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An uncountable Moore-Schmidt theorem
28 November, 2019 in math.DS, math.LO, math.PR, paper | Tags: abstract measure theory, Asgar Jamneshan, cocycles, compact abelian groups, ergodic theory, sigma algebras | by Terence Tao | 7 comments
Asgar Jamneshan and I have just uploaded to the arXiv our paper "An uncountable Moore-Schmidt theorem". This paper revisits a classical theorem of Moore and Schmidt in measurable cohomology of measure-preserving systems. To state the theorem, let be a probability space, and be the group of measure-preserving automorphisms of this space, that is to say the invertible bimeasurable maps that preserve the measure : . To avoid some ambiguity later in this post when we introduce abstract analogues of measure theory, we will refer to measurable maps as concrete measurable maps, and measurable spaces as concrete measurable spaces. (One could also call a concrete probability space, but we will not need to do so here as we will not be working explicitly with abstract probability spaces.)
Let be a discrete group. A (concrete) measure-preserving action of on is a group homomorphism from to , thus is the identity map and for all . A large portion of ergodic theory is concerned with the study of such measure-preserving actions, especially in the classical case when is the integers (with the additive group law).
Let be a compact Hausdorff abelian group, which we can endow with the Borel -algebra . A (concrete measurable) –cocycle is a collection of concrete measurable maps obeying the cocycle equation
for -almost every . (Here we are glossing over a measure-theoretic subtlety that we will return to later in this post – see if you can spot it before then!) Cocycles arise naturally in the theory of group extensions of dynamical systems; in particular (and ignoring the aforementioned subtlety), each cocycle induces a measure-preserving action on (which we endow with the product of with Haar probability measure on ), defined by
This connection with group extensions was the original motivation for our study of measurable cohomology, but is not the focus of the current paper.
A special case of a -valued cocycle is a (concrete measurable) -valued coboundary, in which for each takes the special form
for -almost every , where is some measurable function; note that (ignoring the aforementioned subtlety), every function of this form is automatically a concrete measurable -valued cocycle. One of the first basic questions in measurable cohomology is to try to characterize which -valued cocycles are in fact -valued coboundaries. This is a difficult question in general. However, there is a general result of Moore and Schmidt that at least allows one to reduce to the model case when is the unit circle , by taking advantage of the Pontryagin dual group of characters , that is to say the collection of continuous homomorphisms to the unit circle. More precisely, we have
Theorem 1 (Countable Moore-Schmidt theorem) Let be a discrete group acting in a concrete measure-preserving fashion on a probability space . Let be a compact Hausdorff abelian group. Assume the following additional hypotheses:
(i) is at most countable.
(ii) is a standard Borel space.
(iii) is metrisable.
Then a -valued concrete measurable cocycle is a concrete coboundary if and only if for each character , the -valued cocycles are concrete coboundaries.
The hypotheses (i), (ii), (iii) are saying in some sense that the data are not too "large"; in all three cases they are saying in some sense that the data are only "countably complicated". For instance, (iii) is equivalent to being second countable, and (ii) is equivalent to being modeled by a complete separable metric space. It is because of this restriction that we refer to this result as a "countable" Moore-Schmidt theorem. This theorem is a useful tool in several other applications, such as the Host-Kra structure theorem for ergodic systems; I hope to return to these subsequent applications in a future post.
Let us very briefly sketch the main ideas of the proof of Theorem 1. Ignore for now issues of measurability, and pretend that something that holds almost everywhere in fact holds everywhere. The hard direction is to show that if each is a coboundary, then so is . By hypothesis, we then have an equation of the form
for all and some functions , and our task is then to produce a function for which
for all .
Comparing the two equations, the task would be easy if we could find an for which
for all . However there is an obstruction to this: the left-hand side of (3) is additive in , so the right-hand side would have to be also in order to obtain such a representation. In other words, for this strategy to work, one would have to first establish the identity
for all . On the other hand, the good news is that if we somehow manage to obtain the equation, then we can obtain a function obeying (3), thanks to Pontryagin duality, which gives a one-to-one correspondence between and the homomorphisms of the (discrete) group to .
Now, it turns out that one cannot derive the equation (4) directly from the given information (2). However, the left-hand side of (2) is additive in , so the right-hand side must be also. Manipulating this fact, we eventually arrive at
In other words, we don't get to show that the left-hand side of (4) vanishes, but we do at least get to show that it is -invariant. Now let us assume for sake of argument that the action of is ergodic, which (ignoring issues about sets of measure zero) basically asserts that the only -invariant functions are constant. So now we get a weaker version of (4), namely
for some constants .
Now we need to eliminate the constants. This can be done by the following group-theoretic projection. Let denote the space of concrete measurable maps from to , up to almost everywhere equivalence; this is an abelian group where the various terms in (5) naturally live. Inside this group we have the subgroup of constant functions (up to almost everywhere equivalence); this is where the right-hand side of (5) lives. Because is a divisible group, there is an application of Zorn's lemma (a good exercise for those who are not acquainted with these things) to show that there exists a retraction , that is to say a group homomorphism that is the identity on the subgroup . We can use this retraction, or more precisely the complement , to eliminate the constant in (5). Indeed, if we set
then from (5) we see that
while from (2) one has
and now the previous strategy works with replaced by . This concludes the sketch of proof of Theorem 1.
In making the above argument rigorous, the hypotheses (i)-(iii) are used in several places. For instance, to reduce to the ergodic case one relies on the ergodic decomposition, which requires the hypothesis (ii). Also, most of the above equations only hold outside of a set of measure zero, and the hypothesis (i) and the hypothesis (iii) (which is equivalent to being at most countable) to avoid the problem that an uncountable union of sets of measure zero could have positive measure (or fail to be measurable at all).
My co-author Asgar Jamneshan and I are working on a long-term project to extend many results in ergodic theory (such as the aforementioned Host-Kra structure theorem) to "uncountable" settings in which hypotheses analogous to (i)-(iii) are omitted; thus we wish to consider actions on uncountable groups, on spaces that are not standard Borel, and cocycles taking values in groups that are not metrisable. Such uncountable contexts naturally arise when trying to apply ergodic theory techniques to combinatorial problems (such as the inverse conjecture for the Gowers norms), as one often relies on the ultraproduct construction (or something similar) to generate an ergodic theory translation of these problems, and these constructions usually give "uncountable" objects rather than "countable" ones. (For instance, the ultraproduct of finite groups is a hyperfinite group, which is usually uncountable.). This paper marks the first step in this project by extending the Moore-Schmidt theorem to the uncountable setting.
If one simply drops the hypotheses (i)-(iii) and tries to prove the Moore-Schmidt theorem, several serious difficulties arise. We have already mentioned the loss of the ergodic decomposition and the possibility that one has to control an uncountable union of null sets. But there is in fact a more basic problem when one deletes (iii): the addition operation , while still continuous, can fail to be measurable as a map from to ! Thus for instance the sum of two measurable functions need not remain measurable, which makes even the very definition of a measurable cocycle or measurable coboundary problematic (or at least unnatural). This phenomenon is known as the Nedoma pathology. A standard example arises when is the uncountable torus , endowed with the product topology. Crucially, the Borel -algebra generated by this uncountable product is not the product of the factor Borel -algebras (the discrepancy ultimately arises from the fact that topologies permit uncountable unions, but -algebras do not); relating to this, the product -algebra is not the same as the Borel -algebra , but is instead a strict sub-algebra. If the group operations on were measurable, then the diagonal set
would be measurable in . But it is an easy exercise in manipulation of -algebras to show that if are any two measurable spaces and is measurable in , then the fibres of are contained in some countably generated subalgebra of . Thus if were -measurable, then all the points of would lie in a single countably generated -algebra. But the cardinality of such an algebra is at most while the cardinality of is , and Cantor's theorem then gives a contradiction.
To resolve this problem, we give a coarser -algebra than the Borel -algebra, which we call the reduced -algebra , thus coarsening the measurable space structure on to a new measurable space . In the case of compact Hausdorff abelian groups, can be defined as the -algebra generated by the characters ; for more general compact abelian groups, one can define as the -algebra generated by all continuous maps into metric spaces. This -algebra is equal to when is metrisable but can be smaller for other . With this measurable structure, becomes a measurable group; it seems that once one leaves the metrisable world that is a superior (or at least equally good) space to work with than for analysis, as it avoids the Nedoma pathology. (For instance, from Plancherel's theorem, we see that if is the Haar probability measure on , then (thus, every -measurable set is equivalent modulo -null sets to a -measurable set), so there is no damage to Plancherel caused by passing to the reduced -algebra.
Passing to the reduced -algebra fixes the most severe problems with an uncountable Moore-Schmidt theorem, but one is still faced with an issue of having to potentially take an uncountable union of null sets. To avoid this sort of problem, we pass to the framework of abstract measure theory, in which we remove explicit mention of "points" and can easily delete all null sets at a very early stage of the formalism. In this setup, the category of concrete measurable spaces is replaced with the larger category of abstract measurable spaces, which we formally define as the opposite category of the category of -algebras (with Boolean algebra homomorphisms). Thus, we define an abstract measurable space to be an object of the form , where is an (abstract) -algebra and is a formal placeholder symbol that signifies use of the opposite category, and an abstract measurable map is an object of the form , where is a Boolean algebra homomorphism and is again used as a formal placeholder; we call the pullback map associated to . [UPDATE: It turns out that this definition of a measurable map led to technical issues. In a forthcoming revision of the paper we also impose the requirement that the abstract measurable map be -complete (i.e., it respects countable joins).] The composition of two abstract measurable maps , is defined by the formula , or equivalently .
Every concrete measurable space can be identified with an abstract counterpart , and similarly every concrete measurable map can be identified with an abstract counterpart , where is the pullback map . Thus the category of concrete measurable spaces can be viewed as a subcategory of the category of abstract measurable spaces. The advantage of working in the abstract setting is that it gives us access to more spaces that could not be directly defined in the concrete setting. Most importantly for us, we have a new abstract space, the opposite measure algebra of , defined as where is the ideal of null sets in . Informally, is the space with all the null sets removed; there is a canonical abstract embedding map , which allows one to convert any concrete measurable map into an abstract one . One can then define the notion of an abstract action, abstract cocycle, and abstract coboundary by replacing every occurrence of the category of concrete measurable spaces with their abstract counterparts, and replacing with the opposite measure algebra ; see the paper for details. Our main theorem is then
Theorem 2 (Uncountable Moore-Schmidt theorem) Let be a discrete group acting abstractly on a -finite measure space . Let be a compact Hausdorff abelian group. Then a -valued abstract measurable cocycle is an abstract coboundary if and only if for each character , the -valued cocycles are abstract coboundaries.
With the abstract formalism, the proof of the uncountable Moore-Schmidt theorem is almost identical to the countable one (in fact we were able to make some simplifications, such as avoiding the use of the ergodic decomposition). A key tool is what we call a "conditional Pontryagin duality" theorem, which asserts that if one has an abstract measurable map for each obeying the identity for all , then there is an abstract measurable map such that for all . This is derived from the usual Pontryagin duality and some other tools, most notably the completeness of the -algebra of , and the Sikorski extension theorem.
We feel that it is natural to stay within the abstract measure theory formalism whenever dealing with uncountable situations. However, it is still an interesting question as to when one can guarantee that the abstract objects constructed in this formalism are representable by concrete analogues. The basic questions in this regard are:
(i) Suppose one has an abstract measurable map into a concrete measurable space. Does there exist a representation of by a concrete measurable map ? Is it unique up to almost everywhere equivalence?
(ii) Suppose one has a concrete cocycle that is an abstract coboundary. When can it be represented by a concrete coboundary?
For (i) the answer is somewhat interesting (as I learned after posing this MathOverflow question):
If does not separate points, or is not compact metrisable or Polish, there can be counterexamples to uniqueness. If is not compact or Polish, there can be counterexamples to existence.
If is a compact metric space or a Polish space, then one always has existence and uniqueness.
If is a compact Hausdorff abelian group, one always has existence.
If is a complete measure space, then one always has existence (from a theorem of Maharam).
If is the unit interval with the Borel -algebra and Lebesgue measure, then one has existence for all compact Hausdorff assuming the continuum hypothesis (from a theorem of von Neumann) but existence can fail under other extensions of ZFC (from a theorem of Shelah, using the method of forcing).
For more general , existence for all compact Hausdorff is equivalent to the existence of a lifting from the -algebra to (or, in the language of abstract measurable spaces, the existence of an abstract retraction from to ).
It is a long-standing open question (posed for instance by Fremlin) whether it is relatively consistent with ZFC that existence holds whenever is compact Hausdorff.
Our understanding of (ii) is much less complete:
If is metrisable, the answer is "always" (which among other things establishes the countable Moore-Schmidt theorem as a corollary of the uncountable one).
If is at most countable and is a complete measure space, then the answer is again "always".
In view of the answers to (i), I would not be surprised if the full answer to (ii) was also sensitive to axioms of set theory. However, such set theoretic issues seem to be almost completely avoided if one sticks with the abstract formalism throughout; they only arise when trying to pass back and forth between the abstract and concrete categories.
Central extensions of Lie groups, and cocycle averaging
7 June, 2011 in expository, math.GN, math.GR, math.RT | Tags: cocycles, group extensions, Hilbert's fifth problem, Lie groups | by Terence Tao | 12 comments
In the last few months, I have been working my way through the theory behind the solution to Hilbert's fifth problem, as I (together with Emmanuel Breuillard, Ben Green, and Tom Sanders) have found this theory to be useful in obtaining noncommutative inverse sumset theorems in arbitrary groups; I hope to be able to report on this connection at some later point on this blog. Among other things, this theory achieves the remarkable feat of creating a smooth Lie group structure out of what is ostensibly a much weaker structure, namely the structure of a locally compact group. The ability of algebraic structure (in this case, group structure) to upgrade weak regularity (in this case, continuous structure) to strong regularity (in this case, smooth and even analytic structure) seems to be a recurring theme in mathematics, and an important part of what I like to call the "dichotomy between structure and randomness".
The theory of Hilbert's fifth problem sprawls across many subfields of mathematics: Lie theory, representation theory, group theory, nonabelian Fourier analysis, point-set topology, and even a little bit of group cohomology. The latter aspect of this theory is what I want to focus on today. The general question that comes into play here is the extension problem: given two (topological or Lie) groups and , what is the structure of the possible groups that are formed by extending by . In other words, given a short exact sequence
to what extent is the structure of determined by that of and ?
As an example of why understanding the extension problem would help in structural theory, let us consider the task of classifying the structure of a Lie group . Firstly, we factor out the connected component of the identity as
as Lie groups are locally connected, is discrete. Thus, to understand general Lie groups, it suffices to understand the extensions of discrete groups by connected Lie groups.
Next, to study a connected Lie group , we can consider the conjugation action on the Lie algebra , which gives the adjoint representation . The kernel of this representation consists of all the group elements that commute with all elements of the Lie algebra, and thus (by connectedness) is the center of . The adjoint representation is then faithful on the quotient . The short exact sequence
then describes as a central extension (by the abelian Lie group ) of , which is a connected Lie group with a faithful finite-dimensional linear representation.
This suggests a route to Hilbert's fifth problem, at least in the case of connected groups . Let be a connected locally compact group that we hope to demonstrate is isomorphic to a Lie group. As discussed in a previous post, we first form the space of one-parameter subgroups of (which should, eventually, become the Lie algebra of ). Hopefully, has the structure of a vector space. The group acts on by conjugation; this action should be both continuous and linear, giving an "adjoint representation" . The kernel of this representation should then be the center of . The quotient is locally compact and has a faithful linear representation, and is thus a Lie group by von Neumann's version of Cartan's theorem (discussed in this previous post). The group is locally compact abelian, and so it should be a relatively easy task to establish that it is also a Lie group. To finish the job, one needs the following result:
Theorem 1 (Central extensions of Lie are Lie) Let be a locally compact group which is a central extension of a Lie group by an abelian Lie group . Then is also isomorphic to a Lie group.
This result can be obtained by combining a result of Kuranishi with a result of Gleason; I am recording this argument below the fold. The point here is that while is initially only a topological group, the smooth structures of and can be combined (after a little bit of cohomology) to create the smooth structure on required to upgrade from a topological group to a Lie group. One of the main ideas here is to improve the behaviour of a cocycle by averaging it; this basic trick is helpful elsewhere in the theory, resolving a number of cohomological issues in topological group theory. The result can be generalised to show in fact that arbitrary (topological) extensions of Lie groups by Lie groups remain Lie; this was shown by Gleason. However, the above special case of this result is already sufficient (in conjunction with the rest of the theory, of course) to resolve Hilbert's fifth problem.
Remark 1 We have shown in the above discussion that every connected Lie group is a central extension (by an abelian Lie group) of a Lie group with a faithful continuous linear representation. It is natural to ask whether this central extension is necessary. Unfortunately, not every connected Lie group admits a faithful continuous linear representation. An example (due to Birkhoff) is the Heisenberg-Weyl group
Indeed, if we consider the group elements
for some prime , then one easily verifies that has order and is central, and that is conjugate to . If we have a faithful linear representation of , then must have at least one eigenvalue that is a primitive root of unity. If is the eigenspace associated to , then must preserve , and be conjugate to on this space. This forces to have at least distinct eigenvalues on , and hence (and thus ) must have dimension at least . Letting we obtain a contradiction. (On the other hand, is certainly isomorphic to the extension of the linear group by the abelian group .)
An inverse theorem for the uniformity seminorms associated with the action of F^infty_p
19 January, 2009 in math.DS, paper | Tags: characteristic factor, cocycles, finite fields, Gowers uniformity norm, polynomials, Tamar Ziegler, Vitaly Bergelson | by Terence Tao | 7 comments
Vitaly Bergelson, Tamar Ziegler, and I have just uploaded to the arXiv our paper "An inverse theorem for the uniformity seminorms associated with the action of ". This paper establishes the ergodic inverse theorems that are needed in our other recent paper to establish the inverse conjecture for the Gowers norms over finite fields in high characteristic (and to establish a partial result in low characteristic), as follows:
Theorem. Let be a finite field of characteristic p. Suppose that is a probability space with an ergodic measure-preserving action of . Let be such that the Gowers-Host-Kra seminorm (defined in a previous post) is non-zero.
In the high-characteristic case , there exists a phase polynomial g of degree <k (as defined in the previous post) such that .
In general characteristic, there exists a phase polynomial of degree <C(k) for some C(k) depending only on k such that .
This theorem is closely analogous to a similar theorem of Host and Kra on ergodic actions of , in which the role of phase polynomials is played by functions that arise from nilsystem factors of X. Indeed, our arguments rely heavily on the machinery of Host and Kra.
The paper is rather technical (60+ pages!) and difficult to describe in detail here, but I will try to sketch out (in very broad brush strokes) what the key steps in the proof of part 2 of the theorem are. (Part 1 is similar but requires a more delicate analysis at various stages, keeping more careful track of the degrees of various polynomials.)
Cohomology for dynamical systems
21 December, 2008 in expository, math.AT, math.DS | Tags: coboundaries, cocycles, cohomology, dynamical systems | by Terence Tao | 25 comments
A dynamical system is a space X, together with an action of some group . [In practice, one often places topological or measure-theoretic structure on X or G, but this will not be relevant for the current discussion. In most applications, G is an abelian (additive) group such as the integers or the reals , but I prefer to use multiplicative notation here.] A useful notion in the subject is that of an (abelian) cocycle; this is a function taking values in an abelian group that obeys the cocycle equation
for all and . [Again, if one is placing topological or measure-theoretic structure on the system, one would want to be continuous or measurable, but we will ignore these issues.] The significance of cocycles in the subject is that they allow one to construct (abelian) extensions or skew products of the original dynamical system X, defined as the Cartesian product with the group action . (The cocycle equation (1) is needed to ensure that one indeed has a group action, and in particular that .) This turns out to be a useful means to build complex dynamical systems out of simpler ones. (For instance, one can build nilsystems by starting with a point and taking a finite number of abelian extensions of that point by a certain type of cocycle.)
A special type of cocycle is a coboundary; this is a cocycle that takes the form for some function . (Note that the cocycle equation (1) is automaticaly satisfied if is of this form.) An extension of a dynamical system by a coboundary can be conjugated to the trivial extension by the change of variables .
While every coboundary is a cocycle, the converse is not always true. (For instance, if X is a point, the only coboundary is the zero function, whereas a cocycle is essentially the same thing as a homomorphism from G to U, so in many cases there will be more cocycles than coboundaries. For a contrasting example, if X and G are finite (for simplicity) and G acts freely on X, it is not difficult to see that every cocycle is a coboundary.) One can measure the extent to which this converse fails by introducing the first cohomology group , where is the space of cocycles and is the space of coboundaries (note that both spaces are abelian groups). In my forthcoming paper with Vitaly Bergelson and Tamar Ziegler on the ergodic inverse Gowers conjecture (which should be available shortly), we make substantial use of some basic facts about this cohomology group (in the category of measure-preserving systems) that were established in a paper of Host and Kra.
The above terminology of cocycles, coboundaries, and cohomology groups of course comes from the theory of cohomology in algebraic topology. Comparing the formal definitions of cohomology groups in that theory with the ones given above, there is certainly quite a bit of similarity, but in the dynamical systems literature the precise connection does not seem to be heavily emphasised. The purpose of this post is to record the precise fashion in which dynamical systems cohomology is a special case of cochain complex cohomology from algebraic topology, and more specifically is analogous to singular cohomology (and can also be viewed as the group cohomology of the space of scalar-valued functions on X, when viewed as a G-module); this is not particularly difficult, but I found it an instructive exercise (especially given that my algebraic topology is extremely rusty), though perhaps this post is more for my own benefit that for anyone else.


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No Thanks: Reunite 545 Traumatized Children With Families (OPINION)
By: Kristin Kan, MD
In this February 19, 2019, file photo, children line up to enter a tent at the Homestead Temporary Shelter for Unaccompanied Children in Homestead, Fla. (AP Photo/Wilfredo Lee, File)
United States families are preparing for Thanksgiving and other winter holidays by finding the safest way to celebrate without transmitting COVID-19 to each other.
While the decisions are difficult as each family weighs its own risks, these are the necessary steps to protect loved ones until it will be safer to gather all in-person again. The way Americans celebrate will look different, but thanks to technology, remaining connected is possible.
But the security and gratitude of being together as a family will not occur for 545 children alone and traumatized in this country. American Civil Liberties Union lawyers recently filed with the U.S. Justice Department that 545 detained migrant children have not yet been reunited with their parents.
At the recent presidential debate, when asked about the children separated from their families, President Donald Trump responded dismissively that they have been "so well taken care of."
This follows the Trump administration's implementation of the "zero tolerance" policy of government-sanctioned separation of children from parents in July 2017 until June 2018. It is estimated that approximately 5,500 migrant children were separated from their parents; 40% were younger than 10 years old.
The nation's policy was not only in violation of human rights but also was harmful to children's health.
It has been two years since the policy ended. The lawyers, who had been assigned with reuniting children with parents, have been unable to locate or reach parents of these 545 children.
While parent-child separation is a tragedy experienced around the globe from war, natural disasters, collapsed governments, and trafficking, mandated parent-child separation was an appallingly designed immigration policy.
As a medical asylee evaluator and pediatrician, I have documented the stories of these children's escapes from gang-led targeted violence, extortion, and the murders of relatives killed in their home countries.
From my field of child health research, I know that children with increasing number of traumatic experiences, sometimes known as adverse childhood experiences (ACEs), are at higher risk for devastating, long-term health consequences, including heart disease and stroke, depression, and suicide.
In our previous study of children with ACEs in the U.S., family factors that promote positive parent-child interaction were significant for childhood resilience, or the general capacity for children to recover from substantial challenges.
The U.S.' unpopular policy compounded the damages these children had already faced in dreadful ways. The U.S. must remedy the harm caused to these children and their families. Reunification of the remaining children with their families must remain a priority in order to progress toward repairing the damage.
The U.S. government also needs to provide appropriate rehabilitative mental and medical services to the traumatized children and parents. Guaranteed access to trauma-informed care is necessary so that children can receive services in an environment for recovery instead of re-traumatization.
While the U.S. continues to wrestle with consensus on immigration policy, the rights of children and families in policies and practices need protection, along with the guarantee against repeating this egregious policy ever again.
As the holidays approach, the importance of family safety and health is a key concern. But the policies that represent our country must protect all children and families, including non-citizens, who are guaranteed rights by the U.S. Constitution and international law.
In 1995 at the launch of the Children' Fund, Nelson Mandela stated, "There can be no keener revelation of a society's soul than the way in which it treats its children." Recognizing that to build a future generation, the reversal of the "wrong done to our youth" must be a national priority.
In U.S. history, family separation, unfortunately, is not a new federal strategy, but it cannot be the norm.
Kristin Kan, MD MPH MSc is a pediatrician, researcher, and Assistant Professor of Pediatrics at Ann and Robert H. Lurie Children's Hospital of Chicago and Northwestern University, and a Public Voices Fellow with The OpEd Project.
US Has Reunited 100 Children Taken From Parents Under Trump
Separated Since 2017 Under Trump Policy, One Family…
US Will Reunite 4 Families Separated at Mexico…

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Please find the 2018 band camp documents below. The District 51 Medical/Field Trip forms MUST be turned in on Monday, July 31st.
Field Trip Permission Form and Medical Form – This MUST be turned in on July 31st.
2018 Band Camp Brochure – Lots of information about what happens during band camp, and our evening events!
CHS Marching Band Calendar 2018– Here is our calendar that was mailed out in June. Please note that there were several changes from the preliminary calendar that was distributed in the spring semester.
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After a freshman campaign where she led the Dustdevils in ERA, Melanie Lint will take an increased role on the pitching staff after it lost second-team All-Heartland Conference hurler Delainy Thompson.
The Dustdevils softball team entered this weekend's series against the best team in the Heartland Conference looking to prove itself. After two close road losses Friday, Texas A&M International proved it could hang with St. Mary's. And on Saturday, it showed it can beat them.
The Dustdevils handed the Rattlers just their second conference loss all season with a tight 1-0 victory in the series finale. They scored the lone run in the fourth and held on for the win in San Antonio.
The victory improves the Dustdevils to 13-24 this season while keeping them from dropping below .500 in Heartland Conference play jumping to 10-9. They are just percentage points behind third-place Lubbock Christian (18-9, 8-6 Heartland) and fourth-place Oklahoma Christian (19-16, 9-7) in the league standings.
St. Mary's (25-12) remains on top of the Heartland standings even with the loss as it falls to 13-2 in conference play. They opened the series Friday winning 2-1 and 5-3 over TAMIU after previously handing the school its most lopsided conference outings of 2018 at 8-1 and 4-1 in a doubleheader in Laredo on March 7.
Throughout the campaign, freshman pitcher Melanie Lint has had an impressive first season. But Saturday was her signature moment holding the Rattlers off the scoreboard in the complete-game shutout. Lint threw all seven innings while only giving up three hits and walking two batters. She is now 6-7 with the 10th best ERA in the conference at 2.74.
A little over a month ago, Lint allowed a combined 15 runs in two games to West Texas A&M and UC-Colorado Springs as her ERA ballooned to 5.12. But she has gotten better every time out since, lowering her ERA in all 15 appearances since that game. She has only given up a total of six earned runs during that span in 51 innings, an ERA of 0.82 in those 15 outings.
Meanwhile, it was the offense's job to try to get at least a run on the board, and they managed to do just that. It wasn't as easy as it may sound, as the Rattlers trotted out starting pitcher Staci Johns - the reigning Louisville Slugger/NFCA Division II Pitcher of the Week - who boasted a 13-4 record and the league's third-lowest ERA at 1.69. She even lowered it Saturday to 1.65, but her record gained a defeat in the loss column.
Johns stifled TAMIU just a day earlier in a 2-1 win throwing all seven innings while giving up only one hit and one unearned run with six strikeouts. She wasn't quite as dominant Saturday, giving up a run and five hits while punching out seven.
Through the first three innings, things didn't look good for the Dustdevils against Johns. The sophomore hurler retired the first nine batters she faced working her way through the order. But in the fourth, center fielder Cassie Cannon singled to right to lead off the inning. A sacrifice bunt from second baseman Melanie Gamboa moved her into scoring position for Maddison Schofield and she delivered. The right fielder singled home Cannon for the game's only run.
TAMIU had a chance for an insurance run in the seventh as third baseman Maya Paul led off the frame with a double to left center. But she was picked off on the next play after a fly out for a double play. It proved to be costly as designated hitter Summer Woodson potentially could've brought her home during the next at-bat with a single to left.
First baseman Brandi Giles also had a two-out single in the fifth.
Meanwhile, the Rattlers had only really one opportunity to get to Lint coming in the fifth. A single kicked things off before the runner was moved to second on a ground out. With two outs, another single put runners on second and third before a walk loaded the bases. But Lint got a fly out to center field to get out of danger and strand the bases loaded.
Riding the momentum of beating the top team in the conference, the Dustdevils head to third-place Lubbock Christian Tuesday looking to climb in the standings. In their only games of next week, TAMIU hosts the Lady Chaps in a doubleheader at noon.


text:
Publish dateThursday 3 November 2022 - 20:36
Call for Iran's participation at Bologna Children's Book Fair 2023 issued
IBNA- Iran's Book and Literature House Institute issued a call inviting Iranian publishers and book activists to participate at the 60th Bologna Children's Book Fair (BCBF) scheduled for March 6 to 9 2023.
All active Iranian publishers, print industry unions, cultural institutes, literary agents and children's books illustrators have been addressed by the Book and Literature House institute to register for the event.
Registration for attending Iran's stand at the 60th Bologna Children's Book Fair will continue to November 11 on the website: ketab.ir.
The deadline for submitting the list of appropriate children's books as well as catalogs and brochures is December 1. Also those interested may send the original books not later than January 10 to the Book and Literature House Institute. The books must be published by the permission of Iran's Ministry of Culture and Islamic Guidance.
Since 1963, BCBF is held yearly for four days in March or April in Bologna, Italy. It is the meeting place for all professionals involved with creating and publishing children's books, and is mainly used for the buying and selling of rights, both for translations and for derived products like movies or animated series.
It is also the event where a number of major awards are given, the BolognaRagazzi Awards, in four categories (Fiction, Non-fiction, New Horizons (for the non-Western world) and Opera Prima (for first works).
During the fair, but separate from it, some major awards are announced, including the biannual Hans Christian Andersen Awards and the Astrid Lindgren Memorial Award.
https://www.ibna.ir/vdcjxoet8uqe8vz.92fu.html
ibna.ir/vdcjxoet8uqe8vz.92fu.html


text:
Which Animal Are You Most Likely to Hit While Driving?
by Kelly Roche on October 27, 2017
Roughly one in three drivers say they don't feel confident about knowing how to avoid a collision with a large animal, a new national survey from State Farm Canada finds.
"The unpredictability of these situations, combined with human impulses to try to preserve the lives of these animals makes these situations difficult and dangerous," said State Farm Canada spokesman John Bordignon.
More than 80 per cent of drivers polled say they believe that better public education about how to react to wildlife on the road is needed to prevent collisions that could lead to injuries and fatalities,
According to the survey, when seeing a deer in the middle of a two-lane highway, Canadians are most likely to brake (66 per cent) or take their foot off the gas (55 per cent). More than one-third indicated they would honk their horn and one-quarter said they would swerve.
"In fact, according to police and road safety experts, swerving is not the best strategy when approaching wildlife on the road," said Bordignon.
"Instead, they advise drivers to maintain their line, even if it's toward the animal, and firmly apply the brakes. Swerving could send you into the path of an oncoming vehicle or cause you to lose control of your car."
The survey indicates that Canadians want and need more education on how to deal with wildlife on our roads. The most likely time to encounter wildlife is at dusk or dawn, in October and November, on two-lane rural highways with speeds of 80 km/h or more.
From an insurance perspective, the average auto damage claim after hitting an animal is $4,500.
State Farm Canada's long-time partner and road safety experts, The Traffic Injury Research Foundation (TIRF), have developed an online information centre focused on road safety and wildlife.
The Wildlife Roadsharing Resource Centre (WRRC) profiles tips on wildlife collision prevention, how to respond to animals on the road, tips for when a collision with wildlife is unavoidable and advice on what to do after a collision.
Specifically, TIRF has produced a fact sheet to address some of the common myths and misconceptions around wildlife vehicle collisions.
More than 25 per cent of survey respondents have hit a small animal on the road while driving.
More than 25 per cent have either hit or nearly hit a large animal while driving.
More than half of respondents who said they had hit a large animal had damage to their car.
More than 80 per cent of respondents claim they slow down when they see road signs for wildlife in the area.
Most respondents believe either evening (46 per cent) or night (36 per cent) is the most likely time to hit an animal on the road.
The online survey, conducted in March 2017, polled 3,061 respondents of driving age across Canada.
Infographic courtesy of State Farm Canada
Two Ontario Zoos Ranked as Some of the Cruelest in the World
Brampton residents celebrating group lotto win
Police searching for missing 16-year-old boy
Traffic study identifies most dangerous streets in Brampton
Survey finds half of Canadian drivers don't know what to do after a collision
Survey finds many young Canadians believe driving high not a big deal
Survey finds Canadians want easier access to financial information
Cosmetic Animal Testing Could Soon be Banned in Canada
5 Animal Adventures In The GTA
5 Big New Restaurant Openings of the Summer in Brampton
Anokhi
Honest Restaurant
Little London Cafe
Green Bites Dumplings & Tea Bar
Fan "D" Flame
5 Best free winter activities near Brampton
Top 5 Brunch spots in Brampton
Top 5 Cheap Caribbean Eats in Brampton
Top 5 Indian Takeout in Brampton
Top 5 Cheap Pizza in Brampton
Brunch and Brampton go together like bacon and eggs! Whether you're craving the classics i.e. bacon and eggs or something a little different i.e.


Wine: Upon arrival guests will enjoy a sparkling wine which could in our opinion match any of our counterparts in Champagne, we will also include 2 other sparkling British wines 1 of which we will marry to a cheese.
Whisky or Gin which ever you prefer: Discover the mysteries of Whiskies and what makes single malt and Scottish Whisky so distinct, we will also give some top tips on quality, pricing and purchasing and bring you our top 3 Whiskies. Or why not opt for Gin instead of Whisky, Gin is the fastest growing UK trend and we will provide our top 3 UK Gins from both micro to established distilleries. If you like we can do both Whisky and Gin with a mobile bar and barman to entertain your clients.
Cheeses: What meal would not be complete without cheese? We believe here in the UK we have some of the best Cheese producers in the world! Of course we are famed for our cheddar but there is so much more we can offer here in the UK, let our chefs pick you some of our favourites to inspire and wow your guests, a typical tasting will be 1 blue cheese, 1 soft cheese, 1 cheddar and a mystery cheese all from the UK and using Ewes cows and goats and on occasion buffalo milk.
Depending on the style you would like will depend on the format we would follow, e.g informal guests will enjoy the items at their own leisure using tasting notes and cards, and for formal we would seat guests at tables then serve and introduce each category in turn to the guests matching some of the cheeses with wines and chocolates with Whiskey, for the brave how about a blue cheese and chocolate trust us its delicious!


text:
How to Gain Fat in Your Arms & Legs
How to Lose Underbelly Fat
How to Get Ripped in 90 Days
by Mike Samuels
Carb Cycling With Cardio
Breakdancing as a Way to Lose Weight
Easiest Way for Pear Shapes to Lose Weight
How to Get a Flat Chest for Men
Getting ripped requires a strict diet and intense workout regime. Ninety days may sound like a long time, but getting ripped during this time frame can be challenging. It is possible, however, if you're already in good shape and stick to your plan for the duration, avoiding any slip-ups along the way.
Reduce your current daily calorie intake. Calories are your body's main source of fuel, but to lose fat, you need to burn more calories than you eat. This causes your body to have to burn fat stores for fuel instead of relying on food. According to the Mayo Clinic, dropping 500 calories per day is the best way to start, as this is enough to promote fat loss but not enough to leave you feeling hungry or cause you to lose muscle mass.
Eat foods high in protein, fiber and healthy fats, along with plenty of vegetables, and avoid processed foods and those high in sugars, advises nutritionist Dr. Jonny Bowden, author of "The 150 Healthiest Foods on Earth." According to Bowden, food quality is just as important as calories when getting ripped. High-carbohydrate and high-sugar foods cause a big spike in the hormone insulin, which promotes fat storage and leaves you feeling tired, lethargic and hungry. By contrast, good quality foods, such as meat, fish, fruits, vegetables, nuts and beans, leave you feeling full and satisfied; they also have a much more positive effect on insulin and blood sugar levels.
Combine weight training and cardiovascular work for optimal results. Weight training preserves and builds muscle mass, improving your definition, and also revs up your metabolism. Cardio burns extra calories, helping to speed fat loss. Do three full-body workouts per week, consisting of three sets of eight to 12 repetitions on squats, lunges, dumbbell presses, dumbbell rows and biceps curls for the first 45 days. In the second half of the 90 days, increase your training frequency to four times per week. Do two lower-body workouts of squats, deadlifts, leg curls and calf raises and two upper-body workouts of bench presses, barbell rows, chin-ups and dips. Stick to the same rep and set ranges.
Add in two cardiovascular sessions each week -- one 45 minute, moderate-intensity, steady-state session, such as jogging, swimming or cycling, and one high-intensity workout, including hill sprints, kettlebell circuits or a spinning class. Do this for the first 30 days. From days 31 to 60, do two steady-state sessions and add 10 minutes to your high-intensity sessions. To ramp up progress in the last 30 days, do two steady-state sessions and two high-intensity workouts.
Mayo Clinic: Counting Calories: Get Back to Weight-loss Basics
Always consult a Doctor before beginning any new diet or training plan.
Mike Samuels started writing for his own fitness website and local publications in 2008. He graduated from Peter Symonds College in the UK with A Levels in law, business and sports science, and is a fully qualified personal trainer, sports massage therapist and corrective exercise specialist with accreditations from Premier Global International.
David McNew/Getty Images News/Getty Images
How to Lose Weight & Tone Up Quickly
How to Get Rid of Fat Around Your Organs
How to Get a Beach Body in 3 Months
How to Lose Tummy Flab if You Can't Do Push-Ups or Sit-Ups


Bhubaneswar: The Odisha Minority Alliance (OMA) has honored John Dayal, a leading lay Catholic human rights activist and senior journalist, for his lifetime contribution for the cause of religious minorities in India.
The award was given on December 18 by Ramesh Chandra Majhi, Minister for Scheduled Tribes and Scheduled Caste Development, Other Backward Class and Minority Welfare, Government of Odisha, on behalf of Odisha Minority Alliance (OMA), Bhubaneswar in Bhubaneswar.
More than 300 religious minority leaders, human right defenders, social workers and academicians coming from different parts of Odisha attended the function organized on the occasion of International Minority Day.
OMA, a coalition of religious minorities in Odisha, Eastern India, comprises Christians and Muslims, the state's major minority groups.
Barendra Kumar, convener of OMA, hailed Dayal as a multi-faced human rights crusader, towering leader of the religious minorities in India. His contributions to the commitment and dedication for the cause of minorities remain unparalleled, he added.
Jugal Kishore Ranjit, co-convener of OMA, said Dayal was the first recipient of the award. The alliance plans to award every year a distinguished person for the cause of the minorities.
Dayal, a former member of the National Integration Council, is the founder general secretary of All India Christian Council, past president and current spokesperson of the All India Catholic Council.
He volunteers to probe atrocities on any communities anywhere in the country and defends the rights of violated minority communities on both print and electronic media, Ranjit noted.
"Moreover, he does not mince his words and writings while defending the cause of the minorities. He leads from the front and remains an inspiration for minority communities," the OMA official said. Dayal has shown equal commitment in defending the cause of other religious minority communities; be it Sikh or Muslim. "Hence, the Committee honored Dayal so that the next generation continue his mission and spirit in the challenging times ahead in the country," he added.
Majhi stressed the need for everyone to cooperate in building up society. "It is a good sign that state government has taken initiative to construct 100 hostels for minority students and 25 multipurpose sectors in Odisha," he pointed out.
The Odisha government, he added, would study the possibility of setting up a State Minority Commission. He invited minority community leaders for consultation to decide special budgetary allocations for the minorities welfare according to their priorities.
Dayal, while acknowledging the honor, stressed the need for sustained and collective efforts to address the issues and concerns of the minorities in India. Today they seem more vulnerable than before, he added.
The Catholic lay leader urged minority leaders to come forward to check attacks on their communities. Odisha has witnessed several such attacks, he pointed out.
"We need to multiply our efforts to foster peaceful co-existence of all communities. Challenges have soared up as religious minorities are under threats in several parts. So, we need to be on guard ourselves as seemingly the discourse is not saner for the minorities," Dayal said.
Fr. Ajaya Kumar Singh, human rights activist, urged all to work for the realization of constitutional rights that provide them equal and equitable opportunities as equal citizenship.


Ozone therapy has been a revolution in health and in all aspects. Clinical conditions that the cure would be a doubt, the application of ozone leads to health in a short time.
Oxidative capacity is critical to successful treatment.
Author and co-author of scientific manuscripts and book chapters.


This is a turn-key opportunity to own an established and profitable Restaurant. Vincent's in Afton. Fully equipped, furnished, inventoried and staffed Restaurant. This Restaurant is lucrative and has a history of rewarding profits.(P&L shared with qualified buyers with a signed NDA). This also includes a spacious, very good condition and rented, 1 bedroom apartment.


Almost 400,000 people are suffering in tent cities with conditions only worsening as the rain approaches and disease and infectious outbreaks begin. With as little as $100,000 of tools & 5,000 men clearing their house bases & using their broken house materials, 45,000 temporary homes for the poor could be built in 4 to 6 months. The solution is under our feet but government & leaders struggle to vision doing this. Who will supply the tools? We will!
"300,000 men sit doing nothing while their families suffer. With as little as $100,000 of tools & 5,000 men clearing their house bases & using their broken house materials, 45,000 temporary homes for the poor could be built in 4 to 6 months. The solution is under our feet but govt & leaders struggle to vision doing this. Who will supply the tools? We will!
To provide the basic tools required to clear EQ rubbled homes, salvage the toilet (key goal) and utilise the stable base for rebuilding. Furthermore, an exponential roll-out of the concept is necessary as the impending rainy season presents an abundance of new problems and the likeliness for an epidemic.


text:
Q: "Pot calling the kettle black" ... but what if the kettle isn't black (figuratively speaking)? The pot calling the kettle black is a well accepted idiom in English, and has many equivalents in other languages.
But there are some occasions when this phrase is not quite appropriate. When one uses this idiom, it seems that one is acknowledging that the transgression is equally applicable to both parties being referenced.
What if the accuser (i.e., pot) is known to be guilty of a perceived transgression, but the target (kettle) is unjustly accused?  Is there another appropriate idiom that captures the essence of the situation?

A: The subject here is the pot, not the kettle.
This expression is used to declare that an accuser (the pot) is not innocent themselves, and is essentially being a hypocrite. The actual colour of the kettle is secondary, but it's assumed to be guilty too.
A common expression that accuses hypocrisy without calling other parties into question is:

People who live in glass houses shouldn't throw stones.

A: Attributing one's own faults to others could be considered projection.

A: I don't know of such an idiom, and imagine that you'd need to provide far more detail about the relationship in question for a relevant idiom to be dredged up.
The previously-suggested projection bias term seems to not mesh well with the notion of a transgressor accusing a party known to be innocent.  In common Usenet parlance, when some delusional person accuses sane people of one bad habit or another, that is called 'projection', whether accurately or not I cannot say.
A transgressor who knows the other party is innocent probably cannot be said to be rationalizing, over-generalizing, misconceiving, etc. but perhaps can be said to be blame-shifting or demonizing.
If a third party called two other parties (one guilty, one not) transgressors, that would be called "tarring with the same brush" or "tarring with a broad brush".

redpajama_set_name: RedPajamaStackExchange


Now this is an event to my heart! During the BIG Secondhand SALE next week you can buy yourself some cool secondhand pieces and even help others while doing so. What more could you want?!
Last year's sale was a massive success, with many organizations receiving donations. A car full of stuff went to We Care And Share in Rotterdam, 20 boxes/bags filled with shoes, hats, scarves and gloves were brought to Movement On The Ground, 35 garbage bags with winter coats were dropped off at the refugee center in the former Bijlmer prison, and loads of sports clothes went to Don Bosco's project for homeless youngsters.
Want to donate clothes? Just come by! Want to earn extra karma points? Donate (new!) (thermic) underwear, games and books in English, Arabic, Greek and Farsi, educational kits, toys or mobile phones (preferably with charger).
More than enough reason to get up, donate and score a new outfit!


text:
Clarkesworld Issue 93
Mary Anne Mohanraj (Author) Robert Reed (Author) Tang Fei (Author)
FORMAT
Paperback$6.99(English)

Clarkesworld is a Hugo Award-winning science fiction and fantasy magazine. Each month we bring you a mix of fiction (new and classic works), articles, interviews and art.
Our June 2014 issue contains:
Original Fiction by Robert Reed ("wHole"), Tang Fei ("Pepe"), and Mary Anne Mohanraj ("Communion").
Classic stories by Molly Gloss ("Lambing Season") and Geoff Ryman ("Have Not Have").
Non-fiction by Susan E. Connolly ("The Issue of Gender in Genre Fiction: A Detailed Analysis"), an interview with Chuck Wendig, an Another Word column by Daniel Abraham, and an editorial by Neil Clarke.
5.5 X 0.25 X 8.5 inches | 0.31 pounds
Science Fiction - Collections & Anthologies
"Mary Anne Mohanraj is author of Bodies in Motion (HarperCollins) and fourteen other titles. Bodies in Motion was a finalist for the Asian American Book Awards, a USA Today Notable Book, and has been translated into six languages. She's received a Locus Award, a CFW Breaking Barriers Award, an Illinois Arts Council Fellowship, and more.
Mohanraj is Clinical Associate Professor of fiction and literature at the University of Illinois at Chicago, serves as Executive Director of DesiLit (desilit.org), and directs the Kriti Festival of Art and Literature (kritifestival.org). She founded and served for ten issues as editor-in-chief of Jaggery, a South Asian literary journal (jaggerylit.com). She serves on the board of her local garden club "€" she loves incorporating garden harvests into her recipes "€" and was recently elected to the Oak Park library board.
Mohanraj was born in Sri Lanka in 1971, and moved to America at the age of 2. When she was young, her family would go back often to vis
Robert Reed is an adjunct Professor of English at Marymount University in Arlington, Virginia. Mr. Reed has written earlier books about train wrecks, streamline industrial design, the New York City elevated railroad system, and nineteenth-century Washington, D.C.
Tang Fei, writer, commentator. Member of the Shanghai Writer's Association and the SFWA. Her signature works include Paradise in the Clouds, The Person who Saw Cetus and The Anonymous Banquet. Since 2013, ten of her stories have been translated and published around the world; her novella The Panda Keeper won Best Microfiction at 2019's Smokelong Quarterly, Wu Ding's Journey to the West won the Silver Prize for Most Popular Deduction Fiction at the Speculative Fiction in Translation Awards, and "The Robe" won Best Short Story at the Yinli (China Reader's Choice) SF Awards. Apart from writing, she also dabbles in other art forms such as literary criticism, poetry, installation art and photography. Her commentary pieces have been published in The Economics Observer (China), Hong Kong and Shenzhen Literary Review.
Strange desires & cult classics VIEW LIST (60 BOOKS)


COBRA is an innovative non-mydriatic digital fundus camera that combines all the needed functions for a fast retinal screening. By using a new optical system , COBRA provides high quality retinal pictures.
minimizing the examination time for the patient.
The high resolution CCD sensor (5 MP in the HD version) is both used for the patient alignement (with an IR source) and for the retinal picture acquisition (with a white LED flash and IR).
COBRA is connected to the PC by IEEE1394 protocol (Firewire type A or B), providing a very high speed data transfer.
Patients data are saved in a database, using the Phoenix software. Stand-alone or Network station are both possible. DICOM feature is integrated in Phoenix software.


Your friendly neighborhood Spider-Man has become the all-time favorite Marvel Comics icon for a reason -- he's just a regular guy who's trying to get through the day like the rest of us. Spidey's alter-ego, Peter Parker, makes us think about ourselves, and how crazy things can happen to people who just want to catch a break. Here's a painted bust of Spider-Man, as rendered by the artist who featured him prominently in the groundbreaking Marvels comic series.


Free Zone Alliance. Independent Technology. International page.
Our purpose is to make the works of Source available to anyone who wishes to study.
The idea of Free Zone Technology originated by LRH in 1973.
Captain Bill Robertson was creator of the Free Zone in 1984.
L. Ron Hubbard, a self-taught intuitive genius, founded the philosophy and religion of Scientology in 1952. His writings on how people can better themselves and the world are both brilliant and extraordinarily extensive. He wished his work to be made available to mankind.
We are carrying out his wishes.
There is only one thing that could happen to tech, and that is to say that it would be buried. The remedy would be buried. If it ever went out of sight, this world's done. All you've got to do is invalidate it and put it out of sight and hide it, and it'll come up in the wrong place doing the wrong thing, and mankind will find itself a slave.
So anybody that knows the remedy of this subject, anybody that knows these tecniques, is himself actually under a certain responsibility – that's to make sure that he doesn't remain a sole proprietor. That's all it takes, just don't remain a sole proprietor. Don't ever think that a monopoly of this subject is a safe thing to have. It's not safe. It's not safe for man; it's not safe for this universe.
This universe has long been looking for new ways to make slaves. Well, we've got some new ways to make slaves here. Let's see that none are made.
We welcome your feedback and suggestions. Thank you.
FREE ZONE SCIENTOLOGY - an area not controlled by evil organizations or implanters, but free to expand spiritually (CBR, Sector 9).


text:
\section{INTRODUCTION}
As the energy demand multiplies the world over and the conventional energy resources deplete alarmingly, wind energy utilisation has attained greater
importance from the perspective of sustainable development, as it is renewable, clean and comparatively cost effective. As a result, wind energy has already emerged as an
essential constituent in the global energy mix and is all set to grow to its maximum potential across countries and regions in the years to come. As wind power is directly proportional to
the cube of wind speed, even slightest variations in wind speed will significantly affect the power output from wind energy generators. Since wind is a fluctuating resource in respect of availability and speed, precise wind forecasting becomes essential, especially when wind power penetration grows, for the effective management of electricity grid to ensure quality power
supply. Accurate wind forecasts on different lead time scales help wind farms in real-time grid operations, economic load dispatch planning, reserve requirement decisions, market trading,
maintenance planning and the like.

Wind forecasting continues to be an area of high research interest owing to its practical relevance in the ever-expanding wind energy industry. Costa et al. \cite{costa2008review} have
reviewed the research in short-term wind prediction over 30 years, giving attention to forecasting methods, mathematical, statistical and physical models, as well
as meteorology. Foley et al. \cite{foley2012current} and Okumus et al. \cite{okumus2016current} have conducted an extensive review of the current methods and improvements in the
field of wind power forecasting. Based on the methodology adopted, wind forecasting models are grouped mainly into physical, statistical, data learning and hybrid models. The physical
models, which utilize different atmospheric parameters are useful for identifying recurring patterns and making long-term predictions. Statistical models assume that
the wind speed fluctuations are stochastic. However, it has
recently been demonstrated that the underlying dynamics of apparent random-
like fluctuations of wind speed measurements is deterministic, low-dimensional
and chaotic \cite{sreelekshmi2012deterministic,    drisya2014deterministic,drisya2018diverse}. Hybrid models have been developed recently by combining
different methods such as physical, statistical and machine learning methods to enhance prediction accuracy \cite{meng2016wind,han2017non}. Models based
on artificial neural network and other data learning techniques have also been gaining increased attention in literature in the recent past. Mohandes et al. \cite{mohandes2004support} have
compared a support vector regression (SVR) approach for wind speed prediction favourably against a multi-layer perceptron (MLP) for systems with
orders 1 to 11. Liu et al. \cite{liu2014short} attempted short-term wind speed forecasting using wavelet transform and Support Vector Machines, applying a
genetic algorithm for parameter optimization. Fugon et al. \cite{fugon2008data} applied linear and non-linear data mining algorithms for the short-term wind power
forecasting at three distinct wind farm locations in France. Lahouar et al. \cite{lahouar2017hour} tried out Random Forest model for an hour ahead wind power prediction and tested the model with measured wind data and showed good improvement of forecast accuracy compared to classical neural network prediction. Mohandes et al. \cite{mohandes2012spatial} conducted a study within Saudi Arabia to estimate the mean monthly wind speed at certain locations using the historic mean monthly wind speed data from a number of other locations and reported good agreement between estimated and measured monthly mean wind speed values. Browell et al. \cite{browell2018improved} attempted very short-term wind forecasting by incorporating large-scale meteorological information into a vector autoregressive model and showed improved accuracies in forecasting in different case studies conducted in the United Kingdom.

Various machine learning algorithms have been tested successfully to predict wind speed variations. However, almost all reported studies are location specific as training and testing data are sourced from the same location. Apart from that, application of such models have not been tested for time independence as the test data considered are adjacent in time to the training data. In this work, we investigate the possibility of developing time and location independent models based on machine learning algorithms for wind speed forecasting for the wind energy industry. Such models hold practical value for wind energy industry for locations where sufficient past data are not available for model training. The first objective of this study is to investigate the accuracy of models applied to data moving away from the training data set. The second objective is to analyse the accuracy of cross-location predictions in which models trained using data from one location are tested against data from another location.  Proper training of the forecast model with the available data is a crucial factor for its performance. In the case of wind speed time series, it raises the question of deciding the optimum size of past data required to train the model for producing accurate time ahead predictions, as the duration of wind speed time series is significant since the fluctuation characteristics vary remarkably over different seasons. The
theory of mutual information has been applied to estimate the optimum size of preceding data set to be applied in the training of models and testing of forecasts. The study reported here investigates the efficacy of two uniquely trained and tested machine learning models based on (i) Support Vector Machine (SVM) and (ii) Random Forest (RF) algorithms for  wind speed forecasting in the same-location as well as cross-location scenarios, wherein promising results are obtained.

\begin{table}
	\begin{center}
		\begin{tabular}{ |c|c|c|c| }
			\hline
			Location & Latitude & Longitude \\
			\hline
			L1 & $09^0 45' 30.2''$ & $77^0 10' 41.3''$ \\
			\hline
			L2 & $09^0 59' 09.5''$ & $77^0 11' 50.0''$ \\
			\hline
			L3 &$12^0 01' 32.7''$ & $75^0 20' 32.4''$\\
			\hline
			L4 & $09^0 39' 11.5''$ & $76^0 53' 3.0''$\\
			\hline
			L5 &$10^0 48' 57.7''$ & $76^0 40' 10.3''$\\
			\hline
		\end{tabular}
		\caption{\label{tab.loc} Geographic coordinates of the wind masts used for wind data collection.
		}
	\end{center}
\end{table}

\begin{figure}
	\centering\includegraphics[width=\columnwidth]{./figures/locations.JPG}
	\caption{\label{fig.locations} Geographical locations of the wind measuring masts indicated on 3D map (Courtesy: Google Maps).}
\end{figure}

\section{MACHINE LEARNING MODELS}
Machine learning is a method of improving the performance of a computational software programme by itself with experience. In machine learning, past
experience is fed to the machine as input, and it gives the output as a typical
model that is capable of solving future problems of the same nature. Here,
past experience is collected for the purpose of imparting training. An abstract
target function is determined that well describes the relationship between existing
input and desired output. Subsequently, a machine learning model is selected
to approximate the target function. In the end, a suitable algorithm is used
to build the model from the training examples. In this paper, two different
machine learning models, namely, Support Vector Machine and Random Forest
models have been used for the investigations. The e1071 package in R is used in this research to develop, train and test the models \cite{e1071}.
\subsection{ Support Vector Machine model}
Support Vector Machine (SVM) is a supervised learning method derived from Vapnik's work on statistical learning theory which was initially used for classification problems and later generalized for regression \cite{cristianini2000introduction,cortes1995support}.  It is an optimization technique of finding a surface which maximizes the margin between two classes based on two main ideas namely, the maximization of distance between the classifying surface and the nearest elements called support vector and the transformation of the input dimension into higher dimensional space using a kernel function. SVM method performs classification tasks by constructing hyperplanes in a multidimensional space that separate cases of different class labels. To construct an optimal hyperplane, SVM employs an iterative training algorithm which is used to minimize an error function. In the case of a linear classification problem, the hyperplane can be expressed as
\begin{eqnarray*}
	y_i(w \times x_i+b) \geq 1-\psi_i
\end{eqnarray*}
where $x_i, y_i \in R^n$   are the training data pairs and $w$ the coefficient vector of classification hyperplane, b the offset of the hyperplane from the origin and $\psi_i$ are the positive slack variables \cite{cortes1995support}. The optimum hyperplane is obtained by solving the minimization problem .
\begin{eqnarray*}
	Minimize \sum_{i=1}^{n} \alpha_i \frac{1}{2}\sum_{i=1}^{n}\sum_{i=1}^{n}n \alpha_i \alpha_j y_iy_j(x_ix_j) \\
	subject \, to \sum_{i=1}^{n}n \alpha_i y_j = 0 and 0 \leq \alpha_i \leq C
\end{eqnarray*}
Where $\alpha_i$ are Lagrange multipliers and C the penalty \cite{samui2008slope}. RBF kernel has been used in our present analysis. The SVM can also be used for regression without sacrificing its main features and it is resistant to overfitting.
\subsection{Random Forest model}
The Random Forest (RF) algorithm is a non-parametric ensemble based learning technique used for both classification and regression \cite{breiman2001random}. The decision tree algorithm works on a set of rules and the possible outcomes to form a tree-like structure. However, such a system is prone to error propagation contributed by an incorrect rule which adds the impurity to the subsequent nodes. Random Forest algorithm eliminates error diffusion process inherent in decision trees by constructing multiple trees. Random samples of given data set are generated and fed to several tree-based learners to form a random forest. Splitting condition for each node in a tree is based only on the randomly selected predictor attributes which lower the error rate by avoiding the correlation among the trees. The successful application of random forest regression algorithm has already been reported in many fields like cheminformatics, speech recognition, bioinformatics, classification and prediction in ecology \cite{svetnik2003random,xu2004random,jiang2004joint}. The random forest regression, which is a non-parametric, captures the functional relationship between dependent and independent variables from the features of the data. From a given data set, algorithm generates a forest of $n$ trees as $\{T_1(X),T_2(X),\hdots, T_n(X)\}$, using an $m$ dimensional vector input $X=(x_1,x_2,\hdots ,x_m)$. Every tree $T_i(X)$  generates an outcome $W_i=T_1(X)$. The average of all individual outputs is considered as the response of random forest. The bagging process of selection with replacement is done both on the samples and the attribute. Normally two third of the data will be the size of bootstrap samples, and the rest is known as out-of-bag samples. The combined effect of bootstrap and attribute bagging helps the algorithm to reduce misclassification error.

\begin{figure}
	\centering\includegraphics[width=\columnwidth]{figures/mutual.jpeg}
	\caption{\label{fig.mutual} The mutual information of hourly wind speed time series as function of delay.}
\end{figure}

\begin{figure}
	\centering\includegraphics[width=\columnwidth]{figures/sameloc_3hr_kul.jpeg}
	\caption{\label{fig.sameloc_3hr_kul} Comparison between the actual and forecast wind speeds with repeated 3 hour ahead predictions for the same-location forecasting for location L1, using SVM model.}
\end{figure}

\section{RESULTS AND DISCUSSIONS}

The hourly wind speeds at the height of 80 m above the ground level at five
different windy locations situated in the Indian state of Kerala, represented by L1 to L5 as shown in  3D map given in Fig.~\ref{fig.locations} and summarised in Table~\ref{tab.loc}, measured using
wind masts over a continuous period of two years 2012 and 2013 have been utilised for the analysis in this work. These locations are geographically
distributed in such a way that the locations L2, L3, L4 and L5 are at radial
distances 25 km, 321 km, 34 km and 130 km respectively from the location
L1 and the triangular area formed by the locations L1, L2 and L4 comes to 385
square kilometres.  Two different machine learning forecast models built on SVM and RF algorithms have been employed for the analysis. The  wind speed data for
the first year (2012) have been used for training and validating the models, in
order to ensure effective learning of the dynamics of wind flow fluctuations over
a complete seasonal cycle. The wind speed data for the second year (2013) have been used for the testing of forecast results.

\begin{figure}
	\centering\includegraphics[width=\columnwidth]{figures/sameloc_5hr_kul.jpeg}
	\caption{\label{fig.sameloc_5hr_kul} Comparison between the actual and forecast wind speeds with repeated 5 hour ahead predictions for the same-location forecasting for location L1, using SVM model.}
\end{figure}
\begin{figure}
	\centering\includegraphics[width=\columnwidth]{figures/same_svmrmse1.jpeg}
	\caption{\label{fig.same_svmrmse1} Mean of RMSEs of predictions versus prediction time, for predictions at the locations L1 to L5 using SVM model trained with data from the respective locations. }
\end{figure}

The extent of dependence of a value in a time series on the previous values
can be estimated by the calculation of mutual information between delayed time
series \cite{fraser1986using}. Relying on this, the optimum length of dependency of wind speed
values on the past data has been determined by computing values of mutual
information and the same knowledge made use of in the training of models and
testing of forecasts. The mutual information in the present analysis appears
to become negligible by 72 data points, after which the plot starts
to level-off, as observed in Fig.~\ref{fig.mutual}. It is therefore taken that every wind speed
data point is a function of its previous 72 data points. Hence, the training of SVM
model using the past data has been done for all the wind speed values in the
training data segment, by inputting 72 continuous measures for each wind speed
value ahead. The same approach has been adopted while inputting the previous set
of data for training the RF models as well.

In the first stage, same-location predictions (where data from the same location is used in parts for training and testing) have been examined for all the
five locations, for all hours ahead predictions from 1 hour  up
to 48 hours ahead using SVM model. Each of the one step ahead
predictions is generated by inputting the immediately preceding 72 data points
into the trained model. In 2 and higher hour ahead predictions, one step
ahead predictions are repeated, each time by using the lastly predicted value as
the last of the preceding 72 input points. The predicted time series segments have been compared with actual values along the one year test period, and the deviations analysed using the statistical measure of Root Mean Square Error (RMSE). In the next step,
all possible combinations of cross-location predictions have been experimented,
wherein, SVM model trained with data from one location has been employed to
generate wind speed forecasts at the other four locations by inputting test data
from those four locations respectively. In the subsequent stage, all the above
investigations have been repeated by developing and using the machine learning
model of RF and the results obtained with both the models have
been analysed and compared.

In the typical prediction scenario we input past 72 wind speed data points and obtain one step ahead prediction. Further values are predicted recursively using one step ahead prediction.
Fig.~\ref{fig.sameloc_3hr_kul} shows a typical 3-hour ahead prediction up to 1000 hours ahead of the training data set at location L1 using SVM model.  Similar plot of 5-hour ahead prediction is given in Fig.~\ref{fig.sameloc_5hr_kul}. In both these plots, the predictions are seen remarkably close to the original measured data, except for some over predictions at peaks.
With the SVM model trained using the data in 2012, we obtained predictions up to 48 hours ahead corresponding to each data point in 2013 by inputting 72 previous values. These predictions were compared with actual data to find the RMSE. Fig.~\ref{fig.same_svmrmse1} shows the mean RMSE versus prediction time averaged over predictions with respect to each data point in 2013 for all the five locations. It may be noted that the RMSE is less than 2 m/s up to 48-hour ahead prediction for locations L1 and L3 whereas the same is almost less than 3 m/s for other locations. However, up to 22-hour ahead, predictions show RMSEs less than 2.5 m/s in all the locations.

\begin{figure}
	\centering\includegraphics[width=\columnwidth]{figures/mal_kul_3hr.jpeg}
	\caption{\label{fig.mal_kul_3hr} Comparison between the actual and forecast wind speeds with 3-hour ahead predictions for the cross-location forecasting for location L1, using SVM model trained with data from location L5.}
\end{figure}

\begin{figure}
	\centering\includegraphics[width=\columnwidth]{figures/mal_kul_5hr.jpeg}
	\caption{\label{fig.mal_kul_5hr} Comparison between the actual and forecast wind speeds with 5-hour ahead predictions for the cross-location forecasting for location L1, using SVM model trained with data from location L5.}
\end{figure}

\begin{figure}
	\centering\includegraphics[width=\columnwidth]{figures/kul_rmse1.jpeg}
	\caption{\label{fig.kul_rmse1} Mean of RMSEs of predictions versus prediction time, for cross-location predictions at the locations L2, L3, L4 and L5 using SVM model trained with data from the location L1. }
\end{figure}

\begin{figure}
	\centering\includegraphics[width=\columnwidth]{figures/precentage_SVM1.jpeg}
	\caption{\label{fig.precentage_SVM1} Percentage of cross-location predictions with RMSEs below 1.5 m/s, 2.5 m/s and 3.5 m/s versus prediction time, when using SVM model.}
\end{figure}

\begin{figure}
	\centering\includegraphics[width=\columnwidth]{figures/RF_mal_kul_3hr.jpeg}
	\caption{\label{fig.RF_mal_kul_3hr} Comparison between the actual and forecast wind speeds with 3 hour ahead predictions for the cross-location forecasting for location L1, using RF model trained with data from location L5.}
\end{figure}

\begin{figure}
	\centering\includegraphics[width=\columnwidth]{figures/RF_mal_kul_5hr.jpeg}
	\caption{\label{fig.RF_mal_kul_5hr} Comparison between the actual and forecast wind speeds with 5 hour ahead predictions for the cross-location forecasting for location L1, using RF model trained with data from location L5.}
\end{figure}

\begin{figure}
	\centering\includegraphics[width=\columnwidth]{figures/percentage1.jpeg}
	\caption{\label{fig.percentage1} Percentage of cross-location predictions with RMSEs below 1.5 m/s, 2.5 m/s and 3.5 m/s versus prediction time, when using SVM model (circular points) and RF model (squared points).}
\end{figure}

As a next step, we trained the model with data of one location of the year 2012 and applied to predict, corresponding to each data point in 2013, up to 48 hours ahead for each other location. Two sample predictions, 3-hour and 5-hour ahead, up to 1000 hours ahead of the time of training data are given in Figs.~\ref{fig.mal_kul_3hr}, \ref{fig.mal_kul_5hr}.  When the above investigation is carried out under the cross-location scenario for the
five locations, a total of 5 prediction scenarios, each with predictions for four
locations using the SVM model trained with the data from the other location is
available for analyses.  Fig.~\ref{fig.kul_rmse1} depicts one such scenario, wherein predictions are generated for the locations L2 to L5 using the SVM model trained
with the historic data from the location L1. In this case, it can be seen that the mean RMSE is less than 2.5 m/s for up to 48-hour predictions even in the worst case of location L4.  In a similar fashion, we repeated the cross-prediction sequence by selecting one location for modelling and other locations for prediction. In order to have a better understanding of the efficacy of the cross-location predictions, a percentage-wise representation of all predictions throughout the year 2013 for all possible cross-location prediction situations, that show individual RMSE values less than 1.5 m/s, 2.5 m/s and 3.5 m/s are plotted against the prediction time in Fig.~\ref{fig.precentage_SVM1}.
This plot is useful in two different ways as it helps to determine (i) the length of time ahead predictions that is achievable for a given accuracy of prediction and (ii)  the accuracy levels for a given length of time ahead prediction. For prediction accuracy with RMSE less than 1.5 m/s 75 \% of predictions goes up to 2-hour ahead in time. When the level of prediction accuracy with RMSE is leas than 2.5 m/s, up to 16-hour ahead predictions constitute up to 75\% of the prediction samples. More than 85\% of the 48-hour ahead cross-location predictions are with RMSE less than 3.5 m/s.  In another way of interpreting the above plot is to say that, for example, if 10
hour ahead prediction is considered, around 94\% of prediction samples show
individual RSME values below 3.5 m/s, 80\% of samples show the same value
below 2.5 m/s and 45\% of samples show the same below 1.5 m/s.

In the final phase of the research, the above investigations have been repeated by employing RF model in place of SVM model. The results show
predicted values to match closely with the actual wind time series dynamics
almost as seen as in the case of SVM model, both for same-location as well as cross-location forecasting. The typical cross-location predictions presented in Fig.~\ref{fig.mal_kul_3hr} and Fig.~\ref{fig.mal_kul_5hr} are reproduced in Fig.~\ref{fig.RF_mal_kul_3hr} and Fig.~\ref{fig.RF_mal_kul_5hr} respectively with RF model in place of SVM model for the forecasting, which again show comparable results in terms of wind flow dynamics and forecast accuracy.

In Fig.~\ref{fig.percentage1}, the scenario in Fig.~\ref{fig.precentage_SVM1} for SVM model is reproduced with the corresponding results generated by the RF model overlaid. As can be seen from  Fig.~\ref{fig.percentage1} both models show similar behaviour, especially for lower time ahead predictions. If more stringent levels of forecast accuracy is desired, the SVM model shows
marginal supremacy over the RF model in the shorter time ahead predictions and
vice versa in the longer time ahead predictions.

\section{CONCLUSION}

In this work, we investigated the prospect of employing machine learning based predictive models for the cross-location prediction of wind speed variations. We analysed wind speed data for a period of two years from 5 locations separated by a minimum of 25 km and a maximum of 321 km by using both Support Vector Machine (SVM) and Random Forest (RF) models. The dependency of wind speed on past data has been assessed using the theory of mutual information and the same estimate has been made use of in the intelligent training of models with proper time delay embedding matrix and also in inputting proper length of past data in the testing of forecasts. The results indicate that the models developed and trained here can be effectively used in wind speed forecasting on the same time series at far away points in relation to the training data with respect to time. This time-independent characteristic is helpful in avoiding the need in the usual methods for training of models using the immediate past data every time predictions are attempted. The research further proves that both these models, together with the methods of training and testing followed here, can generate reliable and quality cross-location short-term wind speed forecasts to a duration of 16 to 17 hours from a given point in time across a geographical area as wide as in the present case, with not less than 75\% of such time ahead prediction samples from all along the testing period showing individual RMSE values below 2.5 m/s. In the case of one hour ahead predictions along the one year test period of all the 20 cross-location prediction scenarios from the 5 locations, almost 95\% of such predictions show RMSE values below the same value. The results obtained further show that in cross-location forecasting, the RF model slightly outperforms the SVM model in the longer time ahead predictions when higher levels of accuracies are desired. The promising results obtained in the cross-location forecasting of wind speed point to the possible existence of certain collective characteristics hidden within the surface wind flow dynamics, which deserve to be studied further. From the practical perspective, the research outcome is very promising for supporting the growing wind energy industry, by being able to help develop hardware instruments embedded with trained models for time as well as location independent wind speed forecasting tasks. The cross-location forecast capability makes it possible to predict wind speeds at newly identified locations where sufficient past data are not available for model-building by employing a model trained with historical wind speed data from a different location within that geographical area.

\section*{ACKNOWLEDGEMENT}
The authors acknowledge with gratitude the use of wind data, measured by NIWE (National
Institute of Wind Energy under the Ministry of New and Renewable Energy, Government
of India) for and on behalf of ANERT (Agency for Non-conventional Energy and Rural
Technology under the state government of Kerala in India), in this research work. The authors are also grateful to the campus computing facility of University of Kerala set up under DST-PURDE programme for providing computational facilities. The authors also state that they have no conflicts of interest to declare.

\section*{REFERENCES}
\bibliographystyle{unsrt}

redpajama_set_name: RedPajamaArXiv


An armchair with an organic and rhythmic design with different elements resembling the petals of an open flower.Upholstered in SOLE fabric (100% TREVIRA CS). Padded seat cushion in bi-density HR foam 40-45kg/m3. Padded back cushion in bi-density HR foam 40-45kg/m3....Read moreAn armchair with an organic and rhythmic design with different elements resembling the petals of an open flower.Upholstered in SOLE fabric (100% TREVIRA CS). Padded seat cushion in bi-density HR foam 40-45kg/m3. Padded back cushion in bi-density HR foam 40-45kg/m3. Structure in solid wood and plywood. Also available in other dimensions. Optional deco cushions.
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Like most Jewish festivals, food is a central part of Purim: One of the holiday's four mitzvahs is to hold a festive meal, a Seudat Purim. Poppy seeds are a recurring theme in Purim recipes. Perhaps it's due to the legend that Queen Esther ate seeds during her time at the king's palace. Or perhaps it's simply due to the popularity of the poppy seed hamantaschen, arguably the holiday's most iconic foods. Either way, these five recipes will ensure your Purim meal is festive.
Poppy seeds add a delicate crunch to your sweet potato gnocchi. Recipe via City Mouse Online. Get the recipe here.
These deliciously nutty cookies are perfect for adding to a mishloach manot - the traditional Purim gift basket exchange. Recipe via City Mouse Online. Get the recipe here.
This pear pie gets a Purim upgrade thanks to the poppy seeds in the filling. Recipe via City Mouse Online. Get the recipe here.
Classic poppy seed filling takes many traditional additions, and you can choose your favorite: Think sliced or grated apples, raisins, chocolate, or candied orange peel. Recipe by Vered Guttman. Get the recipe here.
Bursting with flavor and crunch, this Shirazi salad is the Persian version of the Arab/Israeli chopped salad. This version includes pomegranate seeds and poppy seeds in the spirit of the holiday and Queen Esther. Recipe by Vered Guttman. Get the recipe here.


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text:
«Сосна Веймутова» — ботанічна пам'ятка природи місцевого значення в Україні.

Пам'ятка природи зростає біля приміщення КЕЧ на вул. Степана Бандери, 56 у місті Чорткові Тернопільської області.

Статус надано рішенням Тернопільської обласної ради від 8 вересня 2006 р. № 44. Перебуває у віданні Чортківської міської ради.

Площа — 0,01 га.

Під охороною сосна Веймутова віком біля 80 років, діаметром 47 сантиметрів. Це дерево є єдиним у місті і має велику еколого-освітню та естетичну цінність.

Джерела

Посилання

Природоохоронні об'єкти, засновані 2006
Сосни
2006 у Тернопільській області
Вересень 2006

redpajama_set_name: RedPajamaWikipedia


The Eligibility Department responds to your request for eligibility verification by sending a message to your Inbox.
The name of the patient whose eligibility is being verified.
The date the request was submitted.
This message indicates whether or not the patient is eligible and includes an explanation for the determination.
Patient's current Primary Care Physician.
Date the patient became effective with the health plan.
Date the patient was or will be terminated.
Notes or comments from the Eligibility Department.


text:
Q: Laravel Socialite + Making API calls after login Laravel 5, Socialite, and google/apiclient packages.
Source code: https://github.com/svpernova09/meatings
I have socialite working fine with Google for logging users in.
I'm trying to make an API call in a different method to fetch Calendar events as the logged in user. I'm getting stuck with what tokens to use where.
The error I'm getting is:

"error" : "invalid_grant",
"error_description" : "Code was already redeemed."

My method:
public function show($user_id)
{
    $user = $this->user->find($user_id);

    $client = new Google_Client();
    $client->setClientId(env('GOOGLE_CLIENT_ID'));
    $client->setClientSecret(env('GOOGLE_CLIENT_SECRET'));
    $client->setRedirectUri(env('GOOGLE_CALLBACK_URL'));

    $client->authenticate($user->code);
    $service = new Google_Service_Calendar($client);

    $calendarId = $user->calendar_id;
    $optParams = array(
        'maxResults' => 5,
        'orderBy' => 'startTime',
        'singleEvents' => TRUE,
        'timeMin' => date('c'),
    );
    $results = $service->events->listEvents($calendarId, $optParams);
    $events = [];
    if (count($results->getItems()) > 0) {
        foreach ( $results->getItems() as $event ) {
            $events[] = $event;
        }
    }

    return view('users.calendar')->with('events', $events);
}

The Laravel output is:

Google_Auth_Exception in OAuth2.php line 127:
Error fetching OAuth2 access token, message: 'invalid_grant'

$user-code looks like: 4/hfPzDrOHyaEv3asdfadsfasdfDw72nXIl0rt2boUpGj7hM.Um5wPgCeasdfasdfafd1t6qxkmwI
Any guidance would be great. I'm not getting anywhere with the google guides.

A: Calendar uses a different scope than social login. You have to ask for permission again. You can check the documentation of the Calendar API and try it out on Google Playground.
Also Google returns "Code was already redeemed." because you already have an access token for the public information of the user with your code.


Nuwakot: The power supply from the central system has been disrupted with the fire engulfing the Trishuli Fuse Service (no light) at the Trishuli Hydropower Production House of the Nepal Electricity Authority.
The power supply came to a halt when the fire caught the 'incomer' that was installed in power service to supply electricity and a fuse section with seven feeders of distribution at around 10.00 pm on Wednesday.
However, the power generation house has remained safe despite fire outbreak at Fuse Section. The fire was taken under control under half an hour.
The losses caused by the fire are yet to be ascertained as data collection for the same is undergoing.