funding makes it less vulnerable than many other EMs to global/EM turmoil.
For our full, detailed list of country and sector positioning, see Table 1.
Q1 was also a busy time on the frontier, with Vietnamese equities approaching parabolic heights by the end of the quarter. After seeing the markets crest mid-April, we moved Vietnam back to neutral relative to frontier. The long-term fundamentals of the market remain solid and reasonably priced given a growth outlook (0.7x forward PEG); but we expect a cooling off period for at least a few months as fundamentals catch-up to prices. Romania also surged ahead 19% during Q1, fulfilling our forecast for some further outperformance of the market. We are cautious going into the end of the year as inflation is cresting up and the government's fiscal impulse continues unfettered. This could herald upside surprises for interest rates and a potential for a swift reversal of market sentiment. But the market there remains reasonably priced at about 10x trailing earnings and 1.1x P/B and so we will remain constructive a little longer, but are becoming more cautious.
In Argentina, the markets corrected 5.6% during Q1 and now seem to be waiting for the next sign. We are monitoring the inflation numbers closely, which are coming in right at our rule-of-thumb threshold of about 2% monthly CPI to stay neutral on the market. Over the coming months we are looking for a lack of bad news or more price weakness to re-enter the market. Kuwait also outperformed during the quarter (+8.1%), reaffirming our call for an overweight in our annual outlook. We think the positioning relative to other GCC markets remains very positive for Kuwait, but after some solid early year performance we are a little less sanguine on Kuwait's outperformance for the rest of the year. We still think Kuwait has a chance to get flagged by MSCI for watch-list inclusion for an upgrade to emerging markets, but for now it appears that an ultimate upgrade is not likely without a significant uptick in liquidity.
Remaining in the Gulf, markets are aflurry over the prospect of Saudi Arabia's potential to upgrade to emerging markets status. On March 28, FTSE announced that Saudi Arabia would be elevated to secondary emerging market status within their global equity indices. Local brokers and some investors are beginning to hype the potential for MSCI to follow suit this June. We are not so sanguine and see an MSCI announcement of an upgrade as coming late 2018, at the earliest, with mid-2019 still more likely. We also are not excited by Saudi equities, which remain at or slightly above their historical valuations and roughly on par with the rest of their would be emerging market peers. While the reforms occurring within Saudi Arabia are very interesting, and definitely should yield some exciting individual stock opportunities, we are not convinced that this market represents either a growth or value opportunity, and thus remain dissuaded to follow any beta play in the market. For our views on other potential reclassification candidates, as well as a review of recent research suggesting a trading strategy for such index changes, please refer to our recent FIS Foresights piece, Profiting from MSCI Reclassifications.
This report is neither an offer to sell nor a solicitation to invest in any product offered by FIS Group, Inc. and should not be considered as investment advice. This report was prepared for clients and prospective clients of FIS Group and is intended to be used solely by such clients and prospects for educational and illustrative purposes. The information contained herein is proprietary to FIS Group and may not be duplicated or used for any purpose other than the educational purpose for which it has been provided. Any unauthorized use, duplication or disclosure of this report is strictly prohibited.
This report is based on information believed to be correct, but is subject to revision. Although the information provided herein has been obtained from sources which FIS Group believes to be reliable, FIS Group does not guarantee its accuracy, and such information may be incomplete or condensed. Additional information is available from FIS Group upon request.
All performance and other projections are historical and do not guarantee future performance. No assurance can be given that any particular investment objective or strategy will be achieved at a given time and actual investment results may vary over any given time.


Qingdao Eversafe Marine Engineering CO.,LTD is the subsidiary of Qingdao Evergreen Maritime group company, specializes in ship launching, dry docking ,heavy lift with marine airbags.In 2007 years, The founder of Evergreen Maritime, Bob Yu realized that only produce good airbags is not enough , must guide clients to use airbags properly. Then one engineering service team was set up to help clients manager and carry out ship launching, dry docking projects. That team is the precursor of Eversafe Marine.
From 2008 years, Eversafe Marine began to operate independently. At that time, in China most engineering companies were engaged in ship launching, dry docking with airbags, worked heavily on experience, seldom did calculation for projects. Sometimes they succeed , some times they failed but don't know why.
Engineers of Eversafe Marine graduated from universities, they were educated to respect science. They carry out calculations for each project, implement projects cautiously. Gradually Eversafe Marine emerge as focal points due to 100% safety and success ratio of project.
Then in 2008, Eversafe Marine was appointed to launch one Olympic torch vessel by Beijing Government. Subsequently, got contract to haul out one retired submarine with airbags for Chinese Navy.
In 2010 years, Eversafe Marine launched one DWT58000 cargo ship (lightweight 11,800 tonnes) with 76 pieces airbags that created the world record of heaviest ship ever launched with airbags.
In 2011 years, Eversafe Marine salvaged one 6500 CBM LPG vessel in Romania with 20 pieces airbags, saved a new built ship with small cost.
In 2013 years, relocated 4000 tonnes structure with airbags, initiating the marine airbag application in building relocation area.
In 2015 years, created the method of launching vessel from floating carrier deck, launched 20+ barges for clients.
Till now , Eversafe Marine keeps 100% success ratio of undertaken projects, keeps his small size to stay fit and run fast.
Providing superior products and services from concept development through design, manufacturing, delivery, installation and operation. To design, supervise, install, maintain and operate marine projects in a safe and environmentally sound manner.
To generate an attitude of enthusiasm and pride throughout the company, through promoting high-tech products and providing a favourable environment for professional and personal development, and to highly reward it.
Eversafe Marine Engineering gets the National Science and Technology Progress Award for his achievement of marine engineering technology. As the partner of CNOOC, CNPC, China Navy,Eversafe is honored to work with talented people to do creative works. Combining with Nankai University we get powerful technology support and research resource.Technology creating value is our main attitude toward fierce competition.


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Physics Inventions
Physics Experiments And Labs
Just 4 percent of galaxies have neighbors like the Milky Way
How unique is the Milky Way? To find out, a group of researchers led by Stanford University astrophysicist Risa Wechsler compared the Milky Way to similar galaxies and found that just four percent are like the galaxy Earth calls home.
"We are interested in how the Milky Way fits into the broader context of the universe", said Wechsler. "This research helps us understand whether our galaxy is typical or not, and may provide clues to its formation history."
The research team compared the Milky Way to similar galaxies in terms of luminosity–a measure of how much light is emitted–and distance to other bright galaxies. They found galaxies that have two satellites that are as bright and close by as the Milky Way's two closest satellites, the Large and Small Magellanic Clouds, are rare.
Published in the May 20 issue of the Astrophysical Journal, the findings are based on analyses of data collected from the Sloan Digital Sky Survey (SDSS). The work is the first of three papers that study the properties of the Milky Way's two most massive satellites.
Supported in part by the National Science Foundation (NSF), the SDSS is the most extensive survey of the optical sky performed to date.
In more than eight years of operations, SDSS has obtained images covering more than a quarter of the sky, and created 3-dimensional maps containing more than 930,000 galaxies and 120,000 quasars. For this analysis, Wechsler's group studied more than 20,000 galaxies with properties similar to the Milky Way and investigated the galaxies surrounding these Milky Way "twins", to create a "census" of galaxies similar to the Milky Way in the universe.
The work represents one of the most extensive studies of this kind ever performed.
Scientists can also compare the SDSS data to galaxies simulated by a computer model. Since they are currently unable to see all the way back to the Big Bang, this is one way researchers are trying to understand how the universe as we see it today began.
In order to learn more about possible conditions in the early universe, the group performed computer simulations to recreate the universe from specific sets of starting conditions. Then they compared their simulations to the SDSS data set. In this way, the group was able to test different theories of galaxy formation to determine whether or not each would result in a universe that matches what we see today. The results of their simulation matched the result found in the SDSS data set: just four percent of the simulated galaxies had two satellites like the Magellanic Clouds.
"This is an excellent example of data-enabled science," said Nigel Sharp, of NSF's Division of Astronomical Sciences. "Comparing the 'fake' and 'real' Universes is how we discriminate between successful and unsuccessful theories. This work interconnects three of the four legs of science: theory, observation and simulation, for a powerful scientific result."
Their results also lend support to a leading theory of galaxy formation called the Cold Dark Matter (CDM) theory. This theory provides what many consider to be the simplest explanation for the arrangement of galaxies throughout the universe following the Big Bang. It assumes that most of the matter in the Universe consists of material that cannot be observed by its electromagnetic radiation (dark) and whose constituent particles move slowly (cold). Dark matter, an invisible and exotic material of unknown composition, is believed to influence the distribution of galaxies in space and the overall expansion of the universe. The rareness of this aspect of the Milky Way may provide clues to its formation history.
"Because the presence of two galaxies like the Magellanic Clouds is unusual, we can use them to learn more about our own galaxy," said Wechsler. Using their simulation, the team identified a sample of simulated galaxies that had satellites matching the Milky Way's in terms of their locations and speeds.
"The combination of large surveys of the sky like the SDSS and large samples of simulated galaxies provides a new opportunity to learn about the place of our galaxy in the Universe," said Wechsler. "Future surveys will allow us to extend this study to even dimmer satellite galaxies, to build a full picture of the formation of our galaxy."
Source: National Science Foundation
Mohsin ali Science & Technology News Astrophysical Journal, Big Bang, CDM, Cold Dark Matter, Earth, latestinventionsinscience, Magellanic Clouds, Milky Way, National Science Foundation, Nigel Sharp, NSF, physics, physicsinventions, physicsnews, Risa Wechsler, science, sciencenews, SDSS, Sloan Digital Sky Survey, Source National Science Foundation, Stanford University
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Shorea balanocarpoides (called, along with some other species in the genus Shorea, white meranti or yellow meranti) is a species of plant in the family Dipterocarpaceae. It is found in Sumatra, Peninsular Malaysia and Borneo.

References

balanocarpoides
Trees of Sumatra
Trees of Peninsular Malaysia
Trees of Borneo
Endangered plants
Taxonomy articles created by Polbot

redpajama_set_name: RedPajamaWikipedia