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http://motls.blogspot.com/2012/11/obama-romney-trf-poll.html	## Tuesday, November 06, 2012 ... ///// ### Obama-Romney: TRF poll Update: About 1/3 of U.S. TRF readers voted for Obama and 3/5 of them expected Obama to win. Only 1% of TRF readers voted for Obama but expected Romney to win. Among the non-TRF readers, Romney slightly won the popular vote but by the electoral votes, Obama safely defended his presidency. Dow Jones collapsed by more than two percent after the results. This poll is very simple and unsurprising. I want the U.S. readers – which make up 1/2 of the TRF visitors – to report whom they voted for and whom they expect to win. Well, I only mean the U.S. readers who are not crying of being tired of Bronko Báma and Mitt Romney yet. Who did you vote for, whom do you expect to win? I voted for Obama and expect Obama to winI voted for Romney but expect Obama to winI voted for Obama but expect Romney to winI voted for Romney and expect Romney to win pollcode.com free polls If you didn't actually physically vote but you have an opinion, please pretend that you did vote. Your vote counts here. Let me ask Unamerican readers to stay silent because this choice isn't really our business, the business of Unamericans. ;-) I would like to know how politically symmetric or asymmetric the readership of TRF is. #### snail feedback (22) : Why not give those Americans who are tired of the mainstream parties a third choice? I suspect that a number of your readers are Ron Paul Republicans or would choose to vote for Gary Johnson, Virgil Goode, or some other candidate. What's needed is a four party race, not just a three party race. That way votes will be taken away from not just one of the dominant parties, i.e. the Democrats or the Republicans, but both of them. Unfortunately, without realizing it, no matter who you vote for, you are throwing away your vote, for to vote in this duplicitous two-party system is nothing more than an exercise in futility. The proof of that is the last 30 or so years, if you look at the actual policies of each preceding President, you will find that the President that wins, no matter if it is Republican or Democrat, maintains or expands on the polices of the previous President. In fact, in looking at the policy differences you will find that 98%, if not more, of the previous President is maintained by the newly elected President coming into office, no matter which Party comes to power. In other words, there is not enough difference between the Parties or their polices to be meaningful. But thanks to the wonders of marketing, the American Voter actually thinks he or she is being given a choice, that his or her vote actually counts for something, when in fact, it is only an exercise to keep the American public placated through an elaborate political dog and pony show. It is the ultimate method of control, to allow a people to think they can make a difference, to give them hope that if only we can get this man into office things will change, the country will finally be put on the right path.How many years have we heard this very thing? Yes, this is the most important election ever, strangely, every election in the past 30 years have been the most important election ever and it is so vital that you cast your vote so we make sure that the right man gets elected. The stage play is presented to the American People every four years,the actors change, but the script remains the same. Sure there are stage props that are changed out, each candidate has some cosmetic policies that give their supporters the idea that their respective candidate is indeed THE ONE, but as far as substance, as far as real, substantive change taking place due to the election of a Republican or Democrat, there is no substantive differences between them. Your vote has become nothing more than a convenient means of political control, meaningless in terms of results due to the fact that both Parties have rigged the system to such a degree that they dare not allow other voices or opinions to creep into their ideological debate. This country finds itself in its current dismal state due to the fact that the People of this country, unaware of the enormous power structure behind the two Parties, continue to allow the same polices to be maintained and expanded without abatement. These are polices that have brought this country to the brink of ruin, and both the Republicans and Democrats are equally responsible, yet we continue to listen, continue to vote for puppet leaders whose strings are being pulled by the corporate one-percenters behind the curtains. Elections are making us choke Illusions of choice are a joke It's all just a ploy For sheep to enjoy Like rabbits enjoy a good smoke The Limerick King http://www.flickr.com/photos/expd/8116284456/ The quant pundits predict O wins, gut-feel pundits predict R wins. Today Dan Rather has gut feeling Romney will have a good day (win!) due to big turnout. Lubos, what do you think of Nate Silver? If such a strong favoring for O why is O camp sending Biden & Clinton to swing states up to the wire? I'm assuming you mean us in the wide wide world. No problem. You quit interfering in our affairs and we'll keep out of yours. Deal? Finally, a TRF article with no math! Been waiting a long time for that one. ;) At my precinct, in the Heart of Blue state California, there were fewer ballots cast than here on your TRF poll. I don't know if that means anything, but it could be a sign of general malaise among my liberal neighbors. Crossing fingers. Because most states are winner take all, and third party runs generally ensure another four years of crooks and democrats misruling the country. Any other questions? Helen Thomas? as a free man I choose to be optimistic. “The pessimist complains about the wind; the optimist expects it to change; the realist adjusts the sails.” -- William Arthur Ward I see myself as a realist, or at least it's my aim to be one. Sorry, I can't make any deal with you because I don't know who you are and where you're from. Moreover, I think that your "principle" of "no interference in our affairs" is complete bullshit. Everyone affects the affairs of many others in various ways - because everyone has some interests and everyone interacts. That's true for your affairs and that's true for "our" affairs, whoever is "we". I just said that the U.S. president is being chosen by Americans and I just the TRF blog to emulate this habit (although I obviously can't efficiently enforce the rule). Americans are doing many other decisions about themselves, much like Czechs about Czechs or Arabs about Arabs. But none of them is acting in the vacuum. Sovereignty doesn't mean that your affairs will be unaffected by others or by other nations. I think I picked the wrong week to give up heroin. Dear Tom, you will have to hurry up ;-) because on January, the most likely president that we elect is a former communist, which is still good because in the following parliamentary elections, (not only former) socialists and communists will probably secure a constitutional majority. The grass is always greener on the other side of the pond. ;-) Whoa I'm glad I read this. You really opened my eyes. God, you must be smart. Perhaps Lubos will take you on as an assistant. Who said that? And signed my name to it? Must have been Gleick. That magnificent bastard snuck into my computer. All joking aside, Cynthia, I'm a little foggy on what you mean by adjusting the sails. I think you have a point. For cripes sake, Obama running against Romney, both of them knee deep in government take over of your profession. A person would have to be blind not to see it. Still how do you tack against Obama/Romney Care? You have a strategy? Taking the practice to Costa Rica, maybe? So who did the other 39% of Obama voters think would win? Romney did not win the popular vote, he is trailing by 2% so far. If you want to see why he lost, the answer is Christian poor workers didn't vote for him. He ended up with fewer votes than McCain and George Bush despite a larger population. About 10 million white voters stayed home. Before y ou do that, have they lifted the ban on liquor? Sure, a long time ago. It was a one-month-long policy only. I always liked the grass in Amsterdam ... Seriously though I hope that none ever fall victim again to any totalitarian control.	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 1, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.2521609365940094, "perplexity": 3072.9929954349473}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-41/segments/1412037663007.13/warc/CC-MAIN-20140930004103-00173-ip-10-234-18-248.ec2.internal.warc.gz"}
https://www.physicsforums.com/threads/algebra-question-rings-and-ideals.217623/	# Algebra question - rings and ideals 1. Feb 24, 2008 ### quasar987 [SOLVED] Algebra question - rings and ideals 1. The problem statement, all variables and given/known data Let R be a (nonzero) commutative ring with identity and I be an ideal of I. Denote (I) the ideal of R[x] generated by I. The book says that (I) is the set of polynomials with coefficients in I. Why is that? 3. The attempt at a solution Call A the set of polynomials with coefficients in I. R is commutative and so is R[x], therefor (I) is simply given by (I) = {ap(x): a is in I and p(x) in R[x]} So clearly (I) is a subset of A. But for the other inclusion, given b_0+...+b_nx^n in A, we need to find an element a in I and a set {a_0,...,a_n} in R such that aa_i = b_i for all i=1,...,n. How is this achieved?? 2. Feb 24, 2008 ### morphism If b_0+...+b_nx^n is in A, then b_0, ..., b_n are all in I, and thus in (I). The latter is an ideal, so b_kx^k is certainly in (I), and so is the sum of such things. Edit: I don't really see how this follows. I would instead prove that A is an ideal of R that contains I and hence contains (I) by definition. Last edited: Feb 24, 2008 3. Feb 24, 2008 ### quasar987 Of course it does not follows! I was confused.	{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.943153977394104, "perplexity": 1063.3738770816626}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-09/segments/1487501171043.28/warc/CC-MAIN-20170219104611-00182-ip-10-171-10-108.ec2.internal.warc.gz"}
https://mc-stan.org/docs/2_27/stan-users-guide/log-sum-of-exponentials.html	## 15.4 Log sum of exponentials Working on the log scale, multiplication is converted to addition, $\log (a \cdot b) = \log a + \log b.$ Thus sequences of multiplication operations can remain on the log scale. But what about addition? Given $$\log a$$ and $$\log b$$, how do we get $$\log (a + b)$$? Working out the algebra, $\log (a + b) = \log (\exp(\log a) + \exp(\log b)).$ ### 15.4.1 Log-sum-exp function The nested log of sum of exponentials is so common, it has its own name, “log-sum-exp,” $\textrm{log-sum-exp}(u, v) = \log (\exp(u) + \exp(v)).$ so that $\log (a + b) = \textrm{log-sum-exp}(\log a, \log b).$ Although it appears this might overflow as soon as exponentiation is introduced, evaluation does not proceed by evaluating the terms as written. Instead, with a little algebra, the terms are rearranged into a stable form, $\textrm{log-sum-exp}(u, v) = \max(u, v) + \log\big( \exp(u - \max(u, v)) + \exp(v - \max(u, v)) \big).$ Because the terms inside the exponentiations are $$u - \max(u, v)$$ and $$v - \max(u, v)$$, one will be zero and the other will be negative. Because the operation is symmetric, it may be assumed without loss of generality that $$u \geq v$$, so that $\textrm{log-sum-exp}(u, v) = u + \log\big(1 + \exp(v - u)\big).$ Although the inner term may itself be evaluated using the built-in function log1p, there is only limited gain because $$\exp(v - u)$$ is only near zero when $$u$$ is much larger than $$v$$, meaning the final result is likely to round to $$u$$ anyway. To conclude, when evaluating $$\log (a + b)$$ given $$\log a$$ and $$\log b$$, and assuming $$\log a > \log b$$, return $\log (a + b) = \log a + \textrm{log1p}\big(\exp(\log b - \log a)\big).$ ### 15.4.2 Applying log-sum-exp to a sequence The log sum of exponentials function may be generalized to sequences in the obvious way, so that if $$v = v_1, \ldots, v_N$$, then $\begin{eqnarray} \textrm{log-sum-exp}(v) & = & \log \sum_{n = 1}^N \exp(v_n) \\[4pt] & = & \max(v) + \log \sum_{n = 1}^N \exp(v_n - \max(v)). \end{eqnarray}$ The exponent cannot overflow because its argument is either zero or negative. This form makes it easy to calculate $$\log (u_1 + \cdots + u_N)$$ given only $$\log u_n$$. ### 15.4.3 Calculating means with log-sum-exp An immediate application is to computing the mean of a vector $$u$$ entirely on the log scale. That is, given $$\log u$$ and returning $$\log \textrm{mean}(u)$$. $\begin{eqnarray} \log \left( \frac{1}{N} \sum_{n = 1}^N u_n \right) & = & \log \frac{1}{N} + \log \sum_{n = 1}^N \exp(\log u_n) \\[4pt] & = & -\log N + \textrm{log-sum-exp}(\log u). \end{eqnarray}$ where $$\log u = (\log u_1, \ldots, \log u_N)$$ is understood elementwise.	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9405062198638916, "perplexity": 347.77306494820516}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-31/segments/1627046153971.20/warc/CC-MAIN-20210730154005-20210730184005-00714.warc.gz"}
https://www.physicsforums.com/threads/angular-and-linear-acceleration-on-a-wheel.589316/	Angular and Linear Acceleration on a Wheel 1. Mar 22, 2012 PeachBanana 1. The problem statement, all variables and given/known data A 68 cm diameter wheel accelerates uniformly about its center from 150 rpm to 270 rpm in 4.1 s. 1. Determine its angular acceleration. α = 3.1 rad./s^2 2. Determine the radial component of the linear acceleration of a point on the edge of the wheel 1.6 s after it has started accelerating. 2. Relevant equations ω final = ω initial + αt v final = v initial + at ω * r = v 3. The attempt at a solution (20.61174 rad./s)(0.34m) = 7.0079916 m/s (final velocity) (15.7079 rad./s)(0.34m) = 5.340686 m/s (initial velocity) 7.0079916 m/s - 5.340686 m/s / 1.6 s = 1.042066 m/s^2 2. Mar 22, 2012 tiny-tim Hi PeachBanana! No, I think they're asking for the centripetal acceleration (ω2r). 3. Mar 22, 2012 PeachBanana tiny-tim: Thank you so much. That is much clearer now. The way it was worded was strange. Similar Discussions: Angular and Linear Acceleration on a Wheel	{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9287863969802856, "perplexity": 2471.6298430593356}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-43/segments/1508187828356.82/warc/CC-MAIN-20171024090757-20171024110757-00270.warc.gz"}
https://spectrum.library.concordia.ca/978211/	Title: # Determinants of Pseudo-Laplacians on compact Riemannian manifolds and uniform bounds of eigenfunctions on tori Aissiou, Tayeb (2013) Determinants of Pseudo-Laplacians on compact Riemannian manifolds and uniform bounds of eigenfunctions on tori. PhD thesis, Concordia University. Preview Text (application/pdf) Aissiou_PhD_S2014.pdf - Accepted Version 562kB ## Abstract In the first part of this thesis, we derive comparison formulas relating the zeta-regularized determinant of an arbitrary self-adjoint extension of the Laplace operator with domain consisting of smooth functions compactly supported on the complement of a point $P$, to the zeta-regularized determinant of the Laplace operator on $X$. Here $X$ is a compact Riemannian manifold of dimension 2 or 3; $P\in X$. In the second part, we provide a proof of a conjecture by Jakobson, Nadirashvili, and Toth stating that on an n-dimensional flat torus, the Fourier transform of squares of the eigenfunctions $\|phi_j\|^2$ of the Laplacian have uniform $l^n$ bounds that do not depend on the eigenvalue $\lambda_j$. The thesis is based on two published papers that can be found in the bibliography. Divisions: Concordia University > Faculty of Arts and Science > Mathematics and Statistics Thesis (PhD) Aissiou, Tayeb Concordia University Ph. D. Mathematics 2013 Kokotov, Alexey and Korotkin, Dmitri Determinants, Pseudo-Laplacian, Laplacian, Eigenfunctions, Eigenvalues, uniform bounds, L^p, compact manifolds, determinants of Laplacian, self-adjoint, extensions, zeta function, regularized determinant, geometric lemma, 978211 TAYEB AISSIOU 16 Jun 2014 14:06 18 Jan 2018 17:46 All items in Spectrum are protected by copyright, with all rights reserved. The use of items is governed by Spectrum's terms of access. Repository Staff Only: item control page	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.4997118413448334, "perplexity": 1246.1191503711966}, "config": {"markdown_headings": true, "markdown_code": false, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-50/segments/1606141187753.32/warc/CC-MAIN-20201126084625-20201126114625-00012.warc.gz"}
http://www.math.snu.ac.kr/board/index.php?mid=seminars&page=12&sort_index=room&order_type=desc&document_srl=774930	This talk is an introduction to the following problem: If L is a random lattice of R^n and S is a measurable subset, how are the points of L distributed inside S? This is related to a number of areas such as analytic number theory and quantum chaos, but here we focus on the problem itself rather than its applications. I'll discuss the main tools, current progress, and what needs to be done in the short- and long-term.	{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8707975149154663, "perplexity": 204.50793517318183}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-33/segments/1659882573104.24/warc/CC-MAIN-20220817183340-20220817213340-00456.warc.gz"}
http://www.zentralblatt-math.org/zmath/en/advanced/?q=an:0743.11012	Language: Search: Contact Zentralblatt MATH has released its new interface! For an improved author identification, see the new author database of ZBMATH. Query: Fill in the form and click »Search«... Format: Display: entries per page entries Zbl 0743.11012 Deeba, Elias Y.; Rodriguez, Dennis M. Stirling's series and Bernoulli numbers. (English) [J] Am. Math. Mon. 98, No.5, 423-426 (1991). ISSN 0002-9890 For $n=2,3,\ldots$ the following infinite system of recurrences for the Bernoulli numbers $B\sb m$ is shown: $$B\sb m={1\over n(1-n\sp m)}\sum\sp{m-1}\sb{k=0}n\sp k{m\choose k}B\sb k\sum\sp{n- 1}\sb{j=1}j\sp{m-k}.$$ The proof follows by direct computations from the usual generating function of the Bernoulli numbers. [R.F.Tichy (Graz)] MSC 2000: *11B68 Bernoulli numbers, etc. 05A15 Combinatorial enumeration problems Keywords: infinite system of recurrences; Bernoulli numbers; generating function Highlights Master Server	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9875279068946838, "perplexity": 8697.293829985429}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2013-20/segments/1368709337609/warc/CC-MAIN-20130516130217-00090-ip-10-60-113-184.ec2.internal.warc.gz"}
http://cms.math.ca/cjm/kw/isoperimetric%20inequality	location: Publications → journals Search results Search: All articles in the CJM digital archive with keyword isoperimetric inequality Expand all Collapse all Results 1 - 3 of 3 1. CJM Online first Xiao, Jie; Ye, Deping Anisotropic Sobolev Capacity with Fractional Order In this paper, we introduce the anisotropic Sobolev capacity with fractional order and develop some basic properties for this new object. Applications to the theory of anisotropic fractional Sobolev spaces are provided. In particular, we give geometric characterizations for a nonnegative Radon measure $\mu$ that naturally induces an embedding of the anisotropic fractional Sobolev class $\dot{\Lambda}_{\alpha,K}^{1,1}$ into the $\mu$-based-Lebesgue-space $L^{n/\beta}_\mu$ with $0\lt \beta\le n$. Also, we investigate the anisotropic fractional $\alpha$-perimeter. Such a geometric quantity can be used to approximate the anisotropic Sobolev capacity with fractional order. Estimation on the constant in the related Minkowski inequality, which is asymptotically optimal as $\alpha\rightarrow 0^+$, will be provided. Keywords:sharpness, isoperimetric inequality, Minkowski inequality, fractional Sobolev capacity, fractional perimeterCategories:52A38, 53A15, 53A30 2. CJM 2012 (vol 65 pp. 1401) Zhao, Wei; Shen, Yibing A Universal Volume Comparison Theorem for Finsler Manifolds and Related Results In this paper, we establish a universal volume comparison theorem for Finsler manifolds and give the Berger-Kazdan inequality and SantalÃ³'s formula in Finsler geometry. Being based on these, we derive a Berger-Kazdan type comparison theorem and a Croke type isoperimetric inequality for Finsler manifolds. Keywords:Finsler manifold, Berger-Kazdan inequality, Berger-Kazdan comparison theorem, SantalÃ³'s formula, Croke's isoperimetric inequalityCategories:53B40, 53C65, 52A38 3. CJM 1999 (vol 51 pp. 449) Bahn, Hyoungsick; Ehrlich, Paul A Brunn-Minkowski Type Theorem on the Minkowski Spacetime In this article, we derive a Brunn-Minkowski type theorem for sets bearing some relation to the causal structure on the Minkowski spacetime $\mathbb{L}^{n+1}$. We also present an isoperimetric inequality in the Minkowski spacetime $\mathbb{L}^{n+1}$ as a consequence of this Brunn-Minkowski type theorem. Keywords:Minkowski spacetime, Brunn-Minkowski inequality, isoperimetric inequalityCategories:53B30, 52A40, 52A38 top of page \| contact us \| privacy \| site map \|	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8560383915901184, "perplexity": 1984.2086534994678}, "config": {"markdown_headings": true, "markdown_code": false, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2016-36/segments/1471982295103.11/warc/CC-MAIN-20160823195815-00130-ip-10-153-172-175.ec2.internal.warc.gz"}
https://astrobites.org/2018/01/24/hunting-for-new-physics-in-a-black-holes-shadow/	# Hunting for new physics in a black hole’s shadow Authors: Steven B. Giddings & Dimitrios Psaltis First Author’s Institution: University of California, Santa Barbara Status: Submitted to Phys Rev D, open access on the arXiv. For 5 days in April of 2017, 8 radio telescopes on 4 continents all pointed in concert at Sagittarius A, the supermassive black hole at the center of our galaxy. During this observing campaign these 8 telescopes effectively became one Earth-sized radio telescope, the Event Horizon Telescope (EHT). Using hydrogen maser atomic clocks to track the difference in the arrival times of the radio signal at the various telescopes, the far-flung array can emulate a single telescope with an effective diameter equal to that of our planet, a technique called very long baseline interferometry (VLBI). Figure 1. The Event Horizon Telescope network. The nodes are the individual radio telescopes that make up the network, and the connections are the baselines between them. (Image Credit: ESO) The goal of the EHT project is to directly image the immediate environs of a black hole, a region that has been inaccessible with light thus far. The unprecedented angular resolution achieved by the EHT is approximately 50 micro arcseconds (approximately the resolution needed to see an apple on the surface of the moon from your house), not coincidentally the same angular size on the sky as the event horizon of Sgr A and that of the super-massive black hole at the heart of the elliptical galaxy M87. While M87 is much farther away than the Galactic Center, the mass of its central black hole is $\sim 6.5 \times 10 ^ 9$ solar masses, about 1500 times more massive than Sgr A. Since the size of the event horizon scales linearly with the mass of the black hole, the angular sizes subtended on the sky by the event horizons of Sgr A and M87’s black hole end up being comparable. Alongside the recent successes of gravitational wave astronomy, the EHT is another way to probe the ‘strong-field’ gravitational regime and provide long-awaited answers to questions about general relativity. Specifically, the EHT uses mm-wavelength radio astronomy to trace the extremely hot gas that is believed to inhabit the area directly outside the event horizon of the black hole. General relativity predicts that a silhouette, or ‘shadow’, will be seen imprinted onto the image of the hot gas, the distinct signature of the black hole’s event horizon (See Fig. 2). Today’s paper looks at ways to test general relativity, alternative theories of gravity, and the quantum structure of space-time by studying the size and shape of this shadow. Figure 2. At left: A simulated image of Sgr A* showing the hot accretion flow. The light coming from the hot gas is lensed by the strong gravity and forms a ring that encircles the distinctive shadow of the black hole. The ring is brighter on the approaching side and dimmer on the receding side due to Doppler effects. At right: The expected performance of the EHT array during its 2017 observing run. [arxiv:1409.4690] In general relativity, the event horizon of a Schwarzschild (non-spinning) black hole should be perfectly circular and its radius should scale with the black hole’s mass as $2MG/c^2$, where $M$ is mass of the black hole, $G$ is the gravitational constant, and $c$ is the speed of light. In the more astrophysically realistic case where a black hole has spin, described by the Kerr metric, the event horizon will still look very circular unless the spin is exceptionally large and the inclination angle is high (line-of-sight is near the axis of rotation). However, in beyond-GR theories the event horizon can be asymmetric, and the size can vary. In this paper the authors study the observable effects of what they call ‘soft quantum modifications’ on the black hole shadow. What this really means is that instead of the space-time being smooth and well described by general relativity, it takes on a jittery quantized behavior at certain length scales. A bumpy space-time may sound strange, but is not completely uncalled for, and such an approach is well motivated by a variety of outstanding issues (see Bites on: hairy black holes, quantized gravity, and the black hole information paradox). Figure 3. Possible shapes of the event horizon that can result from small perturbations to the black hole’s structure. Left and right show different phases of the same perturbation mode. One should imagine the black hole pulsating back-and-forth between these shapes. The blue circle shows the shape of the event horizon in the regular non-spinning general relativistic (Schwarzschild) case. (Figure 5 in the paper) The authors allow small changes (perturbations) to the structure of the black hole space-time (the metric), of the sort that might be allowed in a reasonable theory of quantum gravity. They then calculate what the shape of the horizon looks like under these perturbations (Fig. 3), and the effect that this has on the path that light takes around the black hole. The authors find that introducing these small changes to the structure of the black hole space-time can have significant and time-dependent (not to mention beautiful) effects on the shape of the shadow that is cast onto the image of the bright gas (see Fig. 4). If these effects exist, they could in some cases be easily distinguished from their cousins, the more staid classical black hole shadows. However, they observe that in their model the dynamical variations in the shadow have a characteristic time-scale that is proportional to $\frac{1}{M},$ with $M$ the mass of the black-hole. In other words, the less massive the black hole, the more time that will pass between noticeable variations in the black hole’s shadow. This period ends up being just too long for observations of Sgr A. That is, while the observations of Sgr A taken in April may be able to resolve strange, non-circular shapes (if there are quantum gravitational perturbations at all!), we will not be able to see the shape of the horizon changing. However, because M87 is so much more massive, its characteristic pulsation period is short enough to capture in a typical EHT observation. Figure 4. A simulated image of the effect of the quantum perturbations on the light coming off the hot gas near the black hole. (Figure 9 in the paper) This paper is a worthwhile and fun exploration of possible effects that a quantum structure of space-time could have on black hole shadows, but there are some limitations. The ‘soft quantum modifications’ were made only for non-spinning (Schwarzschild) black holes. Extending these methods to the spinning case is not trivial, but there are reasons to believe that the results will be at least qualitatively similar. Most importantly however, those searching for hints of a theory beyond General Relativity in black hole shadows now know what to look for. While the EHT observations were performed in April, the results are not out yet. VLBI techniques require significant data processing, and the team only just received the data taken by the South Pole Telescope (the node that provides the longest baseline) via the sneakernet. There are no flights out of the South Pole during the austral winter and too much data to send via the internet (even if it wasn’t the strictly bandwidth limited TDRSS network that provides the South Pole station’s connection!). While it remains to be seen, it’s possible that the first direct image of the event horizon of a black hole is sitting in the data, just waiting to be pieced together, and with it possible clues about the quantum structure of space-time. I am a graduate student at the University of Toronto. Previously I worked on the NASA Swift Observatory sci ops team. My research has focused on the discovery of high-energy multi-messenger transients and my interests lie in using these phenomena as probes of fundamental physics. 1. As an engineer (small e because I never actually did engineering in my career) I’ve always enjoyed following various fundamental physics topics. Among them is Gravity, but being essentially uneducated … I try not to make too much stuff up about things like black holes. So I ask myself simple questions. I wondered if you could notarize or debunk a couple of my imaginary lines of reasoning. For some time I have thought of the edgeless-ness of black holes as reverberating membrane, that it has to be changing shape, not remaining spherical. I think this notion was implanted in my mind many years ago when I had read about how spin would have to affect these things. So, I see this in my mind black holes sort of like the surface falling water droplets … it was hard for me to imagine how the event horizon wouldn’t bounce when matter falls beyond it into the hole, or just naturally resonate with diminishing amplitude relative to past events. Further, I try to invert the picture: I imagine what’s happening to the “droplet” if instead of being perfectly black it were perfectly reflective (a chrome marble with a viscous surface like a water droplet.) Then I can sort of perceive gravity waves in the reverberation of the Ev.H. by watching my reflection. Two merging reverberating chrome droplets are easier for me to imagine merging than field lines in a 2D projection. Is this just crazy? Where this goes for me is into thought experiments like: What’s going on when a teeny black hole falls into a much larger one… I perceive the physics like watching a droplet land in a lake. The camera of my mind sees it in super slo-mo and at a macro focal length. Or is it like a small asteroid landing in the ocean, as seen through a telephoto lens… I’m looking forward to hearing about the VLBA results with great anticipation. Thank you so much for writing about your work. I’m green with envy. • Hi David, The event horizon is not a physical object. It is a mathematical boundary that delimits the region of space inside of which events can never affect that which is outside, and from which even light cannot escape. The reason this paper talks about the event horizon ‘changing shape’, is because, while not physical, the shape of the event horizon effects what can (and cannot) be seen by observers on the outside, and so will change the image that is detected by the Event Horizon Telescope. Conventional general relativity predicts that the event horizon will be perfectly spherical for a non-spinning black hole, and oblong in a very precise way for one that is spinning. This paper explores the idea of a small quantum modification to general relativity that would allow the event horizon to take on other shapes. They then examine the effect that this would have on the image detected by the Event Horizon Telescope, and thus how it could be used to detect physics beyond general relativity. While one can use physical objects and phenomena from our more immediate experiences to imagine black hole dynamics, you must remember that the event horizon is not actually physical. In this case, ask yourself what would the ‘reverberations’ you mention mean for a non-physical entity? And have you followed the analogy too far? Hope this cleared up your question.	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 7, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5754627585411072, "perplexity": 593.5994428632893}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-10/segments/1614178368608.66/warc/CC-MAIN-20210304051942-20210304081942-00356.warc.gz"}
http://www.genealogy.ams.org/id.php?id=146173	Ph.D. Lomonosov Moscow State University 1978 Dissertation: Some Improvements Of Estimates For The Rate Of Convergence In The Central Limit Theorem Mathematics Subject Classification: 60—Probability theory and stochastic processes Students:	{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8187301158905029, "perplexity": 736.9896162617772}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-47/segments/1542039743968.63/warc/CC-MAIN-20181118052443-20181118074443-00089.warc.gz"}
https://motls.blogspot.com/2010/08/new-scientist-attacks-quantum-physics.html	## Monday, August 23, 2010 ... // ### New Scientist attacks quantum physics Well, I can't hide that I really hate the magazine called New Scientist. Ninety-five percent of their articles about the disciplines I care about - and about science per se - are emotional attacks by breathtakingly deluded pompous imbeciles against the scientific principles and scientific achievements that I hold dear - that I consider the pillars of the human knowledge and progress. Nude Socialist has already dedicated a whole issue to attacks on "climate deniers". It systematically promotes crackpots in high-energy physics (and their dumb speculations and misconceptions) and tries to put them on the same level - if not a higher level - with the world's top physicists (and the key findings of physics). Attacks against string theory haven't been revolutionary enough for these new "scientists" so they picked all of quantum physics as their new target today. Two minutes ago, they released the following article: Is quantum theory weird enough for the real world? It's a classic article by anti-quantum zealots who simply refuse to accept, on purely dogmatic grounds, that the postulates of quantum mechanics could be a fundamental part of the reality. Already the subtitle has increased my adrenaline level by a factor of pi: Our most successful theory of nature is bewilderingly remote from reality. But fixing that may require a weirder theory still How it can be "bewilderingly remote from reality" if it is our most successful theory of Nature? It just doesn't make sense. A theory's proximity to reality is defined by its ability to successfully and accurately reproduce and predict the information about the relevant class of phenomena and objects. So it is just a logical contradiction for a successful theory of Nature to be "remote from reality". Moreover, as long as one is doing science, there is no justification for attempts to "fix" a theory that agrees with all the observations and works perfectly consistently at the mathematical level, too. They quote some people with strange Slavic names I've never heard of who are repeating the misconception from the subtitle in some truly "new", bizarre ways. For example, a Časlav Brukner says: We do not have a source for the mathematical formalism of quantum mechanics. We do not have a nice physically plausible set of principles from which to derive it. There are no known, more fundamental principles from which the quantum postulates can be derived simply because the postulates of quantum mechanics are among the most fundamental insights we have about the reality. And they're perfectly "physically plausible". In fact, they're not plausible just a priori. They have been verified and validated by some of the most accurate experiments ever made by living forms on this planet. If someone doesn't find them "physically plausible", obviously, he confuses physics with his own philosophical bigotry. What they really want to say is that the principles of quantum mechanics are not ideologically plausible for anti-quantum bigots with tiny brains and huge mouths. But that's something completely different from a "physical plausibility". The author of the Nude Socialist article, a Richard Webb, improves the statement by the Časlav Brukner in the following way: Quantum physics might be quantum - but as far as we can tell it isn't physics. Holy cattle. A few years ago, it was "just" string theory that was said - by a coalition of Swolins, Smoits, and their mindless fans - not to be physics. But that's no longer enough for the pompous fools of this world who are thriving because almost no one has enough courage to give these arrogant scumbags a proper thrashing. In 2010, even quantum physics fails to be physics! This is just completely insane. Quantum physics is not only physics but, as we have known for 80 years, it is all of physics. Physics is a science about the fundamental phenomena in the real world and all phenomena in the real world are quantum phenomena because the whole world follows the postulates of quantum mechanics. So any classical or otherwise non-quantum physics is bound to be nothing else than an approximation to quantum physics - as long as it is valid at all. Following the very same template that would be used against string theory a few years ago, Richard Webb paints a picture where quantum physics doesn't belong to physics of Tycho Brahe and others. The final paragraph says: Not so with quantum theory. Although it was initially inspired by an idea rooted in the real world - that energy came in small packets called quanta - by the time luminaries such as Erwin Schrödinger and Werner Heisenberg had finished its mathematical formulation, the theory had acquired a life of its own (see chart). Wow. So it's a sin for a theory to acquire a "life of its own". And because it differs from the phenomena that were studied by Tycho Brahe, it surely has to be separated from the real world, right? Incredible. These dozens of paragraphs full of lies and irrationality is the only justification that Richard Webb offers to support some not-exactly-specified but surely "revolutionary" ideas by the crackpots with the Slavic names. If you want to know what is their better theory, you will hear about fantastic theories - except that it's also known that they prohibit physical systems from evolving (among other bugs that are not quoted). Well, that's a pretty serious problem for a theory that would like to replace quantum physics, isn't it? But in the world of the Nude Socialist hype, such a failure doesn't matter. More precisely, it is a virtue. The dirtier trash you write down (and you are), the better image of you will be created by the crackpot would-be science journalists. Several painful paragraphs about the inability of these crackpot theories to reproduce basic properties of the real world follow. When it kind of becomes clear that quantum mechanics hasn't been "replaced" by scientific tools, Richard Webb has an excellent idea how to change the rules of the game: There is another possibility: observation might actually be leading us astray. Exactly. Observations are thoseevil quantum deniers that deny the true reality that has nothing to do with observations! The right new criterion to judge a physics theory is not to compare its predictions with observations but to see what Nude Socialist writes about it. After all, it has been writing pure garbage about science for many years. It has no problem to print a long and vitriolic diatribe claiming that a theory ceases to be scientific - and becomes detached from the reality - if it actually cares about the observations. The reality is very different. At one day, we may find a deeper layer of principles that will imply the postulates of quantum mechanics as we know them today - that will put them into a more comprehensive picture. But it's virtually impossible for these postulates to ever be distorted; they are almost certainly exact. In particular, the world of science - as long as it will be science - will never return back to the classical deterministic confines. Nude Socialists may continue to whine about the imperialist quantum mechanics that controls the world of physics even though it's so evil. And they may brainwash thousands of readers who are not able to use their own brains. But that's the only thing that they can do against the laws of Nature. #### snail feedback (3) : Lubos, In the back of my mind I keep thinking that there is something after all in the various formulations of quantum physics that impedes our understanding of the deep truth of string theories. I am not sure that the fact of the matter is that physics is somewhere between our notions of determinism and indeterminism. Your recent comments on some of the more frontier or fringe articles are very informative and seems to me to have all the ingredients to either solve some of this or understand the issues. I find it remarkable how often our posts share the same concerns even before they are shared- or for that matter what is in the popular news magazines of the day. The PeSla New Scientist is the Daily Mirror of science journalism.	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 1, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.3242957293987274, "perplexity": 1024.0408057485315}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 5, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-13/segments/1552912202525.25/warc/CC-MAIN-20190321132523-20190321154523-00256.warc.gz"}
https://gmatclub.com/forum/stores-x-y-and-z-each-sell-a-certain-item-that-has-a-given-161578.html	GMAT Question of the Day: Daily via email \| Daily via Instagram New to GMAT Club? Watch this Video It is currently 18 Jan 2020, 16:17 ### GMAT Club Daily Prep #### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email. Customized for You we will pick new questions that match your level based on your Timer History Track every week, we’ll send you an estimated GMAT score based on your performance Practice Pays we will pick new questions that match your level based on your Timer History # Stores X, Y, and Z each sell a certain item that has a given Author Message TAGS: ### Hide Tags Intern Joined: 02 Jul 2013 Posts: 18 Schools: LBS MIF '15 Stores X, Y, and Z each sell a certain item that has a given [#permalink] ### Show Tags Updated on: 14 Oct 2013, 06:55 7 48 00:00 Difficulty: 45% (medium) Question Stats: 70% (02:21) correct 30% (02:36) wrong based on 667 sessions ### HideShow timer Statistics Stores X, Y, and Z each sell a certain item that has a given list price. Stores X and Y are located in a state with a 5 percent sales tax, and both sell the item at a 5 percent discount off list price, while Store Z is located in a state with no sales tax and gives no discounts. Store X applies its discounts first and then charges sales tax on the discounted price, while Store Y adds the tax first and then applies the discount to the price with tax. If x and y are the prices, with tax and discount, charged by Stores X and Y, respectively, and z is the price charged by Store Z, which of the following statements correctly describes the relationship among x, y, and z? A. x=y=z B. x=y<z C. x<y<z D. x<z<y E. y<z<x Originally posted by bulletpoint on 14 Oct 2013, 06:24. Last edited by Bunuel on 14 Oct 2013, 06:55, edited 1 time in total. Moved to PS forum. Math Expert Joined: 02 Sep 2009 Posts: 60480 Re: Stores X, Y, and Z each sell a certain item that has a given [#permalink] ### Show Tags 14 Oct 2013, 06:58 15 12 bulletpoint wrote: Stores X, Y, and Z each sell a certain item that has a given list price. Stores X and Y are located in a state with a 5 percent sales tax, and both sell the item at a 5 percent discount off list price, while Store Z is located in a state with no sales tax and gives no discounts. Store X applies its discounts first and then charges sales tax on the discounted price, while Store Y adds the tax first and then applies the discount to the price with tax. If x and y are the prices, with tax and discount, charged by Stores X and Y, respectively, and z is the price charged by Store Z, which of the following statements correctly describes the relationship among x, y, and z? A. x=y=z B. x=y<z C. x<y<z D. x<z<y E. y<z<x Say the price of the item is 100. Then: x = (1000.95)1.05 < 100. y = (1001.05)0.95 < 100. z = 100. So, we have that x=y<z. _________________ ##### General Discussion Senior Manager Joined: 04 Jul 2014 Posts: 293 Location: India GMAT 1: 640 Q47 V31 GMAT 2: 640 Q44 V34 GMAT 3: 710 Q49 V37 GPA: 3.58 WE: Analyst (Accounting) Re: Stores X, Y, and Z each sell a certain item that has a given [#permalink] ### Show Tags 24 Nov 2014, 03:18 2 Hi Bunuel, I tried this on a spreadsheet. I took a common number (100) and did 2 sets of operations for 2 options: option 1 (Store Y) added X% and subtracted Y% from the result of the first operation option 2 (Store X) subtracted Y% and added X% from the result of the first operation Attachment: Capture.PNG [ 1.74 KiB \| Viewed 49104 times ] I always got the same answer. Is this a property that we can by heart? Math Expert Joined: 02 Sep 2009 Posts: 60480 Stores X, Y, and Z each sell a certain item that has a given [#permalink] ### Show Tags 24 Nov 2014, 06:44 8 5 joseph0alexander wrote: Hi Bunuel, I tried this on a spreadsheet. I took a common number (100) and did 2 sets of operations for 2 options: option 1 (Store Y) added X% and subtracted Y% from the result of the first operation option 2 (Store X) subtracted Y% and added X% from the result of the first operation Attachment: Capture.PNG I always got the same answer. Is this a property that we can by heart? Yes, increasing a quantity by x% and then decreasing the result by y% is the same as decreasing by y% and then increasing the result by x%: $$[p(1 + \frac{x}{100})](1 - \frac{y}{100}) = [p(1 -\frac{y}{100})](1 + \frac{x}{100})$$ _________________ Intern Joined: 04 Sep 2012 Posts: 13 Location: United States Concentration: Finance, Technology GMAT 1: 710 Q45 V42 GPA: 3 WE: Securities Sales and Trading (Other) Re: Stores X, Y, and Z each sell a certain item that has a given [#permalink] ### Show Tags 28 Jul 2015, 16:30 Thought process: We're dealing with percents. Increase and decrease. Strategy: Pick numbers and plow through the calculations. Choose 100 or another easy round number. See that x=y<z CHOOSE B ON TO THE NEXT Intern Joined: 20 May 2013 Posts: 1 Re: Stores X, Y, and Z each sell a certain item that has a given [#permalink] ### Show Tags 29 Sep 2016, 03:02 Bunuel Can you please explain if this is correct - If we used the formula instead of successive discounts ie A + B + AB/100 (where A and B are successive discounts/percentages applied to the same quantity) then the ans for final list price value is: X: (-5) + 5 -25/100 (X) => X is the list price Y: 5 - 5 -25/100 (Y) => Y is the list price But seems like the final list price value is different using this formula. Is it incorrect to use it here? Intern Joined: 19 Jan 2016 Posts: 34 Re: Stores X, Y, and Z each sell a certain item that has a given [#permalink] ### Show Tags 09 Oct 2016, 08:03 Hi Bunnel, I tried solving this question by taking the value of the product as 100. A 5% decrease results 95 (discounted price) after we add the tax to this value it is equal to 99.3. If the sales tax is added and then discounted its 101.5. Can you please explain what am i missing here ? Board of Directors Status: Stepping into my 10 years long dream Joined: 18 Jul 2015 Posts: 3556 Re: Stores X, Y, and Z each sell a certain item that has a given [#permalink] ### Show Tags 09 Oct 2016, 08:50 1 nikitamitra wrote: Bunuel Can you please explain if this is correct - If we used the formula instead of successive discounts ie A + B + AB/100 (where A and B are successive discounts/percentages applied to the same quantity) then the ans for final list price value is: X: (-5) + 5 -25/100 (X) => X is the list price Y: 5 - 5 -25/100 (Y) => Y is the list price But seems like the final list price value is different using this formula. Is it incorrect to use it here? Yes, using the formula also we will get the same result. Note that List price of the product is same. So, Try taking the value of each product 'a' and then substutitute in your formula. You will get the result. anuj11 wrote: Hi Bunnel, I tried solving this question by taking the value of the product as 100. A 5% decrease results 95 (discounted price) after we add the tax to this value it is equal to 99.3. If the sales tax is added and then discounted its 101.5. Can you please explain what am i missing here ? You are making a calculation mistake. List price 100. Case 1 : 5% increase then 5% discount. = 105 * 0.95 Case 2 : 5% discount the n 5% increase = 95 1.05 Both will be equal. _________________ My GMAT Story: From V21 to V40 My MBA Journey: My 10 years long MBA Dream My Secret Hacks: Best way to use GMATClub \| Importance of an Error Log! Verbal Resources: All SC Resources at one place \| All CR Resources at one place GMAT Club Inbuilt Error Log Functionality - View More. New Visa Forum - Ask all your Visa Related Questions - here. New! Best Reply Functionality on GMAT Club! Find a bug in the new email templates and get rewarded with 2 weeks of GMATClub Tests for free Check our new About Us Page here. Intern Joined: 15 Nov 2015 Posts: 2 Re: Stores X, Y, and Z each sell a certain item that has a given [#permalink] ### Show Tags 04 Jun 2017, 20:29 Bunuel wrote: bulletpoint wrote: Stores X, Y, and Z each sell a certain item that has a given list price. Stores X and Y are located in a state with a 5 percent sales tax, and both sell the item at a 5 percent discount off list price, while Store Z is located in a state with no sales tax and gives no discounts. Store X applies its discounts first and then charges sales tax on the discounted price, while Store Y adds the tax first and then applies the discount to the price with tax. If x and y are the prices, with tax and discount, charged by Stores X and Y, respectively, and z is the price charged by Store Z, which of the following statements correctly describes the relationship among x, y, and z? A. x=y=z B. x=y<z C. x<y<z D. x<z<y E. y<z<x Say the price of the item is 100. Then: x = (1000.95)1.05 < 100. y = (1001.05)0.95 < 100. z = 100. So, we have that x=y<z. Hi, I understand that Y<Z, but could you please explain why X equals to Y<Z? Retired Moderator Joined: 22 Aug 2013 Posts: 1403 Location: India Re: Stores X, Y, and Z each sell a certain item that has a given [#permalink] ### Show Tags 04 Jun 2017, 22:43 nielsenn wrote: Bunuel wrote: bulletpoint wrote: Stores X, Y, and Z each sell a certain item that has a given list price. Stores X and Y are located in a state with a 5 percent sales tax, and both sell the item at a 5 percent discount off list price, while Store Z is located in a state with no sales tax and gives no discounts. Store X applies its discounts first and then charges sales tax on the discounted price, while Store Y adds the tax first and then applies the discount to the price with tax. If x and y are the prices, with tax and discount, charged by Stores X and Y, respectively, and z is the price charged by Store Z, which of the following statements correctly describes the relationship among x, y, and z? A. x=y=z B. x=y<z C. x<y<z D. x<z<y E. y<z<x Say the price of the item is 100. Then: x = (1000.95)1.05 < 100. y = (1001.05)0.95 < 100. z = 100. So, we have that x=y<z. Hi, I understand that Y<Z, but could you please explain why X equals to Y<Z? Hi x=y<z simply means that x and y are equal to each other, and both are less than z. Target Test Prep Representative Affiliations: Target Test Prep Joined: 04 Mar 2011 Posts: 2806 Re: Stores X, Y, and Z each sell a certain item that has a given [#permalink] ### Show Tags 06 Jun 2017, 16:46 1 bulletpoint wrote: Stores X, Y, and Z each sell a certain item that has a given list price. Stores X and Y are located in a state with a 5 percent sales tax, and both sell the item at a 5 percent discount off list price, while Store Z is located in a state with no sales tax and gives no discounts. Store X applies its discounts first and then charges sales tax on the discounted price, while Store Y adds the tax first and then applies the discount to the price with tax. If x and y are the prices, with tax and discount, charged by Stores X and Y, respectively, and z is the price charged by Store Z, which of the following statements correctly describes the relationship among x, y, and z? A. x=y=z B. x=y<z C. x<y<z D. x<z<y E. y<z<x We are given that Stores X and Y are located in a state with a 5 percent sales tax, and both sell an item at a 5 percent discount off list price, while Store Z is located in a state with no sales tax and gives no discounts. We are also given that Store X applies its discounts first and then charges sales tax on the discounted price, while Store Y adds the tax first and then applies the discount to the price with tax. Let’s determine the prices, x, y, and z and let the original price of the item = 100. Price at Store X: (100)(0.95)(1.05) = $99.75 Price at Store Y: (100)(1.05)(0.95) =$99.75 Price at Store Z: $100 Thus, x = y < z Answer: B _________________ # Jeffrey Miller Head of GMAT Instruction Jeff@TargetTestPrep.com 181 Reviews 5-star rated online GMAT quant self study course See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews If you find one of my posts helpful, please take a moment to click on the "Kudos" button. Intern Joined: 14 Jul 2017 Posts: 25 Re: Stores X, Y, and Z each sell a certain item that has a given [#permalink] ### Show Tags 02 Mar 2018, 00:09 Hi Cant we use the %change formula = x + y + (xy/100) to calculate two successive % change instead of calculating the discount and tax seperately?? Posted from my mobile device Retired Moderator Joined: 22 Aug 2013 Posts: 1403 Location: India Re: Stores X, Y, and Z each sell a certain item that has a given [#permalink] ### Show Tags 02 Mar 2018, 00:15 1 RashmiT wrote: Hi Cant we use the %change formula = x + y + (xy/100) to calculate two successive % change instead of calculating the discount and tax seperately?? Posted from my mobile device Hi Yes we can do that. Discount of 5% would mean -5% change, while tax of 5% would mean +5% change. So, for Store X, it would be = -5 + 5 + (-5)5/100 = - 2.5% change overall and for Store Y, it would be = +5 -5 + 5(-5)/100 = -2.5% change overall So the final values for Stores X and Y would be same Intern Joined: 09 Apr 2018 Posts: 20 Stores X, Y, and Z each sell a certain item that has a given [#permalink] ### Show Tags 14 Sep 2018, 04:45 While this questions is straight, I made a very silly mistake, in a hurry missed that, for y discount is applied to (List Price + Sales Tax), I still feel there is some contradiction in the question stem. Stem says - 1. Stores X, Y, and Z each sell a certain item that has a given list price. 2. X&Y give 5 percent discount off list price. Now this List Price is a given price for ALL X, Y & Z. This clearly means that if LP is a given value (say 100), the Value of Discount on LP is 5% LP in X & Y (=$5), and $0 in Z. In such a case, The S.Ps of all are X: (100 - 5)1.05 =$99.75 Y: (1001.05)- (5% of LP) = 105 - 5 = $100 Z:$100 So, x < y = z Of course this is incorrect given the OA, but I strongly feel there is some contradiction (though minimal) in the question stem. Is it that I am thinking too much or missing something here? Perhaps the question shouldn't have mentioned off list price for the Discount Applied by X and Y. Intern Joined: 06 Jun 2018 Posts: 41 Location: India Schools: IIMA PGPX"20 (D) GMAT 1: 640 Q47 V30 GMAT 2: 540 Q42 V22 GPA: 3.7 Re: Stores X, Y, and Z each sell a certain item that has a given [#permalink] ### Show Tags 20 Oct 2018, 04:42 Bunuel, abhimahna chetan2u - I have got answer correct by considering list price as 100 however where is it mentioned that list price are same ? If list price of x and y is different then B can not be answer and even we do not in that case z will be less or more than x and y. Math Expert Joined: 02 Aug 2009 Posts: 8341 Re: Stores X, Y, and Z each sell a certain item that has a given [#permalink] ### Show Tags 20 Oct 2018, 06:47 NAvinash wrote: Bunuel, abhimahna chetan2u - I have got answer correct by considering list price as 100 however where is it mentioned that list price are same ? If list price of x and y is different then B can not be answer and even we do not in that case z will be less or more than x and y. Hi it is given a certain item that has a list price.. This points to same item and same price.. Otherwise it would a certain item that has a list price for each place/that has a different list price or something to that effect _________________ Intern Joined: 04 Apr 2017 Posts: 22 Re: Stores X, Y, and Z each sell a certain item that has a given [#permalink] ### Show Tags 21 Dec 2018, 06:21 Bunuel wrote: bulletpoint wrote: Stores X, Y, and Z each sell a certain item that has a given list price. Stores X and Y are located in a state with a 5 percent sales tax, and both sell the item at a 5 percent discount off list price, while Store Z is located in a state with no sales tax and gives no discounts. Store X applies its discounts first and then charges sales tax on the discounted price, while Store Y adds the tax first and then applies the discount to the price with tax. If x and y are the prices, with tax and discount, charged by Stores X and Y, respectively, and z is the price charged by Store Z, which of the following statements correctly describes the relationship among x, y, and z? A. x=y=z B. x=y<z C. x<y<z D. x<z<y E. y<z<x Say the price of the item is 100. Then: x = (1000.95)1.05 < 100. y = (1001.05)0.95 < 100. z = 100. So, we have that x=y<z. Can you please clarify how you easily know that (1000.95)*1.05 is < 100 without calculations? Is it by logic? I spent sometime in calculations to reach it? GMAT Club Legend Joined: 12 Sep 2015 Posts: 4214 Re: Stores X, Y, and Z each sell a certain item that has a given [#permalink] ### Show Tags 19 Mar 2019, 07:09 1 Top Contributor bulletpoint wrote: Stores X, Y, and Z each sell a certain item that has a given list price. Stores X and Y are located in a state with a 5 percent sales tax, and both sell the item at a 5 percent discount off list price, while Store Z is located in a state with no sales tax and gives no discounts. Store X applies its discounts first and then charges sales tax on the discounted price, while Store Y adds the tax first and then applies the discount to the price with tax. If x and y are the prices, with tax and discount, charged by Stores X and Y, respectively, and z is the price charged by Store Z, which of the following statements correctly describes the relationship among x, y, and z? A. x=y=z B. x=y<z C. x<y<z D. x<z<y E. y<z<x Let $100 = the list price for all 3 stores Store X$100 plus 5% sales tax = $105$105 minus 5% discount = (0.95)($105) =$99.75 Aside: a 5% discount means the buyer is paying 95% of the cost (thus 95% of $105) Store Y$100 minus 5% discount = $95$95 plus 5% sales tax = (1.05)($95) =$99.75 Store Z $100 We can see that$99.75 = $99.75 <$100 In other words, x = y < z Cheers, Brent _________________ Test confidently with gmatprepnow.com Manager Joined: 09 Mar 2018 Posts: 55 Location: India Schools: CBS Deferred "24 Re: Stores X, Y, and Z each sell a certain item that has a given [#permalink] ### Show Tags 27 Mar 2019, 04:10 for 2 successive decrease and increase in %ages the best formula is $$X+Y+\frac{XY}{100}$$ the sign may vary if it is an increase or decrease. let the original price be 100 then, plugging in values(for store X) : $$5 - 5 + \frac{(-5)(5)}{100}$$ which gives : -0.25% change overall similar will be the case for store Y . hence we can conclude X=Y<Z VP Joined: 18 Dec 2017 Posts: 1001 Location: United States (KS) GMAT 1: 600 Q46 V27 Re: Stores X, Y, and Z each sell a certain item that has a given [#permalink] ### Show Tags 10 Dec 2019, 15:26 bulletpoint wrote: Stores X, Y, and Z each sell a certain item that has a given list price. Stores X and Y are located in a state with a 5 percent sales tax, and both sell the item at a 5 percent discount off list price, while Store Z is located in a state with no sales tax and gives no discounts. Store X applies its discounts first and then charges sales tax on the discounted price, while Store Y adds the tax first and then applies the discount to the price with tax. If x and y are the prices, with tax and discount, charged by Stores X and Y, respectively, and z is the price charged by Store Z, which of the following statements correctly describes the relationship among x, y, and z? A. x=y=z B. x=y<z C. x<y<z D. x<z<y E. y<z<x This question is literally a 500 level question. But the way GMAC words it makes it a 600-700 level question. This is absolute brilliance. If you are comfortable with percentages then you know the sequence does not matter. 5% increase followed by 5% decrease or the other way round will give the exact same result. You can try it. B is the perfect choice. Glad I got it right during the test. ! _________________ The Moment You Think About Giving Up, Think Of The Reason Why You Held On So Long Learn from the Legend himself: All GMAT Ninja LIVE YouTube videos by topic You are missing on great learning if you don't know what this is: Project SC Butler Re: Stores X, Y, and Z each sell a certain item that has a given [#permalink] 10 Dec 2019, 15:26 Display posts from previous: Sort by	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.2994115948677063, "perplexity": 2710.844018973829}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-05/segments/1579250593994.14/warc/CC-MAIN-20200118221909-20200119005909-00284.warc.gz"}
http://math.stackexchange.com/questions/171929/approximate-solution-for-the-root-of-a-non-linear-function	# Approximate solution for the root of a non-linear function I have been working with a system which involves computing the roots of functions that look like $$e^t (g\cos(\omega t) + b) = c$$ where $t$ is the independent variable and the parameters $g$, $\omega$ and $b$ are real and positive and $c$ is real. This, apparently has no analytical solution and I have been doing it in the computer easily. However, for some parts of my research it would be very useful to have some approx. solution. For instance, in the form of a series where successive approx. may be computed. However, I have no idea how to even start. Would anyone Have some guidelines as to how to approach this problem? Thanks very much in advance. Edit: So, the full problem is as follows. Suppose we start with some value $t_0$. Then we want the first root of $$e^{t_1} (g\cos(\omega t_1) + b) = e^{t_0} (g\cos(\omega t_0) + b)$$ ie, the value of $t_1$ that satisfies this equation and is closer to $t_0$. Note that the RHS is simply the number which I previously called $c$. With $t_1$, the next step is to compute $t_2$ from the equation $$e^{t_2} (g\cos(\omega t_2) - b) = e^{t_1} (g\cos(\omega t_1) - b)$$ (note the sign change in $b$). This is the framework of my current problem: find successive roots $t_i$ with the sign in $b$ alternating between each computation. The questions that arise are: for what values of $t_0$ are there roots and are there infinitely many? For instance, if $\omega=3$, $b=0.8$ and $g=1.75$ then $t_0 = 0.174765$ is unstable. It yields roughly $20$ roots and then stop. ## Update Thank you all for the support. As for the instability (cf. @LeonidKovalev's answer), here is an example: This is for $\omega = 3$, $g= 1.75$ and $b = 0.8$. This shows that as time progresses the crossing times begin to grow so that after some time there is no longer a root. Perhaps, and this is a mistake which I apologise for, this instability is brought about by the fact that I am solving a slightly different system in which $\cos\omega t$ is replaced by $\cos(\omega t-\phi)$, with $\phi = \text{atan}(\omega)$ (I thought this would go away by rescaling $t$ appropriately). - If you just write out a function name like cos, $\TeX$ interprets it as a sequence of variable names, which it italicizes. To get the right formatting, you need to use the predefined commands such as \cos. If you need a function name for which there's no predefined command, you can use \operatorname{name}. – joriki Jul 17 '12 at 13:38 You could write out the Taylor series for $\exp t$ and $\cos \omega t$, carry out the multiplication, and truncate after any $t^4$ powers. This will give you an (ugly, and probably not terribly accurate) closed form solution. If you go to orders higher than 4, you run into general unsolvability of polynomials of order $\ge 5$. – Emily Jul 17 '12 at 13:48 "Note that the RHS is simply a positive number" -- why is that? $g\cos (\omega t_0)+b$ could be negative for all I know. – user31373 Jul 18 '12 at 16:28 Oh my! I am sorry Leonid, you are right. My mistake. The RHS may be both pos. and neg. I will correct that in the question. – Gabriel Landi Jul 18 '12 at 19:29 Newton's method comes to mind -- in the form of a series and you have ac losed form of the derivative, so can explicitly make the formula for the next iteration. – gt6989b Jul 20 '12 at 16:28 ## 4 Answers (New answer) Some of this overlaps with the answer by Jayesh Badwaik, but it does not hurt to see two people's perspective. Concerning the sequence $t_k$, let's begin with a simple observation based on Rolle's theorem: there exists $t$ strictly between $t_k$ and $t_{k+1}$ where the derivative of $e^t(g\cos\omega t\pm b)$ vanishes. This means $g\cos\omega t-g\omega \sin\omega t\pm b=0$. If $g\sqrt{1+\omega^2}\le b$, the derivative never changes its sign; therefore in this case you don't even have $t_1$. If $g\sqrt{1+\omega^2}> b$, there are infinitely many solutions which form a periodic pattern. This does not tell us that the sequence $t_k$ is infinite, but if it is infinite, then it grows at least linearly: $t_k\ge Ak+B$. When $g>b$, the function $e^t(g\cos\omega t\pm b)$ is oscillating with increasing amplitude, roughly between $\pm g e^t$. It is not hard to see that in this case there is always $t_{k+1} \in (t_k, t_k+2\pi/\omega]$. So, the sequence $t_k$ is infinite and it grows at linear rate. Notice that this contradicts your observation that the sequence stops with $b=0.8$ and $g=1.75$. I suspect that you ran into overflow issues due to the exponential growth of the function. The case $g=b$ is about the same as $g>b$: here the function does not change sign, but it returns to zero infinitely often. The sequence $t_k$ is infinite and grows at linear rate. In the interval $g< b< g\sqrt{1+\omega^2}$ the elementary observations above do not suffice. Let's step back from the case-by-case analysis and try to see more structure. Let $F(t)=e^t(g\cos\omega t+ b)$. The equation $F(t_{k+1})=F(t_k)$ is invariant under adding an integer multiple of $2\pi/\omega$ to both $t_k,t_{k+1}$. So, we can choose the starting point $t_0$ to be in an interval of length $2\pi/\omega$ of our choice: it appears to be convenient to take the interval between two consecutive local minima of $F$. We can also choose to subtract a multiple of $2\pi/\omega$ from subsequent points $t_k$ to avoid the exponential growth and associated numerical issues. On every other step you want to solve a modified equation with $-b$ in place of $b$: namely, $e^{t_{k+1}} (g\cos(\omega t_{k+1}) - b) = e^{t_k} (g\cos(\omega t_k) - b)$. But this equation can be put in terms of the same function $F$ as follows: $F(t_{k+1}-\pi/\omega)=F(t_k-\pi/\omega)$. I could as well use $+\pi/\omega$ since the integer multiples of $2\pi/\omega$ do not matter. But it seems advisable to jump to the left rather than to the right, to keep the sequence from growing. Here is the algorithm: 1. Start with $s_0$. 2. Find the smallest $s_{k+1}>s_{k}$ such that $F(s_{k+1})=F(s_k)$. If there is no solution, stop. 3. Replace $s_{k+1}$ with $s_{k+1}-\pi/\omega$. 4. Increment $k$ and return to step 2. This process continues for as long as the original process with $t_k$, and $s_k$ agrees with $t_k$ up to an integer multiple of $\pi/\omega$. This algorithm can be useful not just for computations, but also for understanding of what can happen. For example, if $F(s)=F(s+\pi/\omega)$, and this common value of $F$ does not occur in between, then starting with $s_0=s$ we get $s_1=s_2=\dots=s$, and the process goes on forever. Here is a concrete example: $f=e^t(\cos 3t+2)$; the starting point is $(1/3)\cos^{-1}(2(e^{\pi/3}-1)/(e^{\pi/3}+1))$. This example shows that infinite process is possible even if $g<b$. You can get more information by following the algorithm yourself with a printout of the graph of $F$. From the starting point, draw horizontal line to the right until it crosses the graph again (if it does not, the game is over). Then move the point $\pi/\omega$ to the left, adjust the vertical coordinate so that it lies on the graph of $F$, and repeat. After a few tries you should get a pretty good idea of how this dynamical system behaves. (Old answer) First of all, you can divide both sides by c. So let's assume this was done, and our equation is $g\cos\omega t+b = \exp(-t)$. This means we are looking for intersections between the exponential curve and a cosine wave. In general, there may be many intersections, in fact there are infinitely many when $g>b$. Are all of these solutions relevant to your task, or is there a preferred one? If $g<b$, we have an upper and lower bounds for solutions, namely $-\log(b\pm g)$. The number $-\log b$ looks like a good starting point for Newton's method, which can indeed be written in the form of a series. I might be able to say more if you can clarify a) what to do with nonunique solutions, and b) if you know anything about the relative size of the constants involved. For example, is b much larger than g? Etc. - Hi, I really appreciate the answer. So: only the first root is of interest. The parameters are all positive and have the following usual ranges: $0<b<2$, $0<g<10$ and $0<\omega<10$. This is approximate, but shows they are not very different from one another. I will edit the question to post a slightly more general panorama of the question. – Gabriel Landi Jul 18 '12 at 14:32 Let $$y \left( x \right) = \exp( t )\left( g \cos \left ( \omega t \right) + b \right)$$ For $\omega \ll 1$, I don't know if next solution will exist or not. The next solution will only exist if the slope of the function is negative at that point. CASE 1 : $b < g\sqrt{\omega^{2} + 1} \text{ and } \frac{\omega}{t} \gg 1$ Then, let $$\frac{dy}{dt} = y - \exp(t)\left(g \omega \sin\left(\omega t \right) \right)$$ Solving for $\frac{dy}{dt} = 0$ $$\exp( t )\left( g \cos \left ( \omega t \right) + b \right) - \exp(t)\left(g \omega \sin\left(\omega t \right) \right) = 0$$ And reducing it, $$\omega \sin \left( \omega t \right) - \cos\left( \omega t \right) = \frac{b}{g}$$ which implies $$\sin\left(\omega t + \phi \right) = \frac{b}{g\sqrt{\omega^{2} + 1}} = K$$ where $\phi = atan\left( \frac{-1}{\omega}\right)$ and hence, the requirement for $b < g\sqrt{\omega^{2} + 1}$. Hence, $$t_{en} = \frac{asin(K) - \phi + 2n\pi}{\omega}$$ So, now you have maxima and minima. So, now the next value of your variable lies either between the two minima or two maxima, depending on whether the slope is positive or negative at that point. So, suppose, your $t$ is $\theta$ after the extrema. Then, the next value would be $\theta$ before the next same extrema (if $t_{1}$ was $\theta$ after a minima, then $t_{2}$ would be $\theta$ before the next minima), approximately. $\theta = \omega t - 2\pi m$ where $m = \lfloor\frac{\omega t}{2\pi}\rfloor$ and then $$t_{2} = t_{1} + \frac{2\pi - \theta}{\omega}$$ This was the easiest way to calculate approximate formula. But I doubt, it is much useful if you want to apply further analytical tools mainly because of floor function. CASE 2 : for $b > g\sqrt{\omega^{2} + 1}$ I am hoping one can apply a similar procedure using some sort of transformation and back, I am not sure though. Will try to get back to you on it. - Taking Leonid's $c=1$ I would try to divide this problem into two regimes. $\omega >1$ and fast oscillations. If $g+b <1$ then the intersection will happen at the peak of the oscillation and we can approximate as $g+b = e^{-t}$ and solve for $t$. To do better, perturb around this solution. If $g+b >1$ then the solution would be at $g \cos \omega t + b \sim 1$. $\omega <1$ and slow oscillations. If $g+b <1$ then the cosine is nearly fixed and one solves $g+b = e^{-t}$. If $g+b >1$ the intersection happens near $t=\pi/2$. The only region where it will be hard to get an approximation will be the $\omega \sim 1$ regime. One could divide things into quadrants and make conditions on which phase of $\omega t$ the intersection is likely to happen. This is work, might be faster to use your non-linear root finding solutions for the transition region, plot it and fit something to the solution (a quick polynomial for example). - Dividing by $g$, we may assume that $g=1$. I will consider then the equation $$e^t(\cos(\omega\,t)+b)=c,\quad \omega>0,\quad b>0,\quad c\in\mathbb{R}.$$ Case 1: $b>1$. Then $0<b-1\le\cos(\omega\,t)+b\le1+b$ for all $t$. There are no solutions if $c\le0$. If $c>0$ there is a finite number of solutions in the interval $\Bigl[\dfrac{\log c}{b-1},\dfrac{\log c}{1+b}\Bigr]$. Case 2: $b=1$. Then $0\le\cos(\omega\,t)+1\le2$ for all $t$. There are no solutions if $c<0$. If $c=0$ there are infinitely many solutions, given by $t=\dfrac{(2\,k+1)\pi}{\omega}$, $k\in\mathbb{Z}$. If $c>0$ there are two solutions on each interval $\Bigl(\dfrac{(2\,k-1)\pi}{\omega},\dfrac{(2\,k+1)\pi}{\omega}\Bigr)$ with $k\ge\dfrac{\omega}{2\,\pi}\log\dfrac{c}{2}$ (only one if equality holds). Case 3: $0<b<1$. Then $\cos(\omega\,t)+b$ takes both positive and negative values. There are infinitely many solutions for all $c\in\mathbb{R}$. Let $\beta\in(0,\pi/(2\,\omega))$ be such that $\cos(\omega\,\beta)=b$. If $c=0$, then the solutions are $\pm\,\beta+2\,k\,\pi$, $k\in\mathbb{Z}$. If $c>0$ the solutions lie in intervals $\Bigl(-\beta+\dfrac{2\,k\,\pi}{\omega},\beta+\dfrac{2\,k\,\pi}{\omega}\Bigr)$ with $k\ge\dfrac{\omega}{2\,\pi}\log\dfrac{c}{1+b}$. If $c<0$, then the solutions lie in the intervals $\Bigl(\beta+\dfrac{2\,k\,\pi}{\omega},-\beta+\dfrac{2(k+1)\pi}{\omega}\Bigr)$ with $2\,k+1\ge\dfrac{\omega}{\pi}\log\dfrac{\|c\|}{1-b}$. Edit In the above, I have made the error of assuming that the maxima and minima of $e^t(\cos(\omega\,t)+b)$ are attained at points where $\cos(\omega\,t)=\pm1$. The correct statement for Case 2 ($b=1$) when $c>0$ should be: Let $M_k$ be the maximum of $e^t(\cos(\omega\,t)+b)$ on the interval $\Bigl[\dfrac{(2\,k-1)\pi}{\omega},\dfrac{(2\,k+1)\pi}{\omega}\Bigr]$. Then there are two solutions on $\Bigl(\dfrac{(2\,k-1)\pi}{\omega},\dfrac{(2\,k+1)\pi}{\omega}\Bigr)$ for all $k$ such that $M_k\ge c$ (only one if equality holds). Case 3 has to be changed in a similar way. -	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 10, "x-ck12": 0, "texerror": 0, "math_score": 0.9367743134498596, "perplexity": 132.82579778528148}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2016-22/segments/1464049270527.3/warc/CC-MAIN-20160524002110-00005-ip-10-185-217-139.ec2.internal.warc.gz"}
https://birch-lang.org/documentation/library/functions/simulate_negative_binomial/	# simulate_negative_binomial function simulate_negative_binomial(k:Integer, ρ:Real) -> Integer Simulate a negative binomial distribution. • k: Number of successes before the experiment is stopped. • ρ: Probability of success. Returns the number of failures.	{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9564346075057983, "perplexity": 15722.960863415708}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-16/segments/1585371665328.87/warc/CC-MAIN-20200407022841-20200407053341-00422.warc.gz"}
https://arxiv.org/abs/1811.05100	cs.DS # Title:Balancing Relevance and Diversity in Online Bipartite Matching via Submodularity Abstract: In bipartite matching problems, vertices on one side of a bipartite graph are paired with those on the other. In its online variant, one side of the graph is available offline, while the vertices on the other side arrive online. When a vertex arrives, an irrevocable and immediate decision should be made by the algorithm; either match it to an available vertex or drop it. Examples of such problems include matching workers to firms, advertisers to keywords, organs to patients, and so on. Much of the literature focuses on maximizing the total relevance---modeled via total weight---of the matching. However, in many real-world problems, it is also important to consider contributions of diversity: hiring a diverse pool of candidates, displaying a relevant but diverse set of ads, and so on. In this paper, we propose the Online Submodular Bipartite Matching (\osbm) problem, where the goal is to maximize a submodular function $f$ over the set of matched edges. This objective is general enough to capture the notion of both diversity (\emph{e.g.,} a weighted coverage function) and relevance (\emph{e.g.,} the traditional linear function)---as well as many other natural objective functions occurring in practice (\emph{e.g.,} limited total budget in advertising settings). We propose novel algorithms that have provable guarantees and are essentially optimal when restricted to various special cases. We also run experiments on real-world and synthetic datasets to validate our algorithms. Comments: To appear in AAAI 2019 Subjects: Data Structures and Algorithms (cs.DS) Cite as: arXiv:1811.05100 [cs.DS] (or arXiv:1811.05100v1 [cs.DS] for this version) ## Submission history From: Karthik Abinav Sankararaman [view email] [v1] Tue, 13 Nov 2018 04:43:05 UTC (4,135 KB)	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.4828207790851593, "perplexity": 1409.6007001883993}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-30/segments/1563195525973.56/warc/CC-MAIN-20190719012046-20190719034046-00455.warc.gz"}
http://mathhelpforum.com/new-users/203001-possible-primes.html	# Math Help - Possible Primes. 1. ## Possible Primes. Is it possible to either prove or disprove the following? If m is a positive odd integer such that 2m = 2 (mod. m(m-1)) then m is a prime. Examples: 27 = 2 (mod. 42 = 7x6). 7 is prime. 243 = 2 (mod. 1806 = 43x42). 43 is prime. 2. ## Re: Possible Primes. Originally Posted by Stan Is it possible to either prove or disprove the following? If m is a positive odd integer such that 2m = 2 (mod. m(m-1)) then m is a prime. Examples: 27 = 2 (mod. 42 = 7x6). 7 is prime. 243 = 2 (mod. 1806 = 43x42). 43 is prime. Is the following proof valid? Theorem. If m is a positive odd integer such that 2m ≡ 2 (mod. m(m-1)) then m ≡ 3 (mod. 4) and m is a prime. Proof. Let 2m ≡ 2 (mod. m(m-1)) then 2m - 2 =km(m-1) for some positive integer k. This gives 2m-1 – 1 = km(m-1)/2 and since 2m-1 – 1 is odd, (m-1)/2 is odd implying m ≡ 3 (mod. 4). Let p be the least valued prime dividing (m-1)/2 . Then p is odd and 2m-1 ≡ 1 (mod. p). Let d be the order of 2 (mod. p). Then d is a positive integer < p and 2d ≡ 1 (mod. p). So d divides (m-1) and d divides (p-1). This implies there is a prime dividing d, less than p, which divides (m-1)/2 . This contrdicts p is the least valued prime dividing (m-1)/2 . Hence, m is a prime. 3. ## Re: Possible Primes. The proof is invalid. However, there is an updated proof of the theorem in the post ' Primes Conjecture' which may or may not be valid.	{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9480398893356323, "perplexity": 3319.7696831505045}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-41/segments/1412037663135.34/warc/CC-MAIN-20140930004103-00170-ip-10-234-18-248.ec2.internal.warc.gz"}
http://math.stackexchange.com/users/57063/chris-cooney	# Chris Cooney less info reputation 6 bio website location Manchester age 21 member for 1 year, 7 months seen Jul 8 at 7:56 profile views 42 # 7 Questions 2 Expressing a sequence as a recurrence relation 2 Solution to Recurrence Relation 1 Solving a recurrence realtion using backward substitution. 1 Summation of Arithmetic-Geometric Series 0 What is the definition if a distinct cycle in a graph? # 143 Reputation +5 Solving a recurrence realtion using backward substitution. +10 Expressing a sequence as a recurrence relation +10 Solution to Recurrence Relation +5 Summation of Arithmetic-Geometric Series This user has not answered any questions # 8 Tags 0 recurrence-relations × 4 0 logarithms 0 asymptotics × 2 0 summation 0 algorithms 0 sequences-and-series 0 graphing-functions 0 induction # 9 Accounts Stack Overflow 14,017 rep 11033 Mathematics 143 rep 6 Biology 118 rep 3 Super User 106 rep 2 Meta Stack Exchange 101 rep 1	{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8759725689888, "perplexity": 5503.931070077113}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-35/segments/1408500834883.60/warc/CC-MAIN-20140820021354-00384-ip-10-180-136-8.ec2.internal.warc.gz"}
http://harvard.voxcharta.org/tag/particle-acceleration/	# Posts Tagged particle acceleration ## Recent Postings from particle acceleration ### An Efficient Fokker-Planck Solver and its Application to Stochastic Particle Acceleration in Galaxy Clusters Particle acceleration by turbulence plays a role in many astrophysical environments. The non- linear evolution of the underlying cosmic-ray spectrum is complex and can be described by a Fokker-Planck equation, which in general has to be solved numerically. We present here an implementation to compute the evolution of a cosmic-ray spectrum coupled to turbulence considering isotropic particle pitch-angle distributions and taking into account the relevant particle energy gains and losses. Our code can be used in run time and post-processing to very large astrophysical fluid simulations. We also propose a novel method to compress cosmic- ray spectra by a factor of ten, to ease the memory demand in very large simulations. We show a number of code tests, which firmly establish the correctness of the code. In this paper we focus on relativistic electrons, but our code and methods can be easily extended to the case of hadrons. We apply our pipeline to the relevant problem of particle acceleration in galaxy clusters. We define a sub-grid model for compressible MHD-turbulence in the intra- cluster-medium and calculate the corresponding reacceleration timescale from first principles. We then use a magneto-hydrodynamic simulation of an isolated cluster merger to follow the evolution of relativistic electron spectra and radio emission generated from the system over several Gyrs. ### Particle acceleration and wave excitation in quasi-parallel high-Mach-number collisionless shocks: Particle-in-cell simulation We herein investigate shock formation and particle acceleration processes for both protons and electrons in a quasi-parallel high-Mach-number collisionless shock through a long-term, large-scale particle-in-cell simulation. We show that both protons and electrons are accelerated in the shock and that these accelerated particles generate large-amplitude Alfv\’{e}nic waves in the upstream region of the shock. After the upstream waves have grown sufficiently, the local structure of the collisionless shock becomes substantially similar to that of a quasi-perpendicular shock due to the large transverse magnetic field of the waves. A fraction of protons are accelerated in the shock with a power-law-like energy distribution. The rate of proton injection to the acceleration process is approximately constant, and in the injection process, the phase-trapping mechanism for the protons by the upstream waves can play an important role. The dominant acceleration process is a Fermi-like process through repeated shock crossings of the protons. This process is a `fast’ process in the sense that the time required for most of the accelerated protons to complete one cycle of the acceleration process is much shorter than the diffusion time. A fraction of the electrons is also accelerated by the same mechanism, and have a power-law-like energy distribution. However, the injection does not enter a steady state during the simulation, which may be related to the intermittent activity of the upstream waves. Upstream of the shock, a fraction of the electrons is pre-accelerated before reaching the shock, which may contribute to steady electron injection at a later time. ### Unusual Flaring Activity in the Blazar PKS 1424-418 during 2008-2011 Context. Blazars are a subset of active galactic nuclei (AGN) with jets that are oriented along our line of sight. Variability and spectral energy distribution (SED) studies are crucial tools for understanding the physical processes responsible for observed AGN emission. Aims. We report peculiar behaviour in the bright gamma-ray blazar PKS 1424-418 and use its strong variability to reveal information about the particle acceleration and interactions in the jet. Methods. Correlation analysis of the extensive optical coverage by the ATOM telescope and nearly continuous gamma-ray coverage by the Fermi Large Area Telescope is combined with broadband, time-dependent modeling of the SED incorporating supplemental information from radio and X-ray observations of this blazar. Results. We analyse in detail four bright phases at optical-GeV energies. These flares of PKS 1424-418 show high correlation between these energy ranges, with the exception of one large optical flare that coincides with relatively low gamma-ray activity. Although the optical/gamma-ray behaviour of PKS 1424-418 shows variety, the multiwavelength modeling indicates that these differences can largely be explained by changes in the flux and energy spectrum of the electrons in the jet that are radiating. We find that for all flares the SED is adequately represented by a leptonic model that includes inverse Compton emission from external radiation fields with similar parameters. Conclusions. Detailed studies of individual blazars like PKS 1424-418 during periods of enhanced activity in different wavebands are helping us identify underlying patterns in the physical parameters in this class of AGN. ### Unusual Flaring Activity in the Blazar PKS 1424-418 during 2008-2011 [Replacement] Context. Blazars are a subset of active galactic nuclei (AGN) with jets that are oriented along our line of sight. Variability and spectral energy distribution (SED) studies are crucial tools for understanding the physical processes responsible for observed AGN emission. Aims. We report peculiar behaviour in the bright gamma-ray blazar PKS 1424-418 and use its strong variability to reveal information about the particle acceleration and interactions in the jet. Methods. Correlation analysis of the extensive optical coverage by the ATOM telescope and nearly continuous gamma-ray coverage by the Fermi Large Area Telescope is combined with broadband, time-dependent modeling of the SED incorporating supplemental information from radio and X-ray observations of this blazar. Results. We analyse in detail four bright phases at optical-GeV energies. These flares of PKS 1424-418 show high correlation between these energy ranges, with the exception of one large optical flare that coincides with relatively low gamma-ray activity. Although the optical/gamma-ray behaviour of PKS 1424-418 shows variety, the multiwavelength modeling indicates that these differences can largely be explained by changes in the flux and energy spectrum of the electrons in the jet that are radiating. We find that for all flares the SED is adequately represented by a leptonic model that includes inverse Compton emission from external radiation fields with similar parameters. Conclusions. Detailed studies of individual blazars like PKS 1424-418 during periods of enhanced activity in different wavebands are helping us identify underlying patterns in the physical parameters in this class of AGN. ### Synchrotron X-ray emission from old pulsars We study the synchrotron radiation as the observed non-thermal X-ray emission from old pulsars ($\gtrsim1-10$Myr) to investigate the particle acceleration in their magnetospheres. We assume that the power-law component of the observed X-ray spectra is caused by the synchrotron radiation from electrons and positrons in the magnetosphere. We consider two pair production mechanisms of X-ray emitting particles, the magnetic and the photon-photon pair productions. High-energy photons, which ignite the pair production, are emitted via the curvature radiation of the accelerated particles. We use the analytical description for the radiative transfer and estimate the luminosity of the synchrotron radiation. We find that for pulsars with the spin-down luminosity $L_{\rm sd}\lesssim10^{33}$ erg s$^{-1}$, the locations of the particle acceleration and the non-thermal X-ray emission are within $\lesssim10^7$cm from the centre of the neutron star, where the magnetic pair production occurs. For pulsars with the spin-down luminosity $L_{\rm sd}\lesssim10^{31}$ erg s$^{-1}$ such as J0108-1431, the synchrotron radiation is difficult to explain the observed non-thermal component even if we consider the existence of the strong and small-scale surface magnetic field structures. ### SEP acceleration in CME driven shocks using a hybrid code We preform hybrid simulations of super Alfvenic quasi-parallel shock, driven by a Coronal Mass Ejection (CME), propagating in the Outer Coronal or Solar Wind at distances of between 3 to 6 solar radii. The hybrid treatment of the problem enable the study of the shock propagation on the ion time scale, preserving ion kinetics and allowing for a self consistent treatment of the shock propagation and particle acceleration. The CME plasma drags the embedded magnetic field lines stretching from the sun, and propagates out into interplanetary space at a greater velocity than the in-situ solar wind, driving the shock, and producing very energetic particles. Our results show electromagnetic Alfven waves are generated at the shock front. The waves propagate upstream of the shock and are produced by the counter streaming ions of the solar wind plasma being reflected at the shock. A significant fraction of the particles are accelerated in two distinct phases: first, particles drift from the shock and are accelerated in the upstream region and, second, particles arriving at the shock get trapped, and are accelerated at the shock front. A fraction of the particles diffused back to the shock, which is consistent with the Fermi acceleration mechanism. ### Global Numerical Modeling of Energetic Proton Acceleration in a Coronal Mass Ejection Traveling through the Solar Corona [Cross-Listing] The acceleration of protons and electrons to high (sometimes GeV/nucleon) energies by solar phenomena is a key component of space weather. These solar energetic particle (SEP) events can damage spacecraft and communications, as well as present radiation hazards to humans. In-depth particle acceleration simulations have been performed for idealized magnetic fields for diffusive acceleration and particle propagation, and at the same time the quality of MHD simulations of coronal mass ejections (CMEs) has improved significantly. However, to date these two pieces of the same puzzle have remained largely decoupled. Such structures may contain not just a shock but also sizable sheath and pileup compression regions behind it, and may vary considerably with longitude and latitude based on the underlying coronal conditions. In this work, we have coupled results from a detailed global three-dimensional MHD time-dependent CME simulation to a global proton acceleration and transport model, in order to study time-dependent effects of SEP acceleration between 1.8 and 8 solar radii in the 2005 May 13 CME. We find that the source population is accelerated to at least 100 MeV, with distributions enhanced up to six orders of magnitude. Acceleration efficiency varies strongly along field lines probing different regions of the dynamically evolving CME, whose dynamics is influenced by the large-scale coronal magnetic field structure. We observe strong acceleration in sheath regions immediately behind the shock. ### Quasiperiodic acceleration of electrons by a plasmoid-driven shock in the solar atmosphere Cosmic rays and solar energetic particles may be accelerated to relativistic energies by shock waves in astrophysical plasmas. On the Sun, shocks and particle acceleration are often associated with the eruption of magnetized plasmoids, called coronal mass ejections (CMEs). However, the physical relationship between CMEs and shock particle acceleration is not well understood. Here, we use extreme ultraviolet, radio and white-light imaging of a solar eruptive event on 22 September 2011 to show that a CME-induced shock (Alfv\’en Mach number 2.4$^{+0.7}_{-0.8}$) was coincident with a coronal wave and an intense metric radio burst generated by intermittent acceleration of electrons to kinetic energies of 2-46 keV (0.1-0.4 c). Our observations show that plasmoid-driven quasi-perpendicular shocks are capable of producing quasi-periodic acceleration of electrons, an effect consistent with a turbulent or rippled plasma shock surface. ### A fast current-driven instability in relativistic collisionless shocks We report here on a fast current-driven instability at relativistic collisionless shocks, triggered by the perpendicular current carried by the supra-thermal particles as they gyrate around the background magnetic field in the shock precursor. We show that this instability grows faster than any other instability studied so far in this context, and we argue that it is likely to shape the physics of the shock and of particle acceleration in a broad parameter range. ### 3D simulations of the non-thermal broad-band emission from young supernova remnants including efficient particle acceleration Supernova remnants are believed to be the major contributors to Galactic cosmic rays. In this paper, we explore how the non-thermal emission from young remnants can be used to probe the production of energetic particles at the shock (both protons and electrons). Our model couples hydrodynamic simulations of a supernova remnant with a kinetic treatment of particle acceleration. We include two important back-reaction loops upstream of the shock: energetic particles can (i) modify the flow structure and (ii) amplify the magnetic field. As the latter process is not fully understood, we use different limit cases that encompass a wide range of possibilities. We follow the history of the shock dynamics and of the particle transport downstream of the shock, which allows us to compute the non-thermal emission from the remnant at any given age. We do this in 3D, in order to generate projected maps that can be compared with observations. We observe that completely different recipes for the magnetic field can lead to similar modifications of the shock structure, although to very different configurations of the field and particles. We show how this affects the emission patterns in different energy bands, from radio to X-rays and $\gamma$-rays. High magnetic fields ($>100 \mu$G) directly impact the synchrotron emission from electrons, by restricting their emission to thin rims, and indirectly impact the inverse Compton emission from electrons and also the pion decay emission from protons, mostly by shifting their cut-off energies to respectively lower and higher energies. ### Evidence of Electron Acceleration around the Reconnection X-point in a Solar Flare Particle acceleration is one of the most significant features that are ubiquitous among space and cosmic plasmas. It is most prominent during flares in the case of the Sun, with which huge amount of electromagnetic radiation and high-energy particles are expelled into the interplanetary space through acceleration of plasma particles in the corona. Though it has been well understood that energies of flares are supplied by the mechanism called magnetic reconnection based on the observations in X-rays and EUV with space telescopes, where and how in the flaring magnetic field plasmas are accelerated has remained unknown due to the low plasma density in the flaring corona. We here report the first observational identification of the energetic non-thermal electrons around the point of the ongoing magnetic reconnection (X-point); with the location of the X-point identified by soft X-ray imagery and the localized presence of non-thermal electrons identified from imaging-spectroscopic data at two microwave frequencies. Considering the existence of the reconnection outflows that carries both plasma particles and magnetic fields out from the X-point, our identified non-thermal microwave emissions around the X-point indicate that the electrons are accelerated around the reconnection X-point. Additionally, the plasma around the X-point was also thermally heated up to 10 MK. The estimated reconnection rate of this event is ~0.017. ### Extremely efficient Zevatron in rotating AGN magnetospheres A novel model of particle acceleration in the magnetospheres of rotating Active Galactic Nuclei (AGN) is constructed.The particle energies may be boosted up to 10^{21}eV in a two step mechanism: In the first stage, the Langmuir waves are centrifugally excited and amplified by means of a parametric process that efficiently pumps rotational energy to excite electrostatic fields. In the second stage, the electrostatic energy is transferred to particle kinetic energy via Landau damping made possible by rapid "Langmuir collapse". The time scale for parametric pumping of Langmuir waves turns out to be small compared to the kinematic timescale, indicating high efficiency of the first process. The second process of "Langmuir collapse" – the creation of caverns or low density regions – also happens rapidly for the characteristic parameters of the AGN magnetosphere. The Langmuir collapse creates appropriate conditions for transferring electric energy to boost up already high particle energies to much higher values. It is further shown that various energy loss mechanism are relatively weak, and do not impose any significant constraints on maximum achievable energies. ### Filaments in the southern giant lobe of Centaurus A: constraints on nature and origin from modelling and GMRT observations We present results from imaging of the radio filaments in the southern giant lobe of Centaurus A using data from GMRT observations at 325 and 235 MHz, and outcomes from filament modelling. The observations reveal a rich filamentary structure, largely matching the morphology at 1.4 GHz. We find no clear connection of the filaments to the jet. We seek to constrain the nature and origin of the vertex and vortex filaments associated with the lobe and their role in high-energy particle acceleration. We deduce that these filaments are at most mildly overpressured with respect to the global lobe plasma showing no evidence of large-scale efficient Fermi I-type particle acceleration, and persist for ~ 2-3 Myr. We demonstrate that the dwarf galaxy KK 196 (AM 1318-444) cannot account for the features, and that surface plasma instabilities, the internal sausage mode and radiative instabilities are highly unlikely. An internal tearing instability and the kink mode are allowed within the observational and growth time constraints and could develop in parallel on different physical scales. We interpret the origin of the vertex and vortex filaments in terms of weak shocks from transonic MHD turbulence or from a moderately recent jet activity of the parent AGN, or an interplay of both. ### Filaments in the southern giant lobe of Centaurus A: constraints on nature and origin from modelling and GMRT observations [Replacement] We present results from imaging of the radio filaments in the southern giant lobe of Centaurus A using data from GMRT observations at 325 and 235 MHz, and outcomes from filament modelling. The observations reveal a rich filamentary structure, largely matching the morphology at 1.4 GHz. We find no clear connection of the filaments to the jet. We seek to constrain the nature and origin of the vertex and vortex filaments associated with the lobe and their role in high-energy particle acceleration. We deduce that these filaments are at most mildly overpressured with respect to the global lobe plasma showing no evidence of large-scale efficient Fermi I-type particle acceleration, and persist for ~ 2-3 Myr. We demonstrate that the dwarf galaxy KK 196 (AM 1318-444) cannot account for the features, and that surface plasma instabilities, the internal sausage mode and radiative instabilities are highly unlikely. An internal tearing instability and the kink mode are allowed within the observational and growth time constraints and could develop in parallel on different physical scales. We interpret the origin of the vertex and vortex filaments in terms of weak shocks from transonic MHD turbulence or from a moderately recent jet activity of the parent AGN, or an interplay of both. ### Magnetic Field Amplification and Flat Spectrum Radio Quasars We perform time-dependent, spatially-resolved simulations of blazar emission to evaluate several flaring scenarios related to magnetic-field amplification and enhanced particle acceleration. The code explicitly accounts for light-travel-time effects and is applied to flares observed in the flat spectrum radio quasar (FSRQ) PKS 0208-512, which show optical/{\gamma}-ray correlation at some times, but orphan optical flares at other times. Changes in both the magnetic field and the particle acceleration efficiency are explored as causes of flares. Generally, external Compton emission appears to describe the available data better than a synchrotron self-Compton scenario, and in particular orphan optical flares are difficult to produce in the SSC framework. X-ray soft-excesses, {\gamma}-ray spectral hardening, and the detections at very high energies of certain FSRQs during flares find natural explanations in the EC scenario with particle acceleration change. Likewise, optical flares with/without {\gamma}-ray counterparts can be explained by different allocations of energy between the magnetization and particle acceleration, which may be related to the orientation of the magnetic field relative to the jet flow. We also calculate the degree of linear polarization and polarization angle as a function of time for a jet with helical magnetic field. Tightening of the magnetic helix immediately downstream of the jet perturbations, where flares occur, can be sufficient to explain the increases in the degree of polarization and a rotation by >= 180 degree of the observed polarization angle, if light-travel-time effects are properly considered. ### TeV {\gamma}-ray observations of the young synchrotron-dominated SNRs G1.9+0.3 and G330.2+1.0 with H.E.S.S The non-thermal nature of the X-ray emission from the shell-type supernova remnants (SNRs) G1.9+0.3 and G330.2+1.0 is an indication of intense particle acceleration in the shock fronts of both objects. This suggests that the SNRs are prime candidates for very-high-energy (VHE; E $>$ 0.1 TeV) {\gamma}-ray observations. G1.9+0.3, recently established as the youngest known SNR in the Galaxy, also offers a unique opportunity to study the earliest stages of SNR evolution in the VHE domain. The purpose of this work is to probe the level of VHE {\gamma}-ray emission from both SNRs and use this to constrain their physical properties. Observations were conducted with the H.E.S.S. (High Energy Stereoscopic System) Cherenkov telescope array over a more than six-year period spanning 2004-2010. The obtained data have effective livetimes of 67 h for G1.9+0.3 and 16 h for G330.2+1.0. The data are analyzed in the context of the multi-wavelength observations currently available and in the framework of both leptonic and hadronic particle acceleration scenarios. No significant {\gamma}-ray signal from G1.9+0.3 or G330.2+1.0 was detected. Upper limits (99% confidence level) to the TeV flux from G1.9+0.3 and G330.2+1.0 for the assumed spectral index {\Gamma} = 2.5 were set at 5.6 $\times$ 10$^{-13}$ cm$^{-2}$ s$^{-1}$ above 0.26 TeV and 3.2 $\times$ 10$^{-12}$ cm$^{-2}$ s$^{-1}$ above 0.38 TeV, respectively. In a one-zone leptonic scenario, these upper limits imply lower limits on the interior magnetic field to B$_{\mathrm{G1.9}}$ $\gtrsim$ 11 {\mu}G for G1.9+0.3 and to B$_{\mathrm{G330}}$ $\gtrsim$ 8 {\mu}G for G330.2+1.0. In a hadronic scenario, the low ambient densities and the large distances to the SNRs result in very low predicted fluxes, for which the H.E.S.S. upper limits are not constraining. ### Electron-scale shear instabilities: magnetic field generation and particle acceleration in astrophysical jets Strong shear flow regions found in astrophysical jets are shown to be important dissipation regions, where the shear flow kinetic energy is converted into electric and magnetic field energy via shear instabilities. The emergence of these self-consistent fields make shear flows significant sites for radiation emission and particle acceleration. We focus on electron-scale instabilities, namely the collisionless, unmagnetized Kelvin-Helmholtz instability (KHI) and a large-scale dc magnetic field generation mechanism on the electron scales. We show that these processes are important candidates to generate magnetic fields in the presence of strong velocity shears, which may naturally originate in energetic matter outburst of active galactic nuclei and gamma-ray bursters. We show that the KHI is robust to density jumps between shearing flows, thus operating in various scenarios with different density contrasts. Multidimensional particle-in-cell (PIC) simulations of the KHI, performed with OSIRIS, reveal the emergence of a strong and large-scale dc magnetic field component, which is not captured by the standard linear fluid theory. This dc component arises from kinetic effects associated with the thermal expansion of electrons of one flow into the other across the shear layer, whilst ions remain unperturbed due to their inertia. The electron expansion forms dc current sheets, which induce a dc magnetic field. Our results indicate that most of the electromagnetic energy developed in the KHI is stored in the dc component, reaching values of equipartition on the order of $10^{-3}$ in the electron time-scale, and persists longer than the proton time-scale. Particle scattering/acceleration in the self generated fields of these shear flow instabilities is also analyzed. ### Does a strong particle accelerator arise very close to the light cylinder in a pulsar magnetosphere? We examine if an efficient particle acceleration takes place by a magnetic-field-aligned electric field near the light cylinder in a rotating neutron star magnetosphere. Constructing the electric current density with the actual motion of collision-less plasmas, we express the rotationally induced, Goldreich-Julian charge density as a function of position. It is demonstrated that the ‘light cylinder gap’, which emits very high energy photons via curvature process by virtue of a strong magnetic-field-aligned electric field very close to the light cylinder, will not arise in an actual pulsar magnetosphere. ### Jet contributions to the broad-band spectrum of Cyg X-1 in the hard state We apply the jet model developed in the preceding paper of Zdziarski et al.\ to the hard-state emission spectra of Cyg X-1. We augment the model for the analytical treatment of the particle evolution beyond the energy dissipation region, and allow for various forms of the acceleration rate. We calculate the resulting electron and emission spectra as functions of the jet height, along with the emission spectra integrated over the outflow. The model accounts well for the observed radio, infrared, and GeV fluxes of the source, although the available data do not provide unique constraints on the model free parameters. The contribution of the jet emission in the UV–to–X-ray range turns out to be in all the cases negligible compared to the radiative output of the accretion component. Nevertheless, we find out that it is possible to account for the observed flux of Cyg X-1 at MeV energies by synchrotron jet emission, in accord with the recent claims of the detection of strong linear polarization of the source in that range, but only assuming a very efficient particle acceleration leading to the formation of flat electron spectra, and jet magnetic fields much above the equipartition level. ### Jet contributions to the broad-band spectrum of Cyg X-1 in the hard state [Replacement] We apply the jet model developed in the preceding paper of Zdziarski et al. to the hard-state emission spectra of Cyg X-1. We augment the model for the analytical treatment of the particle evolution beyond the energy dissipation region, and allow for various forms of the acceleration rate. We calculate the resulting electron and emission spectra as functions of the jet height, along with the emission spectra integrated over the outflow. The model accounts well for the observed radio, infrared, and GeV fluxes of the source, although the available data do not provide unique constraints on the model free parameters. The contribution of the jet emission in the UV–to–X-ray range turns out to be in all the cases negligible compared to the radiative output of the accretion component. Nevertheless, we find out that it is possible to account for the observed flux of Cyg X-1 at MeV energies by synchrotron jet emission, in accord with the recent claims of the detection of strong linear polarization of the source in that range. However, this is possible only assuming a very efficient particle acceleration leading to the formation of flat electron spectra, and jet magnetic fields much above the equipartition level. ### A Magnetohydrodynamic Model of The M87 Jet. II. Self-consistent Quad-shock Jet Model for Optical Relativistic Motions and Particle Acceleration We describe a new paradigm for understanding both relativistic motions and particle acceleration in the M87 jet: a magnetically dominated relativistic flow that naturally produces four relativistic magnetohydrodynamic (MHD) shocks (forward/reverse fast and slow modes). We apply this model to a set of optical super- and subluminal motions discovered by Biretta and coworkers with the {\em Hubble Space Telescope} during 1994 — 1998. The model concept consists of ejection of a {\em single} relativistic Poynting jet, which possesses a coherent helical (poloidal + toroidal) magnetic component, at the remarkably flaring point HST-1. We are able to reproduce quantitatively proper motions of components seen in the {\em optical} observations of HST-1 with the same model we used previously to describe similar features in radio VLBI observations in 2005 — 2006. This indicates that the quad relativistic MHD shock model can be applied generally to recurring pairs of super/subluminal knots ejected from the upstream edge of the HST-1 complex as observed from radio to optical wavelengths, with forward/reverse fast-mode MHD shocks then responsible for observed moving features. Moreover, we identify such intrinsic properties as the shock compression ratio, degree of magnetization, and magnetic obliquity and show that they are suitable to mediate diffusive shock acceleration of relativistic particles via the first-order Fermi process. We suggest that relativistic MHD shocks in Poynting-flux dominated helical jets may play a role in explaining observed emission and proper motions in many AGNs. ### Acceleration of Relativistic Electrons by MHD Turbulence: Implications for Non-thermal Emission from Black Hole Accretion Disks We use analytic estimates and numerical simulations of test particles interacting with magnetohydrodynamic (MHD) turbulence to show that subsonic MHD turbulence produces efficient second-order Fermi acceleration of relativistic particles. This acceleration is not well-described by standard quasi-linear theory but is a consequence of resonance broadening of wave-particle interactions in MHD turbulence. We provide momentum diffusion coefficients that can be used for astrophysical and heliospheric applications and discuss the implications of our results for accretion flows onto black holes. In particular, we show that particle acceleration by subsonic turbulence in radiatively inefficient accretion flows can produce a non-thermal tail in the electron distribution function that is likely important for modeling and interpreting the emission from low luminosity systems such as Sgr A* and M87. ### A two-zone approach to neutrino production in gamma-ray bursts Gamma-ray bursts (GRB) are the most powerful events in the universe. They are capable of accelerating particles to very high energies, so are strong candidates as sources of detectable astrophysical neutrinos. We study the effects of particle acceleration and escape by implementing a two-zone model in order to assess the production of high-energy neutrinos in GRBs associated with their prompt emission. Both primary relativistic electrons and protons are injected in a zone where an acceleration mechanism operates and dominates over the losses. The escaping particles are re-injected in a cooling zone that propagates downstream. The synchrotron photons emitted by the accelerated electrons are taken as targets for $p\gamma$ interactions, which generate pions along with the $pp$ collisions with cold protons in the flow. The distribution of these secondary pions and the decaying muons are also computed in both zones, from which the neutrino output is obtained. We find that for escape rates lower than the acceleration rate, the synchrotron emission from electrons in the acceleration zone can account for the GRB emission, and the production of neutrinos via $p\gamma$ interactions in this zone becomes dominant for $E_\nu>10^5$ GeV. For illustration, we compute the corresponding diffuse neutrino flux under different assumptions and show that it can reach the level of the signal recently detected by IceCube. ### Mapping the particle acceleration in the cool core of the galaxy cluster RX J1720.1+2638 We present new deep, high-resolution radio images of the diffuse minihalo in the cool core of the galaxy cluster RX ,J1720.1+2638. The images have been obtained with the Giant Metrewave Radio Telescope at 317, 617 and 1280 MHz and with the Very Large Array at 1.5, 4.9 and 8.4 GHz, with angular resolutions ranging from 1" to 10". This represents the best radio spectral and imaging dataset for any minihalo. Most of the radio flux of the minihalo arises from a bright central component with a maximum radius of ~80 kpc. A fainter tail of emission extends out from the central component to form a spiral-shaped structure with a length of ~230 kpc, seen at frequencies 1.5 GHz and below. We observe steepening of the total radio spectrum of the minihalo at high frequencies. Furthermore, a spectral index image shows that the spectrum of the diffuse emission steepens with the increasing distance along the tail. A striking spatial correlation is observed between the minihalo emission and two cold fronts visible in the Chandra X-ray image of this cool core. These cold fronts confine the minihalo, as also seen in numerical simulations of minihalo formation by sloshing-induced turbulence. All these observations provide support to the hypothesis that the radio emitting electrons in cluster cool cores are produced by turbulent reacceleration. ### The relativistic solar particle event of 2005 January 20: prompt and delayed particle acceleration The highest energies of solar energetic nucleons detected in space or through gamma-ray emission in the solar atmosphere are in the GeV range. Where and how the particles are accelerated is still controversial. We search for observational evidence on the acceleration region(s) by comparing the timing of relativistic protons detected at Earth and radiative signatures in the solar atmosphere. To this end a detailed comparison is undertaken of the double-peaked time profile of relativistic protons, derived from the worldwide network of neutron monitors during the large particle event of 2005 January 20, with UV imaging and radio petrography over a broad frequency band from the low corona to interplanetary space. We show that both relativistic proton releases to interplanetary space were accompanied by distinct episodes of energy release and electron acceleration in the corona traced by the radio emission and by brightenings of UV kernels in the low solar atmosphere. The timing of electromagnetic emissions and relativistic protons suggests that the first proton peak was related to the acceleration of gamma-ray emitting protons during the impulsive flare phase, as shown before. The second proton peak occurred together with signatures of magnetic restructuring in the corona after the CME passage. We attribute the acceleration to reconnection and possibly turbulence in large-scale coronal loops. While type II radio emission was observed in the high corona, there is no evidence of a temporal relationship with the relativistic proton acceleration. ### The Supernova Remnant W44: confirmations and challenges for cosmic-ray acceleration The middle-aged supernova remnant (SNR) W44 has recently attracted attention because of its relevance regarding the origin of Galactic cosmic-rays. The gamma-ray missions AGILE and Fermi have established, for the first time for a SNR, the spectral continuum below 200 MeV which can be attributed to neutral pion emission. Confirming the hadronic origin of the gamma-ray emission near 100 MeV is then of the greatest importance. Our paper is focused on a global re-assessment of all available data and models of particle acceleration in W44, with the goal of determining on a firm ground the hadronic and leptonic contributions to the overall spectrum. We also present new gamma-ray and CO NANTEN2 data on W44, and compare them with recently published AGILE and Fermi data. Our analysis strengthens previous studies and observations of the W44 complex environment and provides new information for a more detailed modeling. In particular, we determine that the average gas density of the regions emitting 100 MeV – 10 GeV gamma-rays is relatively high (n= 250 – 300 cm^-3). The hadronic interpretation of the gamma-ray spectrum of W44 is viable, and supported by strong evidence. It implies a relatively large value for the average magnetic field (B > 10^2 microG) in the SNR surroundings, sign of field amplification by shock-driven turbulence. Our new analysis establishes that the spectral index of the proton energy distribution function is p1 = 2.2 +/- 0.1 at low energies and p2 = 3.2 +/- 0.1 at high energies. We critically discuss hadronic versus leptonic-only models of emission taking into account simultaneously radio and gamma-ray data. We find that the leptonic models are disfavored by the combination of radio and gamma-ray data. Having determined the hadronic nature of the gamma-ray emission on firm ground, a number of theoretical challenges remains to be addressed. ### The Supernova Remnant W44: confirmations and challenges for cosmic-ray acceleration [Replacement] The middle-aged supernova remnant (SNR) W44 has recently attracted attention because of its relevance regarding the origin of Galactic cosmic-rays. The gamma-ray missions AGILE and Fermi have established, for the first time for a SNR, the spectral continuum below 200 MeV which can be attributed to neutral pion emission. Confirming the hadronic origin of the gamma-ray emission near 100 MeV is then of the greatest importance. Our paper is focused on a global re-assessment of all available data and models of particle acceleration in W44, with the goal of determining on a firm ground the hadronic and leptonic contributions to the overall spectrum. We also present new gamma-ray and CO NANTEN2 data on W44, and compare them with recently published AGILE and Fermi data. Our analysis strengthens previous studies and observations of the W44 complex environment and provides new information for a more detailed modeling. In particular, we determine that the average gas density of the regions emitting 100 MeV – 10 GeV gamma-rays is relatively high (n= 250 – 300 cm^-3). The hadronic interpretation of the gamma-ray spectrum of W44 is viable, and supported by strong evidence. It implies a relatively large value for the average magnetic field (B > 10^2 microG) in the SNR surroundings, sign of field amplification by shock-driven turbulence. Our new analysis establishes that the spectral index of the proton energy distribution function is p1 = 2.2 +/- 0.1 at low energies and p2 = 3.2 +/- 0.1 at high energies. We critically discuss hadronic versus leptonic-only models of emission taking into account simultaneously radio and gamma-ray data. We find that the leptonic models are disfavored by the combination of radio and gamma-ray data. Having determined the hadronic nature of the gamma-ray emission on firm ground, a number of theoretical challenges remains to be addressed. ### Electric Current Circuits in Astrophysics Cosmic magnetic structures have in common that they are anchored in a dynamo, that an external driver converts kinetic energy into internal magnetic energy, that this magnetic energy is transported as Poynting flux across the magnetically dominated structure, and that the magnetic energy is released in the form of particle acceleration, heating, bulk motion, MHD waves, and radiation. The investigation of the electric current system is particularly illuminating as to the course of events and the physics involved. We demonstrate this for the radio pulsar wind, the solar flare, and terrestrial magnetic storms. ### The Generation of Nonthermal Particles in the Relativistic Magnetic Reconnection of Pair Plasmas Particle acceleration in the magnetic reconnection of electron-positron plasmas is studied by using a particle-in-cell simulation. It is found that a significantly large number of nonthermal particles are generated by the inductive electric fields around an X-type neutral line when the reconnection outflow velocity, which is known to be an Alfv\’{e}n velocity, is on the order of the speed of light. In such a relativistic reconnection regime, we also find that electrons and positrons form a power-law-like energy distribution through their drift along the reconnection electric field under the relativistic Speiser motion. A brief discussion of the relevance of these results to the current sheet structure, which has an antiparallel magnetic field in astrophysical sources of synchrotron radiation, is presented. ### A Numerical Assessment of Cosmic-ray Energy Diffusion through Turbulent Media How and where cosmic rays are produced, and how they diffuse through various turbulent media, represent fundamental problems in astrophysics with far reaching implications, both in terms of our theoretical understanding of high-energy processes in the Milky Way and beyond, and the successful interpretation of space-based and ground based GeV and TeV observations. For example, recent and ongoing detections, e.g., by Fermi (in space) and HESS (in Namibia), of $\gamma$-rays produced in regions of dense molecular gas hold important clues for both processes. In this paper, we carry out a comprehensive numerical investigation of relativistic particle acceleration and transport through turbulent magnetized environments in order to derive broadly useful scaling laws for the energy diffusion coefficients. ### Test-particle acceleration in a hierarchical three-dimensional turbulence model The acceleration of charged particles is relevant to the solar corona over a broad range of scales and energies. High-energy particles are usually detected in concomitance with large energy release events like solar eruptions and flares, nevertheless acceleration can occur at smaller scales, characterized by dynamical activity near current sheets. To gain insight into the complex scenario of coronal charged particle acceleration, we investigate the properties of acceleration with a test-particle approach using three-dimensional magnetohydrodynamic (MHD) models. These are obtained from direct solutions of the reduced MHD equations, well suited for a plasma embedded in a strong axial magnetic field, relevant to the inner heliosphere. A multi-box, multi-scale technique is used to solve the equations of motion for protons. This method allows us to resolve an extended range of scales present in the system, namely from the ion inertial scale of the order of a meter up to macroscopic scales of the order of $10\,$km ($1/100$th of the outer scale of the system). This new technique is useful to identify the mechanisms that, acting at different scales, are responsible for acceleration to high energies of a small fraction of the particles in the coronal plasma. We report results that describe acceleration at different stages over a broad range of time, length and energy scales. ### Relativistic shock acceleration and some consequences This paper summarizes recent progresses in our theoretical understanding of particle acceleration at relativistic shock waves and it discusses two salient consequences: (1) the maximal energy of accelerated particles; (2) the impact of the shock-generated micro-turbulence on the multi-wavelength light curves of gamma-ray burst afterglows. ### Collisionless Relativistic Shocks:current driven turbulence and particle acceleration The physics of collisionless relativistic shocks with a moderate magnetization is presented. Micro-physics is relevant to explain the most energetic radiative phenomena of Nature, namely that of the termination shock of Gamma Ray Bursts. A transition towards Fermi process occurs for decreasing magnetization around a critical value which turns out to be the condition for the scattering to break the mean field inhibition. Scattering is produced by magnetic micro-turbulence driven by the current carried by returning particles, which had not been considered till now, but turns out to be more intense than Weibel’s one around the transition. The current is also responsible for a buffer effect on the motion of the incoming flow, on which the threshold for the onset of turbulence depends. ### Shock-cloud interaction and particle acceleration in SN 1006 The supernova remnant SN 1006 is a powerful source of high-energy particles and evolves in a relatively tenuous and uniform environment, though interacting with an atomic cloud in its northwestern limb. The X-ray image of SN 1006 reveals an indentation in the southwestern part of the shock front and the HI maps show an isolated cloud (southwestern cloud) having the same velocity as the northwestern cloud and whose morphology fits perfectly in the indentation. We performed spatially resolved spectral analysis of a set of small regions in the southwestern nonthermal limb and studied the deep X-ray spectra obtained within the XMM-Newton SN 1006 Large Program. We also analyzed archive HI data, obtained combining single dish and interferometric observations. We found that the best-fit value of the N_H derived from the X-ray spectra significantly increases in regions corresponding to the southwestern cloud, while the cutoff energy of the synchrotron emission decreases. The amount of the N_H variations corresponds perfectly with the HI column density of the southwestern cloud, as measured from the radio data. The decrease in the cutoff energy at the indentation clearly reveals that the back side of the cloud is actually interacting with the remnant. The southwestern limb therefore presents a unique combination of efficient particle acceleration and high ambient density, thus being the most promising region for gamma-ray hadronic emission in SN 1006. We estimate that such emission will be detectable with the Fermi telescope within a few years. ### Relativistic Reconnection: an Efficient Source of Non-Thermal Particles In magnetized astrophysical outflows, the dissipation of field energy into particle energy via magnetic reconnection is often invoked to explain the observed non-thermal signatures. By means of two- and three-dimensional particle-in-cell simulations, we investigate anti-parallel reconnection in magnetically-dominated electron-positron plasmas. Our simulations extend to unprecedentedly long temporal and spatial scales, so we can capture the asymptotic state of the system beyond the initial transients, and without any artificial limitation by the boundary conditions. At late times, the reconnection layer is organized into a chain of large magnetic islands connected by thin X-lines. The plasmoid instability further fragments each X-line into a series of smaller islands, separated by X-points. At the X-points, the particles become unmagnetized and they get accelerated along the reconnection electric field. We provide definitive evidence that the late-time particle spectrum integrated over the whole reconnection region is a power-law, whose slope is harder than -2 for magnetizations sigma>10. Efficient particle acceleration to non-thermal energies is a generic by-product of the long-term evolution of relativistic reconnection in both two and three dimensions. In three dimensions, the drift-kink mode corrugates the reconnection layer at early times, but the long-term evolution is controlled by the plasmoid instability, that facilitates efficient particle acceleration, in analogy to the two-dimensional physics. Our findings have important implications for the generation of hard photon spectra in pulsar winds and relativistic astrophysical jets. ### A CR-hydro-NEI Model of the Structure and Broadband Emission from Tycho's SNR Tycho’s supernova remnant (SNR) is well-established as a source of particle acceleration to very high energies. Constraints from numerous studies indicate that the observed gamma-ray emission results primarily from hadronic processes, providing direct evidence of highly relativistic ions that have been accelerated by the SNR. Here we present an investigation of the dynamical and spectral evolution of Tycho’s SNR by carrying out hydrodynamical simulations that include diffusive shock acceleration of particles in the amplified magnetic field at the forward shock of the SNR. Our simulations provide a consistent view of the shock positions, the nonthermal emission, the thermal X-ray emission from the forward shock, and the brightness profiles of the radio and X-ray emission. We compare these with the observed properties of Tycho to determine the density of the ambient material, the particle acceleration efficiency and maximum energy, the accelerated electron to-proton ratio, and the properties of the shocked gas downstream of the expanding SNR shell. We find that evolution of a typical Type Ia supernova in a low ambient density (n_0 ~ 0.3 cm^{-3}), with an upstream magnetic field of ~5\ microGauss, and with ~16% of the SNR kinetic energy being converted into relativistic electrons and ions through diffusive shock acceleration, reproduces the observed properties of Tycho. Under such a scenario, the bulk of observed gamma-ray emission at high energies is produced by pi^0-decay resulting from the collisions of energetic hadrons, while inverse-Compton emission is significant at lower energies, comprising roughly half of the flux between 1 and 10 GeV. ### Dust Production and Particle Acceleration in Supernova 1987A Revealed with ALMA Supernova (SN) explosions are crucial engines driving the evolution of galaxies by shock heating gas, increasing the metallicity, creating dust, and accelerating energetic particles. In 2012 we used the Atacama Large Millimeter/Submillimeter Array to observe SN 1987A, one of the best-observed supernovae since the invention of the telescope. We present spatially resolved images at 450um, 870um, 1.4mm, and 2.8mm, an important transition wavelength range. Longer wavelength emission is dominated by synchrotron radiation from shock-accelerated particles, shorter wavelengths by emission from the largest mass of dust measured in a supernova remnant (>0.2Msun). For the first time we show unambiguously that this dust has formed in the inner ejecta (the cold remnants of the exploded star’s core). The dust emission is concentrated to the center of the remnant, so the dust has not yet been affected by the shocks. If a significant fraction survives, and if SN 1987A is typical, supernovae are important cosmological dust producers. ### Pulsar wind model for the spin-down behavior of intermittent pulsars [Replacement] Intermittent pulsars are part-time radio pulsars. They have higher slow down rate in the on state (radio-loud) than in the off state (radio-quiet). This gives the evidence that particle wind may play an important role in pulsar spindown. The effect of particle acceleration is included in modeling the rotational energy loss rate of the neutron star. Applying the pulsar wind model to the three intermittent pulsars (PSR B1931+24, PSR J1841-0500, and PSR J1832+0029), their magnetic field and inclination angle are calculated simultaneously. The theoretical braking indices of intermittent pulsars are also given. In the pulsar wind model, the density of the particle wind can always be the Goldreich-Julian density. This may ensure that different on states of intermittent pulsars are stable. The duty cycle of particle wind can be determined from timing observations. It is consistent with the duty cycle of the on state. Inclination angle and braking index observations of intermittent pulsars may help to test different models of particle acceleration. At present, the inverse Compton scattering induced space charge limited flow with field saturation model can be ruled out. ### Pulsar wind model for the spin-down behavior of intermittent pulsars It is observed that intermittent pulsars have higher slow down rate in the on state (radio-loud) than in the off state (radio-quiet). This gives the evidence that particle wind may play an important role in pulsar spindown. The effect of particle acceleration is included in modeling the rotational energy loss rate. Applying the pulsar wind model to the three intermittent pulsars (PSR B1931+24, PSR J1841-0500, and PSR J1832+0029), we calculate their magnetic field and inclination angle simultaneously. The braking index of intermittent pulsars is also predicted. The duty cycle of particle wind determined from timing observations is consistent with the duty cycle of the on state. It is shown that the particle number density may always be the Goldreich-Julian density. This may ensure that different on states of intermittent pulsars are stable. Observations on the inclination angle and braking index of intermittent pulsars may help to test different models of particle acceleration, as well as different models of pulsar magnetosphere. At present, the inverse Compton scattering induced space charge limited flow with field saturation model could already be ruled out. ### The Origin of Galactic Cosmic Rays One century ago Viktor Hess carried out several balloon flights that led him to conclude that the penetrating radiation responsible for the discharge of electroscopes was of extraterrestrial origin. One century from the discovery of this phenomenon seems to be a good time to stop and think about what we have understood about Cosmic Rays. The aim of this review is to illustrate the ideas that have been and are being explored in order to account for the observable quantities related to cosmic rays and to summarize the numerous new pieces of observation that are becoming available. In fact, despite the possible impression that development in this field is somewhat slow, the rate of new discoveries in the last decade or so has been impressive, and mainly driven by beautiful pieces of observation. At the same time scientists in this field have been able to propose new, fascinating ways to investigate particle acceleration inside the sources, making use of multifrequency observations that range from the radio, to the optical, to X-rays and gamma rays. These ideas can now be confronted with data. I will mostly focus on supernova remnants as the most plausible sources of Galactic cosmic rays, and I will review the main aspects of the modern theory of diffusive particle acceleration at supernova remnant shocks, with special attention for the dynamical reaction of accelerated particles on the shock and the phenomenon of magnetic field amplification at the shock. Cosmic ray escape from the sources is discussed as a necessary step to determine the spectrum of cosmic rays at the Earth. In the end of this review I will also discuss the phenomenon of cosmic ray acceleration at shocks propagating in partially ionized media and the implications of this phenomenon in terms of width of the Balmer line emission. ### The Origin of Galactic Cosmic Rays [Replacement] One century ago Viktor Hess carried out several balloon flights that led him to conclude that the penetrating radiation responsible for the discharge of electroscopes was of extraterrestrial origin. One century from the discovery of this phenomenon seems to be a good time to stop and think about what we have understood about Cosmic Rays. The aim of this review is to illustrate the ideas that have been and are being explored in order to account for the observable quantities related to cosmic rays and to summarize the numerous new pieces of observation that are becoming available. In fact, despite the possible impression that development in this field is somewhat slow, the rate of new discoveries in the last decade or so has been impressive, and mainly driven by beautiful pieces of observation. At the same time scientists in this field have been able to propose new, fascinating ways to investigate particle acceleration inside the sources, making use of multifrequency observations that range from the radio, to the optical, to X-rays and gamma rays. These ideas can now be confronted with data. I will mostly focus on supernova remnants as the most plausible sources of Galactic cosmic rays, and I will review the main aspects of the modern theory of diffusive particle acceleration at supernova remnant shocks, with special attention for the dynamical reaction of accelerated particles on the shock and the phenomenon of magnetic field amplification at the shock. Cosmic ray escape from the sources is discussed as a necessary step to determine the spectrum of cosmic rays at the Earth. In the end of this review I will also discuss the phenomenon of cosmic ray acceleration at shocks propagating in partially ionized media and the implications of this phenomenon in terms of width of the Balmer line emission. ### Origin of Nonthermal Emission from the Fermi Bubbles and Mechanisms of Particle Acceleration There We analyse processes of particle acceleration in the Fermi Bubbles. The goal of our investigations is to obtain restrictions for acceleration mechanisms. Our analysis of the three processes: acceleration from background plasma, re-acceleration of relativistic electrons emitted by supernova remnants, and acceleration by shocks generated by processes of star tidal disruption in the Galactic Center, showed that the model of multi-shock acceleration does not have serious objections at present and therefore seems us more attractive than others. ### Particle acceleration by shocks in supernova remnants Particle acceleration occurs on a range of scales from AU in the heliosphere to Mpc in clusters of galaxies and to energies ranging from MeV to EeV. A number of acceleration processes have been proposed, but diffusive shock acceleration (DSA) is widely invoked as the predominant mechanism. DSA operates on all these scales and probably to the highest energies. DSA is simple, robust and predicts a universal spectrum. However there are still many unknowns regarding particle acceleration. This paper focuses on the particular question of whether supernova remnants (SNR) can produce the Galactic CR spectrum up to the knee at a few PeV. The answer depends in large part on the detailed physics of diffusive shock acceleration. ### Linking accretion flow and particle acceleration in jets - II. Self-similar jet models with full relativistic MHD gravitational mass We present a new, semi-analytic formalism to model the acceleration and collimation of relativistic jets in a gravitational potential. The gravitational energy density includes the kinetic, thermal, and electromagnetic mass contributions. The solutions are close to self-similar throughout the integration, from very close to the black hole to the region where gravity is unimportant. The field lines are tied to the conditions very close to the central object and eventually overcollimate, possibly leading to a collimation shock. This collimation shock could provide the conditions for diffusive shock acceleration, leading to the observed electron populations with a power-law energy distribution in jets. We provide the derivation, a detailed analysis of a solution, and describe the effects the parameters have on the properties of the solutions, such as the Lorentz factor and location of the collimation shock. We also discuss the deviations from self-similarity. By comparing the new gravity term with the gravity term obtained from a non-relativistic formalism in a previous work, we show they are equivalent in the non-relativistic limit. This equivalence shows the approach taken in that work is valid and allows us to comment on its limitations. ### Vortical field amplification and particle acceleration at rippled shocks Supernova Remnants (SNRs) shocks are believed to accelerate charged particles and to generate strong turbulence in the post-shock flow. From high-energy observations in the past decade, a magnetic field at SNR shocks largely exceeding the shock-compressed interstellar field has been inferred. We outline how such a field amplification results from a small-scale dynamo process downstream of the shock, providing an explicit expression for the turbulence back-reaction to the fluid whirling. The spatial scale of the $X-$ray rims and the short time-variability can be obtained by using reasonable parameters for the interstellar turbulence. We show that such a vortical field saturation is faster than the acceleration time of the synchrotron emitting energetic electrons. ### Three-dimensional relativistic pair plasma reconnection with radiative feedback in the Crab Nebula [Replacement] The discovery of rapid synchrotron gamma-ray flares above 100 MeV from the Crab Nebula has attracted new interest in alternative particle acceleration mechanisms in pulsar wind nebulae. Diffuse shock-acceleration fails to explain the flares because particle acceleration and emission occur during a single or even sub-Larmor timescale. In this regime, the synchrotron energy losses induce a drag force on the particle motion that balances the electric acceleration and prevents the emission of synchrotron radiation above 160 MeV. Previous analytical studies and 2D particle-in-cell (PIC) simulations indicate that relativistic reconnection is a viable mechanism to circumvent the above difficulties. The reconnection electric field localized at X-points linearly accelerates particles with little radiative energy losses. In this paper, we check whether this mechanism survives in 3D, using a set of large PIC simulations with radiation reaction force and with a guide field. In agreement with earlier works, we find that the relativistic drift kink instability deforms and then disrupts the layer, resulting in significant plasma heating but few non-thermal particles. A moderate guide field stabilizes the layer and enables particle acceleration. We report that 3D magnetic reconnection can accelerate particles above the standard radiation reaction limit, although the effect is less pronounced than in 2D with no guide field. We confirm that the highest energy particles form compact bunches within magnetic flux ropes, and a beam tightly confined within the reconnection layer, which could result in the observed Crab flares when, by chance, the beam crosses our line of sight. ### Three-dimensional relativistic pair plasma reconnection with radiative feedback in the Crab Nebula The discovery of rapid synchrotron gamma-ray flares above 100 MeV from the Crab Nebula has attracted new interest in alternative particle acceleration mechanisms in pulsar wind nebulae. Diffuse shock-acceleration fails to explain the flares because particle acceleration and emission occur during a single or even sub-Larmor timescale. In this regime, the synchrotron energy losses induce a drag force on the particle motion that balances the electric acceleration and prevents the emission of synchrotron radiation above 160 MeV. Previous analytical studies and 2D particle-in-cell (PIC) simulations indicate that relativistic reconnection is a viable mechanism to circumvent the above difficulties. The reconnection electric field localized at X-points linearly accelerates particles with little radiative energy losses. In this paper, we check whether this mechanism survives in 3D, using a set of large PIC simulations with radiation reaction force and with a guide field. In agreement with earlier works, we find that the relativistic drift kink instability deforms and then disrupts the layer, resulting in significant plasma heating but few non-thermal particles. A moderate guide field stabilizes the layer and enables particle acceleration. We report that 3D magnetic reconnection can accelerate particles above the standard radiation reaction limit, although the effect is less pronounced than in 2D with no guide field. We confirm that the highest energy particles form compact bunches within magnetic flux ropes, and a beam tightly confined within the reconnection layer, which could result in the observed Crab flares when, by chance, the beam crosses our line of sight. ### Cosmic Ray acceleration and Balmer emission from RCW 86 (G315.4-2.3) [Replacement] Context. Observation of Balmer lines from the region around the forward shock of supernova remnants (SNR) may provide valuable information on the shock dynamics and the efficiency of particle acceleration at the shock. Aims. We calculated the Balmer line emission and the shape of the broad Balmer line for parameter values suitable for SNR RCW 86 (G315.4-2.3) as a function of the cosmic-ray (CR) acceleration efficiency and of the level of thermal equilibration between electrons and protons behind the shock. This calculation aims at using the width of the broad Balmer-line emission to infer the CR acceleration efficiency in this remnant. Methods. We used the recently developed nonlinear theory of diffusive shock-acceleration in the presence of neutrals. The semianalytical approach we developed includes a description of magnetic field amplification as due to resonant streaming instability, the dynamical reaction of accelerated particles and the turbulent magnetic field on the shock, and all channels of interaction between neutral hydrogen atoms and background ions that are relevant for the shock dynamics. Results. We derive the CR acceleration efficiency in the SNR RCW 86 from the Balmer emission. Since our calculation used recent measurements of the shock proper motion, the results depend on the assumed distance to Earth. For a distance of 2 kpc the measured width of the broad Balmer line is compatible with the absence of CR acceleration. For a distance of 2.5 kpc, which is a widely used value in current literature, a CR acceleration efficiency of 5-30% is obtained, depending upon the electron-ion equilibration and the ionization fraction upstream of the shock. By combining information on Balmer emission with the measured value of the downstream electron temperature, we constrain the CR acceleration efficiency to be ~20%. ### Cosmic Ray acceleration and Balmer emission from RCW 86 (G315.4-2.3) Context. Observation of Balmer lines from the region around the forward shock of supernova remnants may provide precious information on the shock dynamics and on the efficiency of particle acceleration at the shock. Aims. We calculate the Balmer line emission and the shape of the broad Balmer line for parameters values suitable for SNR RCW 86 (G315.4-2.3), as a function of the cosmic ray (CR) acceleration efficiency and of the level of thermal equilibration between electrons and protons behind the shock. This calculation aims at using the width of the broad Balmer line emission to infer the CR acceleration efficiency in this remnant. Methods. We use the recently developed non-linear theory of diffusive shock acceleration in the presence of neutrals. The semi-analytical approach that we have developed includes a description of magnetic field amplification as due to resonant streaming instability, the dynamical reaction of both accelerated particles and turbulent magnetic field on the shock, and all channels of interaction between neutral hydrogen atoms and background ions that are relevant for the shock dynamics. Results. We derive from Balmer emission the CR acceleration efficiency in the SNR RCW 86. Since our calculation uses recent measurements of the shock proper motion, the results depend on the assumed distance to Earth. For a distance of 2 kpc the measured width of the broad Balmer line is compatible with the absence of CR acceleration. For a distance of 2.5 kpc, which is a widely used value in current literature, a CR acceleration efficiency of 5-30% is obtained, depending upon the electron-ion equilibration and the ionization fraction upstream of the shock. When information on Balmer emission is combined with the measured value of the downstream electron temperature, the CR acceleration efficiency can be constrained to be ~20%. ### Particle acceleration by binary black holes We explore multi-black hole spacetimes from the perspective of ultra-high energy particle collisions. Such a discussion is limited to spacetimes containing single black hole so far. We deal with Majumdar-Papapetrou solution representing binary system consisting of two identical black holes. We consider particles following timelike geodesics that are confined to move on equatorial plane towards the axis of symmetry. We consider collision between two particles moving in the opposite directions at the location midway between the black holes on the axis. We show that the center of mass energy of collision between the particles increases with the decrease in the separation between the black holes and shows divergence in the limit where separation goes to zero. Whether or not high energy collisions can occur in the more general setting like colliding black holes, in the intermediate region when distance the black holes is small can in principle be verified in the numerical relativity simulations.	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8950698971748352, "perplexity": 1275.941827204507}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-23/segments/1405997891953.98/warc/CC-MAIN-20140722025811-00185-ip-10-33-131-23.ec2.internal.warc.gz"}
http://physics.stackexchange.com/questions/35005/how-could-the-unit-of-a-constant-be-unit-of-tension-n-1	# How could the unit of a constant be unit of tension $N^{-1}$? From my pervious Question:What are the units of the quantities in the Einstein field equation? i noticed that the unit of this constant $\frac {G}{c^4}$ is the unit of tenstion $$\frac {m^3}{kg.s^2}\frac {s^4}{m^4}=\frac {s^2}{kg.m}={N^{-1}}$$ How could the unit of a constant be unit of tension $N^{-1}$!? - First of all, the inverse newton is the unit of inverse tension ($1/F$, one over force), not tension itself. Second, it follows from dimensional analysis. It's the constant that has to multiply the energy density (energy per cubic meter) to get the curvature (one per squared meter). Clearly, the ratio taken in one way is "energy per meter" i.e. force or tension, and the coefficient is the inverse to it, so it has to be inverse tension. What you seem to confuse are the words "constant" and "dimensionless". These are different things. A "constant" is something that isn't allowed to change in time (or depend on space or other things). A "dimensionless" quantity is a quantity with no units. These are two totally different things. There can be dimensionful constants, like your $G/c^4$ or the mass of the electron $m_0$, among infinitely many other examples. They don't depend on time but they do require units (e.g. the electron mass requires a unit of mass, e.g. a kilogram). And there can also be dimensionless quantities that are non-constant, like the albedo of the Earth's surface or the inflation rate. They don't need units because they're "ratios" of various things of the same type, but they do depend on time because the numerators and denominators do. - Using G,$\hbar$, and c together you can make any unit you want, so it isn't surprising that you get inverse Newtons from G,c and $\hbar$. What is somewhat interesting is that you get it without using $\hbar$. This means that there is a fundamental force unit in General Relativity, and you should understand what it means. The proper way to understand it is using some standard unit intuition. The combinations $G\over c^2$ and $G\over c^3$ are the conversion factors from kg to m and s respectively. They tells you the mass of a black hole when you multiply by (half) the Schwarzschild radius, or by the time it takes light to cross the Schwarzschild radius (time and space are interchangable in relativity). $$c^3/G has units kg/s, and it tells you how many seconds it takes to cross the event horizon of a black hole, per kg of mass. You noticed that this quantity, times c, is a force. A force is a flow of momentum from one place to another. One way of making a force is to have a certain amount of water smack into a wall with velocity v. In this case, the force is the amount of water hitting the wall (in Kg/s) times the velocity (in m/s). The Kg/s unit c^3/G is the maximum amount of mass you can fit into a region of size 1 light-second. Multiplying by c, you get the maximum momentum you can transmit into a wall per second, since this is the maximum mass times the maximum velocity. So this constant is like a rough measure of the maximum force you can exert. The value is large: 1.24 \times 10^{44} N. This is the intuition for the quantity, but when you boost an object, it becomes skinnier, and there is no limit to how skinny you can make a black hole. If you make a black pancake moving at ultra-relativistic speeds, you can exert a larger force than this by as much as you want, so this "maximum force" business is a total fake. - What is somewhat interesting and also funny is that you get planck force without even using planck constant. a. the Planck mass, denoted by m_P, is the unit of mass in the system of natural units known as Planck units. It is defined so that:$$m_p=\sqrt {\frac{\hbar G}{c}}$$b. planck time:$$t_p=\sqrt {\frac{\hbar G}{c^5}}$$c. planck force:$$F_p=m_p.c/t_p=c^4/G$$in other words:$$R_{\mu\nu}-\frac {1}{2}g_{\mu\nu}R+g_{\mu\nu}\Lambda=\frac {8\pi }{F_p}T_{\mu\nu} - @Ron Maimon how is it possible!? – funny Aug 27 '12 at 11:17	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9560925364494324, "perplexity": 514.4392248395832}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2015-48/segments/1448398464396.78/warc/CC-MAIN-20151124205424-00082-ip-10-71-132-137.ec2.internal.warc.gz"}
https://proofwiki.org/wiki/Algebraic_Element_of_Field_Extension_is_Root_of_Unique_Monic_Polynomial_of_Minimal_Degree	# Algebraic Element of Field Extension is Root of Unique Monic Polynomial of Minimal Degree ## Theorem Let $L / K$ be a field extension. Let $\alpha \in L$ be algebraic over $K$. Then there exists a unique monic polynomial $f \in K \sqbrk x$ of smallest degree such that $\map f \alpha = 0$, called the minimal polynomial. ## Proof ### Existence Follows from Well-Ordering Principle and because $K$ is a field. $\Box$ ### Uniqueness Let $f$ and $g$ be two such monic polynomial. Then: $\map f \alpha - \map g \alpha = 0$ Aiming for a contradiction, suppose $f - g \ne 0$. Let $a$ be the leading coefficient of $f-g$. Then $\dfrac 1 {a} \paren {f - g}$ is another such polynomial of strictly smaller degree. Thus $f - g = 0$. $\blacksquare$	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9281524419784546, "perplexity": 269.5928703982144}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-40/segments/1600402127075.68/warc/CC-MAIN-20200930141310-20200930171310-00785.warc.gz"}
https://forum.allaboutcircuits.com/threads/having-trouble-reading-low-high-from-this-sound-sensor.157845/	# Having trouble reading low/high from this sound sensor #### zirconx Joined Mar 10, 2010 97 Hi,I'm having some trouble getting accurate readings from this sound sensor. It runs on 3-5v, and signals LOW when sound is above an (adjustable) threshold. I'm reading the output pin on my voltmeter as well as a Pine64 SBC. (similar to a Raspberry Pi). A couple links on this particular sensor: https://www.electronicshub.org/interfacing-sound-sensor-with-arduino/ http://henrysbench.capnfatz.com/henrys-bench/arduino-sensors-and-input/arduino-sound-detection-sensor-tutorial-and-user-manual/ I bought it from here: https://www.banggood.com/Microphone-Sound-Sensor-Module-Voice-Sensor-High-Sensitivity-Sound-Detection-Module-Whistle-Module-p-1235446.html The problem I am having is the signal does not go low enough. When powered by 5v, I get a 5v signal when there is no sound. When there is sound (I'm using a tone generator app on my phone), the signal goes to 3v. I would expect it to go to 0v. When powered by 3.3v (which is how I will use it on the Pine64), a LOW signal is only 1.8v. This is not low enough to trigger a LOW reading on my Pine64. I tried adding a resistor to ground. That adjusts the HIGH/LOW signals downward, but not enough that I can get a reliable reading either way. The sound indicator LED on the board seems to light reliably and solid when I provide the test tone signal. When I turn the adjustment knob most of the way down, I can get a 0v signal, but then it never goes HIGH either (it's too sensitive). Am I using this wrong? Do you think I got a bad batch (I've tried two of them)? Thanks for any help. #### Attachments • 3 MB Views: 6 #### spinnaker Joined Oct 29, 2009 7,835 Did you try blocking the microphone to rule out any ambient sound? #### sghioto Joined Dec 31, 2017 1,038 When powered by 3.3v (which is how I will use it on the Pine64), a LOW signal is only 1.8v. From the voltage readings the output may be oscillating. Can you put a scope on the output? What are the readings when not connected to the Pine64? SG #### zirconx Joined Mar 10, 2010 97 I have tried it unconnected to the Pine64, the readings were (pretty much) the same. I agree from the voltage readings it seems like it could be oscillating. I don't have a scope but the voltage readings look stable. They match what the audio-signal indicator LED is showing on the board - it's on solid, and the voltage seems to be a solid 1.8v, for example. I don't see the LED flickering. I didn't try blocking the mic, but the LED audio-signal indicator seems to be working. In a quiet room the LED is off (and I read 3.3v). Then I turn on the tone generator and the LED goes solid, and the voltage drops to 1.8v. If I had an analog input I could work with this, but the Pine64 doesn't have any. Given this circuit (thatI found on one of the pages I linked earlier), is there anything I could check or do differently? #### Raymond Genovese Joined Mar 5, 2016 1,658 It is a very cheap unit and you could have a crappy pot on it, or something else. Look at the schematic here https://www.electronicshub.org/interfacing-sound-sensor-with-arduino/ Can you put your meter on the analog out point and see if it systematically changing with sound? With no power, can you see if the pot is systematically changing or jumping? edited to add: you posted the schematic as I was typing. So that LM393 is function as a simple comparator INA and INB with the pot setting the value to decide if OUT goes low or stays high. Checking the analog out is one thing as I mention. Checking the pot is another. Last edited: #### sghioto Joined Dec 31, 2017 1,038 I don't see the LED flickering. If the oscillation is fast enough you would not notice any flickering. You really need to look at the output with a scope. Edit: You are checking the unit with a tone generator. So the unit will be switching ON and OFF at the signal frequency. SG #### zirconx Joined Mar 10, 2010 97 If the oscillation is fast enough you would not notice any flickering. You really need to look at the output with a scope. Edit: You are checking the unit with a tone generator. So the unit will be switching ON and OFF at the signal frequency. SG Hmm it was a 600hz tone, you think the unit might be switching on and off at that frequency? I also tried blowing into the mic and got the same result. This $43 "scope" would probably let me see what is happening, right? It has a 200Khz bandwidth. https://www.amazon.com/Quimat-Oscilloscope-BNC-Clip-Assembled-Finished/dp/B077D62Z1P #### sghioto Joined Dec 31, 2017 1,038 This$43 "scope" would probably let me see what is happening, right? Yes, In fact I have that exact unit. Hmm it was a 600hz tone, you think the unit might be switching on and off at that frequency? Yes I do. SG #### Raymond Genovese Joined Mar 5, 2016 1,658 The digital out should oscillate with a 600 Hz tone. If you are reading the output of the 393 digitally, it should be a series of lows and highs - that would be working normally. How do you think it should work? Are you saying that the pine never sees a low with the tone on? #### KeithWalker Joined Jul 10, 2017 796 I have tried it unconnected to the Pine64, the readings were (pretty much) the same. I agree from the voltage readings it seems like it could be oscillating. I don't have a scope but the voltage readings look stable. They match what the audio-signal indicator LED is showing on the board - it's on solid, and the voltage seems to be a solid 1.8v, for example. I don't see the LED flickering. I didn't try blocking the mic, but the LED audio-signal indicator seems to be working. In a quiet room the LED is off (and I read 3.3v). Then I turn on the tone generator and the LED goes solid, and the voltage drops to 1.8v. If I had an analog input I could work with this, but the Pine64 doesn't have any. Given this circuit (thatI found on one of the pages I linked earlier), is there anything I could check or do differently? The comparator is not oscillating. The AC signal from the microphone is not detected so the comparator is being turned on and off by positive and negative half cycles of the amplified AC signal. That's not a very good design. #### Raymond Genovese Joined Mar 5, 2016 1,658 The problem I am having is the signal does not go low enough. When powered by 5v, I get a 5v signal when there is no sound. When there is sound (I'm using a tone generator app on my phone), the signal goes to 3v. I would expect it to go to 0v. When powered by 3.3v (which is how I will use it on the Pine64), a LOW signal is only 1.8v. This is not low enough to trigger a LOW reading on my Pine64. Can you please respond to this query @zirconx : How are you determining that it is not triggering a low reading on your pine? Are reading the sound bit and it is NEVER 0 while the tone is being presented? Can you post the code fragment whereby you made the determination that it can't trigger a low reading? I am asking because the sound bit should be changing from 1 to 0 and 1 to 0 and so on when you are presenting the tone. Are you saying that it NEVER goes low or assuming that it will not be read as a low because you see 1.8V on the meter? I am saying that your pine should be reading a series of 1 and 0 in the presence of the tone if it is working correctly. #### zirconx Joined Mar 10, 2010 97 Can you please respond to this query @zirconx : How are you determining that it is not triggering a low reading on your pine? Are reading the sound bit and it is NEVER 0 while the tone is being presented? Can you post the code fragment whereby you made the determination that it can't trigger a low reading? I am asking because the sound bit should be changing from 1 to 0 and 1 to 0 and so on when you are presenting the tone. Are you saying that it NEVER goes low or assuming that it will not be read as a low because you see 1.8V on the meter? I am saying that your pine should be reading a series of 1 and 0 in the presence of the tone if it is working correctly. Indeed this is what was happening. I have a software program written in nodejs that writes the pin value to console whenever the value changes. When I had a resistor hooked up between signal and ground, to bring the output lower, I did get oscillating 1's and 0's from my program. I thought that was because the voltage was near the threshold of LOW/HIGH, but perhaps it was just oscillating due to the tone. I will do some more testing with different sounds, I don't recall if I tried my blowing on the mic test at that point. My plan is to couple the mic (probably with a zip tie) to a water pipe and be able to tell when the shower/tub is on. I know that when I had only the voltmeter hooked up, blowing on the mic caused the voltage to change from 3.3v to 1.8v. Which still doesn't seem right. Yes, In fact I have that exact unit. Yes I do. SG I'm also considering this one: https://www.amazon.com/SainSmart-Portable-Handheld-Digital-Oscilloscope/dp/B074QBQNB7 If I could find a decent deal on a "real" scope for close to that price I'd get it instead. I looked in the Marketplace here but didn't see anything. #### Raymond Genovese Joined Mar 5, 2016 1,658 So, the voltmeter will produce something like an average. With something like a 600 Hz square wave, that is as you would expect. After reading a little more carefully, I began to suspect that it was working just fine. They are more like a clap switch in a digital mode - just plain sound detection. You can get a little better with A to D and the analog out (but you still are sampling a wave), but if you do not have that, you will have to program your away around what you want to do. #### zirconx Joined Mar 10, 2010 97 Ok so after reading through all this, and doing some more testing, I think you are right, it's working correctly. I expected the sensor to go LOW and stay there while there was sound, but like you said, it probably doesn't work that way. I am seeing oscillating 1's and 0's out of my program whenever there is sound above the threshold. So I think I can work with that in software - If the state hasn't changed for 1 second and it's HIGH, then the water is off. If the state has changed within the last second, then the water is on. Thanks for all the help. #### Raymond Genovese Joined Mar 5, 2016 1,658 My plan is to couple the mic (probably with a zip tie) to a water pipe and be able to tell when the shower/tub is on. You still may be able to do it, but you are going to have to sample the port over a period of time and get an average value. Do that for no water running and water running. How long to sample can be determined empirically. Compare the averages at different time periods - maybe a second or two is all you need. BUT, any increase in sound levels from "no water running" will look like "water running". Bang on the pipes and it will look like water running from the program's point of view. The power of the technique is limited. #### zirconx Joined Mar 10, 2010 97 Yea you are right, the ON state needs to be more than just has it changed in the last second, it needs to be has it continued to change for the last several seconds. That will omit banging on the pipes, etc. My measurements don't need to be precise, +/- 10 seconds is fine. #### Yaakov Joined Jan 27, 2019 1,612 #### spinnaker Joined Oct 29, 2009 7,835 Ok so after reading through all this, and doing some more testing, I think you are right, it's working correctly. I expected the sensor to go LOW and stay there while there was sound, but like you said, it probably doesn't work that way. I am seeing oscillating 1's and 0's out of my program whenever there is sound above the threshold. So I think I can work with that in software - If the state hasn't changed for 1 second and it's HIGH, then the water is off. If the state has changed within the last second, then the water is on. Thanks for all the help. Probably represents a sound level. Is there a proper datasheet on this thing instead of someone's project that needs to be weeded through? Wait based on the schematic (if it is correct) that does not make sense. #### djsfantasi Joined Apr 11, 2010 6,335 When using sound as a control signal (I.e. a digital output), there is additional processing beyond mere detection required. Just detecting sound levels alone will oscillate. Plus, you have the issue of background noise. First, I’d experiment to determine the level of background noise. Then, in the output stream, I’d use an op amp as a differential amplifier subtract out the background noise and keep the voltage differential between background and detected noise. This is how you’d eliminate the 3.3V you’re seeing when the water isn’t running. I’d wire the op amp to magnify the remaining signal to full scale. Then, the signal IS going to vary. So I’d add an envelope follower to integrate the signal. Since you’re talking about a ten second window, you have a broad range of RC values to perform the integration. #### djsfantasi Joined Apr 11, 2010 6,335 When using sound as a control signal (I.e. a digital output), there is additional processing beyond mere detection required. Just detecting sound levels alone will oscillate. Plus, you have the issue of background noise. First, I’d experiment to determine the level of background noise. Then, in the output stream, I’d use an op amp as a differential amplifier subtract out the background noise and keep the voltage differential between background and detected noise. I’d wire the op amp to magnify the remaining signal to full scale. Then, the signal IS going to vary. So I’d add an envelope follower OR! You’re reading this with an Arduinos, right? Don’t use digitalRead(). Use analogRead() with an analog pin. Then, in your sketch, you can subtract the 3.3V or just ignore anything below 3.3V. Then, I’d take several measurements (with a slight delay) and average the results. This rolling average will produce a number at which sound is continuously detected.	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5296377539634705, "perplexity": 1055.8684436712988}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-24/segments/1590347396163.18/warc/CC-MAIN-20200527204212-20200527234212-00481.warc.gz"}
https://arxiv.org/abs/0706.3866	### Current browse context: cond-mat.mes-hall (what is this?) # Title: Hall Transport in Granular Metals and Effects of Coulomb Interactions Abstract: We present a theory of Hall effect in granular systems at large tunneling conductance $g_{T}\gg 1$. Hall transport is essentially determined by the intragrain electron dynamics, which, as we find using the Kubo formula and diagrammatic technique, can be described by nonzero diffusion modes inside the grains. We show that in the absence of Coulomb interaction the Hall resistivity $\rho_{xy}$ depends neither on the tunneling conductance nor on the intragrain disorder and is given by the classical formula $\rho_{xy}=H/(n^* e c)$, where $n^*$ differs from the carrier density $n$ inside the grains by a numerical coefficient determined by the shape of the grains and type of granular lattice. Further, we study the effects of Coulomb interactions by calculating first-order in $1/g_T$ corrections and find that (i) in a wide range of temperatures $T \gtrsim \Ga$ exceeding the tunneling escape rate $\Ga$, the Hall resistivity $\rho_{xy}$ and conductivity $\sig_{xy}$ acquire logarithmic in $T$ corrections, which are of local origin and absent in homogeneously disordered metals; (ii) large-scale Altshuler-Aronov'' correction to $\sig_{xy}$, relevant at $T\ll\Ga$, vanishes in agreement with the theory of homogeneously disordered metals. Comments: 29 pages, 16 figures Subjects: Mesoscale and Nanoscale Physics (cond-mat.mes-hall); Strongly Correlated Electrons (cond-mat.str-el) Journal reference: Phys. Rev. B 77, 045116 (2008) DOI: 10.1103/PhysRevB.77.045116 Cite as: arXiv:0706.3866 [cond-mat.mes-hall] (or arXiv:0706.3866v1 [cond-mat.mes-hall] for this version) ## Submission history From: Maxim Kharitonov [view email] [v1] Tue, 26 Jun 2007 16:42:05 GMT (601kb)	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8397781252861023, "perplexity": 2211.779783266692}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-39/segments/1505818689806.55/warc/CC-MAIN-20170923231842-20170924011842-00676.warc.gz"}
http://illuminations.nctm.org/Activity.aspx?id=3510	## Equivalent Fractions 3-5 Standards: Math Content: Number and Operations Create equivalent fractions by dividing and shading squares or circles, and match each fraction to its location on the number line. ### Modes Along the top, choose Square or Circle. ### How to Use • Use the sliders to increase or decrease the number of columns and rows (for Squares) or the number of sectors (for Circles). • Once the shape is divided as you want it, click on the sections to color them. Make the green and blue fractions equivalent to the red fraction. • Click on the Check buttons to see if your fractions match. (Note that all fractions must use a different denominator. You will get a message that says, "Use a different denominator," if you make an equivalent fraction that does not use a different denominator.) • Equivalent Fractions will automatically be added to the table. • To delete a row, use the Trash Can icon in the table. • To erase all recordings, use the Reset Table button. • Use the New Fraction button to generate a new red fraction. • The Build Your Own option can be used to create a red fraction of your choosing. In the panel along the right side, choose the Build Your Own option. Create a fraction whose denominator is a prime number. • How many equivalent fractions can you create? Is it possible to create a fraction such that no equivalent fractions could be created with this applet? • Find at least one. • Can you describe the fractions for which this is possible? ### Fraction Game 3-5, 6-8 This applet allows students to individually practice working with relationships among fractions and ways of combining fractions. ### Fraction Models 3-5, 6-8 Explore different representations for fractions including improper fractions, mixed numbers, decimals, and percentages. Additionally, there are length, area, region, and set models.	{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8657375574111938, "perplexity": 1764.0772264777206}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2015-35/segments/1440644064420.15/warc/CC-MAIN-20150827025424-00241-ip-10-171-96-226.ec2.internal.warc.gz"}
http://profmattstrassler.com/articles-and-posts/particle-physics-basics/fields-and-their-particles-with-math/	# Fields and Their Particles: With Math Getting a rough understanding of the basics of particle physics — our current understanding of the most elementary aspects of the universe — isn’t that hard. If you’ve had a class on physics at the advanced pre-university or beginning university level, it’s even easier. If math terrifies you, try the non-math version of this presentation [sorry, that version won’t be ready for a while yet.] But if you can handle algebra, sines and cosines, and (perhaps not even necessary) the simplest aspects of calculus, then you can learn how fields work and how particles arise. There’s one leap of faith you’ll need, which involves learning a tiny bit about what quantum mechanics does. I won’t explain it in math, I’ll just tell you the answers. But once you accept that one point, everything else will follow. Here are the articles 1,2. The ball attached to a spring: 3,4,5. Waves (classical formula and equations of motion, and quantum waves) 6,7. Fields and their particles Once you’ve read these, don’t miss How the Higgs Field Works ### 21 responses to “Fields and Their Particles: With Math” 1. If people could just realize that $$\epsilon_0$$ and $$\mu_0$$ are the essential properties of the space. Just like the lengths are the properties of the space. That is all. But it turned out to be the hardest thing to realize. Length, time, $$\epsilon_0$$ and $$\mu_0$$, is everything we need to start with, concerning space. To accept them as axioms, for which Maxwell already discovered the fundamental relation: The change of a photon position in time is equal to the reciprocal value of the $$\displaystyle \sqrt{ \epsilon_0 \cdot \mu_0}$$ $$\epsilon_0$$ and $$\mu_0$$ are something that was discovered, measured, long time ago. They are electromagnetic properties. Of the space. Photon also has electromagnetic properties. [i]Electromagnetic[/i] is that what [i]attaches[/i] energy and space, what enables the propagation of a photon, what enables photon’s existence in the way it exists – as a linearly propagating EM-energy-oscillation, which has the wavelength (spatial property), and the period of oscillation (time property). The time in which a photon makes one full EM-oscillation is $$\displaystyle \Delta t = \Delta s \cdot \sqrt{\epsilon_0 \cdot \mu_0}$$. Any photon will propagate with the velocity $$\displaystyle \frac{1}{\sqrt{ \epsilon_0 \cdot \mu_0}}$$, regardless of its energy. A photon’s energy is $$\Delta E = h \cdot \nu \Rightarrow \Delta E \cdot \Delta t = h$$. The equation $$\Delta E \cdot \Delta t = h$$ is the law that each photon has to obey. In the above text are given all that is necessary to derive all of the most important equations in physics, using simple infinitesimal calculus, because all of the essential properties of space and of a photon can and do change continually. A photons mass, non-inertial mass, is [tex]\Delta m = \Delta E \cdot \epsilon_0 \cdot \mu_0[\tex], that is, it is the measure of coupling, the convolution of photons elementary energy and epsilon-mu-space. http://www.thenakedscientists.com/forum/index.php?topic=46034.0 Best regards, Zordim • Best regards to you too, but please keep this silliness to your own website. 2. There is nothing silly about it. The last sound science was the explanation of photoelectric effect. After that, the whole century of silliness passed. Enough with that. Stop embarrassing yourself. • thank you for your comment. I’d like to see you build a transistor or a laser or a GPS system with your theory of the world. And meanwhile, what business is it of yours if I embarrass myself? Go run your own website. 3. The transistor was made with clever experimenting, based upon accidental discovery, and only after it was made and tested, it was also modeled mathematically, using the “in”, “fancy” theory of that time, the QM. That model is as good as Ptolemy-helicoids which described the movement of the heaven-bodies – it describes, but explains nothing. Does not enable any theoretical analysis on which one could rely in order to make modifications/improvements. The same was with the laser. And, concerning the GPS systems, the equations that I have derived, simply, accurately and comprehensibly, from their fundamental, elementary level physical origin, are the equations upon which the future GPS systems will be made, and the engineers will know completely and exactly why and what are they doing when they make them. The kids in high-school will soon, easily, and with understanding, derive the Newton’s principles, relativity equations, Newton’s gravitation law, … . And, as an electrotechnics engineer (electronics with telecommunications as the main course of study) and Computer Systems expert, I’ve significantly contributed in making the state-of-the-art thermo-optical DWDM TC devices (nxn SVTs, EDFA GTC, several versions of AWGs, several versions of ROADMs), through which, me and you exchange these messages today. I spent 4 years, 10-12h per day in the test&measurement lab, measuring, testing, evaluating, programming the lasers, power monitors, spectrum analysers, polarizers, robotic-measurement-stages, performing measurements, creating and automating the evaluation procedures,… And I can tell you, not even the q of quantum mechanics was used to develop them. Only experiments, and good old classical physics. Because, practically, QM is of no use. It is only for showing off, when presenting results in journals and on conferences. I won’t bother you any more, but, please, stop embarrassing yourself. It is not what a clever man should do. • Ravi Its not true that QM was used to explain the workings of the transistor only after it was made. There was this PBS documentary in the early 2000s which described, for example, how Bardeen worked out the effect of surface electron states on the resistance at the interfaces between the semiconductors. Besides, even to understand the propagation of electrons in simple metals, as well as the inertness of certain elements and insulators, one needs QM. In fact for a lot of macroscopic properties and phenomenon (magnetism, rigidity of solids, chemical reactivity of elements, etc) one needs to invoke some QM principles even at the qualitative level! 4. We agree on one thing: one of us is embarrassing himself. 5. miu miu 手帳 6. John Howard Thank you for your efforts … The comments, questions and your responses contain learning value. So, any comment (including this) which is not relevant or contains negative learning value should be deleted or placed in ‘lol’ category. lol! 7. Great content, thanks for sharing !! 8. In case you have just about any concerns regarding in which and how to use bracelets with beads ( you can e-mail us on the site. There are various sites on the Internet that showcase a huge number of designs with relevant pictures to bring you exactly what you are looking for. How can a bride incorporate their theme when choosing their wedding jewellery. You need to keep in mind your body structure in the process of selecting wedding jewellery. For women and men of the decade, silver earrings among other types of jewellery is very popular. way to clean and care for it. Now connect your alternator wire towards the regulating wiring harness. High amplifier alternators are often useful for EMS automobiles, commercial trucks, excavators, chilled trucks, industrial equipment, and mass transit automobiles. Quartz is very famous among many jewellery wearers. This unique feature of hallmarking the stones makes it easy to distinguish a real diamond from a fake one. 9. Pingback: Higgs Boson Mass \| Page 2 10. Pingback: Higgs Boson Mass \| Page 2	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5666799545288086, "perplexity": 1743.544119983361}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 5, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2015-48/segments/1448398468971.92/warc/CC-MAIN-20151124205428-00223-ip-10-71-132-137.ec2.internal.warc.gz"}
https://yazin.org/teleport/logs/mini-waypoint-attempt-4/	# Mini Waypoint Attempt 4 February 26, 2017 I took it out for a flight and it was stable in steady flight. Whenever it banked though, it would roll like crazy and then eventually settle down. I’d watched a video earlier on PID tuning and recognized the symptoms immediately. Still, I decided to let it fly in AUTO mode and see what happens. It flew really really far away, and then crashed on it’s way back. I was also surprised when I inspected the logs to find that it’d been overridden (I did some flying after the crash, and memory in the APM is circular and overrides previous logs when it runs out). • PID tuning, specifically adjusting the ‘P’ (Proportional) value for Roll down from 0.4 to 0.2. If it’s still too high, I’ll adjust accordingly.	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.4936400055885315, "perplexity": 2539.4248457356903}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-21/segments/1620243989006.71/warc/CC-MAIN-20210509153220-20210509183220-00095.warc.gz"}
http://etsf.polytechnique.fr/node/1635	# NIR dyes based on [M(R,R timdt)(2)] metal-dithiolenes: Additivity of M, R, and R contributions to tune the NIR absorption (M = Ni, Pd, Pt; R,R timdt = monoreduced form of disubstituted imidazolidine-2,4,5-trithione) Title NIR dyes based on [M(R,R timdt)(2)] metal-dithiolenes: Additivity of M, R, and R contributions to tune the NIR absorption (M = Ni, Pd, Pt; R,R timdt = monoreduced form of disubstituted imidazolidine-2,4,5-trithione) Publication Type Journal Article Year of Publication 2003 Aragoni, MC, Arca, M, Cassano, T, Denotti, C, Devillanova, FA, Frau, R, Isaia, F, Lelj, F, Lippolis, V, Nitti, L, Romaniello, P, Tommasi, R, Verani, G Journal EUROPEAN JOURNAL OF INORGANIC CHEMISTRY Issue 10 Pagination 1939-1947 Date Published MAY Keywords paper Abstract {With the aim of preparing new dyes for Q-switching and/or mode-locking Nd-based lasers, such as Nd:YLF and Nd:YAG (emission wavelengths 1053 and 1064 nm, respectively), the syntheses of about 30 new neutral dithiolenemetal complexes belonging to the class {[}M(R,R'timdt)(2)] have been carried out {[}M = Ni (4a-c; 4g-j), Pd (5a-j), Pt (6a-j); R,R'timdt = monoreduced form of disubstituted imidazolidine-2,4,5-trithione]. The examination of the effects induced on the intense NIR absorption by changing M, R, and R' has allowed for the recognition of the additive contributions (Deltalambda) of the central metal ion and of the substituents to the lambda(max)(M,R,R') max position of the NIR absorption maximum, which is in the region of 1000 nm. The high Deltalambda values due to aromatic substituents have been elucidated by means of Hybrid-DFT calculations performed on the model compound {[}Ni(H(2)timdt)(Ph,H-timdt)]. Both the k(max)(M,R,R') values and the molar extinction coefficients vary with the solvent. Complex 5f {[}M = Pd Full Text	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5098193287849426, "perplexity": 21140.713365585638}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-30/segments/1563195528687.63/warc/CC-MAIN-20190723022935-20190723044935-00326.warc.gz"}
http://math.stackexchange.com/users/108/jacob?tab=reputation	Jacob Reputation 338 Next privilege 500 Rep. Access review queues 1 5 12 Impact ~26k people reached • 0 posts edited # 338 Reputation 5 Apr 16 +5 17:49 upvote How many numbers between 1 and 1000 can be divided by both $a$ and $b$ 0 Mar 15 There were no net reputation changes on this day 10 Jan 29 +10 15:04 2 events Explanation of method for showing that 0 / 0 is undefined 10 Jan 12 5 Dec 18 '14 5 Nov 14 '14 5 Nov 3 '14 5 Aug 13 '14 5 Aug 12 '14 5 Aug 8 '14 10 Aug 5 '14 5 Jun 4 '14 5 May 13 '14 5 May 9 '14 5 Jan 28 '14 5 Nov 4 '13 5 Aug 30 '13 5 Aug 15 '13 5 Jun 19 '13 5 Sep 24 '11 5 Sep 23 '11 5 Sep 4 '11 5 Aug 11 '11 5 Jul 23 '11 5 Jun 27 '11 5 Jun 26 '11 5 May 15 '11 5 Mar 27 '11 5 Oct 30 '10 12 Oct 29 '10	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7019142508506775, "perplexity": 25600.72174156528}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2015-18/segments/1429246641054.14/warc/CC-MAIN-20150417045721-00044-ip-10-235-10-82.ec2.internal.warc.gz"}
http://brilliant.org/explorations/joy-problem-solving/operator-searches/b-premium/?element_id=clicked_locked_chapter_btn_from_explorations_topic_page	Back to all chapters # Operator Searches Solve problems in reverse using the rules of arithmetic! # A preview of "Operator Searches"Join Brilliant Premium Operator searches are puzzles for equations that can be solved with a mix of logic, creativity, and number theory. Of course $$8 + 8 + 8 + 8 = 32,$$ but what operators can you use to make the equation below true? $8 \ \ \ 8 \ \ \ 8 \ \ \ 8 \ \ \ 8 \ \ \ = \ \ \ 32$ Here are some of the solutions that we've come up with. Can you find any others? \begin{align} (8 + 8)\times (8 + 8) \div 8 &= 32 \\ (8\times8\times8) ÷ (8 + 8)&= 32 \\ 8- 8 \div 8 - 8 \div 8 &=3 \times 2 \end{align} Here is one last example to get your mind racing! Using any operators (and parentheses if needed), can you make this true? Get creative! $1\, \square\, 1\, \square\, 1\, \square\, 1\, = 5$ ×	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9997487664222717, "perplexity": 1429.8111863894603}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-26/segments/1498128323970.81/warc/CC-MAIN-20170629121355-20170629141355-00450.warc.gz"}
https://www.techwhiff.com/issue/which-of-the-following-sentences-is-punctuated-correctly--60580	Which of the following sentences is punctuated correctly? A. Doctors are concerned about the rising death rate from asthma, they are unsure of its cause. B. Doctors are concerned about the rising death rate, from asthma, they are unsure of its cause. C. Doctors are concerned about the rising death rate from asthma; they are unsure of its cause. D. Doctors are concerned about the rising death rate from asthma they are unsure of its cause. Question: Which of the following sentences is punctuated correctly? A. Doctors are concerned about the rising death rate from asthma, they are unsure of its cause. B. Doctors are concerned about the rising death rate, from asthma, they are unsure of its cause. C. Doctors are concerned about the rising death rate from asthma; they are unsure of its cause. D. Doctors are concerned about the rising death rate from asthma they are unsure of its cause. The dance crew, after performing for the crowd, wash the paint from their faces. Which subject-verb agreement rule applies to this sentence? use a singular verb with a singular subject use a plural verb with a plural subject use a plural verb with a collective subject functioning as individual parts use a singular verb with a collective subject functioning as a unit The dance crew, after performing for the crowd, wash the paint from their faces. Which subject-verb agreement rule applies to this sentence? use a singular verb with a singular subject use a plural verb with a plural subject use a plural verb with a collective subject functioning as individual parts... In order to achieve a win-win solution, all parties involved should negotiate a solution. True or False ? In order to achieve a win-win solution, all parties involved should negotiate a solution. True or False ?... Normalmente, Marta por la mañana se despierta a las siete, pero no puede levantarse hasta las siete y media. Se ducha y después se viste. Luego desayuna y se cepilla los dientes. Después, se peina y se maquilla. Entonces sale para sus clases. Después de las clases, almuerza con sus amigos y por la tarde estudia en la biblioteca. Regresa a casa, cena y ve un poco la televisión. Por la noche, generalmente se acuesta a las diez y por último, se duerme. almorzar ducharse peinarse ver la televisi Normalmente, Marta por la mañana se despierta a las siete, pero no puede levantarse hasta las siete y media. Se ducha y después se viste. Luego desayuna y se cepilla los dientes. Después, se peina y se maquilla. Entonces sale para sus clases. Después de las clases, almuerza con sus amigos y por ... Which of the following describes how farmers use GPS devices? -to produce insect-resistant plants -to locate their herds -to use chemicals more efficiently -to produce disease-resistant plants Which of the following describes how farmers use GPS devices? -to produce insect-resistant plants -to locate their herds -to use chemicals more efficiently -to produce disease-resistant plants... Distance: Jack and Jill start from the same point and walk in'opposite directions. Jack walks 2 kmh faster than Jill. After 3 hours they are 30 kilometers apart. How fast did each walk? Distance: Jack and Jill start from the same point and walk in'opposite directions. Jack walks 2 kmh faster than Jill. After 3 hours they are 30 kilometers apart. How fast did each walk?... Which modified box plot represents the data set? 10, 12, 2, 4, 24, 2, 7, 7, 9 Which modified box plot represents the data set? 10, 12, 2, 4, 24, 2, 7, 7, 9... Why was appeasement a foreign policy failure for Great Britain and France? O A. The United States was committed to drawing Germany into a military conflict. O B. The formation of the Tripartite Pact forced Germany to rapidly secure new lands. O C. German leaders could not be trusted to honor agreements with other countries. O D. The Soviet Union began to expand into territories Germany agreed to leave. SUBMIT Why was appeasement a foreign policy failure for Great Britain and France? O A. The United States was committed to drawing Germany into a military conflict. O B. The formation of the Tripartite Pact forced Germany to rapidly secure new lands. O C. German leaders could not be trusted to honor agreeme... 5. Granny Goodwitch boards a bus at the local shopping center. The bus travels an average speed of 30 miles/hour. It takes her bus 11.5 minutes to complete the trip to the bus terminal. Along the way the bus makes 13 stops at 30 seconds a stop. How far is the local shopping center from the bus terminal? 5. Granny Goodwitch boards a bus at the local shopping center. The bus travels an average speed of 30 miles/hour. It takes her bus 11.5 minutes to complete the trip to the bus terminal. Along the way the bus makes 13 stops at 30 seconds a stop. How far is the local shopping center from the bus termi... To mix a particular shade of purple paint, red paint and blue paint are mixed in the ratio 5:3. To make 20 gallons of this shade of purple paint, how many gallons of red and blue paint should be used? To mix a particular shade of purple paint, red paint and blue paint are mixed in the ratio 5:3. To make 20 gallons of this shade of purple paint, how many gallons of red and blue paint should be used?... Need help ASAP. 5. Beavers are sometimes trapped for their fur. What could be one effect of increased trapping of beavers in an area? a. Biodiversity among the area’s fish would increase. b. The number of herons and kingfishers would decrease. c. There would be more nesting areas for waterfowl. d. More trees would be cut down. Need help ASAP. 5. Beavers are sometimes trapped for their fur. What could be one effect of increased trapping of beavers in an area? a. Biodiversity among the area’s fish would increase. b. The number of herons and kingfishers would decrease. c. There would be more nesting areas for waterfowl. d.... In chapter 1 from Summer of the Mariposas. Odilia and her sisters encounter a dead body. How does each girl respond to finding the dead body? What aspect of her character does this reveal? In chapter 1 from Summer of the Mariposas. Odilia and her sisters encounter a dead body. How does each girl respond to finding the dead body? What aspect of her character does this reveal?... What is the lcm and gcm of 12:56 what is the lcm and gcm of 12:56... Which statement about reaction rates is true? (A)Changing the temperature cannot speed up a reaction rate. (B)Changing the amount of reactants will not change the reaction rate. (C)Changing the surface area affects the reaction rate. (D)A catalyst slows down the reaction rate. Which statement about reaction rates is true? (A)Changing the temperature cannot speed up a reaction rate. (B)Changing the amount of reactants will not change the reaction rate. (C)Changing the surface area affects the reaction rate. (D)A catalyst slows down the reaction rate.... P(A)= .50 P(B)=.80 P(A and B)=.20 what is P(B/A) P(A)= .50 P(B)=.80 P(A and B)=.20 what is P(B/A)... By S. E. Forman 1911 THE MATCH There never was a time when the world was without fire, but there was a time when men did not know how to kindle fire; and after they learned how to kindle one, it was a long, long time before they learned how to kindle one easily. In these days we can kindle a fire without any trouble, because we can easily get a match; but we must remember that the match is one of the most wonderful things in the world, and that it took men thousands of years to learn how to make By S. E. Forman 1911 THE MATCH There never was a time when the world was without fire, but there was a time when men did not know how to kindle fire; and after they learned how to kindle one, it was a long, long time before they learned how to kindle one easily. In these days we can kindle a fire wi... Solve 3(m+5)–6=3(m+3) AQR solve 3(m+5)–6=3(m+3) AQR... Solve the following inequality. \|3n-2\|-2<1 Solve the following inequality. \|3n-2\|-2<1...	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.16482171416282654, "perplexity": 5753.287283942668}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-06/segments/1674764500671.13/warc/CC-MAIN-20230208024856-20230208054856-00061.warc.gz"}
http://dlmcn.com/rat-root-th.htm	Your continued donations keep Wikipedia running! # Rational root theorem In algebra, the rational root theorem states a constraint on solutions (also called "roots") to the polynomial equation an xn + an−1 xn −1 + ... + a1 x + a0 = 0 with integer coefficients. Let an be nonzero. Then each rational solution x can be written in the form x = p/q for p and q satisfying two properties: • p is an integer factor of the constant term a0, and • q is an integer factor of the leading coefficient an. Thus, a list of possible rational roots of the equation can be derived using the formulae x = ± p/q. For example, every rational solution of the equation 3x3 − 5x2 + 5x − 2 = 0 must be among the numbers 1/3, −1/3, 2/3, −2/3, 1, −1, 2, −2. These root candidates can be tested using the Horner scheme. If a root r1 is found, the Horner scheme will also yield a polynomial of degree n − 1 whose roots, together with r1, are exactly the roots of the original polynomial. It may also be the case that none of the candidates is a solution; in this case the equation has no rational solution. The fundamental theorem of algebra states that any polynomial with integral (or real, or even complex) coefficients must have at least one root in the set of complex numbers. Any polynomial of odd degree (degree being n in the example above) with real coefficients must have a root in the set of real numbers. If the equation lacks a constant term a0, then 0 is one of the rational roots of the equation. The theorem is a special case (for a single linear factor) of Gauss's lemma on the factorization of polynomials.	{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.971195638179779, "perplexity": 340.7562368922775}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-05/segments/1516084892238.78/warc/CC-MAIN-20180123191341-20180123211341-00429.warc.gz"}
http://chimera.labs.oreilly.com/books/1234000001552/ch04.html	Chapter 4. Pitch and the Frequency Domain So far we have learned about some basic properties of sound: timing and volume. To do more complex things, such as sound equalization (e.g., increasing the bass and decreasing the treble), we need more complex tools. This section explains some of the tools that allow you to do these more interesting transformations, which include the ability to simulate different sorts of environments and manipulate sounds directly with JavaScript. Pitch and playbackRate The Web Audio API provides a playbackRate parameter on each AudioSourceNode. This value can be set to affect the pitch of any sound buffer. Note that the pitch as well as the duration of the sample will be affected in this case. There are sophisticated methods that try to affect pitch independent of duration, but this is quite difficult to do in a general-purpose way without introducing blips, scratches, and other undesirable artifacts to the mix. As discussed in “Basics of Musical Pitch”, to compute the frequencies of successive semitones, we simply multiply the frequency by the semitone ratio 21/12. This is very useful if you are developing a musical instrument or using pitch for randomization in a game setting. The following code plays a tone at a given frequency offset in semitones: function playNote(semitones) { // Assume a new source was created from a buffer. var semitoneRatio = Math.pow(2, 1/12); source.playbackRate.value = Math.pow(semitoneRatio, semitones); source.start(0); } As we discussed earlier, our ears perceive pitch exponentially. Treating pitch as an exponential quantity can be inconvenient, since we often deal with awkward values such as the twelfth root of two. Instead of doing that, we can use the detune parameter to specify our offset in cents. Thus you can rewrite the above function using detune in an easier way: function playNote(semitones) { // Assume a new source was created from a buffer. source.detune.value = semitones * 100; source.start(0); } If you pitch shift by too many semitones (e.g., by calling playNote(24);), you will start to hear distortions. Because of this, digital pianos include multiple samples for each instrument. Good digital pianos avoid pitch bending at all, and include a separate sample recorded specifically for each key. Great digital pianos often include multiple samples for each key, which are played back depending on the velocity of the key press. Multiple Sounds with Variations A key feature of sound effects in games is that there can be many of them simultaneously. Imagine you’re in the middle of a gunfight with multiple actors shooting machine guns. Each machine gun fires many times per second, causing tens of sound effects to be played at the same time. Playing back sound from multiple, precisely-timed sources simultaneously is one place the Web Audio API really shines. Now, if all of the machine guns in your game sounded exactly the same, that would be pretty boring. Of course the sound would vary based on distance from the target and relative position [more on this later in “Spatialized Sound”], but even that might not be enough. Luckily the Web Audio API provides a way to easily tweak the previous example in at least two simple ways: 1. With a subtle shift in time between bullets firing 2. By changing pitch to better simulate the randomness of the real world Using our knowledge of timing and pitch, implementing these two effects is pretty straightforward: function shootRound(numberOfRounds, timeBetweenRounds) { var time = context.currentTime; // Make multiple sources using the same buffer and play in quick succession. for (var i = 0; i < numberOfRounds; i++) { var source = this.makeSource(bulletBuffer); source.playbackRate.value = 1 + Math.random() * RANDOM_PLAYBACK; source.start(time + i * timeBetweenRounds + Math.random() * RANDOM_VOLUME); } } The Web Audio API automatically merges multiple sounds playing at once, essentially just adding the waveforms together. This can cause problems such as clipping, which we discuss in “Clipping and Metering”. This example adds some variety to AudioBuffers loaded from sound files. In some cases, it is desirable to have fully synthesized sound effects and no buffers at all [see “Procedurally Generated Sound”]. Oscillator-Based Direct Sound Synthesis As we discussed early in this book, digital sound in the Web Audio API is represented as an array of floats in AudioBuffers. Most of the time, the buffer is created by loading a sound file, or on the fly from some sound stream. In some cases, we might want to synthesize our own sounds. We can do this by creating audio buffers programmatically using JavaScript, which simply evaluate a mathematical function at regular periods and assign values to an array. By taking this approach, we can manually change the amplitude and frequency of our sine wave, or even concatenate multiple sine waves together to create arbitrary sounds [recall the principles of fourier transformations from “Understanding the Frequency Domain”]. Though possible, doing this work in JavaScript is inefficient and complex. Instead, the Web Audio API provides primitives that let you do this with oscillators: OscillatorNode. These nodes have configurable frequency and detune [see the “Basics of Musical Pitch”]. They also have a type that represents the kind of wave to generate. Built-in types include the sine, triangle, sawtooth, and square waves, as shown in Figure 4-4. Oscillators can easily be used in audio graphs in place of AudioBufferSourceNodes. An example of this follows: function play(semitone) { // Create some sweet sweet nodes. var oscillator = context.createOscillator(); oscillator.connect(context.destination); // Play a sine type curve at A4 frequency (440hz). oscillator.frequency.value = 440; oscillator.detune.value = semitone * 100; // Note: this constant will be replaced with "sine". oscillator.type = oscillator.SINE; oscillator.start(0); } In addition to these basic wave types, you can create a custom wave table for your oscillator by using harmonic tables. This lets you efficiently create wave shapes that are much more complex than the previous ones. This topic is very important for musical synthesis applications, but is outside of the scope of this book.	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 4, "x-ck12": 0, "texerror": 0, "math_score": 0.2410825788974762, "perplexity": 1740.458642132963}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 5, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-13/segments/1490218186608.9/warc/CC-MAIN-20170322212946-00129-ip-10-233-31-227.ec2.internal.warc.gz"}
http://www.msri.org/web/msri/scientific/colloquia-seminars	Mathematical Sciences Research Institute Home > Scientific > Colloquia & Seminars 1. Joint NSF Webinar - mandatory for US-based Postdocs Location: MSRI: Baker Board Room Updated on Sep 22, 2016 03:03 PM PDT 2. Working Seminar: Ozawa's proof of Gromov's polynomial growth theorem Location: MSRI: Simons Auditorium Created on Sep 22, 2016 10:09 AM PDT 3. Working Seminar: Projection complexes, rotating families, and beyond Location: MSRI: Baker Board Room Created on Sep 13, 2016 10:03 AM PDT 4. Local rigidity of uniform lattices Location: MSRI: Simons Auditorium Speakers: Arie Levit (Weizmann Institute of Science) A lattice is topologically locally rigid (t.l.r) if small deformations of it are isomorphic lattices. Uniform lattices in Lie groups were shown to be t.l.r by Weil [60']. We show that uniform lattices are t.l.r in any compactly generated topological group G. A lattice is locally rigid (l.r) is small deformations arise from conjugation. It is a classical fact due to Weil [62'] that lattices in semi-simple Lie groups are l.r. Relying on our t.l.r results and on recent work by Caprace-Monod we prove l.r for uniform lattices in the isometry groups of proper geodesically complete CAT(0) spaces, with the exception of SL2(R) factors which occurs already in the classical case. Moreover we are able to extend certain finiteness results due to Wang to this more general context of CAT(0) groups. In the talk I will explain the above notions and results, and present some ideas from the proofs. This is a joint work with Tsachik Geladner. Created on Sep 23, 2016 10:44 AM PDT 1. Working Seminar: Ozawa's proof of Gromov's polynomial growth theorem Created on Sep 22, 2016 10:10 AM PDT 2. Working Seminar: Projection complexes, rotating families, and beyond Location: MSRI: Baker Board Room Created on Sep 13, 2016 10:04 AM PDT 3. Member Seminar: Automorphisms of RAAGs: vast or skimpy? Location: MSRI: Simons Auditorium Speakers: Vincent Guirardel (Institut de Recherche Mathematique (IRMAR)) Say that a group G involves all finite groups if for every finite group F, some finite index subgroup of G maps onto F. For instance, for n>2, SL_n(Z) does not involve all finite groups, whereas Out(F_n) does for n>1. The family of groups Out(A) of outer automorphisms of right angled Artin groups "interpolates" between SL_n(Z) and Out(F_n), and the goal of this talk is to describe the boundary between these 2 behaviours, within this family of groups. We also study other "vastness" properties like SQ-universality, of having many quasimorphisms, and we prove that the boundary happens to be the same. This is a joint work with Andrew Sale. Updated on Sep 14, 2016 10:13 AM PDT 4. Working Seminar: Median Spaces Location: MSRI: Simons Auditorium Created on Sep 13, 2016 09:55 AM PDT 5. Working Seminar: Counting problems in groups and spaces, and random walks Location: MSRI: Simons Auditorium Created on Sep 13, 2016 09:39 AM PDT 6. Common Lunch Location: MSRI: Commons Room Created on Aug 25, 2016 01:46 PM PDT Location: MSRI: Baker Board Room Created on Aug 25, 2016 02:07 PM PDT 8. Working Seminar: Out(Fn) - complexes Location: MSRI: Simons Auditorium Created on Sep 13, 2016 09:48 AM PDT 9. Postdoc Seminar I Location: MSRI: Simons Auditorium Updated on Aug 26, 2016 09:23 AM PDT 10. Postdoc Seminar II Location: MSRI: Simons Auditorium Created on Aug 26, 2016 09:30 AM PDT 11. Working Seminar: Projection complexes, rotating families, and beyond Location: MSRI: Baker Board Room Created on Sep 13, 2016 10:09 AM PDT 12. Member Seminar: Discontinuous Motions of limit sets Location: MSRI: Simons Auditorium Speakers: Mahan Mj (Tata Institute of Fundamental Research) It is well known, thanks to work of Mane-Sad-Sullivan that for a parametrized family of quasifuchsian groups (or equivalently convex cocompact discrete surface subgroups of PSl(2,C)) the limit set moves holomorphically on the Riemann sphere. We shall discuss what happens when a sequence of such groups converges to a non-quasifuchsian group. A discontinuity phenomenon was discovered in joint work with Caroline Series. In further work with Ken'ichi Ohshika, we characterize when precisely these discontinuities arise. Updated on Sep 20, 2016 03:59 PM PDT 13. Working Seminar: Median Spaces Location: MSRI: Simons Auditorium Created on Sep 13, 2016 09:56 AM PDT 14. Working Seminar: Counting problems in groups and spaces, and random walks Location: MSRI: Simons Auditorium Created on Sep 13, 2016 09:40 AM PDT 15. Common Lunch Location: MSRI: Commons Room Created on Aug 25, 2016 01:47 PM PDT Location: MSRI: Baker Board Room Created on Aug 25, 2016 02:07 PM PDT 17. Working Seminar: Out(Fn) - complexes Location: MSRI: Simons Auditorium Created on Sep 13, 2016 09:48 AM PDT 18. Postdoc Seminar I Location: MSRI: Simons Auditorium Created on Aug 26, 2016 09:24 AM PDT 19. Postdoc Seminar II Location: MSRI: Simons Auditorium Created on Aug 26, 2016 09:31 AM PDT 20. Working Seminar: Projection complexes, rotating families, and beyond Location: MSRI: Baker Board Room Created on Sep 13, 2016 10:10 AM PDT 21. Member Seminar: Cannon-Thurston maps for hyperbolic free group extensions Location: MSRI: Simons Auditorium Speakers: Ilya Kapovich (University of Illinois at Urbana-Champaign) Let $F_N$ be a free group of finite rank $N\ge 3$ and let $\Gamma\le Out(F_N)$ be a finitely generated "convex cocompact" subgroup, that is, such that the orbit map from $\Gamma$ to the free factor complex of $F_N$ is a quasi-isometric embedding. Assume also that $\Gamma$ is purely atoroidal. In this case $\Gamma$ determines an extension group $E_\Gamma$ of $\Gamma$ with the quotient $E_\Gamma/F_N=\Gamma$, and it is known by a result of Dowdall and Taylor that the group $E_\Gamma$ is then word-hyperbolic. By a general result of Mitra the inclusion of $F_N$ in $E_\Gamma$ extends to a continuous surjective $F_N$-equivariant map between their hyperbolic boundaries $j: \partial F_N\to \partial E_\Gamma$, called the Cannon-Thurston map. We analyze the structure of this map and prove that the map is finite-to-one, with multiplicity at most $2N$. The talk is based on a joint paper with Spencer Dowdall and Sam Taylor. Updated on Sep 20, 2016 03:53 PM PDT 22. Working Seminar: Median Spaces Location: MSRI: Simons Auditorium Created on Sep 13, 2016 09:57 AM PDT 23. Working Seminar: Counting problems in groups and spaces, and random walks Location: MSRI: Simons Auditorium Created on Sep 13, 2016 09:40 AM PDT 24. Common Lunch Location: MSRI: Commons Room Created on Aug 25, 2016 01:48 PM PDT Location: MSRI: Baker Board Room Created on Aug 25, 2016 02:09 PM PDT 26. Working Seminar: Out(Fn) - complexes Location: MSRI: Simons Auditorium Created on Sep 13, 2016 09:54 AM PDT 27. Postdoc Seminar I Location: MSRI: Simons Auditorium Created on Aug 26, 2016 09:24 AM PDT 28. Postdoc Seminar II Location: MSRI: Simons Auditorium Created on Aug 26, 2016 09:31 AM PDT 29. Working Seminar: Projection complexes, rotating families, and beyond Location: MSRI: Baker Board Room Created on Sep 13, 2016 10:11 AM PDT 30. Working Seminar: Projection complexes, rotating families, and beyond Location: MSRI: Baker Board Room Created on Sep 13, 2016 10:11 AM PDT 31. Member Seminar Location: MSRI: Simons Auditorium Created on Aug 25, 2016 01:59 PM PDT 32. Working Seminar: Counting problems in groups and spaces, and random walks Location: MSRI: Simons Auditorium Updated on Sep 13, 2016 09:41 AM PDT 33. Common Lunch Location: MSRI: Commons Room Created on Aug 25, 2016 01:49 PM PDT Location: MSRI: Commons Room Created on Sep 13, 2016 09:50 AM PDT Location: MSRI: Baker Board Room Created on Aug 25, 2016 02:10 PM PDT 36. Postdoc Seminar I Location: MSRI: Simons Auditorium Updated on Aug 26, 2016 09:25 AM PDT 37. Postdoc Seminar II Location: MSRI: Simons Auditorium Created on Aug 26, 2016 09:32 AM PDT 38. Working Seminar: Projection complexes, rotating families, and beyond Location: MSRI: Baker Board Room Created on Sep 13, 2016 10:12 AM PDT 39. Member Seminar Location: MSRI: Simons Auditorium Created on Aug 25, 2016 01:59 PM PDT 40. Working Seminar: Counting problems in groups and spaces, and random walks Location: MSRI: Simons Auditorium Created on Sep 13, 2016 09:42 AM PDT 41. Common Lunch Location: MSRI: Commons Room Created on Aug 25, 2016 01:50 PM PDT Location: MSRI: Baker Board Room Created on Aug 25, 2016 02:11 PM PDT 43. Postdoc Seminar I Location: MSRI: Simons Auditorium Created on Aug 26, 2016 09:26 AM PDT 44. Postdoc Seminar II Location: MSRI: Simons Auditorium Created on Aug 26, 2016 09:32 AM PDT 45. Working Seminar: Projection complexes, rotating families, and beyond Location: MSRI: Baker Board Room Created on Sep 13, 2016 10:13 AM PDT 46. Member Seminar Location: MSRI: Simons Auditorium Created on Aug 25, 2016 02:00 PM PDT 47. Working Seminar: Counting problems in groups and spaces, and random walks Location: MSRI: Simons Auditorium Created on Sep 13, 2016 09:43 AM PDT 48. Common Lunch Location: MSRI: Commons Room Created on Aug 25, 2016 01:50 PM PDT Location: MSRI: Baker Board Room Updated on Sep 16, 2016 12:18 PM PDT 50. Postdoc Seminar I Location: MSRI: Simons Auditorium Created on Aug 26, 2016 09:34 AM PDT 51. Postdoc Seminar II Location: MSRI: Simons Auditorium Created on Aug 26, 2016 09:33 AM PDT 52. Working Seminar: Projection complexes, rotating families, and beyond Location: MSRI: Baker Board Room Created on Sep 13, 2016 10:14 AM PDT 53. Member Seminar Location: MSRI: Simons Auditorium Created on Aug 25, 2016 02:01 PM PDT 54. Working Seminar: Counting problems in groups and spaces, and random walks Location: MSRI: Simons Auditorium Created on Sep 13, 2016 09:43 AM PDT 55. Common Lunch Location: MSRI: Commons Room Created on Aug 25, 2016 01:52 PM PDT 56. Working Seminar: Projection complexes, rotating families, and beyond Location: MSRI: Baker Board Room Created on Sep 13, 2016 10:15 AM PDT 57. Member Seminar Location: MSRI: Simons Auditorium Created on Aug 25, 2016 02:01 PM PDT 58. Working Seminar: Counting problems in groups and spaces, and random walks Location: MSRI: Simons Auditorium Created on Sep 13, 2016 09:44 AM PDT 59. Common Lunch Location: MSRI: Commons Room Created on Aug 25, 2016 01:53 PM PDT Location: MSRI: Baker Board Room Created on Aug 25, 2016 02:12 PM PDT 61. Postdoc Seminar I Location: MSRI: Simons Auditorium Created on Aug 26, 2016 09:26 AM PDT 62. Postdoc Seminar II Location: MSRI: Simons Auditorium Created on Aug 26, 2016 09:34 AM PDT seminar 1. SeminarPostdoc Seminar II: Job talk: from the torus up Updated on Sep 15, 2016 01:18 PM PDT 2. SeminarPostdoc Seminar I: What is an L^2-Betti number? Updated on Sep 15, 2016 01:18 PM PDT 3. SeminarWorking Seminar: Out(Fn) - complexes Created on Sep 13, 2016 09:47 AM PDT 4. SeminarGraduate Student Seminar: Special cube complexes Updated on Sep 19, 2016 09:03 AM PDT 5. SeminarTopology Seminar: Thurston norm via Fox Calculus Created on Sep 16, 2016 01:51 PM PDT 6. SeminarTopology Seminar: Thurston norm via Fox Calculus Created on Sep 16, 2016 01:52 PM PDT 7. SeminarWorking seminar: Median spaces: Non-embedding into L^1 warm-up Updated on Sep 16, 2016 12:11 PM PDT 8. SeminarCommon Lunch Created on Aug 25, 2016 01:44 PM PDT 9. SeminarWorking Seminar: Counting problems in groups and spaces, and random walks Created on Sep 08, 2016 11:33 AM PDT 10. SeminarJob Market Panel Created on Sep 16, 2016 11:22 AM PDT 11. SeminarWorking Seminar: Median Spaces Updated on Sep 15, 2016 02:08 PM PDT 12. SeminarMember Seminar: Counting lattice points with respect to the Lipschitz metric Updated on Sep 13, 2016 09:50 AM PDT 13. SeminarWorking Seminar: Projection complexes, rotating families, and beyond Created on Sep 13, 2016 10:02 AM PDT 14. SeminarPostdoc Seminar II: Homology of finite covers of graphs and surfaces Updated on Sep 09, 2016 01:22 PM PDT 15. SeminarPostdoc Seminar I: The best of Simplicial Volume Updated on Sep 09, 2016 01:21 PM PDT 16. SeminarBerkeley Math Dept. Colloquium: Geometry and Analysis on Nilpotent Lie Groups Created on Sep 13, 2016 09:20 AM PDT 17. SeminarWorking Seminar: Out(Fn) - complexes Created on Sep 09, 2016 08:37 AM PDT 18. SeminarGraduate Student Seminar: asymptotic cones Updated on Sep 13, 2016 09:29 AM PDT 19. SeminarCommon Lunch Created on Aug 25, 2016 01:41 PM PDT 20. SeminarWorking Seminar: Counting problems in groups and spaces, and random walks Created on Sep 08, 2016 11:32 AM PDT 21. SeminarWorking Seminar: Median Spaces Created on Sep 07, 2016 11:09 AM PDT 22. SeminarMember Seminar: Filling inequalities for lattices in symmetric spaces Updated on Sep 01, 2016 08:49 AM PDT 23. SeminarDelone sets in non-abelian groups: Substitutive tilings of the hyperbolic plane Updated on Sep 09, 2016 08:35 AM PDT 24. SeminarWorking Seminar: Projection complexes, rotating families, and beyond Created on Aug 31, 2016 02:36 PM PDT 25. SeminarDelone sets in non-abelian groups: Bilipschitz equivalence of Delone sets in certain Lie groups Updated on Sep 09, 2016 08:34 AM PDT 26. SeminarDelone sets in non-abelian groups: What is "approximate geometric group theory”? Updated on Sep 09, 2016 08:34 AM PDT 27. SeminarPostdoc Seminar II: Connecting Measurable and Geometric Group Theory Updated on Sep 02, 2016 02:10 PM PDT 28. SeminarPostdoc Seminar I: What is a simple closed curve in a free group?: Curve graph analogues for free group automorphisms. Updated on Sep 02, 2016 02:10 PM PDT 29. SeminarWorking Seminar: Out(Fn) - complexes Updated on Sep 01, 2016 01:30 PM PDT	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.36903896927833557, "perplexity": 14003.795871716502}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2016-40/segments/1474738660887.60/warc/CC-MAIN-20160924173740-00174-ip-10-143-35-109.ec2.internal.warc.gz"}
http://beltoforion.de/article.php?a=magnetic_pendulum	The Magnetic Pendulum Demonstrating the butterfly effect with a magnetic pendulum Introducing the Magnetic Pendulum This article is based on an article named "Experimente zum Chaos" (translated.: "Experiments on Chaos") [1] from the the German magazine Specktrum der Wissenschaft (German version of the Scientific American magazine). The article dates back to 1994, and introduces among other things a simulation showing the chaotic motion of a pendulum under the influence of gravity and three magnets. For some reason, this simulation fascinated me and so I wrote a program implementing it. This article will describe the program and the science behind simulating the magnetic pendulum. The simulation is based on computing the motion of a metallic pendulum under the influence of three magnets. A color image is obtained by integrating the equations of motion for all possible starting points in a two dimensional grid and coloring the starting point with the color of the magnet over which the pendulum came to a rest. Since this involves lengthy integration of the pendulum trail it may take some time to complete the calculation. A few hours is not unusual for a typical image in HD size (1980 x 1080 pixels). On a modern GPU such a task could be done in real time but this simulation does not make use of this technology. • An interest in chaos theory. • For understanding the code i recommend a basic understanding of C++ and MFC. • Hardware OpenGL support is required for the rendering. What you get: • A software for creating pretty high resolution images • Configure models with any number of magnets using INI files • You can abort and continue calculations and make use of multiple processors for speeding up the computations. The Butterfly Effect The simulation is a good example for the so called butterfly effect. For those of you that are unfamiliar with that phrase, here is the brief explanation taken directly from Wikipedia [1]: So how does this all apply to the magnets and pendulum simulation? We will come to that later. We will examine the equations of motion, the integration algorithms and the software itself. But before we do I will show you something even better: A video explaining it indepth. The following video was created by Aldo Cavini Benedetti who did a great job in explaining what the magnets and pendulum simulation is all about. If you watch to the end you will will see that it's actually so simple that even cats understand it: Simulation overview By now you should have an idea where we are heading. The next sections describe a numerical model that demonstrates how small changes in the initial conditions of the simulation can result in large variations of the results. The result is an unpredictability of the simulation result since even the smallest change in the environment might effect the outcome dramatically. Let's start with the details. The classical model assumes having a magnetic pendulum which is attracted by three magnets with each magnet having a distinct color. The magnets are located underneath the pendulum on a circle centered at the pendulum mount-point. They are strong enough to attract the pendulum in a way that it will not come to rest in the center position. The following picture illustrates the model when watched from above. Colored circles symbolize magnets, the cross in the middle the pendulum mount point. The simulation will calculate the route taken by the pendulum under the influence of all three sources plus gravity and friction. Due to energy loss caused by friction, the pendulum will earlier or later stop over one of the magnets. The starting point is then colored with the color of this very same magnet. Doing this for all pixels will result in a pretty map showing a pattern composed of red, green, and blue pixels. The results are shown in the images 1 and 3. The white spot in the middle of image 3 is caused by the pendulum coming to rest in the middle. This is due to the parameters used in this example. Since I'm not a big fan of low color images, adding more color seemed to be necessary. The only information available for each pixel is the color of the magnet, right? And, if you search the internet, you will quickly find that most codes implementing this simulation stop here, but a little more code can greatly improve the results. Remember, for each pixel, we are calculating the whole trace of the pendulum. So it may be a good idea to translate some of the information from the trace into color information. The most obvious is of course the length of the trace. So using the trace length for determining the pixel brightness seems a logical step. (OK, I admit this is not my idea since it was already done in the original version published in Scientific American.) Doing this can be done by using color scaling functions, taking both trace length and maximum trace length as the parameters. The scaling is applied to the source color. In general, the application can use any function, but according to my experience, the following three are useful: As you can see, the result is quite interesting. At least if you have an interest in chaos theory. (If not I wonder why you are still reading.) Starting points resulting in longer traces are shown in darker colors, adding additional complexity to the image. The application allows you to define custom formulas for the color scaling since they will be interpreted using a math expression parser. Simplifications The pendulum is a simplified 2D version, assuming the force pulling it back to the centre is following Hookes law (proportional to the distance). This is a simplification, sparing me the effort of calculating rotation angles, cross products, and the whole stuff I would need otherwise. If you won't tell anyone, I could tell you that implementing it physically correct would not be that much additional work, and in fact, I once made a version doing this. But don't forget, my primary objective was getting a picture for my wall, and the physically correct version would have to be mapped to a sphere not a plane. Since I can't hang a sphere on my wall, I'll stick to the 2D version. Of course, the 2D version is valid for small elongations only. Magnets are assumed to cause a force proportional to the inverse square of the pendulum distance. In principle, this is akin to the Law of gravity or Coloumbs law. All those laws are very similar, but of course, here we are dealing with (hypothetic) magnetic monopoles, not masses or charges. That assumption is in line with what everyone does when it comes to the pendulum and magnets simulation. In reality, Magnets are dipoles. A dipole causes forces proportional to 1/r³ rather than 1/r². The force calculation does not take this into account although simulating a dipole by two monopole sources would be an option too. The Pendulum is assumed to be made up of iron neglecting eddy currents that would be induced in reality. Equations of motion The pendulum movement is calculated by integrating twice over the accelerations acting on the pendulum. Normally, one would not talk about accelerations but forces. According to Newton's second law of motion, the force necessary to move a body equals mass times acceleration. We solve that equation for the acceleration: $$\nonumber\vec{F} = m \vec{a}$$ $$\nonumber\vec{a} = {\vec{F} \over m}$$ Since our initial conditions provide a starting position and a starting velocity (assumed to be null), all we need is to calculate accelerations. For simplicity, mass is assumed to equal one mass unit. Talking about units, I should mention that the simulation in general does not care much about physical units. This is no problem since using real units would just impose scaling factors on the parameters. The following equations list all accelerations relevant for the simulation: Acceleration caused by the pullback of the pendulum: $$\nonumber\vec{a}_g = k_g \cdot \vec{r}$$ Accelleration caused by a single magnet: $$\nonumber\vec{a}_m = k_m \cdot \frac{\vec{r}}{\|\vec{r}\|^3}$$ Decelleration caused by friction: $$\nonumber \vec{a}_f = -k_f \cdot \vec{v}$$ Total acceleration of the pendulum: $$\nonumber \vec{a}_t = \vec{a}_g + \Big( \sum_{m=1}^3{\vec{a}_m} \Big) - \vec{a}_f$$ wobei: • $$\vec{a}_t$$ - Total acceleration of the pendulum • $$\vec{a}_g$$ - Acceleration caused by the pullback of the pendulum • $$\vec{a}_m$$ - Accelleration caused by the magnet m • $$\vec{a}_f$$ - Decelleration caused by friction • $$k_f$$ - Coefficient of friction • $$k_g$$ - Strength of the pendulum pullback • $$k_m$$ - Strength of the the magnet • $$\vec{r}$$ - Position vector of the pendulum Integration of the Pendulum trace Given an initial pendulum position and an initial pendulum velocity, all that is left to do is find a suitable integration scheme and follow the pendulum's trail. For this simulation, the Beeman integration algorithm was used. Applying this scheme does not require much code, and it is pretty accurate. Putting the algorithm into pseudo code looks like this: while tracing pendulum position += Velocity acceleration = 0 for all force sources acceleration += acceleration_caused_by_source if (pendulum is close to source and velocity is small) then stop_magnet = source_index break end if end for acceleration -= acceleration_caused_by_friction velocity += acceleration trace_length += length(velocity) store stop_magnet store trace_length end while Implementing the code for tracing the route taken by the pendulum into C++ looks like: for (int ct=0; ct<m_nMaxSteps && bRunning; ++ct) { // compute new position pos[0] += vel[0]dt + sqr(dt) (2.0/3.0 * (acc)[0] - 1.0 / 6.0 (acc_p)[0]); pos[1] += vel[1]dt + sqr(dt) * (2.0/3.0 * (acc)[1] - 1.0 / 6.0 (acc_p)[1]); (acc_n) = 0.0; // reset accelleration // Calculate Force, we deal with Forces proportional // to the distance or the inverse square of the distance for (std::size_t i=0; i<src_num; ++i) { const Source &src( m_vSources[i] ); r = pos - src.pos; if (src.type==Source::EType::tpLIN) { //--------------------------------------- // Hooke's law: _ // _ r _ // m * a = - k * \|r\| * --- = -k * r // \|r\| // (acc_n)[0] -= src.mult r[0]; (acc_n)[1] -= src.mult r[1]; } else { //--------------------------------------- // Magnet Forces: _ // _ r // m * a = k * ----- // \|r³\| // double dist( sqrt( sqr(src.pos[0] - pos[0]) + sqr(src.pos[1] - pos[1]) + sqr(m_fHeight) ) ); (acc_n)[0] -= (src.mult / (distdistdist)) r[0]; (acc_n)[1] -= (src.mult / (distdistdist)) r[1]; } // Check abort condition if (ct>m_nMinSteps && abs(r)<src.size && abs(vel)<m_fAbortVel) { bRunning = false; stop_mag = (int)i; break; } } // for all sources //-------------------------------------------------------------- // 3.) Friction proportional to velocity (acc_n)[0] -= vel[0] m_fFriction; (acc_n)[1] -= vel[1] m_fFriction; //-------------------------------------------------------------- // 4.) Beeman integration for velocities vel[0] += dt * ( 1.0/3.0 * (acc_n)[0] + 5.0/6.0 (acc)[0] - 1.0/6.0 (acc_p)[0] ); vel[1] += dt ( 1.0/3.0 * (acc_n)[1] + 5.0/6.0 (acc)[1] - 1.0/6.0 (*acc_p)[1] ); //-------------------------------------------------------------- // 5.) flip the acc buffer tmp = acc_p; acc_p = acc; acc = acc_n; acc_n = tmp; } You might also like:	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 6, "x-ck12": 0, "texerror": 0, "math_score": 0.6911516189575195, "perplexity": 1023.5562610912385}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-09/segments/1487501170823.55/warc/CC-MAIN-20170219104610-00360-ip-10-171-10-108.ec2.internal.warc.gz"}
https://www.semanticscholar.org/author/J.-Wei/145172108	• Publications • Influence Ground State of N Coupled Nonlinear Schrödinger Equations in Rn,n≤3 • Mathematics • 2 March 2005 We establish some general theorems for the existence and nonexistence of ground state solutions of steady-state N coupled nonlinear Schrödinger equations. The sign of coupling constants βij’s isExpand • 351 • 17 • PDF On a two-dimensional elliptic problem with large exponent in nonlinearity • Mathematics • 1 February 1994 A semilinear elliptic equation on a bounded domain in R2 with large exponent in the nonlinear term is studied in this paper. We investigate positive solutions obtained by the variational method. ItExpand • 112 • 15 • PDF Spikes in two coupled nonlinear Schrödinger equations • Mathematics • 1 July 2005 Here we study the interaction and the configuration of spikes in a double condensate by analyzing least energy solutions of two coupled nonlinear Schrodinger equations which model Bose–EinsteinExpand • 169 • 14 • PDF The stability of spike solutions to the one-dimensional Gierer—Meinhardt model • Mathematics • 15 March 2001 Abstract The stability properties of an N-spike equilibrium solution to a simplified form of the Gierer–Meinhardt activator–inhibitor model in a one-dimensional domain is studied asymptotically inExpand • 204 • 13 On Single Interior Spike Solutions Of Gierer-Meinhardt System: Uniqueness And Spectrum Estimates • J. Wei • Mathematics • 1 August 1999 We study the interior spike solutions to a steady state problem of the shadow system of the Gierer–Meinhardt system arising from biological pattern formation. We first show that at a non-degenerateExpand • 156 • 12 • PDF Asymptotic behavior of a nonlinear fourth order eigenvalue problem • J. Wei • Mathematics • 31 December 1996 Our purpose in this paper is to study the asymptotic behavior of the nonlinear eigenvalue problem, where {Omega} is a smooth bounded domain in R{sup 4}, {line_integral}(u) is an nonnegative smoothExpand • 60 • 11 Self-similar solutions for the anisotropic affine curve shortening problem • Mathematics • 1 November 2001 Abstract. Similarity between the roles of the group $SL(2,\bf R)$ on the equation for self-similar solutions of the anisotropic affine curve shortening problem and of the conformal group of $S^2$ onExpand • 53 • 10 Concentration on curves for nonlinear Schrödinger Equations • Mathematics • 2007 We consider the problem where p > 1, e > 0 is a small parameter, and V is a uniformly positive, smooth potential. Let Γ be a closed curve, nondegenerate geodesic relative to theExpand • 148 • 10 • PDF Convergence for a Liouville equation • Mathematics • 30 September 2001 Abstract. In this paper, we study the asymptotic behavior of solutions of the Dirichlet problem for the Liouville equation ¶¶ $-\Delta u= \lambda {{K(x)e^u} \over {\int_{\Omega}K(x)e^u}}$¶¶on aExpand • 105 • 10 Spikes in Two-component Systems of Nonlinear Schrodinger Equations with Trapping Potentials • Physics • 15 October 2006 Abstract Recently, two-component systems of nonlinear Schrodinger equations with trap potentials have been well-known to describe a binary mixture of Bose–Einstein condensates called a doubleExpand • 96 • 9	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8549379110336304, "perplexity": 2536.2007440307257}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-10/segments/1614178381989.92/warc/CC-MAIN-20210308052217-20210308082217-00006.warc.gz"}
https://link.springer.com/article/10.1007/s10040-016-1391-1	## Introduction Worldwide, many deltas are sinking due to reduced aggradation and compaction and soil loss resulting from fluid withdrawal, drainage, and oxidation of organic matter (Syvitski et al. 2009). Drainage of organic soils has resulted in soil subsidence due to changes in physical conditions and enhanced rates of microbial decomposition (Hirano et al. 2012; Rojstaczer and Deverel 1993; Stephens et al. 1984). In total, 14–20 % of the world’s organic soils or peatlands are currently drained for agriculture or forestry (Strack 2008). Organic soils or histosols are defined by the Food and Agriculture Organization as having 40 cm or more of organic materials with an organic carbon content of 12–18 % or more. The terms organic soil and peat are often used interchangeably and generally refer to a soil which formed under saturated wetland conditions and is acidic and rich in humus. Peat soils cover an estimated 400 million ha, equivalent to 3 % of the Earth’s land surface (Kaat and Joosten 2009), with most peatlands occurring in the northern hemisphere. Farming and subsidence of peats has been studied in multiple locations. The oldest records are from the Netherlands where peat soils were drained starting between the 9th and 14th centuries. Schorthorst (1977) documented subsidence rates varying from 0.17 to 0.7 cm yr–1 since the 1800s in these peat soils. Stephens et al. (1984) summarized worldwide subsidence rates which ranged from less than 0.5 to 10 cm yr–1 in California, Louisiana, Michigan, New York, Indiana and Florida in the USA and the Netherlands, Republic of Ireland, Norway, England (UK), Israel and Russia. Subsidence in agricultural peatlands has also been studied and estimated in New Zealand (Schipper and McLeod 2002), Southeast Asia (e.g. Hooijer et al. 2012) and Italy (Zanello et al. 2011; Gambolati et al. 2006). Reported causes of peat subsidence include (1) shrinkage due to dewatering, (2) consolidation due to loss of buoyant force and loading, (3) wind and water erosion, (4) oxidation of soil organic matter and (5) burning. Ewing and Vepraskas (2006) differentiated between relatively larger rates of primary subsidence or shrinkage upon drainage and lower rates of secondary subsidence or oxidation. During the 1970s, Schorthorst (1977) reported that compaction, shrinkage, and microbial oxidation caused 28, 20, and 52 % of subsidence in the Netherlands, respectively. US Department of Agriculture and University of Florida researchers extensively studied subsidence in Florida Everglades peats (Stephens et al. 1984) and reported that oxidation accounted for 53 % of historical subsidence. Florida researchers also demonstrated the relation of subsidence and carbon dioxide production (Stephens and Stewart 1976), soil temperature and moisture (Knipling et al. 1970; Volk 1973) and microbial activity (Tate 1979, 1980a, 1980b). Stephens et al. (1984) and Couwenberg and Hooijer (2013) reported an inverse correlation of subsidence rates, and oxidative carbon loss, to depth to groundwater. ### Sacramento-San Joaquin Delta Substantial understanding and quantification of subsidence has occurred since the early 1900s in the Sacramento-San Joaquin Delta, California, USA (hereafter Delta; Fig. 1). Subsidence of organic and highly organic mineral soils (hereafter referred to as organic soils or peat) is a primary landscape-altering process that threatens Delta infrastructure and water supply for over 25 million Californians. Drainage and cultivation of Delta soils since 1850 resulted in subsidence on over 60 islands from 1 to over 8 m (Thompson 1957; Deverel and Leighton 2010; Fig. 2). Key factors influencing subsidence include percent soil organic matter, depth of peat, year of initial drainage and management practices such as burning or growing crops that leave the soil exposed to wind erosion (Deverel and Leighton 2010). The overall objectives of this paper are to: (1) summarize the state of the science for oxidative subsidence of Delta peat soils and report the analysis of recent land-surface elevation data, refinement and recalibration of the subsidence model SUBCALC, (2) estimate present-day subsidence rates and (3) preliminarily assess rice cultivation for stopping or reducing subsidence. Delta peat soils formed from decaying wetland plants (Atwater 1982; Shlemon and Begg 1975; Drexler et al. 2009a). During the 6,000–7,000 years prior to the 1850s, about 5 billion m3 of tidal marsh sediment accumulated in the Delta (Deverel and Leighton 2010; Mount and Twiss 2005). Since the mid-19th century, half of this volume disappeared (Deverel and Leighton 2010; Mount and Twiss 2005). Present-day soils reflect organic matter accumulation through millennia, spatially variable fluvial deposition and oxidation; thus, soil type and organic matter content vary substantially (Deverel and Leighton 2010). Highly organic mineral surface soils generally predominate in the western and northern Delta and true surface organic soils, or histosols predominate in the central, eastern and southern-central Delta. The lowest organic matter content soils, which subside at relatively low rates, generally predominate in areas drained prior to 1880 near the Sacramento River where there was greater fluvial deposition (Deverel and Leighton 2010). Higher subsidence rates are associated with more recently drained and higher-organic matter soils in the central Delta where there was less fluvial deposition (Deverel and Leighton 2010). Using data presented in Atwater (1982) and boring logs, Deverel and Leighton (2010) and Deverel et al. (2015) presented maps of peat thickness. The thickest peat resides in the western and northwestern Delta where thicknesses range to over 7 m on Sherman Island (Fig. 1). Three to over 7 m of peat remains on Ryer, southern Grand, western Brannan, and Twitchell islands (Fig. 1). For most of the central, eastern and southern-central Delta, less than 1–2 m of peat remains (see Fig. 4 in Deverel et al. 2015). Deverel and Rojstaczer (1996) reported that microbial oxidation of organic matter is the primary present-day cause of subsidence. Consistently, Rojstaczer and Deverel (1995) and Deverel and Leighton (2010) demonstrated that spatial variations in soil organic matter content ranged from 4 to 60 % and explained over 55 % of the variation in average subsidence rates from 1978 to 2006. Deverel and Leighton (2010) assessed recent and historic causes of and factors affecting subsidence rates using elevation and soils data collected during 2006 and data reported in Rojstaczer et al. (1991), Rojstaczer and Deverel (1995), Deverel and Rojstaczer (1996) and the University of California (Weir 1950). Deverel and Leighton (2010) developed a computer model, SUBCALC, and geographic information system (GIS) to simulate Delta-wide subsidence. The SUBCALC model was calibrated using historic land-surface elevation data collected on three islands in the central Delta (Bacon and Mildred islands and Jones Tract) by Weir (1950) and Sherman Island in the western Delta (Rojstaczer et al. 1991). Subsidence rates have decreased with time associated with decreasing soil organic matter content and changing land-management practices (Deverel and Leighton 2010). Prior to the early 1960s, burning and wind erosion caused soil loss. Burning no longer occurs, and there is minimal wind erosion. Wind erosion was associated with high-velocity spring winds and bare asparagus fields (Schultz and Carlton 1959; Schultz et al. 1963; Carlton and Schultz 1966). Asparagus was widely planted in the Delta during the 1920s through the 1950s. Due to economic reasons, since the 1960s, asparagus cultivation decreased to a small area. Model results and their agreement with measurements demonstrate that oxidation accounts for the majority of recent subsidence and the remaining portion is due to consolidation (Deverel and Leighton 2010). The application of Michaelis–Menton kinetics was used to simulate oxidation of soil organic carbon. Consistently, Volk (1973) reported that Michaelis–Menton kinetics appropriately described oxidation of peat soils in the Florida Everglades. Little has been documented about consolidation, a secondary cause of organic soil subsidence. Water in organic soils is held in three phases: (1) intercellular, (2) inter-particle water in micropores, and (3) bound or absorbed. Consolidation expulses pore water and particles rearrange (Hobbs 1986). As farmers deepened drainage ditches to compensate for land-surface elevation loss due to oxidation, wind erosion and burning, organic soils consolidated due to dewatering resulting from increased drainage-ditch depth, which reduces pore pressure and buoyancy, thus transferring load to the soil skeleton. Drexler et al. (2009b) presented evidence for consolidation below the upper oxidized layer on farmed subsided islands. To estimate consolidation of subsurface deposits, Deverel and Leighton (2010) assumed compaction proceeds similar to dewatering and irreversible consolidation of a vertical soil column as described by Terzaghi (1925). They employed Terzaghi’s effective stress principle and extensometer data on Twitchell Island to estimate consolidation in SUBCALC using a linear model relating compaction to the change in hydraulic head. The estimated percentages of the different causes of subsidence came from model simulations of elevation change data from the 1920s to 2006. Since the late 1990s, researchers have investigated large-scale and small-scale spatial and temporal trends of subsidence on Delta islands and levees using remotely sensed data. Attempts to use satellite radar data for investigating oxidative subsidence of organic soils suffered from rapid decorrelation in agricultural areas (Cohen et al. 1998; Brooks et al. 2012)—for example, Brooks et al. (2012) showed limited ability to estimate subsidence on Delta island interiors (see Fig. 2 in their paper) presumably due to decorrelation. The Brooks et al. (2012) estimates were primarily for Delta levees around the periphery of islands where decorrelation has less of an effect. The applicability of satellite InSar is primarily limited to more stable structures such as levees. More recently, the relatively longer L-band (23.8 cm) wavelength of the UAVSAR, combined with regular acquisitions, high spatial resolution and data processing techniques developed for low coherence regions, show promise for application of radar interferometry to monitor subsidence in Delta agricultural lands on island interiors at sub-centimeter vertical resolution levels on organic soils (Jones et al. 2011, 2012). UAVSAR data have been used to estimate rates of elevation change on Sherman Island organic soils (Priyanka Sharma, Jet Propulsion Laboratory, unpublished data, 2015). Values ranged from 0 to 5 cm yr–1 and the spatially averaged rate was 1.5 cm yr–1. The UAVSAR-estimated rates were generally consistent with ground-based estimates described here and Deverel and Leighton (2010) and Rojstaczer and Deverel (1995). Terrestrial light detection and ranging technology (Terrestrial LiDAR) has also been used in the Delta to quantify short-term local-scale levee deformation (e.g. Bawden et al. 2014). #### Effects of subsidence and mitigation By reducing the landmass and resistance to hydraulic pressure from adjacent channels, subsidence has contributed to levee failure and island inundation. Weir (1950) reported the results of land surveys and field observations on three central Delta islands from 1922 to 1948 where elevations declined 1.8–2.3 m, resulting in elevations ranging from 3 to 3.4 m below sea level. Weir (1950) warned about increased seepage, levee instability and island flooding associated with subsidence. At the time of Weir’s publication, 50 islands had flooded primarily due to overtopping of levees. From 1930 to the early 1980s, over 50 Delta islands or tracts flooded—the majority due to levee foundation instability (Prokopovitch 1985)—whereas from 1900 to 2006, over 100 island levees failed (Gaddie et al. 2006; Florsheim and Dettinger 2007), causing local infrastructural damage which historically cost hundreds of millions of dollars (Prokopovitch 1985). The flooding of the 4,860-ha Jones Tract due to a levee breach that occurred during the early morning of June 2004 illustrates recent consequences. About $90 million were expended by the State of California to close the levee breach and complete removal of 197 million m3 of flood water by December 2004. Before island reclamation was complete, litigation began when BNSF Railway alleged that the State of California’s operation of the State Water Project resulted in channel scour that induced levee failure. Jones Tract landowners and others joined in the lawsuit. In its statement of decision and judgement, the State Superior Court ruled against the plaintiffs, dismissed the theory of State-Water-Project channel scour and stated that: “Subsidence resulting from the loss of peat soil over the years makes Delta islands more susceptible to flooding due to levee failure”. Island flooding in the western Delta may also cause eastward movement of saline water into the Delta, and thus impede water exports—for example, levee failure and flooding on Brannan-Andrus Island (Fig. 1) in June 1972 caused movement of salt water into the Delta (Cook and Coleman 1973), resulting in cessation of state and federal water exports. An additional 370 million m3 of water was released from reservoirs to mitigate the salinity intrusion. The total cost of flooding was over$97 million in 2015 dollars. Delta subsidence will continue until management practices are adopted that stop subsidence or the organic deposits disappear. Continuing subsidence can make farming more difficult and expensive. For example, as peat disappears, drainage ditches may be excavated into underlying mineral sediments which can be unstable. Also, greater seepage due to increased hydraulic gradients and flow under levees is resulting in larger marginally or non-farmable acreage (Deverel et al. 2015). Hydraulic forces on and seepage through and under levees will increase with continuing subsidence and sea level rise (Deverel et al. 2007a, 2014, 2015). Increased seepage under levees onto islands will decrease levee stability. Deverel et al. (2007b) predicted that seepage onto Twitchell Island (Fig. 1) will increase by 22–34 % during the next several decades. Levee failure or instability from seepage occurs when hydraulic gradients are large enough to erode or move levee internal and/or foundational materials. The Delta Risk Management Strategy (CDWR 2009) estimated the combined probability of levee failure and island flooding from earthquake, high-water flooding, and sunny-day levee failure for most of the deeply subsided central and western Delta ranges from 53 % to over 84 % during the next 20 years. Economic costs of future Delta levee failures were estimated in billions of dollars. Island drainage volumes and dissolved organic carbon loads will increase with continuing subsidence (Deverel et al. 2007a) and drainage costs will increase due to greater pumping lifts and volumes. Oxidation of organic soils generates dissolved organic carbon which forms, upon treatment for drinking, carcinogenic disinfection byproducts (Fleck et al. 2004; Deverel et al. 2007b). Winter and spring rains and irrigation mobilize dissolved organic carbon and trihalomethane precursor loads into island drainage water (Deverel et al. 2007b). Ongoing oxidative subsidence therefore perpetuates the annual cycle of generation of dissolved organic carbon in soil and mobilization to drainage water which is exported to Delta channels which deliver drinking water to 25 million Californians via the State Water Project (CDWR 2015). Similar processes apparently operate to generate methyl mercury, and data presented in Heim et al. (2009) indicate that methyl mercury loads from Delta islands will increase with continuing subsidence. Managed and permanently flooded wetlands will stop and reverse the effects of subsidence (Deverel et al. 1998, 2014; Miller et al. 2000, 2008). These wetlands accumulate carbon, and accretion rates are about 3 cm yr–1 (Deverel et al. 2014); wetlands near levees will reduce seepage onto islands (Deverel et al. 2014). Agriculture is the predominant land use in the Delta and is important to the local economy. However, current farming practices which require an aerated root zone cause subsidence by exposing organic soils to oxygen; therefore, agricultural practices that stop subsidence are highly desirable. The original impetus for investigating rice as a subsidence mitigation land use came from Miller et al. (2000) who indicated that wetlands which were flooded from early spring through midsummer resulted in no net carbon loss. Rice growers use a similar water management practice, flooding rice fields during the warmest months when soil oxidation rates are highest. In the past, cool night temperatures precluded Delta rice cultivation; however, development of cold-tolerant rice varieties resulted in increased Delta rice production with yields generally comparable to other rice-growing areas in California. Rice has been successfully grown on about 3,000 acres on central and eastern Delta islands since the mid-1990s. Heightened recent interest in subsidence mitigation prompted further investigation into rice production on state-owned Twitchell Island in 2009. Micrometeorological data presented by Hatala et al. (2012) and soil nitrogen dynamics reported by Kirk et al. (2015) suggest that rice cultivation will greatly reduce oxidative subsidence in Delta organic soils. Extensometer and leveling data collected in rice fields and an adjacent cornfield are reported here. #### Need for dissemination of quality information Misinformation about present-day Delta subsidence points to the need for collection and dissemination of high quality information. For example, in the Economic Sustainability Plan, the Delta Protection Commission (2012) cited work which attempted to delineate areas of active subsidence based on comparison of 2007 LiDAR data (CDWR 2007) and USGS Quadrangle maps surveyed between 1974 and 1976 (California Central Valley Flood Control Association 2011). The accuracy of the 2007 LiDAR data is about ±0.15 m. The error due to estimating the elevations from the 1974 and 1976 quadrangle contour maps is about one-half of the contour interval (1.5 m) for the topographic maps or 0.76 m (J. Vukovitch, USGS, Denver, personal communication, 1996). During 1974 to 2007, subsidence rates ranged from about 1–3 cm per yr–1, resulting in 0.3–0.9 m of elevation change which is similar to the estimation error from the Quadrangle maps and LiDAR data. Since publication of Deverel and Leighton (2010), additional land-surface elevation-change data has been collected on selected Delta islands; also, greenhouse gas emissions have been measured. While there is a need to assess, analyze and synthesize these data and improve subsidence modeling capability, the overall approach taken here was to collect and analyze land-surface elevation data in rice, corn and pasture fields, refine and recalibrate SUBCALC and estimate present-day Delta subsidence rates. ## Data sources and methods ### Land-surface elevation data #### Extensometer data To monitor small-scale variations in land surface elevation during 2009–2015, HydroFocus personnel installed and operated two extensometers on Twitchell Island, one in a rice field and one in the cornfield adjacent to the rice field (Fig. 1). The cornfield was converted to a wetland in 2014. At the extensometer location on Sherman Island (Fig. 1) described in Deverel and Rojstaczer (1996), new instrumentation recorded elevation changes starting in 2011. At all locations, land-surface elevations were measured relative to the extensometer structure which was anchored below the peat. In the rice field, a steel base support pipe was driven to refusal into the mineral layer underlying the peat soil. A modified sedimentation-erosion table (SET; Boumans and Day 1993) was inserted into a grooved stainless steel sleeve in the base support pipe which ensured instrument stability and replacement to the exact same position after movement to accommodate field operations. The SET arm extended horizontally about 1 m and was adjusted to level. A metal rod with a 5-inch-diameter (12.7 cm) metal disk that rested on the ground freely moved vertically in a sleeve on a metal plate at the end of the arm. HydroFocus personnel fastened a Macro Sensors GHSI 750 linear variable differential transformer (LVDT) to the rod above the plate. The piston arm rested on the plate so that the sensor body would move with the rod and the piston arm would remain stationary. A Campbell CR510 data logger recorded LVDT measurements every 15 min. In the cornfield, HydroFocus personnel constructed an extensometer similar to the one described in Deverel and Rojstaczer (1996). #### Leveling data Annual leveling surveys were conducted at seven locations in the Twitchell Island rice fields during 2009–2013 (Fig. 1) by California Department of Water Resources personnel. Spirit leveling surveys in multiple directions relative to fixed monuments anchored in the mineral material were conducted in the spring of each year after cultivation and before flooding. Land-surface elevations were determined using GPS in 2001 and 2012 at seven monitoring-well locations on Twitchell Island (Fig. 1). ### Modeling of delta subsidence Deverel and Leighton (2010) developed the computer model, SUBCALC, to integrate available data and quantify and simulate subsidence rates and causes. SUBCALC simulates aerobic microbial oxidation of organic carbon, consolidation, wind erosion and burning. Present-day subsidence is the result of oxidation and consolidation. SUBCALC simulates microbial oxidation of soil organic carbon to carbon dioxide using Michaelis–Menton (M–M) enzyme kinetics in which the rate of soil organic-matter oxidation is limited by soil organic carbon content (Browder and Volk 1978): $$\frac{V}{V_{\max }}=\frac{\left[S\right]}{K_{\mathrm{m}}+\left[S\right]}$$ (1) Michaelis-Menton equation (Eq. 1) parameters, K m (the M–M constant) and V max, (the maximum oxidation rate), and effects of temperature were originally estimated based on data reported in Deverel and Rojstaczer (1996). The [S] term (substrate concentration term) is the soil organic carbon fraction. For each annual time step, the different contributions to subsidence (e.g. oxidation and consolidation) were estimated based on newly calculated mass of organic matter and bulk densities (Deverel and Leighton 2010). To estimate the consolidation of subsurface deposits, it was assumed that compaction processes are similar to dewatering and irreversible consolidation of a vertical soil column as described by Terzaghi (1925). The use of Terzaghi’s effective stress principle is generally restricted by assumptions of Newtonian behavior of the liquid phase. Water in organic soil does not strictly follow Newtonian mechanical principles, especially during large changes in stress; however, it was assumed that for a small increment of stress change, dewatering would generally follow Newtonian behavior. SUBCALC simulates this process using a linear equation relating compaction to the change in hydraulic head based on data from the Twitchell Island extensometer (Kerr et al. 2003). Effects of varying depth to groundwater were accounted for using the relation of subsidence rates to depth to groundwater described in Stephens et al. (1984). Substantial detail is provided for the original model in Deverel and Leighton (2010, see their Appendix B in their ‘Supplemental materials’ section). In light of recently available data for land-surface elevation changes and greenhouse-gas emissions from drained Delta organic soils, SUBCALC was modified and re-calibrated for site specific data (Table 1). Specifically, data in Table 1 and information presented in Davidson et al. (2012) were used to estimate V max for Eq. 2 as follows. $${V}_{\max_{\mathrm{x}}}={a}_{\mathrm{x}}\times {e}^{-\mathrm{E}{\mathrm{a}}_{\mathrm{x}}/RT}$$ (2) Where a x is the pre-exponential factor, Eax is the activation energy for the soil organic carbon oxidation reaction, T is soil temperature and R is the universal gas constant. Values for a x and Eax were initially extracted from Davidson et al. (2012). Site recorded soil temperatures shown in Table 1 were used. Using the fraction organic carbon values and calculated V max values, K m (Eq. 1) was used as a calibration term to match carbon fluxes and subsidence rates in Table 1. A linear relationship between calculated/calibrated K m values and soil organic matter content arose. The regression equation was used to estimate K m from soil organic matter content values for estimating Delta-wide subsidence rates. ### Estimation of current subsidence rates The primary spatially variable inputs for SUBCALC are depth to groundwater, soil temperature and soil organic matter content. Michaelis–Menton inputs are calculated from soil temperature and soil organic matter content. The depth of the organic soil where oxidation is simulated to occur is determined by the depth to groundwater and the oxidation rate is governed by depth-to-groundwater/carbon loss-subsidence relations described in Stephens et al. (1984) and Couwenberg and Hooijer (2013). The depth to groundwater was estimated from soil surveys described in the following. #### Depth to groundwater Depth to groundwater on Delta subsided islands is controlled primarily by networks of drainage ditches that feed to island drainage pumping stations that in turn continuously discharge drainage water to Delta channels. Drainage ditches collect water that seeps from adjacent channels and deep percolation of applied irrigation water. There are few depth to groundwater measurements in Delta organic soils and, in general, groundwater levels have been maintained at about 0.8–1.2 m below land surface as the result of drainage system operation. Based on the first author’s experience in working in the organic soils throughout the Delta since the early 1980s, depth to groundwater has not changed substantially over time in most places. Also, data presented in Deverel et al. (2015) indicate lack of change in Delta groundwater levels since the late 1980s. To estimate depth to groundwater throughout the Delta for input to the SUBCALC model, information was obtained for each soil type from the soil surveys for Sacramento, San Joaquin, Solano, Yolo, and Contra Costa counties. The soil surveys have an average, or range, of depth to water value for each soil type. Depth to groundwater values were incorporated into a GIS file used to generate a map of estimated depth to groundwater (USDA Soil Survey Staff, Natural Resources Conservation Service 2006, 2007; Welch 1977; McElhiney 1992; Tugel 1993). #### Soil organic matter content and bulk density Soil organic matter content percentages provided in soil surveys were modified with the results for recently collected soil samples on Twitchell, Staten, Bacon and Sherman islands. Due to oxidation of soil organic matter since collection of data for the soil surveys, available data indicate that present-day soil organic matter content is likely equal to or lower than the mid-range values used to map soil organic matter content in Deverel and Leighton (2010). Soil organic matter determinations on Twitchell and Staten islands during 2012 through 2014 and on Bacon and Sherman islands in 2006 were compared with values reported in the soil surveys and a regression relation was used to estimate present-day values (Figs. 3 and 4). Data presented in Drexler et al. (2009b) for soil percent organic matter and bulk density (Fig. 5) were used to develop a regression relation for estimating initial soil bulk density in SUBCALC. #### Soil temperature Spatially referenced monthly near-surface air temperature data were obtained from sources described by Maurer et al. (2002). Data included daily minimum and maximum temperature observations at National Oceanic and Atmospheric Administration (NOAA) Cooperative Observer (co-op) stations. Co-op stations occur at a density of approximately one per 700 km2. For the Maurer dataset, these observations were spatially interpolated into a 1/8 ° (degrees latitude-longitude) square grid and averaged monthly. For each mapped grid cell overlaying Delta organic soils, an annual average temperature for the period 2007–2010 was calculated from all monthly averages. This period was chosen because the 1950–1999 data exhibit an upward trend. It was assumed that the 2007–2010 data adequately represent present-day Delta temperatures. Each soil feature in the GIS shapefile from this study had a temperature assigned to it from its corresponding grid cell. Air and soil temperature data from Knox et al. (2015) and Hatala et al. (2012) were compared to adjust the air temperatures for SUBCALC model input. On average, soil temperature was 1.2 °C greater than air temperature. This difference was used to convert air to soil temperature for input into Arrhenius function calculations within SUBCALC (Eq. 2). #### Mapping of present-day subsidence Spatially variable present-day subsidence rates were estimated using the recalibrated SUBCALC model and ArcGIS Spatial Analyst. It was assumed that oxidation and consolidation are the only present-day causes of subsidence. It was also assumed that there will be zero subsidence in rice-growing areas and permanently flooded wetlands, and the subsidence rate is zero where the soil organic matter content is less than or equal to 2 %. ## Results ### Recently measured and estimated subsidence rates #### Extensometer and leveling data Twitchell Island cornfield extensometer and observation-well data (Fig. 6) illustrate seasonal variations in land-surface elevations associated with groundwater-level fluctuations from 2009 through 2013. Groundwater levels rose during fall primarily due to decreased crop evapotranspiration and winter precipitation recharge. Groundwater levels decreased in the spring with diminishing rain and increasing evapotranspiration. Using land-surface elevation measurements at times of equal groundwater levels in October 2009 and December 2013, an average inelastic subsidence rate of 0.83 cm yr–1 was estimated. The soil organic matter content was 39.7 % (Table 1). For the seven locations where elevations were determined at observation wells in 2001 and 2012, subsidence rates ranged from 0.11 to 1.94 cm yr–1 in agricultural fields where estimated soil organic matter content ranged from 6 to 20 %. Generally consistent with extensometer data, the average of all seven measurements during 2001–2012 was 0.7 cm yr–1. The Sherman Island extensometer was located next to a drainage pumping station which maintained groundwater levels relatively constant with time since April 2011 (Fig. 7). The inelastic subsidence rate during April 2011 to April 2015 was 0.52 cm yr–1. Soil organic matter content was 16.9 % in 2015 (Table 1). #### Twitchell rice leveling and extensometer data The results of surveying in Twitchell Island rice fields indicated average elevation changes ranging from −1.7 to 2.1 cm yr–1 from 2009–2013. The average elevation-change rate for all seven locations in the rice fields was 0.05 cm yr–1. Spatial variations in rates are primarily due to land disturbance resulting from agricultural activities which include disking for weed control and preparation for planting, harvest and subsequent incorporation of plant residues. During 2012–2015, extensometer data from the Twitchell Island experimental rice field exhibits elastic and inelastic land-surface elevations and changes associated with seasonal cycles in groundwater level changes (Fig. 8). Flooded conditions were maintained in the rice fields during the growing season (late spring through late summer) and during the winter. Fields were drained before seeding in the spring and harvest in late summer/early fall. Six periods of flooding and draining are evident from 2012–2015 (Fig. 8). The 2012 data illustrate key events in the rice cultivation cycle. Land surface elevation initially followed the decline in the groundwater levels as the field was dewatered prior to planting. After planting and through the growing season, groundwater levels were about 20 cm below land surface at the observation well. During that period, land-surface elevations steadily increased. At the end of the growing season, the field was dewatered for harvest in September and groundwater levels and land-surface elevations decreased. The SET was moved off the field for harvesting and cultivation. When the SET was returned later to the exact same location in the field on 6 December 2012, land surface had risen by 17 mm, relative to the previous measurement on 11 November 2012 due to increased groundwater levels resultant from flooding and land disturbance. The water table was maintained through the winter at roughly the same level as during the growing season. The field was dewatered for preparation for planting beginning in late February at which point land-surface elevations declined to about the same level measured in November 2012 as shown by the manual measurement in March 2012. Similar oscillations were observed during 2013–2015. Net changes in land-surface elevations were estimated from the data shown in Fig. 8 by comparing annual land-surface elevation measurements at times when groundwater levels were equal. Land-surface elevations measured when the groundwater levels were shallowest (0.2 m) and deepest (1.15 m) indicated an overall average net accretion of about 0.8 cm yr–1 (Fig. 9). Specifically, the average accretion rates for the shallow (0.2 m) and deep groundwater depths (1.15 m) were 0.47 and 1.2 cm yr–1, respectively. The average accretion rate for all measurements was 0.84 cm yr–1. ### Estimation of Delta-wide subsidence #### Distribution of soil organic matter Figure 3 indicates that relative to values reported in the soil surveys, average soil organic matter has decreased over time and that average values are likely about 72 % of the reported values where there is over 20 % soil organic matter content; however, Fig. 4 indicates that overall, the medians of recently measured values were slightly lower than the mid-range of soil-survey reported values as indicated by the slope of 0.96. The average soil organic-matter percentage values in Fig. 10 were based on the data from soil surveys. Mapped soil organic matter content varied from less than 6 % to over 52 % throughout the Delta (Fig. 10). The distribution of soil organic matter reflects geomorphologic and subsidence history. Highly organic mineral surface soils generally predominate in the western and northern Delta and organic soils are prevalent in the central, eastern and south-central Delta. The lowest organic matter content soils generally prevail in areas drained prior to 1880 near the Sacramento River. In contrast, central and eastern Delta islands, where higher organic-matter soils dominate, were reclaimed during the late 19th century or early 20th century. Prior to reclamation, islands near the Sacramento River (e.g. Sherman Island) were subject to greater fluvial deposition relative to the more quiescent environment in the central and eastern Delta. #### Distribution of soil temperature There is little spatial variation in near-surface annual air temperature. Average annual temperatures ranged from 16.25 to 17.25 °C for the entire Delta. #### Distribution of depth to groundwater There are generally small variations in depth to groundwater in the Delta due to the influence of drainage systems. Based on information in the soil surveys, average depth to groundwater ranged from 0.8 to 1.2 m for most of the organic-soil area. Exceptions included the western Delta (notably Sherman and Jersey islands where pasture is the predominant land use). In these areas, depth to groundwater levels varied from 0 to 0.8 m. #### Estimated subsidence rates The SUBCALC model was re-calibrated for data for land-surface elevation change and greenhouse gas emissions (Table 1) collected throughout the Delta (Fig. 1). Average depth to groundwater varied from 0.50 to 1.39 m and soil organic matter content varied from 14.9 to 39.7 %. There was a small average annual temperature variation among the sites (14.9–16.4 °C) and therefore small variability in V max. The values of K m varied inversely with soil organic matter content. The root-mean square error (RMSE) was calculated as a goodness of fit parameter. For subsidence where depth to groundwater, soil temperature and soil-organic matter content are known, RMSE values indicated that model predictions were accurate within ±0.10 cm yr–1, whereas carbon fluxes were accurately predicted within ±0.006 g C cm–2 yr–1. Estimated present-day subsidence rates, which varied from 0.28 to 1.8 cm yr–1 based on inputs for depth to groundwater, average annual soil temperature and soil organic matter content are shown in Fig. 11. The highest rates (over 0.9 cm yr–1) correspond to high organic-matter soils in the central Delta where estimated soil organic matter content was over 40 % (Figs. 10 and 11). Rates generally equal to or lower than 0.9 cm yr–1 corresponded to the western Delta where soil organic matter content generally ranged from less than 6 to over 17 %. Estimated subsidence was also low or nil in the northern, eastern and southern Delta where organic matter contents were generally less than 15 %. At locations where rice cultivation and wetlands have been implemented (Sherman, Twitchell, Brack, Canal Ranch, Wright Elmwood), zero subsidence was assumed; active subsidence occurs where there is peat at or below elevation –2 m and the highest rates occur below –4 m (Fig. 11). ## Discussion ### Subsidence rates Measured present-day subsidence rates vary substantially in the Delta and are primarily related to soil organic matter content and secondarily to water- and land-management practices, which determine depth to groundwater. Deverel and Leighton (2010) measured land-surface elevations at 51 locations in 2006 where Weir and colleagues determined elevations in 1978 on Bacon Island (Fig. 1). Subsidence rates ranged from 1.5 to 3.0 cm yr–1 where soil organic matter content varied from 15 to over 60 %. On Sherman Island, Deverel and Leighton (2010) resurveyed power-pole foundations in 2006 originally surveyed in 1988 by Rojstaczer et al. (1991) and reported subsidence rates ranging from 0.6 to 2 cm yr–1 where soil organic matter content varied from 3 to 20 %. Figure 11 shows generally lower rates for most of the Delta relative to those reported by Deverel and Leighton (2010). Two key factors explain lower subsidence rates: lower soil organic matter content resultant from ongoing oxidation, and recalibration of SUBCALC with more recent data for subsidence and carbon emissions. For example on Bacon Island (Fig. 1), Deverel and Leighton (2010) reported soil organic matter contents over 60 %. Using the adjusted values described in the ‘Data sources and methods’ section resulted in lower present-day average organic matter content and subsidence rates for the eastern portion of Bacon Island as ranging from 0.9 to 1.4 cm yr–1. The average subsidence rate was 1.3 cm yr–1. For comparison, Deverel and Leighton (2010) reported an average rate of 2.2 cm yr–1 for this area from 1978 to 2006. Within any soil type, soil organic matter content can vary substantially (Fig. 4). The SUBCALC-based subsidence maps presented here therefore provide spatially averaged rates that are representative of areas of similar soil organic matter content at the level of tens to hundreds of hectares. To better assess SUBCALC-simulated present-day subsidence rates for varying organic matter content, on Bacon Island, present-day rates were simulated at the locations where Deverel and Leighton (2010) reported 1978–2006 subsidence rates ranging from 1.5 to 3.8 cm yr–1 and the average rate was 2.2 cm yr–1, whereas soil organic matter content ranged from 14 to 60 % and the average soil organic matter content was 39 %. SUBCALC present-day rates ranged from 0.7 to 2.0 cm yr–1 for the same range of organic matter content percentages, with the average rate being 1.2 cm yr–1. A similar comparison was made between SUBCALC-simulated present-day subsidence rates and Sherman Island 1988–2006 subsidence rates, also reported in Deverel and Leighton (2010). Among Sherman Island measurement points, subsidence rates ranged from 0.6 to 2.0 cm yr–1 and the average rate was 1.2 cm yr–1, while soil organic matter content ranged from 3 to 20 % with an average of 10 %. SUBCALC present-day rates ranged from 0.3 to 0.6 cm yr–1 for the same range of organic matter content percentages, and the average rate was 0.4 cm yr–1. These comparisons illustrated the likely variation within a central (Bacon) and western (Sherman) Delta island and indicates that current subsidence rates are lower than rates in previous decades. Priyanka Sharma and colleagues (P. Sharma, Jet Propulsion Laboratory, California Institute of Technology, personal communication, 2015) used UAVSAR data to estimate subsidence rates from 2009 to 2014 over all of Sherman Island. Reported rates ranged from 0 to 5 cm yr–1 and averaged 1.5 cm yr–1. By comparison, SUBCALC-simulated subsidence rates ranged from 0.3 to 1.1 cm yr–1 and averaged 0.5 cm yr–1 at Sherman Island. Within the Sharma study, the UAVSAR method was found to have over-predicted the subsidence rate (0.7 cm yr–1) at the location of an extensometer, which measured a rate of 0.4 cm yr–1 over the same period. The reported uncertainty in the UAVSAR estimates is about ≤ 0.2 cm yr–1. ### Rice as subsidence-mitigation land use Direct (elevation-change measurements) and indirect estimates (micrometeorological and organic-matter mineralization) of subsidence and accretion are generally consistent in preliminarily evaluations indicating that rice stops or greatly reduces subsidence by providing above- and below-ground plant residue which is incorporated into the soil and by reducing the rate of peat oxidation under saturated conditions. Data derived from leveling surveys and the extensometer demonstrate substantial temporal and spatial variability in land-surface elevation changes and indicate a small net accretion rate. These data illustrate the difficulty in estimating short-term land-surface elevation changes in this and other systems where there is land disturbance and elastic shrinking/swelling changes associated with short-term and seasonal groundwater elevation and soil moisture content changes (e.g. Zanello et al. 2011). Similar difficulties were noted with data collected by Weir (1950) in Deverel and Leighton (2010). Longer-term, high-quality land-surface elevation measurements for rice will provide more definitive answers. Reported subsidence estimates in the Twitchell Island rice fields from indirect methods indicate small rates of subsidence. Based on the eddy-covariance determination of carbon loss, Hatala et al. (2012) estimated subsidence in the Twitchell Island rice field at 0.1 to 0.14 cm yr–1 during 2 years. During a 1-year study, Kirk et al. (2015) estimated soil organic matter-nitrogen mineralization rates at four locations in the Twitchell Island rice field and used these with soil carbon:nitrogen ratios to estimate subsidence rates ranging from 0.07 to 0.11 cm yr–1, in close agreement with results reported by Hatala et al. There is uncertainty in these indirect estimates. In estimating subsidence rates using nitrogen mineralization from peat, Kirk et al. (2015) determined the annual nitrogen budget and by accounting for fertilizer application and plant uptake, calculated the annual mineralized nitrogen as a source to plant nitrogen uptake. Nitrogen from groundwater was estimated in situ using groundwater and soil-water samples in mesocosms. Kirk et al. (2015) assumed that groundwater nitrogen contributions resulted from mineralization during the year of investigation. Given low hydraulic conductivity and high porosity of the organic soils, groundwater nitrogen likely resulted from mineralization during previous years. Additionally, Kirk et al. (2015) applied an fmin factor of 0.67 based on Deverel and Leighton (2010), a factor that is not applicable because any subsidence in rice fields results from oxidation of the organic soil. In Deverel and Leighton (2010), the value of 0.67 was the estimated fraction of organic soil oxidation contributing to subsidence originally reported in Deverel and Rojstaczer (1996). The remaining fraction was attributed to consolidation due to deepening of drainage ditches. Because the rice field drainage ditches have not been altered, the sole cause of subsidence would be oxidation of soil organic matter. Removing the groundwater contribution and fmin factor from the Kirk et al. (2015) calculations resulted in a subsidence rate of about 0.02 cm yr1; furthermore, Kirk et al. (2015) used a plant nitrogen uptake efficiency of 50 % derived from the literature for mineral soils and fertilizer and stated that the values could range as high at 70 %. Using the 70 % value in Kirk et al.’s (2015) calculation and removing the groundwater contribution and the fmin factor denominator resulted in accretion (0.001 cm yr1) to a small amount of subsidence (0.01 cm yr1). Hatala et al. (2012) estimated the net carbon balance (carbon dioxide sequestered – methane emitted + planted seed – harvested grain) and used data for soil bulk density and soil carbon to estimate subsidence rates in rice during 2009–2011. The range of carbon balance values presented was used here to estimate subsidence values as low as 0.07 cm yr1. Using data presented in Knox et al. (2015) for 2013, subsidence rates ranging from 0.02 to 0.13 cm yr1 were estimated. The lower range of estimates of subsidence and accretion based on the data published in Hatala et al. (2012), Knox et al. (2015) and Kirk et al. (2015), are more consistent with measured land-surface elevation changes which indicate a small rate of overall accretion. Qualitatively and in light of uncertainty, the preponderance of evidence summarized here preliminarily indicates that rice cultivation greatly reduces subsidence or may slightly reverse the effects of subsidence. Longer-term data will provide improved quantification of the long-term subsidence mitigation benefit due to rice cultivation. Knox and colleagues (S. Knox, University of California-Berkeley, personal communication, 2016) presented results of 6 years of eddy covariance measurements of CO2 and CH4 fluxes in the Twitchell Island rice field. These data show heretofore unreported substantial annual variability in photosynthesis and methane fluxes driven primarily by variability in soil temperatures and resulted in substantial variability in soil carbon budgets. ### Mitigation The primary Delta subsidence mitigation tools are rice cultivation and permanently flooded wetlands. As demonstrated here and elsewhere (e.g. Miller et al. 2008; Deverel et al. 2014), both of these land use practices stop, greatly reduce or reverse the effects of subsidence. The work described here and in Deverel et al. (2014) provide guidance for implementation of these land-use changes. Areas below elevations of –2 m are candidate areas for implementation because there is active subsidence occurring (Fig. 11). Moreover and consistently, Deverel et al. (2015) demonstrated that artesian conditions prevail below –2 m and 81 % of wet, non- or marginally farmable areas were at or below –2 m. Implementation of rice and wetlands in these areas will prevent or reduce subsidence and associated consequences. ## Summary and conclusions Subsidence due primarily to oxidation of soil organic matter in the Sacramento-San Joaquin Delta affects sustainability of California’s water supply system and local agriculture. By reducing the landmass and resistance to hydraulic pressure from adjacent channels, subsidence has contributed to levee failure and island inundation which potentially affects water for use by over 25 million Californians and irrigation of millions of hectares of agricultural land. Since the mid-nineteenth century, oxidation has resulted in up to 8 m of subsidence. Subsidence rates have declined with time due to the disappearance of about 2.5 billion m3 of organic soil and consequent decreases in soil organic matter content and changing management practices. Present-day Delta subsidence rates have not heretofore been extensively recorded or estimated. Land-surface elevation data were collected to assess present-day subsidence rates and preliminarily evaluate rice as a land use for subsidence mitigation. To depict Delta-wide present-day rates of subsidence, the previously developed and reported SUBCALC model was revisited and calibrated using recent subsidence rates and carbon flux data. The primary inputs to the SUBCALC model include depth to groundwater, soil organic matter content and soil temperatures which were spatially estimated using multiple data sources. These inputs were used to map estimated subsidence rates. Land-surface elevation change data was collected and evaluated relative to indirect estimates of subsidence and accretion using carbon and nitrogen flux data for rice. Extensometer data in a cornfield on Twitchell Island demonstrate seasonal variations in land-surface elevations associated with groundwater-level fluctuations from 2009 through 2013 and an inelastic subsidence rate of 0.83 cm yr–1. Leveling data resulted in a similar estimated subsidence rate of 0.7 cm yr–1 from 2000–2012 on Twitchell Island. The Sherman Island extensometer data indicated a rate of 0.52 cm yr–1 where there was lower soil organic matter content. Calibration of the SUBCALC model indicated accuracy of ±0.10 cm yr–1 where depth to groundwater, soil organic matter content and temperature are known, while regional estimates of subsidence based on spatial variations in estimated soil organic matter content, depth to groundwater and soil temperature range from less than 0.3 to over 1.8 cm yr–1. The primary uncertainty is the distribution of soil organic matter content which results in spatial averaging in the mapping of subsidence rates at the level of tens to hundreds of hectares. Analysis of leveling and extensometer data in the Twitchell Island rice field resulted in an estimated accretion rate of 0.02 to 0.8 cm yr–1. Indirect estimates based on measurements of carbon fluxes and nitrogen mineralization resulted in estimates of low subsidence rates to low accretion rates. The preponderance of evidence presented here preliminarily demonstrates that rice will stop or greatly reduce subsidence for most of the Delta. Areas below elevations of –2 m are candidate areas for implementation because there is active subsidence occurring at rates greater than 0.4 cm yr–1.	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6681725978851318, "perplexity": 6378.705742609971}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-40/segments/1664030337731.82/warc/CC-MAIN-20221006061224-20221006091224-00600.warc.gz"}
https://codefreshers.com/palindrome-basis-solution-codeforces/	# [Solution] Palindrome Basis solution codeforces Palindrome Basis solution codeforces – You are given a positive integer 𝑛n. Let’s call some positive integer 𝑎a without leading zeroes palindromic if it remains the same after reversing the order of its digits. Find the number of distinct ways to express 𝑛n as a sum of positive palindromic integers. Two ways are considered different if the frequency of at least one palindromic integer is different in them. For example, 5=4+15=4+1 and 5=3+1+15=3+1+1 are considered different but 5=3+1+15=3+1+1 and 5=1+3+15=1+3+1 are considered the same. ## [Solution] Palindrome Basis solution codeforces Formally, you need to find the number of distinct multisets of positive palindromic integers the sum of which is equal to 𝑛n. Since the answer can be quite large, print it modulo 109+7109+7. Input The first line of input contains a single integer 𝑡t (1𝑡1041≤t≤104) denoting the number of testcases. Each testcase contains a single line of input containing a single integer 𝑛n (1𝑛41041≤n≤4⋅104) — the required sum of palindromic integers. ## [Solution] Palindrome Basis solution codeforces For each testcase, print a single integer denoting the required answer modulo 109+7109+7. Example input Copy 2 5 12 output Copy 7 74 ## Palindrome Basis solution codeforces For the first testcase, there are 77 ways to partition 55 as a sum of positive palindromic integers: • 5=1+1+1+1+15=1+1+1+1+1 • 5=1+1+1+25=1+1+1+2 • 5=1+2+25=1+2+2 • 5=1+1+35=1+1+3 • 5=2+35=2+3 • 5=1+45=1+4 • 5=55=5 For the second testcase, there are total 7777 ways to partition 1212 as a sum of positive integers but among them, the partitions 12=2+1012=2+1012=1+1+1012=1+1+10 and 12=1212=12 are not valid partitions of 1212 as a sum of positive palindromic integers because 1010 and 1212 are not palindromic. So, there are 7474 ways to partition 1212 as a sum of positive palindromic integers.	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5359242558479309, "perplexity": 1038.4200948409389}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-21/segments/1652662530066.45/warc/CC-MAIN-20220519204127-20220519234127-00642.warc.gz"}
https://www.physicsforums.com/threads/energie-lost-of-the-universe.31286/	# Energie lost of the universe 1. Jun 16, 2004 ### Mikado I am wonderring is there a known solution to the problem that all the light emitted by the stars must come out of the univers (if it is finite). All the energie is then lost and if the univers loses energie, it loses mass hence is bound to disappear someday... if there will be an end, there was a begining In other words is the univers subject to the laws of conservation of energie, mass and even momentum? Is there a shape or any property of the univers that eliminates this problem of energie loss? 2. Jun 17, 2004 ### Adrian Baker Why do you say the energy 'was lost' when light is emitted by the stars - it isn't, it just travels through the Universe as Photons of light. Energy is conserved in the Universe as a whole, yes. Don't forget, Energy and mass can be seen as the same thing (E=mc^2), and changing mass to energy does not therefore break conservation laws. The latest evidence for the future of the Universe is continual expansion for infinite time. 3. Jun 17, 2004 ### LURCH I think the biggest problem with your question is in understanding the concept that the light does not have to leave the universe just because the universe is finite. If the universe is finite, its boundaries are defined by how far its farthest component has traveled, and this includes the photons emitted by Stars. 4. Jun 17, 2004 ### HallsofIvy Staff Emeritus It is quite possible for the universe to be finite and still have no boundaries in the same way the surface of a sphere is finite but has no boundaries. Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook Have something to add? Similar Discussions: Energie lost of the universe	{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8570031523704529, "perplexity": 1093.1350340085878}, "config": {"markdown_headings": true, "markdown_code": false, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-09/segments/1487501172831.37/warc/CC-MAIN-20170219104612-00293-ip-10-171-10-108.ec2.internal.warc.gz"}
https://openstax.org/books/principles-microeconomics-3e/pages/3-2-shifts-in-demand-and-supply-for-goods-and-services?message=retired	Principles of Microeconomics 3e # 3.2Shifts in Demand and Supply for Goods and Services Principles of Microeconomics 3e3.2 Shifts in Demand and Supply for Goods and Services ### Learning Objectives By the end of this section, you will be able to: • Identify factors that affect demand • Graph demand curves and demand shifts • Identify factors that affect supply • Graph supply curves and supply shifts The previous module explored how price affects the quantity demanded and the quantity supplied. The result was the demand curve and the supply curve. Price, however, is not the only factor that influences buyers’ and sellers’ decisions. For example, how is demand for vegetarian food affected if, say, health concerns cause more consumers to avoid eating meat? How is the supply of diamonds affected if diamond producers discover several new diamond mines? What are the major factors, in addition to the price, that influence demand or supply? Visit this website to read a brief note on how marketing strategies can influence supply and demand of products. ### What Factors Affect Demand? We defined demand as the amount of some product a consumer is willing and able to purchase at each price. That suggests at least two factors that affect demand. Willingness to purchase suggests a desire, based on what economists call tastes and preferences. If you neither need nor want something, you will not buy it, and if you really like something, you will buy more of it than someone who does not share your strong preference for it. Ability to purchase suggests that income is important. Professors are usually able to afford better housing and transportation than students, because they have more income. Prices of related goods can affect demand also. If you need a new car, the price of a Honda may affect your demand for a Ford. Finally, the size or composition of the population can affect demand. The more children a family has, the greater their demand for clothing. The more driving-age children a family has, the greater their demand for car insurance, and the less for diapers and baby formula. These factors matter for both individual and market demand as a whole. Exactly how do these various factors affect demand, and how do we show the effects graphically? To answer those questions, we need the ceteris paribus assumption. ### The Ceteris Paribus Assumption A demand curve or a supply curve is a relationship between two, and only two, variables: quantity on the horizontal axis and price on the vertical axis. The assumption behind a demand curve or a supply curve is that no relevant economic factors, other than the product’s price, are changing. Economists call this assumption ceteris paribus, a Latin phrase meaning “other things being equal.” Any given demand or supply curve is based on the ceteris paribus assumption that all else is held equal. A demand curve or a supply curve is a relationship between two, and only two, variables when all other variables are kept constant. If all else is not held equal, then the laws of supply and demand will not necessarily hold, as the following Clear It Up feature shows. ### Clear It Up #### When does ceteris paribus apply? We typically apply ceteris paribus when we observe how changes in price affect demand or supply, but we can apply ceteris paribus more generally. In the real world, demand and supply depend on more factors than just price. For example, a consumer’s demand depends on income and a producer’s supply depends on the cost of producing the product. How can we analyze the effect on demand or supply if multiple factors are changing at the same time—say price rises and income falls? The answer is that we examine the changes one at a time, assuming the other factors are held constant. For example, we can say that an increase in the price reduces the amount consumers will buy (assuming income, and anything else that affects demand, is unchanged). Additionally, a decrease in income reduces the amount consumers can afford to buy (assuming price, and anything else that affects demand, is unchanged). This is what the ceteris paribus assumption really means. In this particular case, after we analyze each factor separately, we can combine the results. The amount consumers buy falls for two reasons: first because of the higher price and second because of the lower income. ### How Does Income Affect Demand? Let’s use income as an example of how factors other than price affect demand. Figure 3.5 shows the initial demand for automobiles as D0. At point Q, for example, if the price is $20,000 per car, the quantity of cars demanded is 18 million. D0 also shows how the quantity of cars demanded would change as a result of a higher or lower price. For example, if the price of a car rose to$22,000, the quantity demanded would decrease to 17 million, at point R. The original demand curve D0, like every demand curve, is based on the ceteris paribus assumption that no other economically relevant factors change. Now imagine that the economy expands in a way that raises the incomes of many people, making cars more affordable. How will this affect demand? How can we show this graphically? Return to Figure 3.5. The price of cars is still $20,000, but with higher incomes, the quantity demanded has now increased to 20 million cars, shown at point S. As a result of the higher income levels, the demand curve shifts to the right to the new demand curve D1, indicating an increase in demand. Table 3.4 shows clearly that this increased demand would occur at every price, not just the original one. Figure 3.5 Shifts in Demand: A Car Example Increased demand means that at every given price, the quantity demanded is higher, so that the demand curve shifts to the right from D0 to D1. Decreased demand means that at every given price, the quantity demanded is lower, so that the demand curve shifts to the left from D0 to D2. Price Decrease to D2 Original Quantity Demanded D0 Increase to D1$16,000 17.6 million 22.0 million 24.0 million $18,000 16.0 million 20.0 million 22.0 million$20,000 14.4 million 18.0 million 20.0 million $22,000 13.6 million 17.0 million 19.0 million$24,000 13.2 million 16.5 million 18.5 million $26,000 12.8 million 16.0 million 18.0 million Table 3.4 Price and Demand Shifts: A Car Example Now, imagine that the economy slows down so that many people lose their jobs or work fewer hours, reducing their incomes. In this case, the decrease in income would lead to a lower quantity of cars demanded at every given price, and the original demand curve D0 would shift left to D2. The shift from D0 to D2 represents such a decrease in demand: At any given price level, the quantity demanded is now lower. In this example, a price of$20,000 means 18 million cars sold along the original demand curve, but only 14.4 million sold after demand fell. When a demand curve shifts, it does not mean that the quantity demanded by every individual buyer changes by the same amount. In this example, not everyone would have higher or lower income and not everyone would buy or not buy an additional car. Instead, a shift in a demand curve captures a pattern for the market as a whole. In the previous section, we argued that higher income causes greater demand at every price. This is true for most goods and services. For some—luxury cars, vacations in Europe, and fine jewelry—the effect of a rise in income can be especially pronounced. A product whose demand rises when income rises, and vice versa, is called a normal good. A few exceptions to this pattern do exist. As incomes rise, many people will buy fewer generic brand groceries and more name brand groceries. They are less likely to buy used cars and more likely to buy new cars. They will be less likely to rent an apartment and more likely to own a home. A product whose demand falls when income rises, and vice versa, is called an inferior good. In other words, when income increases, the demand curve shifts to the left. ### Other Factors That Shift Demand Curves Income is not the only factor that causes a shift in demand. Other factors that change demand include tastes and preferences, the composition or size of the population, the prices of related goods, and even expectations. A change in any one of the underlying factors that determine what quantity people are willing to buy at a given price will cause a shift in demand. Graphically, the new demand curve lies either to the right (an increase) or to the left (a decrease) of the original demand curve. Let’s look at these factors. Changing Tastes or Preferences From 1980 to 2021, the per-person consumption of chicken by Americans rose from 47 pounds per year to 97 pounds per year, and consumption of beef fell from 76 pounds per year to 59 pounds per year, according to the U.S. Department of Agriculture (USDA). Changes like these are largely due to movements in taste, which change the quantity of a good demanded at every price: that is, they shift the demand curve for that good, rightward for chicken and leftward for beef. Changes in the Composition of the Population The proportion of elderly citizens in the United States population is rising. It rose from 9.8% in 1970 to 12.6% in 2000, and will be a projected (by the U.S. Census Bureau) 20% of the population by 2030. A society with relatively more children, like the United States in the 1960s, will have greater demand for goods and services like tricycles and day care facilities. A society with relatively more elderly persons, as the United States is projected to have by 2030, has a higher demand for nursing homes and hearing aids. Similarly, changes in the size of the population can affect the demand for housing and many other goods. Each of these changes in demand will be shown as a shift in the demand curve. Changes in the Prices of Related Goods Changes in the prices of related goods such as substitutes or complements also can affect the demand for a product. A substitute is a good or service that we can use in place of another good or service. As electronic books, like this one, become more available, you would expect to see a decrease in demand for traditional printed books. A lower price for a substitute decreases demand for the other product. For example, in recent years as the price of tablet computers has fallen, the quantity demanded has increased (because of the law of demand). Since people are purchasing tablets, there has been a decrease in demand for laptops, which we can show graphically as a leftward shift in the demand curve for laptops. A higher price for a substitute good has the reverse effect. Other goods are complements for each other, meaning we often use the goods together, because consumption of one good tends to enhance consumption of the other. Examples include breakfast cereal and milk; notebooks and pens or pencils, golf balls and golf clubs; gasoline and sport utility vehicles; and the five-way combination of bacon, lettuce, tomato, mayonnaise, and bread. If the price of golf clubs rises, since the quantity demanded of golf clubs falls (because of the law of demand), demand for a complement good like golf balls decreases, too. Similarly, a higher price for skis would shift the demand curve for a complement good like ski resort trips to the left, while a lower price for a complement has the reverse effect. Changes in Expectations about Future Prices or Other Factors that Affect Demand While it is clear that the price of a good affects the quantity demanded, it is also true that expectations about the future price (or expectations about tastes and preferences, income, and so on) can affect demand. For example, if people hear that a hurricane is coming, they may rush to the store to buy flashlight batteries and bottled water. If people learn that the price of a good like coffee is likely to rise in the future, they may head for the store to stock up on coffee now. We show these changes in demand as shifts in the curve. Therefore, a shift in demand happens when a change in some economic factor (other than price) causes a different quantity to be demanded at every price. The following Work It Out feature shows how this happens. ### Work It Out #### Shift in Demand A shift in demand means that at any price (and at every price), the quantity demanded will be different than it was before. Following is an example of a shift in demand due to an income increase. Step 1. Draw the graph of a demand curve for a normal good like pizza. Pick a price (like P0). Identify the corresponding Q0. See an example in Figure 3.6. Figure 3.6 Demand Curve We can use the demand curve to identify how much consumers would buy at any given price. Step 2. Suppose income increases. As a result of the change, are consumers going to buy more or less pizza? The answer is more. Draw a dotted horizontal line from the chosen price, through the original quantity demanded, to the new point with the new Q1. Draw a dotted vertical line down to the horizontal axis and label the new Q1. Figure 3.7 provides an example. Figure 3.7 Demand Curve with Income Increase With an increase in income, consumers will purchase larger quantities, pushing demand to the right. Step 3. Now, shift the curve through the new point. You will see that an increase in income causes an upward (or rightward) shift in the demand curve, so that at any price the quantities demanded will be higher, as Figure 3.8 illustrates. Figure 3.8 Demand Curve Shifted Right With an increase in income, consumers will purchase larger quantities, pushing demand to the right, and causing the demand curve to shift right. ### Summing Up Factors That Change Demand Figure 3.9 summarizes six factors that can shift demand curves. The direction of the arrows indicates whether the demand curve shifts represent an increase in demand or a decrease in demand. Notice that a change in the price of the good or service itself is not listed among the factors that can shift a demand curve. A change in the price of a good or service causes a movement along a specific demand curve, and it typically leads to some change in the quantity demanded, but it does not shift the demand curve. Figure 3.9 Factors That Shift Demand Curves (a) A list of factors that can cause an increase in demand from D0 to D1. (b) The same factors, if their direction is reversed, can cause a decrease in demand from D0 to D1. When a demand curve shifts, it will then intersect with a given supply curve at a different equilibrium price and quantity. We are, however, getting ahead of our story. Before discussing how changes in demand can affect equilibrium price and quantity, we first need to discuss shifts in supply curves. ### How Production Costs Affect Supply A supply curve shows how quantity supplied will change as the price rises and falls, assuming ceteris paribus so that no other economically relevant factors are changing. If other factors relevant to supply do change, then the entire supply curve will shift. Just as we described a shift in demand as a change in the quantity demanded at every price, a shift in supply means a change in the quantity supplied at every price. In thinking about the factors that affect supply, remember what motivates firms: profits, which are the difference between revenues and costs. A firm produces goods and services using combinations of labor, materials, and machinery, or what we call inputs or factors of production. If a firm faces lower costs of production, while the prices for the good or service the firm produces remain unchanged, a firm’s profits go up. When a firm’s profits increase, it is more motivated to produce output, since the more it produces the more profit it will earn. When costs of production fall, a firm will tend to supply a larger quantity at any given price for its output. We can show this by the supply curve shifting to the right. Take, for example, a messenger company that delivers packages around a city. The company may find that buying gasoline is one of its main costs. If the price of gasoline falls, then the company will find it can deliver messages more cheaply than before. Since lower costs correspond to higher profits, the messenger company may now supply more of its services at any given price. For example, given the lower gasoline prices, the company can now serve a greater area, and increase its supply. Conversely, if a firm faces higher costs of production, then it will earn lower profits at any given selling price for its products. As a result, a higher cost of production typically causes a firm to supply a smaller quantity at any given price. In this case, the supply curve shifts to the left. Consider the supply for cars, shown by curve S0 in Figure 3.10. Point J indicates that if the price is $20,000, the quantity supplied will be 18 million cars. If the price rises to$22,000 per car, ceteris paribus, the quantity supplied will rise to 20 million cars, as point K on the S0 curve shows. We can show the same information in table form, as in Table 3.5. Figure 3.10 Shifts in Supply: A Car Example Decreased supply means that at every given price, the quantity supplied is lower, so that the supply curve shifts to the left, from S0 to S1. Increased supply means that at every given price, the quantity supplied is higher, so that the supply curve shifts to the right, from S0 to S2. Price Decrease to S1 Original Quantity Supplied S0 Increase to S2 $16,000 10.5 million 12.0 million 13.2 million$18,000 13.5 million 15.0 million 16.5 million $20,000 16.5 million 18.0 million 19.8 million$22,000 18.5 million 20.0 million 22.0 million $24,000 19.5 million 21.0 million 23.1 million$26,000 20.5 million 22.0 million 24.2 million Table 3.5 Price and Shifts in Supply: A Car Example Now, imagine that the price of steel, an important ingredient in manufacturing cars, rises, so that producing a car has become more expensive. At any given price for selling cars, car manufacturers will react by supplying a lower quantity. We can show this graphically as a leftward shift of supply, from S0 to S1, which indicates that at any given price, the quantity supplied decreases. In this example, at a price of $20,000, the quantity supplied decreases from 18 million on the original supply curve (S0) to 16.5 million on the supply curve S1, which is labeled as point L. Conversely, if the price of steel decreases, producing a car becomes less expensive. At any given price for selling cars, car manufacturers can now expect to earn higher profits, so they will supply a higher quantity. The shift of supply to the right, from S0 to S2, means that at all prices, the quantity supplied has increased. In this example, at a price of$20,000, the quantity supplied increases from 18 million on the original supply curve (S0) to 19.8 million on the supply curve S2, which is labeled M. ### Other Factors That Affect Supply In the example above, we saw that changes in the prices of inputs in the production process will affect the cost of production and thus the supply. Several other things affect the cost of production, too, such as changes in weather or other natural conditions, new technologies for production, and some government policies. Changes in weather and climate will affect the cost of production for many agricultural products. For example, in 2014 the Manchurian Plain in Northeastern China, which produces most of the country's wheat, corn, and soybeans, experienced its most severe drought in 50 years. A drought decreases the supply of agricultural products, which means that at any given price, a lower quantity will be supplied. Conversely, especially good weather would shift the supply curve to the right. When a firm discovers a new technology that allows the firm to produce at a lower cost, the supply curve will shift to the right, as well. For instance, in the 1960s a major scientific effort nicknamed the Green Revolution focused on breeding improved seeds for basic crops like wheat and rice. By the early 1990s, more than two-thirds of the wheat and rice in low-income countries around the world used these Green Revolution seeds—and the harvest was twice as high per acre. A technological improvement that reduces costs of production will shift supply to the right, so that a greater quantity will be produced at any given price. Government policies can affect the cost of production and the supply curve through taxes, regulations, and subsidies. For example, the U.S. government imposes a tax on alcoholic beverages that collects about $8 billion per year from producers. Businesses treat taxes as costs. Higher costs decrease supply for the reasons we discussed above. Other examples of policy that can affect cost are the wide array of government regulations that require firms to spend money to provide a cleaner environment or a safer workplace. Complying with regulations increases costs. A government subsidy, on the other hand, is the opposite of a tax. A subsidy occurs when the government pays a firm directly or reduces the firm’s taxes if the firm carries out certain actions. From the firm’s perspective, taxes or regulations are an additional cost of production that shifts supply to the left, leading the firm to produce a lower quantity at every given price. Government subsidies reduce the cost of production and increase supply at every given price, shifting supply to the right. The following Work It Out feature shows how this shift happens. ### Work It Out #### Shift in Supply We know that a supply curve shows the minimum price a firm will accept to produce a given quantity of output. What happens to the supply curve when the cost of production goes up? Following is an example of a shift in supply due to a production cost increase. (We’ll introduce some other concepts regarding firm decision-making in Chapters 7 and 8.) Step 1. Draw a graph of a supply curve for pizza. Pick a quantity (like Q0). If you draw a vertical line up from Q0 to the supply curve, you will see the price the firm chooses. Figure 3.11 provides an example. Figure 3.11 Supply Curve You can use a supply curve to show the minimum price a firm will accept to produce a given quantity of output. Step 2. Why did the firm choose that price and not some other? One way to think about this is that the price is composed of two parts. The first part is the cost of producing pizzas at the margin; in this case, the cost of producing the pizza, including cost of ingredients (e.g., dough, sauce, cheese, and pepperoni), the cost of the pizza oven, the shop rent, and the workers' wages. The second part is the firm’s desired profit, which is determined, among other factors, by the profit margins in that particular business. (Desired profit is not necessarily the same as economic profit, which will be explained in Chapter 7.) If you add these two parts together, you get the price the firm wishes to charge. The quantity Q0 and associated price P0 give you one point on the firm’s supply curve, as Figure 3.12 illustrates. Figure 3.12 Setting Prices The cost of production and the desired profit equal the price a firm will set for a product. Step 3. Now, suppose that the cost of production increases. Perhaps cheese has become more expensive by$0.75 per pizza. If that is true, the firm will want to raise its price by the amount of the increase in cost ($0.75). Draw this point on the supply curve directly above the initial point on the curve, but$0.75 higher, as Figure 3.13 shows. Figure 3.13 Increasing Costs Leads to Increasing Price Because the cost of production and the desired profit equal the price a firm will set for a product, if the cost of production increases, the price for the product will also need to increase. Step 4. Shift the supply curve through this point. You will see that an increase in cost causes an upward (or a leftward) shift of the supply curve so that at any price, the quantities supplied will be smaller, as Figure 3.14 illustrates. Figure 3.14 Supply Curve Shifts When the cost of production increases, the supply curve shifts upwardly to a new price level. ### Summing Up Factors That Change Supply Changes in the cost of inputs, natural disasters, new technologies, and the impact of government decisions all affect the cost of production. In turn, these factors affect how much firms are willing to supply at any given price. Figure 3.15 summarizes factors that change the supply of goods and services. Notice that a change in the price of the product itself is not among the factors that shift the supply curve. Although a change in price of a good or service typically causes a change in quantity supplied or a movement along the supply curve for that specific good or service, it does not cause the supply curve itself to shift. Figure 3.15 Factors That Shift Supply Curves (a) A list of factors that can cause an increase in supply from S0 to S1. (b) The same factors, if their direction is reversed, can cause a decrease in supply from S0 to S1. Because demand and supply curves appear on a two-dimensional diagram with only price and quantity on the axes, an unwary visitor to the land of economics might be fooled into believing that economics is about only four topics: demand, supply, price, and quantity. However, demand and supply are really “umbrella” concepts: demand covers all the factors that affect demand, and supply covers all the factors that affect supply. We include factors other than price that affect demand and supply by using shifts in the demand or the supply curve. In this way, the two-dimensional demand and supply model becomes a powerful tool for analyzing a wide range of economic circumstances.	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.2368406355381012, "perplexity": 1107.2332602657057}, "config": {"markdown_headings": true, "markdown_code": false, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-06/segments/1674764500017.27/warc/CC-MAIN-20230202101933-20230202131933-00777.warc.gz"}
https://www.statistics-lab.com/%E7%BB%9F%E8%AE%A1%E4%BB%A3%E5%86%99%E9%9A%8F%E6%9C%BA%E8%BF%87%E7%A8%8B%E4%BD%9C%E4%B8%9A%E4%BB%A3%E5%86%99stochastic-process%E4%BB%A3%E8%80%83notion-of-stochastic-processes/	### 统计代写\|随机过程作业代写stochastic process代考\|Notion of Stochastic Processes statistics-lab™ 为您的留学生涯保驾护航在代写随机过程stochastic process方面已经树立了自己的口碑, 保证靠谱, 高质且原创的统计Statistics代写服务。我们的专家在代写随机过程stochastic process方面经验极为丰富，各种代写随机过程stochastic process相关的作业也就用不着说。 • Statistical Inference 统计推断 • Statistical Computing 统计计算 • (Generalized) Linear Models 广义线性模型 • Statistical Machine Learning 统计机器学习 • Longitudinal Data Analysis 纵向数据分析 • Foundations of Data Science 数据科学基础 ## 统计代写\|随机过程作业代写stochastic process代考\|Notion of Stochastic Processes Loosely speaking, the mathematical description of a random phenomenon as it changes in time is a stochastic process. Since the last century there has been greater realisation that stochastic (or non-deterministic) models are more realistic than deterministic models in many situations. Observations taken at different time points rather than those taken at a fixed period of time began to draw the attention of scientists. The physicists and communication engineers played a leading role in the development of dynamic indeterminism. Many a phenomenon occurring in physical and life sciences are studied not only as a random phenomenon but also as one changing with time or space. Similar considerations are also made in other areas such as social sciences, economics and management sciences, and so on. The scope of applications of stochastic processes which are functions of time or space or both is ever increasing. A stochastic process is a family of random variables $\left{X_{t}\right}$, where $t$ takes values in the index set $T$ (sometimes called a parameter set or a time set). The values of $X$, are called the state space and will be denoted by $S$. If $T$ is countable then the stochastic process is called a stochastic sequence (or discrete parameter stochastic process). If $S$ is countable then the stochastic process is called a discrete state (space) process. If $S$ is a subset of the real line the stochastic process is called a real valued process. If $T$ takes continuously uncountable number of values like $(0, \infty)$ or $(-\infty, \infty)$ the stochastic process is called a continuous time process. To emphasize its dependence on $t$ and sample point $w$, we shall denote the stochastic process by $X(t, w), t \in T, w \in \Omega$ i.e. for each $w \in \Omega, X_{t}=X(t$, $w)$ is a function of $t$. This graph is known as the “typical sample function” or “realization of the stochastic process” $X(t, w)$. ## 统计代写\|随机过程作业代写stochastic process代考\|Different Types of Stochastic Processes Following are the most important types of stochastic processes we come across: 1. Independent stochastic sequence (Discrete time process) $T={1,2,3, \ldots}$ and $\left{X_{t}, t \in T\right}$ are independent random variables. 2. Renewal process (Discrete time process) Here $T={0,1,2,3, \ldots], S=[0, \infty]$. If $X_{n}$ are i.i.d. non-negative random variables and $S_{n}=X_{1}+\ldots+X_{n}$ then $\left{S_{n}\right}$ forms a discrete time (renewal process). 3. Independent increment process (Continuous time process) $T=\left{t_{0}, \infty\right}$, where $t_{0}$ be any real number (+or $-$ ). For every $$t_{0}<t_{1}<\ldots<t_{n}, t_{i} \in T, i=1,2, \ldots, n$$ if $X_{t_{0}}, X_{t_{1}}-X_{t_{0}}, X_{t_{2}}-X_{t_{1}}, \ldots, X_{t_{n}}-X_{t_{n-1}}$ are independent for all possible choices of $(1.1)$, then the stochastic process $\left{X_{1}, t \in T\right}$ is called independent increment stochastic process. 4. Markov process If $P\left[X_{l_{n+1}} \in A \mid X_{l_{n}}=a_{n}, X_{t_{n-1}}=a_{n-1}, \ldots, X_{t_{0}}=a_{0}\right]$ $=P\left[X_{t_{n+1}} \in A \mid X_{t_{n}}=a_{n}\right]$ holds for all choices of $$t_{0}<t_{1}<t_{2}<\ldots<t_{n+1}, t_{i} \in T \cdot i=0,1,2, \ldots, n+1$$ and $A \in . D$, the Borel field of the state space $S$, then $\left{X_{t}, t \in T\right}$ is called a Markov process. 5. Martingale or fair game process If $\quad E\left[X_{t_{n+1}} \mid X_{t_{n}}=a_{n}, X_{t_{n-1}}=a_{n-1}, \ldots, X_{t_{0}}=a_{0}\right]=a_{n}$ i.e. $E\left[X_{t_{n+1}} \mid X_{t_{n}}, \ldots, X_{t_{0}}\right]=X_{t_{n}}$ a.s. for all choices of the partition (1.1), then $\left{X_{t}, t \in T\right}$ is called a Martingale process. 6. Stationary process If the joint distribution of $\left(X_{t_{1}+t_{h}}, \ldots, X_{t_{n}+h}\right)$ are the same for all $h>0$ and $$t_{1}<t_{2}<\ldots<t_{n}, t_{i} \in T, t_{i}+h \in T$$ then $\left{X_{t}, t \in T\right}$ is called a stationary process (strictly stationary process). ## 统计代写\|随机过程作业代写stochastic process代考\|Examples of stationary processes (a) Electrical pulses in communication theory are often postulated to describe a stationary process. Of course, in any physical system there is a transient period at the beginning of a signal. Since typically this has a short duration compared to the signal length, a stationary model may be appropriate. In electrical communication theory, often both the electrical potential and the current are represented as complex variables. Here we may encounter complex-valued stationary processes. (b) The spatial and/or planar distributions of stars of galaxies, plants and animals, are often stationary. Time parameter set $T$ might be Euclidean space, the surface of a sphere or the plane. A stationary distribution may be postulated for the height of a wave and $T$ is taken to be a set of longitudes and latitudes, again two dimensional. (c) Economic time series, such as unemployment, gross national product, national income etc., are often assumed to correspond to a stationary process, at least after some correction for long-term growth has been made. ## 统计代写\|随机过程作业代写stochastic process代考\|Different Types of Stochastic Processes 1. 独立随机序列（离散时间过程）吨=1,2,3,…和\left{X_{t}, t \in T\right}\left{X_{t}, t \in T\right}是独立的随机变量。 2. 更新过程（离散时间过程）这里 $T={0,1,2,3, \ldots], S=[0, \infty].一世FX_{n}一种r和一世.一世.d.n这n−n和G一种吨一世在和r一种nd这米在一种r一世一种bl和s一种ndS_{n}=X_{1}+\ldots+X_{n}吨H和n\left{S_{n}\right}$ 形成一个离散时间（更新过程）。 3. 独立增量过程（Continuous time process） T=\left{t_{0}, \infty\right}T=\left{t_{0}, \infty\right}，在哪里吨0是任何实数（+或−）。对于每一个吨0<吨1<…<吨n,吨一世∈吨,一世=1,2,…,n 如果X吨0,X吨1−X吨0,X吨2−X吨1,…,X吨n−X吨n−1对于所有可能的选择都是独立的(1.1)，然后是随机过程\left{X_{1}, t \in T\right}\left{X_{1}, t \in T\right}称为独立增量随机过程。 4. 马尔可夫过程 If磷[Xln+1∈一种∣Xln=一种n,X吨n−1=一种n−1,…,X吨0=一种0] =磷[X吨n+1∈一种∣X吨n=一种n]适用于所有选择吨0<吨1<吨2<…<吨n+1,吨一世∈吨⋅一世=0,1,2,…,n+1 和一种∈.D, 状态空间的 Borel 场小号，然后\left{X_{t}, t \in T\right}\left{X_{t}, t \in T\right}称为马尔科夫过程。 5. 鞅或公平博弈过程 If和[X吨n+1∣X吨n=一种n,X吨n−1=一种n−1,…,X吨0=一种0]=一种n IE和[X吨n+1∣X吨n,…,X吨0]=X吨n至于分区（1.1）的所有选择，那么\left{X_{t}, t \in T\right}\left{X_{t}, t \in T\right}称为鞅过程。 6. 平稳过程如果联合分布(X吨1+吨H,…,X吨n+H)所有人都一样H>0和吨1<吨2<…<吨n,吨一世∈吨,吨一世+H∈吨然后\left{X_{t}, t \in T\right}\left{X_{t}, t \in T\right}称为平稳过程（strictly平稳过程）。 ## 统计代写\|随机过程作业代写stochastic process代考\|Examples of stationary processes (a) 通信理论中的电脉冲通常被假设为描述一个平稳的过程。当然，在任何物理系统中，信号开始时都有一个瞬态周期。由于与信号长度相比，这通常具有较短的持续时间，因此固定模型可能是合适的。在电通信理论中，通常电势和电流都表示为复变量。在这里，我们可能会遇到复值平稳过程。 (b) 星系、植物和动物的恒星的空间和/或平面分布通常是静止的。时间参数集吨可能是欧几里得空间、球面或平面。 (c) 经济时间序列，例如失业、国民生产总值、国民收入等，通常被假定为对应于一个平稳过程，至少在对长期增长进行了一些修正之后。 ## 广义线性模型代考 statistics-lab作为专业的留学生服务机构，多年来已为美国、英国、加拿大、澳洲等留学热门地的学生提供专业的学术服务，包括但不限于Essay代写，Assignment代写，Dissertation代写，Report代写，小组作业代写，Proposal代写，Paper代写，Presentation代写，计算机作业代写，论文修改和润色，网课代做，exam代考等等。写作范围涵盖高中，本科，研究生等海外留学全阶段，辐射金融，经济学，会计学，审计学，管理学等全球99%专业科目。写作团队既有专业英语母语作者，也有海外名校硕博留学生，每位写作老师都拥有过硬的语言能力，专业的学科背景和学术写作经验。我们承诺100%原创，100%专业，100%准时，100%满意。 ## MATLAB代写 MATLAB 是一种用于技术计算的高性能语言。它将计算、可视化和编程集成在一个易于使用的环境中，其中问题和解决方案以熟悉的数学符号表示。典型用途包括：数学和计算算法开发建模、仿真和原型制作数据分析、探索和可视化科学和工程图形应用程序开发，包括图形用户界面构建MATLAB 是一个交互式系统，其基本数据元素是一个不需要维度的数组。这使您可以解决许多技术计算问题，尤其是那些具有矩阵和向量公式的问题，而只需用 C 或 Fortran 等标量非交互式语言编写程序所需的时间的一小部分。MATLAB 名称代表矩阵实验室。MATLAB 最初的编写目的是提供对由 LINPACK 和 EISPACK 项目开发的矩阵软件的轻松访问，这两个项目共同代表了矩阵计算软件的最新技术。MATLAB 经过多年的发展，得到了许多用户的投入。在大学环境中，它是数学、工程和科学入门和高级课程的标准教学工具。在工业领域，MATLAB 是高效研究、开发和分析的首选工具。MATLAB 具有一系列称为工具箱的特定于应用程序的解决方案。对于大多数 MATLAB 用户来说非常重要，工具箱允许您学习应用专业技术。工具箱是 MATLAB 函数（M 文件）的综合集合，可扩展 MATLAB 环境以解决特定类别的问题。可用工具箱的领域包括信号处理、控制系统、神经网络、模糊逻辑、小波、仿真等。	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9733552932739258, "perplexity": 1287.1977942344063}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-14/segments/1679296945279.63/warc/CC-MAIN-20230324082226-20230324112226-00567.warc.gz"}
http://link.springer.com/article/10.1007%2Fs10940-012-9171-0	Journal of Quantitative Criminology , Volume 29, Issue 1, pp 103–121 # Capital Punishment and Deterrence: Understanding Disparate Results Original Paper DOI: 10.1007/s10940-012-9171-0 Durlauf, S.N., Fu, C. & Navarro, S. J Quant Criminol (2013) 29: 103. doi:10.1007/s10940-012-9171-0 ## Abstract ### Objectives Investigate how different model assumptions have driven the conflicting findings in the literature on the deterrence effect of capital punishment. ### Methods The deterrence effect of capital punishment is estimated across different models that reflect the following sources of model uncertainty: (1) the uncertainty about the probability model generating the aggregate murder rate equation, (2) the uncertainty about the determinants of an individual’s choice of committing a murder or not, (3) the uncertainty about state level heterogeneity, and (4) the uncertainty about the exchangeability between observations with zero murder case and those with positive murder cases. ### Results First, the estimated deterrence effects exhibit great dispersion across models. Second, a particular subset of models—linear models with constant coefficients—always predict a positive deterrence effect. All other models predict negative deterrence effects. Third, the magnitudes of the point estimates of deterrence effects differ mainly because of the choice of linear versus logistic specifications. ### Conclusions The question about the deterrence effect of capital punishment cannot be answered independently from substantive assumptions on what determines individual behavior. The need for judgment cannot be escaped in empirical work. ### Keywords Capital punishmentDeterrenceModel uncertainty	{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8968272805213928, "perplexity": 6473.435547743191}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2016-44/segments/1476988721555.36/warc/CC-MAIN-20161020183841-00138-ip-10-171-6-4.ec2.internal.warc.gz"}
http://tex.stackexchange.com/questions/99482/how-to-delete-borders-rules-in-a-table-defined-with-the-cals-package	# How to delete borders (rules) in a table defined with the cals package? I recently discovered the less known cals package for defining tables HTML-style. Here is all documentation I found: I can create nice tables but following the directions to delete vertical cell borders does not work. Can anybody help? Here is a working example: \documentclass{report} \listfiles %tables in CALS markup \usepackage{cals} %calculate with \textwidth etc. \usepackage{calc} \newlength{\lengthw} \begin{document} \setlength{\lengthw}{\textwidth-5cm} \begin{table}[ht] \caption{Aantal uitgangen} \begin{calstable} \colwidths{{\lengthw}{5cm}} \def\cals@cs@width{0pt} %this should delete column borders but is does not! \brow \alignL\cell{} \alignC\cell{\vfil Aantal uitgangen}\erow } \brow \alignL\cell{\vfil$aantal\ gebruikers < 50$} \alignC\cell{\vfil 1 of 2 uitgangen (cfr. 7.1.2)} \erow \brow \alignL\cell{\vfil$50 \leq aantal\ gebruikers < 500$} \alignC\cell{\vfil 2} \erow \brow \alignL\cell{\vfil$500 \leq aantal\ gebruikers < 1000$} \alignC\cell{\vfil 3} \erow \brow \alignL\cell{\vfil $1000 \times n \leq aantal\ gebruikers < 1000 \times (n+1)$ \\met $n = 1, 2, 3, \dots$} \alignC\cell{\vfil$n+3$} \erow \end{calstable} \end{table} \end{document} - – Claudio Fiandrino Feb 22 '13 at 19:26 Because the macro \cals@cs@width has the character @ in its name, you need to enclose the part where you use it with \makeatletter and \makeatother. (→ What do \makeatletter and \makeatother do?) \makeatletter \def\cals@cs@width{0pt}% \makeatother If you use this in the preamble (after loading the cals package) of your document, you won’t need to repeat it every time. If you want to decide for every table whether you want vertical rules (I’d advise against it), you are better off using an @-less macro that you also define in the preamble of your document. \makeatletter \newcommand{\calsNoVertRules}{% \renewcommand{\cals@cs@width}{0pt}% } \makeatother Now you can simply use \calsNoVertRules to switch vertical rules off. - This indeed did the trick! Many thanks for the very instructive answer. Hoping to see more cals package users here. – Serge Stroobandt Feb 22 '13 at 19:21 \documentclass{report} \listfiles %tables in CALS markup \usepackage{cals} %calculate with \textwidth etc. \usepackage{calc} \newlength{\lengthw} %my suggestion \makeatletter \begin{document} \setlength{\lengthw}{\textwidth-5cm} \begin{table}[ht] \caption{Aantal uitgangen} \begin{calstable} \colwidths{{\lengthw}{5cm}} %\def\cals@cs@width{0pt} %this should delete column borders but is does not! %my suggestion %\def\cals@borderT{0.4pt} %borderTop %\def\cals@borderB{0.4pt} %borderBottom %\def\cals@borderL{0pt} %borderLeft \def\cals@borderR{0pt} %borderRight \brow \alignL\cell{} \alignC\cell{\vfil Aantal uitgangen}\erow } \brow \alignL\cell{\vfil$aantal\ gebruikers < 50$} \alignC\cell{\vfil 1 of 2 uitgangen (cfr. 7.1.2)} \erow \brow \alignL\cell{\vfil$50 \leq aantal\ gebruikers < 500$} \alignC\cell{\vfil 2} \erow \brow \alignL\cell{\vfil$500 \leq aantal\ gebruikers < 1000$} \alignC\cell{\vfil 3} \erow \brow \alignL\cell{\vfil $1000 \times n \leq aantal\ gebruikers < 1000 \times (n+1)$ \\met $n = 1, 2, 3, \dots$} \alignC\cell{\vfil$n+3$} \erow \end{calstable} \end{table} \end{document} - In order to improve your answer, you may want to show how your solution works with a complete document. Usually, this makes clear to the reader how to proceed. – Claudio Fiandrino Jan 28 '14 at 14:55 Sorry, I'm a beginner :) – Attila Kosa Jan 28 '14 at 14:57 No problems at all :) If you improve your answer, I'll be very happy to upvote it. – Claudio Fiandrino Jan 28 '14 at 14:58	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8204466104507446, "perplexity": 6186.752001836906}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 5, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2015-48/segments/1448398461390.54/warc/CC-MAIN-20151124205421-00245-ip-10-71-132-137.ec2.internal.warc.gz"}
http://aimsciences.org/article/doi/10.3934/dcds.2011.29.873	# American Institute of Mathematical Sciences 2011, 29(3): 873-891. doi: 10.3934/dcds.2011.29.873 ## On uniform convergence in ergodic theorems for a class of skew product transformations 1 Department of Statistics, University of Warwick, Coventry, CV4 7AL, United Kingdom Received October 2009 Revised August 2010 Published November 2010 Consider a class of skew product transformations consisting of an ergodic or a periodic transformation on a probability space $(M, \B,\mu)$ in the base and a semigroup of transformations on another probability space (Ω,$\F,P)$ in the fibre. Under suitable mixing conditions for the fibre transformation, we show that the properties ergodicity, weakly mixing, and strongly mixing are passed on from the base transformation to the skew product (with respect to the product measure). We derive ergodic theorems with respect to the skew product on the product space. The main aim of this paper is to establish uniform convergence with respect to the base variable for the series of ergodic averages of a function $F$ on $M\times$Ω along the orbits of such a skew product. Assuming a certain growth condition for the coupling function, a strong mixing condition on the fibre transformation, and continuity and integrability conditions for $F,$ we prove uniform convergence in the base and $\L^p(P)$-convergence in the fibre. Under an equicontinuity assumption on $F$ we further show $P$-almost sure convergence in the fibre. Our work has an application in information theory: It implies convergence of the averages of functions on random fields restricted to parts of stair climbing patterns defined by a direction. Citation: Julia Brettschneider. On uniform convergence in ergodic theorems for a class of skew product transformations. Discrete & Continuous Dynamical Systems - A, 2011, 29 (3) : 873-891. doi: 10.3934/dcds.2011.29.873 ##### References: [1] R. Adler and P. Shields, Skew products of Bernoulli shifts with rotations,, Israel J. Math., 12 (1972), 215. doi: 10.1007/BF02790748. [2] R. Adler and P. Shields, Skew products of Bernoulli shifts with rotations. II,, Israel J. Math., 19 (1974), 228. doi: 10.1007/BF02757718. [3] H. Anzai, Ergodic skew product transformations on the torus,, Osaka Math. J., 3 (1951), 83. [4] H. Bauer, Über die Beziehungen einer abstrakten Theorie des Riemann-Integrals zur Theorie Radonscher Maße,, Math. Z., 65 (1956), 448. doi: 10.1007/BF01473893. [5] A. Bellow and V. Losert, The weighted pointwise ergodic theorem and the individual ergodic theorem along subsequences,, Trans. Am. Math. Soc., 288 (1985), 307. doi: 10.1090/S0002-9947-1985-0773063-8. [6] J. R. Blum and D. L. Hanson, On the mean ergodic theorem for subsequences,, Bull. Am. Math. Soc., 66 (1969), 308. doi: 10.1090/S0002-9904-1960-10481-8. [7] J. Brettschneider, Shannon-MacMillan theorems for random fields along curves and lower bounds for surface-order large deviations,, Prob. Th. Rel. Fields, 142 (2007), 443. doi: 10.1007/s00440-007-0112-z. [8] F. Chersi and A. Volčič, $\lambda$-Equidistributed sequences of partitions and a theorem of the De Bruijn-Post type,, Annali di Matematica Pura ed Applicata, 162 (1992), 23. doi: 10.1007/BF01759997. [9] N. G. de Bruijn and K. A. Post, A remark on uniformly distributed sequences and Riemann integrability,, Indag. Math., 30 (1968), 149. [10] J. L. Doob, "Measure Theory,", Springer-Verlag, (1993). [11] F. den Hollander and M. Keane, Ergodic properties of color records,, Physica A, 138 (1986), 183. doi: 10.1016/0378-4371(86)90179-2. [12] N. Friedman, Mixing on sequences,, Can. J. Math., 35 (1983), 339. [13] H. Furstenberg, Strict ergodicity and transformation of the torus,, Amer. J. Math., 83 (1961), 573. doi: 10.2307/2372899. [14] H.-O. Georgii, "Gibbs Measures and Phase Transitions,", W. de Gruyter, (1988). [15] H.-O. Georgii, Mixing properties of induced random transformations,, Ergod. Th. and Dynam. Systems, 17 (1997), 839. doi: 10.1017/S0143385797086343. [16] O. Hauptmann and C. Pauc, "Differential - und Integralrechnung, Band III," 2. Auflage,, Göschen Lehrbücherei, 26 (1955). [17] P. Hellekalek and G. Larcher, On the ergodicity of a class of skew products,, Israel J. Math., 54 (1986), 301. doi: 10.1007/BF02764958. [18] P. Hellekalek and G. Larcher, On Weyl sums and skew products over irrational rotations,, Theoret. Comput. Sci., 65 (1989), 189. doi: 10.1016/0304-3975(89)90043-1. [19] K. Jacobs, "Measure and Integral,", Academic Press, (1978). [20] S. Kakutani, Random ergodic theorems and Markov processes with a stable distribution, in, in, (1951), 247. [21] A. Katok and B. Hasselblatt, "Introduction to the Modern Theory of Dynamical Systems,", Cambridge Univ. Press, (1995). [22] U. Krengel, "Ergodic theorems,", W. de Gruyter, (1985). [23] M. Lemańczyk and E. Lesigne, Ergodicity of Rokhlin cocycles,, J. Anal. Math., 85 (2001), 43. doi: 10.1007/BF02788075. [24] L. H. Loomis, Linear functional and content,, Amer. J. Math., 76 (1954), 68. doi: 10.2307/2372407. [25] I. Meilijson, Mixing properties of a class of skew-products,, Israel J. Math., 19 (1974), 266. doi: 10.1007/BF02757724. [26] J. Milnor, On the entropy geometry of cellular automata,, Complex Syst., 2 (1988), 357. [27] I. Oren, Ergodicity of cylinder flows arising from irregularities of distribution,, Israel J. Math., 44 (1983), 127. doi: 10.1007/BF02760616. [28] D. A. Pask, Skew products over the irrational rotation,, Israel J. Math., 69 (1990), 65. doi: 10.1007/BF02764730. [29] C. Pauc, Intégrale de partition et intégrale topologique. Familles dérivantes topologiques,, C. r. Acad. Sci. Paris, 230 (1950), 810. [30] P. Walters, "An Introduction to Ergodic Theory,", Springer-Verlag, (1982). [31] H. Weyl, Über die Gleichverteilung von Zahlen mod Eins,, Math. Ann., 77 (): 313. doi: 10.1007/BF01475864. [32] Q. Zhang, On skew products of irrational rotations with tori,, in, 5 (1996), 435. show all references ##### References: [1] R. Adler and P. Shields, Skew products of Bernoulli shifts with rotations,, Israel J. Math., 12 (1972), 215. doi: 10.1007/BF02790748. [2] R. Adler and P. Shields, Skew products of Bernoulli shifts with rotations. II,, Israel J. Math., 19 (1974), 228. doi: 10.1007/BF02757718. [3] H. Anzai, Ergodic skew product transformations on the torus,, Osaka Math. J., 3 (1951), 83. [4] H. Bauer, Über die Beziehungen einer abstrakten Theorie des Riemann-Integrals zur Theorie Radonscher Maße,, Math. Z., 65 (1956), 448. doi: 10.1007/BF01473893. [5] A. Bellow and V. Losert, The weighted pointwise ergodic theorem and the individual ergodic theorem along subsequences,, Trans. Am. Math. Soc., 288 (1985), 307. doi: 10.1090/S0002-9947-1985-0773063-8. [6] J. R. Blum and D. L. Hanson, On the mean ergodic theorem for subsequences,, Bull. Am. Math. Soc., 66 (1969), 308. doi: 10.1090/S0002-9904-1960-10481-8. [7] J. Brettschneider, Shannon-MacMillan theorems for random fields along curves and lower bounds for surface-order large deviations,, Prob. Th. Rel. Fields, 142 (2007), 443. doi: 10.1007/s00440-007-0112-z. [8] F. Chersi and A. Volčič, $\lambda$-Equidistributed sequences of partitions and a theorem of the De Bruijn-Post type,, Annali di Matematica Pura ed Applicata, 162 (1992), 23. doi: 10.1007/BF01759997. [9] N. G. de Bruijn and K. A. Post, A remark on uniformly distributed sequences and Riemann integrability,, Indag. Math., 30 (1968), 149. [10] J. L. Doob, "Measure Theory,", Springer-Verlag, (1993). [11] F. den Hollander and M. Keane, Ergodic properties of color records,, Physica A, 138 (1986), 183. doi: 10.1016/0378-4371(86)90179-2. [12] N. Friedman, Mixing on sequences,, Can. J. Math., 35 (1983), 339. [13] H. Furstenberg, Strict ergodicity and transformation of the torus,, Amer. J. Math., 83 (1961), 573. doi: 10.2307/2372899. [14] H.-O. Georgii, "Gibbs Measures and Phase Transitions,", W. de Gruyter, (1988). [15] H.-O. Georgii, Mixing properties of induced random transformations,, Ergod. Th. and Dynam. Systems, 17 (1997), 839. doi: 10.1017/S0143385797086343. [16] O. Hauptmann and C. Pauc, "Differential - und Integralrechnung, Band III," 2. Auflage,, Göschen Lehrbücherei, 26 (1955). [17] P. Hellekalek and G. Larcher, On the ergodicity of a class of skew products,, Israel J. Math., 54 (1986), 301. doi: 10.1007/BF02764958. [18] P. Hellekalek and G. Larcher, On Weyl sums and skew products over irrational rotations,, Theoret. Comput. Sci., 65 (1989), 189. doi: 10.1016/0304-3975(89)90043-1. [19] K. Jacobs, "Measure and Integral,", Academic Press, (1978). [20] S. Kakutani, Random ergodic theorems and Markov processes with a stable distribution, in, in, (1951), 247. [21] A. Katok and B. Hasselblatt, "Introduction to the Modern Theory of Dynamical Systems,", Cambridge Univ. Press, (1995). [22] U. Krengel, "Ergodic theorems,", W. de Gruyter, (1985). [23] M. Lemańczyk and E. Lesigne, Ergodicity of Rokhlin cocycles,, J. Anal. Math., 85 (2001), 43. doi: 10.1007/BF02788075. [24] L. H. Loomis, Linear functional and content,, Amer. J. Math., 76 (1954), 68. doi: 10.2307/2372407. [25] I. Meilijson, Mixing properties of a class of skew-products,, Israel J. Math., 19 (1974), 266. doi: 10.1007/BF02757724. [26] J. Milnor, On the entropy geometry of cellular automata,, Complex Syst., 2 (1988), 357. [27] I. Oren, Ergodicity of cylinder flows arising from irregularities of distribution,, Israel J. Math., 44 (1983), 127. doi: 10.1007/BF02760616. [28] D. A. Pask, Skew products over the irrational rotation,, Israel J. Math., 69 (1990), 65. doi: 10.1007/BF02764730. [29] C. Pauc, Intégrale de partition et intégrale topologique. Familles dérivantes topologiques,, C. r. Acad. Sci. Paris, 230 (1950), 810. [30] P. Walters, "An Introduction to Ergodic Theory,", Springer-Verlag, (1982). [31] H. Weyl, Über die Gleichverteilung von Zahlen mod Eins,, Math. Ann., 77 (): 313. doi: 10.1007/BF01475864. [32] Q. Zhang, On skew products of irrational rotations with tori,, in, 5 (1996), 435. [1] Matúš Dirbák. Minimal skew products with hypertransitive or mixing properties. Discrete & Continuous Dynamical Systems - A, 2012, 32 (5) : 1657-1674. doi: 10.3934/dcds.2012.32.1657 [2] Zuohuan Zheng, Jing Xia, Zhiming Zheng. Necessary and sufficient conditions for semi-uniform ergodic theorems and their applications. Discrete & Continuous Dynamical Systems - A, 2006, 14 (3) : 409-417. doi: 10.3934/dcds.2006.14.409 [3] Roy Adler, Bruce Kitchens, Michael Shub. Stably ergodic skew products. Discrete & Continuous Dynamical Systems - A, 1996, 2 (3) : 349-350. doi: 10.3934/dcds.1996.2.349 [4] Jory Griffin, Jens Marklof. Limit theorems for skew translations. 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Journal of Modern Dynamics, 2008, 2 (2) : 339-358. doi: 10.3934/jmd.2008.2.339 [10] Tanja Eisner, Jakub Konieczny. Automatic sequences as good weights for ergodic theorems. Discrete & Continuous Dynamical Systems - A, 2018, 38 (8) : 4087-4115. doi: 10.3934/dcds.2018178 [11] C.P. Walkden. Stable ergodicity of skew products of one-dimensional hyperbolic flows. Discrete & Continuous Dynamical Systems - A, 1999, 5 (4) : 897-904. doi: 10.3934/dcds.1999.5.897 [12] François Ledrappier, Omri Sarig. Unique ergodicity for non-uniquely ergodic horocycle flows. Discrete & Continuous Dynamical Systems - A, 2006, 16 (2) : 411-433. doi: 10.3934/dcds.2006.16.411 [13] P.E. Kloeden, Victor S. Kozyakin. The perturbation of attractors of skew-product flows with a shadowing driving system. Discrete & Continuous Dynamical Systems - A, 2001, 7 (4) : 883-893. doi: 10.3934/dcds.2001.7.883 [14] Saša Kocić. Reducibility of skew-product systems with multidimensional Brjuno base flows. 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Discrete & Continuous Dynamical Systems - A, 2018, 38 (6) : 2687-2716. doi: 10.3934/dcds.2018113 2017 Impact Factor: 1.179	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6202527284622192, "perplexity": 4287.596954002076}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-51/segments/1544376823817.62/warc/CC-MAIN-20181212091014-20181212112514-00086.warc.gz"}
https://www.physicsforums.com/threads/normalised-wavefunction-to-calculate-the-expectation.398226/	# Normalised wavefunction to calculate the expectation 1. Apr 25, 2010 ### roshan2004 Do we have to use normalised wavefunction to calculate the expectation and probability of finding the particle? If yes, why? 2. Apr 25, 2010 ### clem Re: Normalisation The probabiliity of the particle being anywhere must be one. 3. Apr 25, 2010 ### roshan2004 Re: Normalisation I know about it, but I have seen using normalised wavefunction in calculating the expectation only so? 4. Apr 25, 2010 ### SpectraCat Re: Normalisation The measurement postulate defines the expectation value of an arbitrary Hermitian operator A for an arbitrary wavefunction $$\Psi$$ as: $$<A>=\frac{<\Psi\|\hat{A}\|\Psi>}{<\Psi\|\Psi>}$$ this is valid for all wavefunctions, including unnormalized ones. If the wavefunction is normalized, the integral in the denominator is just 1, so you only need the numerator. Last edited: Apr 25, 2010 5. Apr 25, 2010 ### Staff: Mentor Re: Normalisation Of course, the denominator is just the normalization integral. So one way or another, you end up normalizing the wave function. Either you or somebody else does it beforehand, or you do it as part of finding the expectation value. 6. Apr 25, 2010 ### LostConjugate Re: Normalisation To take the expectation value of an operator you first act on the function (quantum state) with the operator, which gives you a new function. Then you dot the new function with the original function to see how much of the new function is linear with the original function. If you think of the functions as vectors this is how much the new vector lies along the original vector. However the dot product could have any amplitude if the function is not normalized, which is not of much interest. If we then normalize the result or start with a normalized function then a result of 1 means the new vector is linear with the original vector and 0 means it is orthogonal. And everything in between 0 and 1 means there is a percentage that is linear and orthogonal and we know exactly what that is. Last edited: Apr 25, 2010	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9595250487327576, "perplexity": 679.3919489088321}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-43/segments/1539583511897.56/warc/CC-MAIN-20181018173140-20181018194640-00323.warc.gz"}
https://testbook.com/question-answer/the-distance-between-the-points-6-4-and-3-0--6076f881db06664a2787ae4a	# The distance between the points (6, - 4) and (3, 0) is 1. 5 2. 2 3. 3 4. 4 5. None of these Option 1 : 5 ## Detailed Solution Concept: If P(x1, y1) and Q(x2, y2) are two points in a 2D plane then the distance between the points P(x1, y1) and Q(x2, y2) is given by: $$PQ = \sqrt {{{\left( {{x_2} - {x_1}} \right)}^2} + {{\left( {{y_2} - {y_1}} \right)}^2}}$$ Calculation: Here, we have to find the distance between the points (6, - 4) and (3, 0). Let, P = (6, - 4) and Q = (3, 0) As we know that, the distance between the points P(x1, y1) and Q(x2, y2) is given by: $$PQ = \sqrt {{{\left( {{x_2} - {x_1}} \right)}^2} + {{\left( {{y_2} - {y_1}} \right)}^2}} = \sqrt {{{\left( {3 - 6} \right)}^2} + {{\left( {0 - \left( { - 4} \right)} \right)}^2}} = 5\;\rm units$$ Hence, the distance between the given points is 5 units.	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8617970943450928, "perplexity": 1123.302229102444}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-05/segments/1642320304749.63/warc/CC-MAIN-20220125005757-20220125035757-00370.warc.gz"}
http://physics.stackexchange.com/users/8579/boris?tab=reputation	# Boris less info reputation 15 bio website molecular.cz/~fackovec location Prague, Czech Republic age 25 member for 3 years, 1 month seen Jan 10 '13 at 17:45 profile views 18 # 306 Reputation 110 May 19 '13 +100 02:08 assoc Association Bonus +10 02:08 upvote What does it mean for two objects to “touch”? 25 Nov 15 '12 +25 19:09 2 events Energy formula for separating $O_2$ from mixture of $O_2$, $NH_3$ and $H_2O$ 5 Oct 21 '12 +5 16:16 upvote Density of classical states in quantum theory 15 Sep 14 '12 10 Sep 8 '12 10 Jun 19 '12 10 Apr 21 '12 50 Apr 16 '12 50 Apr 15 '12 20 Apr 10 '12	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.1706164926290512, "perplexity": 7810.221171511696}, "config": {"markdown_headings": true, "markdown_code": false, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2015-22/segments/1432207930259.97/warc/CC-MAIN-20150521113210-00159-ip-10-180-206-219.ec2.internal.warc.gz"}
https://moodle-1819.wooster.edu/course/info.php?id=716&lang=km	### Scientific Computing FA18 (CSCI-10000-01) CSCI 10000. SCIENTIFIC COMPUTING The purpose of this course is to show some of the connections between computer science and other disciplines such as mathematics and the natural sciences. We will study the fundamental computer science concepts for the design and implementation of solutions to problems that can be solved through approximations, simulations, interpolations, and recursive formulas. [MNS]	{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8879420161247253, "perplexity": 590.6732346743314}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-39/segments/1631780057018.8/warc/CC-MAIN-20210920040604-20210920070604-00476.warc.gz"}
https://www.electro-tech-online.com/threads/noobie-question-about-using-a-diode-to-protect-power-to-a-looper-pedal.151850/	# Noobie question about using a diode to protect power to a Looper pedal Status Not open for further replies. ##### Member I am building a Looper that runs on 9 volts, sleeve positive. Is it easy to put in a diode to protect against reversing the power by mistake? Do I put the diode in the negative connection from the DC jack (tip), and which way does the band face? Also, how do I select a diode? I'm looking at an inexpensive 1N4007 1A 1000V General Purpose Rectifier Diode. Will that work? If not, what am I looking for? #### jpanhalt ##### Well-Known Member Diodes can be configured as simply protective. That is, they short the input (adding a resistor maybe advised) when the polarity is reversed. They can also be configured to facilitate either polarity. A bridge rectifier does that. The disadvantage is the small voltage drop you get. If your circuit needs 5V, the drop from a 9V battery can be tolerated. What is a "Looper?" Can you provide the circuit you plan that will let us correct it? #### dr pepper ##### Well-Known Member A diode can go in either lead, but traditionally it goes in the positive, the silver band towards the device being supplied, in this case the looper. What Jp was saying is that sometimes the diode is placed inside the device to be protected across the supply inversely connected, so that if you power the thing with the wrong polarity the diode conducts and effectively shorts out the supply, blowing a fuse and protecting it, only if there isnt a fuse, and there often isnt problems are going to arise. Jp a looper is a sampler, you pressa button it samples audio, then when you next press the button it sstops ampling audio then plays what it has just sampled over and over, you can sort of record & play your own accompaniment as you go, very popular for street performers. ##### Member Thanks for the quick reply jpanhalt. The type of Looper I am building is for electric guitar pedal effects. It uses five Clickless Bypass Relay type circuits wired together in series to put effects in and out of the signal chain. They run at 9 volts. The relays run at less than 1 mA, and the led that shows if the loop is engaged can be around 2 mA but I tested a 20 mA Led on one relay circuit already and it works. The relay peaks at 23 mA (not including the Led) when it switches. My concern is that I may plug in a 2.1 mm sleeve negative 9 volts, and fry the whole thing. There is no diodes on the circuit boards. I just wanted to block 9 volts from going to the circuits negative connection in case I use the wrong AC/DC adapter. ##### Member Thanks dr pepper. Ok I get what jp is saying now. That makes sense with a fuse. Yes your right about a looper being a sampler. I think looper is also slang maybe for an effect switching system as the simple ones just loop the effects in and out of "the loop" in series. I would have thought that the diode would work on the negative connection of the power jack as then it would block the 9volts + from reaching the circuit. #### Nigel Goodwin ##### Super Moderator If you post a circuit diagram we can tell you where to place the diode (it's simple and obvious), but we can't do that from vague descriptions. #### dr pepper ##### Well-Known Member Your right it would work in the - line, its just the majority of that kind of thing that I have seen its in the +. Edit: thinking about it the diode needs to go in the +, if you put it in the - then ground will be lifted by a diode drop - 0.6v, this could cause ground loop issues if you have other effects units in the system, or even just between the loop and the amp. ##### Member Great info thanks dr pepper. I understand how to wire the diode now. (It's obvious too, like Nigel Goodwin says. I'll try to find a diagram too, Nigel) So If I put a diode in line with the positive lead to the circuit, is there a small voltage drop there? Also, can I use any diode as long as it is rated for more than the 9 volts and (about) 200mA? (I'm going to assume that it's not a Zener diode that I need but a Rectifier Diode?) I'm making an order of misc. parts that I need for my projects, and I would like to add a handfull of diodes for my various projects specifically for this safety feature. Apart from the Zener Diodes, this company offers: 1N4007 1A 1000V General Purpose Rectifier Diode - $0.09 each 1N5408 General Purpose Rectifier Diode 3A 1000V - 10-Pack -$1.90 Power Supply Rectifier Diode 6A 1000V - Used as a rectifier in higher current power supplies, also known as 6A10 - $0.48 each 1N4148 Logic Diode (DO-41 case style) -$0.04 each 1N914 Small Signal Fast Switching Diode - $0.06 each 1N4935 Fast Recovery Rectifier Diode 200V 1A DO-41 -$0.19 each Mike. ##### Member Thanks Pommie. I'll look at Sparkfun's website. crutschow, that's an interesting part! Does the "drain" pin also connect to the "drain" flange? Can I ground it just by soldering the drain pin to ground and sticking it in the enclosure with velcro or double sided sticky tape? Or should I screw it to the back of the enclosure? #### Nigel Goodwin ##### Super Moderator As you don't know where to stick a diode, you don't want to be confusing yourself trying to use an FET instead EVERYTHING commercial uses a simple diode, and the 0.7V drop is of no consequence at all. As we've said before, post a circuit and we'll show you exactly where and how to connect the diode. #### crutschow ##### Well-Known Member Does the "drain" pin also connect to the "drain" flange? Yes, they are connected together. That pin is the substrate connection to the MOSFET chip, which is soldered to the flange. Can I ground it just by soldering the drain pin to ground and sticking it in the enclosure with velcro or double sided sticky tape? Or should I screw it to the back of the enclosure? As I stated in post #13, "The P-MOSFET Drain goes to the positive input voltage supply, the Gate goes to ground, and the Source goes to the positive circuit power." Why do you think the drain goes to ground? Since the MOSFET will be dissipating very little power when operating it doesn't need to be mounted to the enclosure. Any convenient way to mount it is fine (even just using the leads). But as noted by others, if the 0.7V drop of a diode is of no consequence in your circuit than just use a diode. #### dr pepper ##### Well-Known Member At the risk of being burned I'll explain how its done commercially with 0 volt drop (and this has already been mentioned). Put a diode across the supply terminals of the looper in reverse, so the silver strip goes to the +, and the other side to -, then you put a fuse, or fusible resistor inline with the supply (before the diode). Then if you power the device in reverse the diode will turn on and blow the fuse. Obviously a fuse or some means of disconnecting the supply is important here. ##### Member ok that makes sense with a fuse, dr pepper. crutschow, I see that I got the P-MOSFET connections wrong, but if the Drain is connected to the positive connection, and the Drain is also the Flange and I screw it to the enclosure, and the flange is then grounded, it will ground the Drain! That's why I thought the Drain goes to ground! (unless I'm getting this wrong!) Nigel, here is a diagram of the Lace Looper from Mammoth Electronics, available in 3, 4, or 5 loops and lots of powdercoat options. Can be ordered with mechanical switches or Clickless Bypass Circuits. Comes with the Clickless circuits for that option. (Mine was around \$112.00 for 5 loops and powdercoat with the clickless option. The Clickless circuits are preassembled). Note: The Send and Return are labeled backwards according to the connections on the Clickless circuit boards. Last edited: #### crutschow ##### Well-Known Member I see that I got the P-MOSFET connections wrong, but if the Drain is connected to the positive connection, and the Drain is also the Flange and I screw it to the enclosure, and the flange is then grounded, it will ground the Drain! That's why I thought the Drain goes to ground! (unless I'm getting this wrong!) The MOSFET flange cannot be connected to ground. That's why you must not screw the flange to the enclosure without an electrical insulator between the flange and the enclosure along with an insulator for the screw (or use a nylon nut and bolt). #### crutschow ##### Well-Known Member Obviously a fuse or some means of disconnecting the supply is important here. That's why I like a MOSFET for reverse protection with a near zero forward voltage drop (you can get MOSFETs with only a few milliohms of forward resistance), it doesn't require a fuse. Status Not open for further replies. Replies 2 Views 613 Replies 1 Views 644 Replies 5 Views 622 Replies 8 Views 3K Replies 3 Views 990	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5503981709480286, "perplexity": 2306.56135181598}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-04/segments/1610703531702.36/warc/CC-MAIN-20210123001629-20210123031629-00736.warc.gz"}
http://math.stackexchange.com/questions/456448/pushout-in-set-example-2-6-2-2-in-david-spivaks-book	# Pushout in Set example 2.6.2.2. in David Spivak's Book Trying to understand Example 2.6.2.2. on page 50 of David I. Spivak's book "Category Theory for Scientists," Spivak gives $X$ as the interval $[0..1]=\{x\in\mathbb{R}\|\,0\le x\le 1\}$, $Y$ as the interval $[1..2]=\{x\in\mathbb{R}\|\,1\le x\le 2\}$, and $W$ as the singleton set $\{1\}$. He then states that the pushout $X\overset{f}{\longleftarrow}W\overset{g}{\longrightarrow}$, where $f$ and $g$ are the "obvious" maps $(1_W\mapsto 1_X)$ and $(1_W\mapsto 1_Y)$, is $[0..2]=\{x\in\mathbb{R}\|\,0\le x\le 2\}$, "as expected." But it looks to me like the pushout is supposed to be the quotient of $X\sqcup W\sqcup Y$ by an equivalence relation generated by the "obvious" functions, which would make the pushout a set with two elements, each of which is an equivalence class in $X\sqcup W\sqcup Y$; the first equivalence class being $1_W$, $1_X$, $1_Y$ and the second equivalence class being $[0..1)\cup(1..2]=\{x\in\mathbb{R}\|\,0\le x\lt 1\}\cup\{x\in\mathbb{R}\|\,1\lt x\le 2\}$. Where am I going wrong? Details of my reasoning follow. I read the pushout as any set isomorphic to the fiber sum, which is the quotient set of the triple disjoint union $X\sqcup W\sqcup Y$ by the equivalence relation generated by the equivalences $w\, {\raise.17ex\hbox{$\scriptstyle\mathtt{\sim}$}}f(w)$ and $w\, {\raise.17ex\hbox{$\scriptstyle\mathtt{\sim}$}}g(w)$ (quoting loosely from the book, Definition 2.6.2.1, page 50). The equivalences, here, seem to need some interpretation. Because equivalences are defined only in the cartesian product of a set with itself (definition 2.6.1.1, page 47), I interpret the ${\raise.17ex\hbox{$\scriptstyle\mathtt{\sim}$}}$ relation to actually be in the cartesian product set $(X\sqcup W\sqcup Y)\times (X\sqcup W\sqcup Y)$; and the notation $w\, {\raise.17ex\hbox{$\scriptstyle\mathtt{\sim}$}}f(w)$ to actually mean $w_W\, {\raise.17ex\hbox{$\scriptstyle\mathtt{\sim}$}}f(w)_X$, where $w_W$ is the element $w$ in the disjoint union $X\sqcup W\sqcup Y$ that "remembers" it was included from set $W$, and $f(w)_X$ is the element $f(w)$ in the disjoint union $X\sqcup W\sqcup Y$ that "remembers" it was included from set $X$, both by the canonical inclusion maps from $W$ and $X$ into the disjoint union. Ditto for $w\, {\raise.17ex\hbox{$\scriptstyle\mathtt{\sim}$}}g(w)$, which I take to actually mean $w_W\, {\raise.17ex\hbox{$\scriptstyle\mathtt{\sim}$}}g(w)_Y$. Under that interpretation (the only reasonable one I can see for the relation), I find that the three elements $1_W$, $1_X$, $1_Y$ form one equivalence class in $X\sqcup W\sqcup Y$, and that all other points, namely $[0..1)_X\cup(1..2]_Y=\{x_X\|\,x\in\mathbb{R}\|\,0\le x\lt 1\}\cup\{y_Y\|\,y\in\mathbb{R},1\lt y\le 2\}$ form another equivalence class. Therefore, I see two elements in the fiber sum, i.e., the pushout. I can't find a way to make Spivak's claimed pushout $[0..2]=\{x\in\mathbb{R}\|\,0\le x\le 2\}$ isomorphic to the fiber sum because the fiber sum puts $1$ in one equivalence class and all other points in another equivalence class. What have I missed? - In the example in your question, the two "obvious" functions each contain one pair, so the relevant equivalence relation is generated by those two pairs, namely $(1_W,1_X)$ and $(1_W,1_Y)$, where I've used subscripts to indicate which of the three sets the element comes from. The equivalence relation thus consists of these two pairs, the pair $(1_X,1_Y)$, the three pairs obtained from these by reversing the order of components, and all pairs of the form $(a,a)$ for $a\in X\sqcup Y\sqcup W$. When you form the quotient by this equivalence relation, you identify the $1$'s of the three given sets, but there are no further identifications. In particular, distinct elements in the $[0..1)$ in $X$ and the $(1..2]$ in $Y$ remain distinct in the pushout.	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.920701801776886, "perplexity": 117.27918086699577}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2015-22/segments/1432207930866.66/warc/CC-MAIN-20150521113210-00089-ip-10-180-206-219.ec2.internal.warc.gz"}
https://worldwidescience.org/topicpages/a/amyloid+precursor+protein.html	#### Sample records for amyloid precursor protein 1. Copper Promotes the Trafficking of the Amyloid Precursor Protein* OpenAIRE Acevedo, Karla M.; Hung, Ya Hui; Dalziel, Andrew H.; Li, Qiao-Xin; Laughton, Katrina; Wikhe, Krutika; Rembach, Alan; Roberts, Blaine; Masters, Colin L.; Ashley I. Bush; Camakaris, James 2010-01-01 Accumulation of the amyloid β peptide in the cortical and hippocampal regions of the brain is a major pathological feature of Alzheimer disease. Amyloid β peptide is generated from the sequential protease cleavage of the amyloid precursor protein (APP). We reported previously that copper increases the level of APP at the cell surface. Here we report that copper, but not iron or zinc, promotes APP trafficking in cultured polarized epithelial cells and neuronal cells. In SH-SY5Y neuronal cells ... 2. Amyloid Precursor Protein Processing in Alzheimer’s Disease Directory of Open Access Journals (Sweden) 2012-03-01 Full Text Available How to Cite this Article: Bhadbhade A, Cheng DW. Amyloid Precursor Protein Processing in Alzheimer’s Disease. Iranian Journal of Child Neurology2012;6(1:1-5.Alzheimer’s disease (AD is a progressive neurodegenerative disorder and a leading cause of dementia. The AD is characterized by presence of intraneuronal tangles and extracellular plaques in the brain. The plaques are composed of dense and mostly insoluble deposits of amyloid beta peptide (Aβ, formed by sequential cleavage of the Amyloid Precursor Protein (APP, by two pathways amyloidogenic and non-amyloidogenic. Tangles are composed of paired helical fragments, which aggregate to form, microtubular protein tau. Although Aβ plaques are established to be the cause of the disease, there exist genetic factors and other pathological identifications in addition to these which are an integral part of the disease. This article gives an overview into the mechanism of APP action, genetic factors and other pathological identifications contributing to Alzheimer’s disease formation.References Brookmeyer R, Gray S, Kawas C. Projections of Alzheimer’s disease in the United States and the public health impact of delaying disease onset. American Journal of Public Health 1998;88(9:1337. Hebert LE, Scherr PA, Bienias JL, Bennett DA, Evans DA. Alzheimer disease in the US population. Arch Neurol 2003;60(8:1119-22. Möller HJ, Graeber M. The case described by Alois Alzheimer in 1911. European Archives of Psychiatry and Clinical Neuroscience 1998:248(3:111-122. Selkoe D J. (2002. Deciphering the genesis and fate of amyloid beta-protein yields novel therapies for Alzheimer disease. J Clinic Investigat 2002;110(10: 1375-82. Wolfe MS. Tau mutations in neurodegenerative diseases. J Biolog Chem 2009;284(10:6021. Selkoe DJ. Alzheimer’s disease: genes, proteins, and therapy. Physiological reviews 2001;81(2:741. Selkoe DJ. The cell biology of [beta]-amyloid precursor protein and presenilin in Alzheimer 3. AMYPdb: A database dedicated to amyloid precursor proteins Directory of Open Access Journals (Sweden) Delamarche Christian 2008-06-01 Full Text Available Abstract Background Misfolding and aggregation of proteins into ordered fibrillar structures is associated with a number of severe pathologies, including Alzheimer's disease, prion diseases, and type II diabetes. The rapid accumulation of knowledge about the sequences and structures of these proteins allows using of in silico methods to investigate the molecular mechanisms of their abnormal conformational changes and assembly. However, such an approach requires the collection of accurate data, which are inconveniently dispersed among several generalist databases. Results We therefore created a free online knowledge database (AMYPdb dedicated to amyloid precursor proteins and we have performed large scale sequence analysis of the included data. Currently, AMYPdb integrates data on 31 families, including 1,705 proteins from nearly 600 organisms. It displays links to more than 2,300 bibliographic references and 1,200 3D-structures. A Wiki system is available to insert data into the database, providing a sharing and collaboration environment. We generated and analyzed 3,621 amino acid sequence patterns, reporting highly specific patterns for each amyloid family, along with patterns likely to be involved in protein misfolding and aggregation. Conclusion AMYPdb is a comprehensive online database aiming at the centralization of bioinformatic data regarding all amyloid proteins and their precursors. Our sequence pattern discovery and analysis approach unveiled protein regions of significant interest. AMYPdb is freely accessible 1. 4. Betaine suppressed Aβ generation by altering amyloid precursor protein processing. Science.gov (United States) Liu, Xiu-Ping; Qian, Xiang; Xie, Yue; Qi, Yan; Peng, Min-Feng; Zhan, Bi-Cui; Lou, Zheng-Qing 2014-07-01 Betaine was an endogenous catabolite of choline, which could be isolated from vegetables and marine products. Betaine could promote the metabolism of homocysteine in healthy subjects and was used for hyperlipidemia, coronary atherosclerosis, and fatty liver in clinic. Recent findings shown that Betaine rescued neuronal damage due to homocysteine induced Alzheimer's disease (AD) like pathological cascade, including tau hyperphosphorylation and amyloid-β (Aβ) deposition. Aβ was derived from amyloid precursor protein (APP) processing, and was a triggering factor for AD pathological onset. Here, we demonstrated that Betaine reduced Aβ levels by altering APP processing in N2a cells stably expressing Swedish mutant of APP. Betaine increased α-secretase activity, but decreased β-secretase activity. Our data indicate that Betaine might play a protective role in Aβ production. 5. Therapeutic Potential of Secreted Amyloid Precursor Protein APPsα Science.gov (United States) Mockett, Bruce G.; Richter, Max; Abraham, Wickliffe C.; Müller, Ulrike C. 2017-01-01 Cleavage of the amyloid precursor protein (APP) by α-secretase generates an extracellularly released fragment termed secreted APP-alpha (APPsα). Not only is this process of interest due to the cleavage of APP within the amyloid-beta sequence, but APPsα itself has many physiological properties that suggest its great potential as a therapeutic target. For example, APPsα is neurotrophic, neuroprotective, neurogenic, a stimulator of protein synthesis and gene expression, and enhances long-term potentiation (LTP) and memory. While most early studies have been conducted in vitro, effectiveness in animal models is now being confirmed. These studies have revealed that either upregulating α-secretase activity, acutely administering APPsα or chronic delivery of APPsα via a gene therapy approach can effectively treat mouse models of Alzheimer’s disease (AD) and other disorders such as traumatic head injury. Together these findings suggest the need for intensifying research efforts to harness the therapeutic potential of this multifunctional protein. 6. Divalent cation tolerance protein binds to β-secretase and inhibits the processing of amyloid precursor protein Institute of Scientific and Technical Information of China (English) Runzhong Liu; Haibo Hou; Xuelian Yi; Shanwen Wu; Huan Zeng 2013-01-01 The deposition of amyloid-beta is a pathological hallmark of Alzheimer's disease. Amyloid-beta is derived from amyloid precursor protein through sequential proteolytic cleavages by β-secretase (beta-site amyloid precursor protein-cleaving enzyme 1) and γ-secretase. To further elucidate the roles of beta-site amyloid precursor protein-cleaving enzyme 1 in the development of Alzheimer's disease, a yeast two-hybrid system was used to screen a human embryonic brain cDNA library for proteins directly interacting with the intracellular domain of beta-site amyloid precursor protein-cleaving enzyme 1. A potential beta-site amyloid precursor protein-cleaving enzyme 1- interacting protein identified from the positive clones was divalent cation tolerance protein. Immunoprecipitation studies in the neuroblastoma cell line N2a showed that exogenous divalent cation tolerance protein interacts with endogenous beta-site amyloid precursor protein-cleaving enzyme 1. The overexpression of divalent cation tolerance protein did not affect beta-site amyloid precursor protein-cleaving enzyme 1 protein levels, but led to increased amyloid precursor protein levels in N2a/APP695 cells, with a concomitant reduction in the processing product amyloid precursor protein C-terminal fragment, indicating that divalent cation tolerance protein inhibits the processing of amyloid precursor protein. Our experimental findings suggest that divalent cation tolerance protein negatively regulates the function of beta-site amyloid precursor protein-cleaving enzyme 1. Thus, divalent cation tolerance protein could play a protective role in Alzheimer's disease. 7. Amyloid precursor protein is trafficked and secreted via synaptic vesicles. Directory of Open Access Journals (Sweden) Teja W Groemer Full Text Available A large body of evidence has implicated amyloid precursor protein (APP and its proteolytic derivatives as key players in the physiological context of neuronal synaptogenesis and synapse maintenance, as well as in the pathology of Alzheimer's Disease (AD. Although APP processing and release are known to occur in response to neuronal stimulation, the exact mechanism by which APP reaches the neuronal surface is unclear. We now demonstrate that a small but relevant number of synaptic vesicles contain APP, which can be released during neuronal activity, and most likely represent the major exocytic pathway of APP. This novel finding leads us to propose a revised model of presynaptic APP trafficking that reconciles existing knowledge on APP with our present understanding of vesicular release and recycling. 8. Altered β-Amyloid Precursor Protein Isoforms in Mexican Alzheimer’s Disease Patients Directory of Open Access Journals (Sweden) V. J. Sánchez-González 2006-01-01 Full Text Available Objective: To determine the β-amyloid precursor protein (βAPP isoforms ratio as a risk factor for Alzheimer’s Disease and to assess its relationship with demographic and genetic variables of the disease. 9. B-Amyloid Precursor Protein Staining of the Brain in Sudden Infant and Early Childhood Death DEFF Research Database (Denmark) Jensen, Lisbeth Lund; Banner, Jytte; Ulhøi, Benedicte Parm 2013-01-01 To develop and validate a scoring method for assessing β-amyloid precursor protein (APP) staining in cerebral white matter and to investigate the occurrence, amount and deposition pattern based on the cause of death in infants and young children.......To develop and validate a scoring method for assessing β-amyloid precursor protein (APP) staining in cerebral white matter and to investigate the occurrence, amount and deposition pattern based on the cause of death in infants and young children.... 10. Amyloid precursor-like protein 1 (APLP1) exhibits stronger zinc-dependent neuronal adhesion than amyloid precursor protein and APLP2. Science.gov (United States) Mayer, Magnus C; Schauenburg, Linda; Thompson-Steckel, Greta; Dunsing, Valentin; Kaden, Daniela; Voigt, Philipp; Schaefer, Michael; Chiantia, Salvatore; Kennedy, Timothy E; Multhaup, Gerhard 2016-04-01 The amyloid precursor protein (APP) and its paralogs, amyloid precursor-like protein 1 (APLP1) and APLP2, are metalloproteins with a putative role both in synaptogenesis and in maintaining synapse structure. Here, we studied the effect of zinc on membrane localization, adhesion, and secretase cleavage of APP, APLP1, and APLP2 in cell culture and rat neurons. For this, we employed live-cell microscopy techniques, a microcontact printing adhesion assay and ELISA for protein detection in cell culture supernatants. We report that zinc induces the multimerization of proteins of the amyloid precursor protein family and enriches them at cellular adhesion sites. Thus, zinc facilitates the formation of de novo APP and APLP1 containing adhesion complexes, whereas it does not have such influence on APLP2. Furthermore, zinc-binding prevented cleavage of APP and APLPs by extracellular secretases. In conclusion, the complexation of zinc modulates neuronal functions of APP and APLPs by (i) regulating formation of adhesion complexes, most prominently for APLP1, and (ii) by reducing the concentrations of neurotrophic soluble APP/APLP ectodomains. Earlier studies suggest a function of the amyloid precursor protein (APP) family proteins in neuronal adhesion. We report here that adhesive function of these proteins is tightly regulated by zinc, most prominently for amyloid precursor-like protein 1 (APLP1). Zinc-mediated APLP1 multimerization, which induced formation of new neuronal contacts and decreased APLP1 shedding. This suggests that APLP1 could function as a zinc receptor processing zinc signals to stabilized or new neuronal contacts. 11. Amyloid precursor protein modulates β-catenin degradation Directory of Open Access Journals (Sweden) Chen Yuzhi 2007-12-01 Full Text Available Abstract Background The amyloid precursor protein (APP is genetically associated with Alzheimer's disease (AD. Elucidating the function of APP should help understand AD pathogenesis and provide insights into therapeutic designs against this devastating neurodegenerative disease. Results We demonstrate that APP expression in primary neurons induces β-catenin phosphorylation at Ser33, Ser37, and Thr41 (S33/37/T41 residues, which is a prerequisite for β-catenin ubiquitinylation and proteasomal degradation. APP-induced phosphorylation of β-catenin resulted in the reduction of total β-catenin levels, suggesting that APP expression promotes β-catenin degradation. In contrast, treatment of neurons with APP siRNAs increased total β-catenin levels and decreased β-catenin phosphorylation at residues S33/37/T41. Further, β-catenin was dramatically increased in hippocampal CA1 pyramidal cells from APP knockout animals. Acute expression of wild type APP or of familial AD APP mutants in primary neurons downregulated β-catenin in membrane and cytosolic fractions, and did not appear to affect nuclear β-catenin or β-catenin-dependent transcription. Conversely, in APP knockout CA1 pyramidal cells, accumulation of β-catenin was associated with the upregulation of cyclin D1, a downstream target of β-catenin signaling. Together, these data establish that APP downregulates β-catenin and suggest a role for APP in sustaining neuronal function by preventing cell cycle reactivation and maintaining synaptic integrity. Conclusion We have provided strong evidence that APP modulates β-catenin degradation in vitro and in vivo. Future studies may investigate whether APP processing is necessary for β-catenin downregulation, and determine if excessive APP expression contributes to AD pathogenesis through abnormal β-catenin downregulation. 12. Manipulations of Amyloid Precursor Protein Cleavage Disrupt the Circadian Clock in Aging Drosophila OpenAIRE Blake, Matthew R.; Holbrook, Scott D.; Kotwica-Rolinska, Joanna; Chow, Eileen; Kretzschmar, Doris; Giebultowicz, Jadwiga M. 2015-01-01 Alzheimer’s disease (AD) is a neurodegenerative disease characterized by severe cognitive deterioration. While causes of AD pathology are debated, a large body of evidence suggests that increased cleavage of Amyloid Precursor Protein (APP) producing the neurotoxic Amyloid-β (Aβ) peptide plays a fundamental role in AD pathogenesis. One of the detrimental behavioral symptoms commonly associated with AD is the fragmentation of sleep-activity cycles with increased nighttime activity and daytime n... 13. Copper binding to the Alzheimer’s disease amyloid precursor protein OpenAIRE Kong, Geoffrey K.-W.; Miles, Luke A.; Crespi, Gabriela A. N.; Morton, Craig J.; Ng, Hooi Ling; Barnham, Kevin J.; McKinstry, William J.; Cappai, Roberto; Michael W. Parker 2007-01-01 Alzheimer’s disease is the fourth biggest killer in developed countries. Amyloid precursor protein (APP) plays a central role in the development of the disease, through the generation of a peptide called Aβ by proteolysis of the precursor protein. APP can function as a metalloprotein and modulate copper transport via its extracellular copper binding domain (CuBD). Copper binding to this domain has been shown to reduce Aβ levels and hence a molecular understanding of the interaction between me... 14. Schisandrin B protects PC12 cells by decreasing the expression of amyloid precursor protein and vacuolar protein sorting 35 Institute of Scientific and Technical Information of China (English) Mingmin Yan; Shanping Mao; Huimin Dong; Baohui Liu; Qian Zhang; Gaofeng Pan; Zhiping Fu 2012-01-01 PC12 cell injury was induced using 20 μM amyloid β-protein 25-35 to establish a model of Alzheimer's disease.The cells were then treated with 5, 10, and 25 μM Schisandrin B.Methylthiazolyldiphenyl-tetrazolium bromide assays and Hoechst 33342 staining results showed that with increasing Schisandrin B concentration, the survival rate of PC12 cells injured by amyloid β-protein 25-35 gradually increased and the rate of apoptosis gradually decreased.Reverse transcription-PCR, immunocytochemical staining and western blot results showed that with increasing Schisandrin B concentration, the mRNA and protein expression of vacuolar protein sorting 35 and amyloid precursor protein were gradually decreased.Vacuolar protein sorting 35 and amyloid precursor protein showed a consistent trend for change.These findings suggest that 5, 10, and 25 μM Schisandrin B antagonizes the cellular injury induced by amyloid β-protein 25-35 in a dose-dependent manner.This may be caused by decreasing the expression of vacuolar protein sorting 35 and amyloid precursor protein.PC12 cell injury was induced using 20 μM amyloid β-protein 25-35 to establish a model of Alzheimer's disease.The cells were then treated with 5, 10, and 25 μM Schisandrin B.Methylthiazolyldiphenyl-tetrazolium bromide assays and Hoechst 33342 staining results showed that with increasing Schisandrin B concentration, the survival rate of PC12 cells injured by amyloid β-protein 25-35 gradually increased and the rate of apoptosis gradually decreased.Reverse transcription-PCR, immunocytochemical staining and western blot results showed that with increasing Schisandrin B concentration, the mRNA and protein expression of vacuolar protein sorting 35 and amyloid precursor protein were gradually decreased.Vacuolar protein sorting 35 and amyloid precursor protein showed a consistent trend for change.These findings suggest that 5, 10, and 25 μM Schisandrin B antagonizes the cellular injury induced by amyloid β-protein 25 15. Exons 16 and 17 of the amyloid precursor protein gene in familial inclusion body myopathy. Science.gov (United States) Sivakumar, K; Cervenáková, L; Dalakas, M C; Leon-Monzon, M; Isaacson, S H; Nagle, J W; Vasconcelos, O; Goldfarb, L G 1995-08-01 Accumulation of beta-amyloid protein (A beta) occurs in some muscle fibers of patients with inclusion body myopathy and resembles the type of amyloid deposits seen in the affected tissues of patients with Alzheimer's disease and cerebrovascular amyloidosis. Because mutations in exons 16 and 17 of the beta-amyloid precursor protein (beta APP) gene on chromosome 21 have been identified in patients with early-onset familial Alzheimer's disease and Dutch-type cerebrovascular amyloidosis, we searched for mutations of the same region in patients with familial inclusion body myopathy. Sequencing of both alleles in 8 patients from four unrelated families did not reveal any mutations in these exons. The amyloid deposition in familial forms of inclusion body myopathy may be either due to errors in other gene loci, or it is secondary reflecting altered beta APP metabolism or myocyte degeneration and cell membrane degradation. 16. Schisandrin B protects PC12 cells by decreasing the expression of amyloid precursor protein and vacuolar protein sorting 35. Science.gov (United States) Yan, Mingmin; Mao, Shanping; Dong, Huimin; Liu, Baohui; Zhang, Qian; Pan, Gaofeng; Fu, Zhiping 2012-03-25 PC12 cell injury was induced using 20 μM amyloid β-protein 25-35 to establish a model of Alzheimer's disease. The cells were then treated with 5, 10, and 25 μM Schisandrin B. Methylthiazolyldiphenyl-tetrazolium bromide assays and Hoechst 33342 staining results showed that with increasing Schisandrin B concentration, the survival rate of PC12 cells injured by amyloid β-protein 25-35 gradually increased and the rate of apoptosis gradually decreased. Reverse transcription-PCR, immunocytochemical staining and western blot results showed that with increasing Schisandrin B concentration, the mRNA and protein expression of vacuolar protein sorting 35 and amyloid precursor protein were gradually decreased. Vacuolar protein sorting 35 and amyloid precursor protein showed a consistent trend for change. These findings suggest that 5, 10, and 25 μM Schisandrin B antagonizes the cellular injury induced by amyloid β-protein 25-35 in a dose-dependent manner. This may be caused by decreasing the expression of vacuolar protein sorting 35 and amyloid precursor protein. 17. Novel effects of FCCP [carbonyl cyanide p-(trifluoromethoxy)phenylhydrazone] on amyloid precursor protein processing. Science.gov (United States) Connop, B P; Thies, R L; Beyreuther, K; Ida, N; Reiner, P B 1999-04-01 Amyloidogenic processing of the beta-amyloid precursor protein (APP) has been implicated in the pathology of Alzheimer's disease. Because it has been suggested that catabolic processing of the APP holoprotein occurs in acidic intracellular compartments, we studied the effects of the protonophore carbonyl cyanide p-(trifluoromethoxy)phenylhydrazone (FCCP) and the H+-ATPase inhibitor bafilomycin A1 on APP catabolism in human embryonic kidney 293 cells expressing either wild-type or "Swedish" mutant APP. Unlike bafilomycin A1, which inhibits beta-amyloid production in cells expressing mutant but not wild-type APP, FCCP inhibited beta-amyloid production in both cell types. Moreover, the effects of FCCP were independent of alterations in total cellular APP levels or APP maturation, and the concentrations used did not alter either cellular ATP levels or cell viability. Bafilomycin A1, which had no effect on beta-amyloid production in wild-type cells, inhibited endocytosis of fluorescent transferrin, whereas concentrations of FCCP that inhibited beta-amyloid production in these cells had no effect on endosomal function. Thus, in wild-type-expressing cells it appears that the beta-amyloid peptide is not produced in the classically defined endosome. Although bafilomycin A1 decreased beta-amyloid release from cells expressing mutant APP but not wild-type APP, it altered lysosomal function in both cell types, suggesting that in normal cells beta-amyloid is not produced in the lysosome. Although inhibition of beta-amyloid production by bafilomycin A1 in mutant cells may occur via changes in endosomal/lysosomal pH, our data suggest that FCCP inhibits wild-type beta-amyloid production by acting on a bafilomycin A1-insensitive acidic compartment that is distinct from either the endosome or the lysosome. 18. Beta-secretase-cleaved amyloid precursor protein in Alzheimer brain: a morphologic study DEFF Research Database (Denmark) Sennvik, Kristina; Bogdanovic, N; Volkmann, Inga 2004-01-01 beta-amyloid (Abeta) is the main constituent of senile plaques seen in Alzheimer's disease. Abeta is derived from the amyloid precursor protein (APP) via proteolytic cleavage by proteases beta- and gamma-secretase. In this study, we examined content and localization of beta-secretase-cleaved APP...... the beta-sAPP immunostaining to be stronger and more extensive in gray matter in Alzheimer disease (AD) cases than controls. The axonal beta-sAPP staining was patchy and unevenly distributed for the AD cases, indicating impaired axonal transport. beta-sAPP was also found surrounding senile plaques... 19. Specific Inhibition of β-Secretase Processing of the Alzheimer Disease Amyloid Precursor Protein. Science.gov (United States) Ben Halima, Saoussen; Mishra, Sabyashachi; Raja, K Muruga Poopathi; Willem, Michael; Baici, Antonio; Simons, Kai; Brüstle, Oliver; Koch, Philipp; Haass, Christian; Caflisch, Amedeo; Rajendran, Lawrence 2016-03-08 Development of disease-modifying therapeutics is urgently needed for treating Alzheimer disease (AD). AD is characterized by toxic β-amyloid (Aβ) peptides produced by β- and γ-secretase-mediated cleavage of the amyloid precursor protein (APP). β-secretase inhibitors reduce Aβ levels, but mechanism-based side effects arise because they also inhibit β-cleavage of non-amyloid substrates like Neuregulin. We report that β-secretase has a higher affinity for Neuregulin than it does for APP. Kinetic studies demonstrate that the affinities and catalytic efficiencies of β-secretase are higher toward non-amyloid substrates than toward APP. We show that non-amyloid substrates are processed by β-secretase in an endocytosis-independent manner. Exploiting this compartmentalization of substrates, we specifically target the endosomal β-secretase by an endosomally targeted β-secretase inhibitor, which blocked cleavage of APP but not non-amyloid substrates in many cell systems, including induced pluripotent stem cell (iPSC)-derived neurons. β-secretase inhibitors can be designed to specifically inhibit the Alzheimer process, enhancing their potential as AD therapeutics without undesired side effects. 20. Cerebrolysin decreases amyloid-beta production by regulating amyloid protein precursor maturation in a transgenic model of Alzheimer's disease. Science.gov (United States) Rockenstein, Edward; Torrance, Magdalena; Mante, Michael; Adame, Anthony; Paulino, Amy; Rose, John B; Crews, Leslie; Moessler, Herbert; Masliah, Eliezer 2006-05-15 Cerebrolysin is a peptide mixture with neurotrophic effects that might reduce the neurodegenerative pathology in Alzheimer's disease (AD). We have previously shown in an amyloid protein precursor (APP) transgenic (tg) mouse model of AD-like neuropathology that Cerebrolysin ameliorates behavioral deficits, is neuroprotective, and decreases amyloid burden; however, the mechanisms involved are not completely clear. Cerebrolysin might reduce amyloid deposition by regulating amyloid-beta (Abeta) degradation or by modulating APP expression, maturation, or processing. To investigate these possibilities, APP tg mice were treated for 6 months with Cerebrolysin and analyzed in the water maze, followed by RNA, immunoblot, and confocal microscopy analysis of full-length (FL) APP and its fragments, beta-secretase (BACE1), and Abeta-degrading enzymes [neprilysin (Nep) and insulin-degrading enzyme (IDE)]. Consistent with previous studies, Cerebrolysin ameliorated the performance deficits in the spatial learning portion of the water maze and reduced the synaptic pathology and amyloid burden in the brains of APP tg mice. These effects were associated with reduced levels of FL APP and APP C-terminal fragments, but levels of BACE1, Notch1, Nep, and IDE were unchanged. In contrast, levels of active cyclin-dependent kinase-5 (CDK5) and glycogen synthase kinase-3beta [GSK-3beta; but not stress-activated protein kinase-1 (SAPK1)], kinases that phosphorylate APP, were reduced. Furthermore, Cerebrolysin reduced the levels of phosphorylated APP and the accumulation of APP in the neuritic processes. Taken together, these results suggest that Cerebrolysin might reduce AD-like pathology in the APP tg mice by regulating APP maturation and transport to sites where Abeta protein is generated. This study clarifies the mechanisms through which Cerebrolysin might reduce Abeta production and deposition in AD and further supports the importance of this compound in the potential treatment of early AD. 1. Insights into the physiological function of the β-amyloid precursor protein: beyond Alzheimer's disease. Science.gov (United States) Dawkins, Edgar; Small, David H 2014-06-01 The β-amyloid precursor protein (APP) has been extensively studied for its role as the precursor of the β-amyloid protein (Aβ) of Alzheimer's disease. However, the normal function of APP remains largely unknown. This article reviews studies on the structure, expression and post-translational processing of APP, as well as studies on the effects of APP in vitro and in vivo. We conclude that the published data provide strong evidence that APP has a trophic function. APP is likely to be involved in neural stem cell development, neuronal survival, neurite outgrowth and neurorepair. However, the mechanisms by which APP exerts its actions remain to be elucidated. The available evidence suggests that APP interacts both intracellularly and extracellularly to regulate various signal transduction mechanisms. This article reviews studies on the structure, expression and post-translational processing of β-amyloid precursor protein (APP), as well as studies on the effects of APP in vitro and in vivo. We conclude that the published data provide strong evidence that APP has a trophic function. APP is likely to be involved in neural stem cell development, neuronal survival, neurite outgrowth and neurorepair. However, the mechanisms by which APP exerts its actions remain to be elucidated. The available evidence suggests that APP interacts both intracellularly and extracellularly to regulate various signal transduction mechanisms. 2. Cellular prion protein expression is not regulated by the Alzheimer's amyloid precursor protein intracellular domain. Directory of Open Access Journals (Sweden) Victoria Lewis Full Text Available There is increasing evidence of molecular and cellular links between Alzheimer's disease (AD and prion diseases. The cellular prion protein, PrP(C, modulates the post-translational processing of the AD amyloid precursor protein (APP, through its inhibition of the β-secretase BACE1, and oligomers of amyloid-β bind to PrP(C which may mediate amyloid-β neurotoxicity. In addition, the APP intracellular domain (AICD, which acts as a transcriptional regulator, has been reported to control the expression of PrP(C. Through the use of transgenic mice, cell culture models and manipulation of APP expression and processing, this study aimed to clarify the role of AICD in regulating PrP(C. Over-expression of the three major isoforms of human APP (APP(695, APP(751 and APP(770 in cultured neuronal and non-neuronal cells had no effect on the level of endogenous PrP(C. Furthermore, analysis of brain tissue from transgenic mice over-expressing either wild type or familial AD associated mutant human APP revealed unaltered PrP(C levels. Knockdown of endogenous APP expression in cells by siRNA or inhibition of γ-secretase activity also had no effect on PrP(C levels. Overall, we did not detect any significant difference in the expression of PrP(C in any of the cell or animal-based paradigms considered, indicating that the control of cellular PrP(C levels by AICD is not as straightforward as previously suggested. 3. Presentation of amyloidosis in carriers of the codon 692 mutation in the amyloid precursor protein gene (APP692) NARCIS (Netherlands) F. Forey; H.L.J. Tanghe (Hervé); M.F. Niermeijer (Martinus); C.M. van Duijn (Cock); J.C. van Swieten (John); F. van Harskamp (Frans); I. de Koning (Inge); M. Cruts (Marc); C. de Jonghe (Chris); S. Kumar-Singh (Samir); A. Tibben (Arend); C. van Broeckhoven (Christine); A. Hofman (Albert) 2000-01-01 textabstractSeveral mutations in the amyloid precursor protein (APP) gene may lead to either Alzheimer's disease or cerebral haemorrhage due to congophilic amyloid angiopathy (CAA). A single family is known in which both types of pathology are expressed because of a missense mutati 4. Sorting by the cytoplasmic domain of the amyloid precursor protein binding receptor SorLA DEFF Research Database (Denmark) Nielsen, Morten S; Gustafsen, Camilla; Madsen, Peder 2007-01-01 -formation with the amyloid precursor protein it downregulates generation of Alzheimer's disease-associated Abeta-peptide. The receptor is mainly located in vesicles, suggesting a function in protein sorting and transport. Here we examined SorLA's trafficking using full-length and chimeric receptors and find that its...... established that the AP-1 adaptor complex is essential to SorLA's transport between Golgi membranes and endosomes. Our results further implicate the GGA proteins in SorLA trafficking and provide evidence that SNX1 and Vps35, as parts of the retromer complex or possibly in a separate context, are engaged... 5. Structure and Synaptic Function of Metal Binding to the Amyloid Precursor Protein and its Proteolytic Fragments Science.gov (United States) Wild, Klemens; August, Alexander; Pietrzik, Claus U.; Kins, Stefan 2017-01-01 Alzheimer’s disease (AD) is ultimately linked to the amyloid precursor protein (APP). However, current research reveals an important synaptic function of APP and APP-like proteins (APLP1 and 2). In this context various neurotrophic and neuroprotective functions have been reported for the APP proteolytic fragments sAPPα, sAPPβ and the monomeric amyloid-beta peptide (Aβ). APP is a metalloprotein and binds copper and zinc ions. Synaptic activity correlates with a release of these ions into the synaptic cleft and dysregulation of their homeostasis is linked to different neurodegenerative diseases. Metal binding to APP or its fragments affects its structure and its proteolytic cleavage and therefore its physiological function at the synapse. Here, we summarize the current data supporting this hypothesis and provide a model of how these different mechanisms might be intertwined with each other. PMID:28197076 6. Brain Endothelial Cells Produce Amyloid β from Amyloid Precursor Protein 770 and Preferentially Secrete the O-Glycosylated Form* Science.gov (United States) Kitazume, Shinobu; Tachida, Yuriko; Kato, Masaki; Yamaguchi, Yoshiki; Honda, Takashi; Hashimoto, Yasuhiro; Wada, Yoshinao; Saito, Takashi; Iwata, Nobuhisa; Saido, Takaomi; Taniguchi, Naoyuki 2010-01-01 Deposition of amyloid β (Aβ) in the brain is closely associated with Alzheimer disease (AD). Aβ is generated from amyloid precursor protein (APP) by the actions of β- and γ-secretases. In addition to Aβ deposition in the brain parenchyma, deposition of Aβ in cerebral vessel walls, termed cerebral amyloid angiopathy, is observed in more than 80% of AD individuals. The mechanism for how Aβ accumulates in blood vessels remains largely unknown. In the present study, we show that brain endothelial cells expressed APP770, a differently spliced APP mRNA isoform from neuronal APP695, and produced Aβ40 and Aβ42. Furthermore, we found that the endothelial APP770 had sialylated core 1 type O-glycans. Interestingly, Ο-glycosylated APP770 was preferentially processed by both α- and β-cleavage and secreted into the media, suggesting that O-glycosylation and APP processing involved related pathways. By immunostaining human brain sections with an anti-APP770 antibody, we found that APP770 was expressed in vascular endothelial cells. Because we were able to detect O-glycosylated sAPP770β in human cerebrospinal fluid, this unique soluble APP770β has the potential to serve as a marker for cortical dementias such as AD and vascular dementia. PMID:20952385 7. Cannabidiol promotes amyloid precursor protein ubiquitination and reduction of beta amyloid expression in SHSY5YAPP+ cells through PPARγ involvement. Science.gov (United States) Scuderi, Caterina; Steardo, Luca; Esposito, Giuseppe 2014-07-01 The amyloidogenic cascade is regarded as a key factor at the basis of Alzheimer's disease (AD) pathogenesis. The aberrant cleavage of amyloid precursor protein (APP) induces an increased production and a subsequent aggregation of beta amyloid (Aβ) peptide in limbic and association cortices. As a result, altered neuronal homeostasis and oxidative injury provoke tangle formation with consequent neuronal loss. Cannabidiol (CBD), a Cannabis derivative devoid of psychotropic effects, has attracted much attention because it may beneficially interfere with several Aβ-triggered neurodegenerative pathways, even though the mechanism responsible for such actions remains unknown. In the present research, the role of CBD was investigated as a possible modulating compound of APP processing in SHSY5Y(APP+) neurons. In addition, the putative involvement of peroxisome proliferator-activated receptor-γ (PPARγ) was explored as a candidate molecular site responsible for CBD actions. Results indicated the CBD capability to induce the ubiquitination of APP protein which led to a substantial decrease in APP full length protein levels in SHSY5Y(APP+) with the consequent decrease in Aβ production. Moreover, CBD promoted an increased survival of SHSY5Y(APP+) neurons, by reducing their long-term apoptotic rate. Obtained results also showed that all, here observed, CBD effects were dependent on the selective activation of PPARγ. 8. β-Amyloid precursor protein: function in stem cell development and Alzheimer's disease brain. Science.gov (United States) Small, David H; Hu, Yanling; Bolós, Marta; Dawkins, Edgar; Foa, Lisa; Young, Kaylene M 2014-01-01 Stem cell therapy may be a suitable approach for the treatment of many neurodegenerative diseases. However, one major impediment to the development of successful cell-based therapies is our limited understanding of the mechanisms that instruct neural stem cell behaviour, such as proliferation and cell fate specification. The β-amyloid precursor protein (APP) of Alzheimer's disease (AD) may play an important role in neural stem cell proliferation and differentiation. Our recent work shows that in vitro, APP stimulates neural stem or progenitor cell proliferation and neuronal differentiation. The effect on proliferation is mediated by an autocrine factor that we have identified as cystatin C. As cystatin C expression is also reported to inhibit the development of amyloid pathology in APP transgenic mice, our finding has implications for the possible use of cystatin C for the therapy of AD. 9. The intact Kunitz domain protects the amyloid precursor protein from being processed by matriptase-2. Science.gov (United States) Beckmann, Anna-Madeleine; Glebov, Konstantin; Walter, Jochen; Merkel, Olaf; Mangold, Martin; Schmidt, Frederike; Becker-Pauly, Christoph; Gütschow, Michael; Stirnberg, Marit 2016-08-01 Proteolytic processing of the amyloid precursor protein (APP) leads to amyloid-β (Aβ) peptides. So far, the mechanism of APP processing is insufficiently characterized at the molecular level. Whereas the knowledge of Aβ generation by several proteases has been expanded, the contribution of the Kunitz-type protease inhibitor domain (KPI) present in two major APP isoforms to the complex proteolytic processing of APP is poorly understood. In this study, we have identified KPI-containing APP as a very potent, slow-binding inhibitor for the membrane-bound proteolytic regulator of iron homeostasis matriptase-2 by forming stable complexes with its target protease in HEK cells. Inhibition and complex formation depend on the intact KPI domain. By inhibiting matriptase-2, KPI-containing APP is protected from matriptase-2-mediated proteolysis within the Aβ region, thus preventing the generation of N-terminally truncated Aβ. 10. The role of the E2 copper binding domain in the cell biology of the amyloid precursor protein OpenAIRE Blanthorn-Hazell, Sophee 2015-01-01 Alzheimer’s disease is a neurodegenerative disorder characterised by the accumulation, in the brain, of neurotoxic amyloid beta-(Aβ) peptides. These peptides are generated from the amyloid precursor protein (APP) via the amyloidogenic proteolytic pathway which also leads to the formation of soluble APP beta (sAPPβ). Alternatively, APP can be cleaved by the non-amyloidogenic pathway in which an α-secretase activity cleaves the protein within the Aβ region generating soluble APP alpha (sAPPα). ... 11. Amyloid precursor protein (APP) affects global protein synthesis in dividing human cells. Science.gov (United States) Sobol, Anna; Galluzzo, Paola; Liang, Shuang; Rambo, Brittany; Skucha, Sylvia; Weber, Megan J; Alani, Sara; Bocchetta, Maurizio 2015-05-01 Hypoxic non-small cell lung cancer (NSCLC) is dependent on Notch-1 signaling for survival. Targeting Notch-1 by means of γ-secretase inhibitors (GSI) proved effective in killing hypoxic NSCLC. Post-mortem analysis of GSI-treated, NSCLC-burdened mice suggested enhanced phosphorylation of 4E-BP1 at threonines 37/46 in hypoxic tumor tissues. In vitro dissection of this phenomenon revealed that Amyloid Precursor Protein (APP) inhibition was responsible for a non-canonical 4E-BP1 phosphorylation pattern rearrangement-a process, in part, mediated by APP regulation of the pseudophosphatase Styx. Upon APP depletion we observed modifications of eIF-4F composition indicating increased recruitment of eIF-4A to the mRNA cap. This phenomenon was supported by the observation that cells with depleted APP were partially resistant to silvestrol, an antibiotic that interferes with eIF-4A assembly into eIF-4F complexes. APP downregulation in dividing human cells increased the rate of global protein synthesis, both cap- and IRES-dependent. Such an increase seemed independent of mTOR inhibition. After administration of Torin-1, APP downregulation and Mechanistic Target of Rapamycin Complex 1 (mTORC-1) inhibition affected 4E-BP1 phosphorylation and global protein synthesis in opposite fashions. Additional investigations indicated that APP operates independently of mTORC-1. Key phenomena described in this study were reversed by overexpression of the APP C-terminal domain. The presented data suggest that APP may be a novel regulator of protein synthesis in dividing human cells, both cancerous and primary. Furthermore, APP appears to affect translation initiation using mechanisms seemingly dissimilar to mTORC-1 regulation of cap-dependent protein synthesis. 12. Inhibition of beta-site amyloid precursor protein-cleaving enzyme and beta-amyloid precursor protein genes in SK-N-SH cells Institute of Scientific and Technical Information of China (English) Suqin Gao; Lin Sun; Enji Han; Hongshun Qi; Jinbo Feng; Shunliang Xu; Wen Xia 2009-01-01 BACKGROUND:Previous studies have demonstrated that Piper futokadsura stem selectively inhibits expression of amyloid precursor protein (APP) at the mRNA level.In addition,the piperlonguminine (A) and dihydropiperlonguminine (B) components (1:0.8),which can be separated from Futokadsura stem,selectively inhibit expression of the APP at mRNA and protein levels.OBJECTIVE:Based on previous findings,the present study investigated the effects of β-site amyloid precursor protein cleaving enzyme (BACE1) and APP genes on the production of β-amyloid peptide 42 (Aβ42) in human neuroblastoma cells (SK-N-SH cells) using small interfering RNAs (siRNAs) and A/B components separated from Futokadsura stem,respectively.DESIGN,TIME AND SETTING:A gene interference-based randomized,controlled,in vitro experiment was performed at the Key Laboratory of Cardiovascular Remodeling and Function Research,Ministries of Education and Public Health,and Institute of Pharmacologic Research,School of Pharmaceutical Science & Department of Biochemistry,School of Medicine,Shandong University between July 2006 and December 2007.MATERIALS:SK-N-SH cells were provided by Shanghai Institutes of Biological Sciences,Chinese Academy of Sciences,Shanghai,China;mouse anti-human BACE1 monoclonal antibody was purchased from R&D Systems,USA;mouse anti-human APP monoclonal antibody was purchased from Cell Signaling Technology,USA;and horseradish peroxidase (HRP)-conjugated goat anti-mouse IgG was provided by Sigma,USA.METHODS:The human BACE1 cDNA sequence was obtained from NCBI website (www.ncbi.nlm.nih.gov/sites/entrez).Three pairs of siRNAs,specific to human BACE1 gene,were synthesized through the use of Silencer? pre-designed siRNA specification,and were transfected into SK-N-SH cells with siPORT NeoFX transfection agent to compare the effects of different concentrations of siRNAs (10-50 nmol/L) on SK-N-SH cells.Futokadsura stem was separated and purified with chemical methods,and the crystal was composed of 13. FKBP12 regulates the localization and processing of amyloid precursor protein in human cell lines Fan-Lun Liu; Ting-Yi Liu; Fan-Lu Kung 2014-03-01 One of the pathological hallmarks of Alzheimer’s disease is the presence of insoluble extracellular amyloid plaques. These plaques are mainly constituted of amyloid beta peptide (A), a proteolytic product of amyloid precursor protein (APP). APP processing also generates the APP intracellular domain (AICD). We have previously demonstrated that AICD interacts with FKBP12, a peptidyl-prolyl cis-trans isomerase (PPIase) ubiquitous in nerve systems. This interaction was interfered by FK506, a clinically used immunosuppressant that has recently been reported to be neuroprotective. To elucidate the roles of FKBP12 in the pathogenesis of Alzheimer’s disease, the effect of FKBP12 overexpression on APP processing was evaluated. Our results revealed that APP processing was shifted towards the amyloidogenic pathway, accompanied by a change in the subcellular localization of APP, upon FKBP12 overexpression. This FKBP12-overexpression-induced effect was reverted by FK506. These findings support our hypothesis that FKBP12 may participate in the regulation of APP processing. FKBP12 overexpression may lead to the stabilization of a certain isomer (presumably the cis form) of the Thr668-Pro669 peptide bond in AICD, therefore change its affinity to flotillin-1 or other raft-associated proteins, and eventually change the localization pattern and cause a shift in the proteolytic processing of APP. 14. Consequences of Inhibiting Amyloid Precursor Protein Processing Enzymes on Synaptic Function and Plasticity Directory of Open Access Journals (Sweden) Hui Wang 2012-01-01 Full Text Available Alzheimer's disease (AD is a neurodegenerative disease, one of whose major pathological hallmarks is the accumulation of amyloid plaques comprised of aggregated β-amyloid (Aβ peptides. It is now recognized that soluble Aβ oligomers may lead to synaptic dysfunctions early in AD pathology preceding plaque deposition. Aβ is produced by a sequential cleavage of amyloid precursor protein (APP by the activity of β- and γ-secretases, which have been identified as major candidate therapeutic targets of AD. This paper focuses on how Aβ alters synaptic function and the functional consequences of inhibiting the activity of the two secretases responsible for Aβ generation. Abnormalities in synaptic function resulting from the absence or inhibition of the Aβ-producing enzymes suggest that Aβ itself may have normal physiological functions which are disrupted by abnormal accumulation of Aβ during AD pathology. This interpretation suggests that AD therapeutics targeting the β- and γ-secretases should be developed to restore normal levels of Aβ or combined with measures to circumvent the associated synaptic dysfunction(s in order to have minimal impact on normal synaptic function. 15. Selective translational control of the Alzheimer amyloid precursor protein transcript by iron regulatory protein-1. Science.gov (United States) Cho, Hyun-Hee; Cahill, Catherine M; Vanderburg, Charles R; Scherzer, Clemens R; Wang, Bin; Huang, Xudong; Rogers, Jack T 2010-10-08 Iron influx increases the translation of the Alzheimer amyloid precursor protein (APP) via an iron-responsive element (IRE) RNA stem loop in its 5'-untranslated region. Equal modulated interaction of the iron regulatory proteins (IRP1 and IRP2) with canonical IREs controls iron-dependent translation of the ferritin subunits. However, our immunoprecipitation RT-PCR and RNA binding experiments demonstrated that IRP1, but not IRP2, selectively bound the APP IRE in human neural cells. This selective IRP1 interaction pattern was evident in human brain and blood tissue from normal and Alzheimer disease patients. We computer-predicted an optimal novel RNA stem loop structure for the human, rhesus monkey, and mouse APP IREs with reference to the canonical ferritin IREs but also the IREs encoded by erythroid heme biosynthetic aminolevulinate synthase and Hif-2α mRNAs, which preferentially bind IRP1. Selective 2'-hydroxyl acylation analyzed by primer extension analysis was consistent with a 13-base single-stranded terminal loop and a conserved GC-rich stem. Biotinylated RNA probes deleted of the conserved CAGA motif in the terminal loop did not bind to IRP1 relative to wild type probes and could no longer base pair to form a predicted AGA triloop. An AGU pseudo-triloop is key for IRP1 binding to the canonical ferritin IREs. RNA probes encoding the APP IRE stem loop exhibited the same high affinity binding to rhIRP1 as occurs for the H-ferritin IRE (35 pm). Intracellular iron chelation increased binding of IRP1 to the APP IRE, decreasing intracellular APP expression in SH-SY5Y cells. Functionally, shRNA knockdown of IRP1 caused increased expression of neural APP consistent with IRP1-APP IRE-driven translation. 16. Yeast Two-Hybrid Screening for Proteins that Interact with the Extracellular Domain of Amyloid Precursor Protein. Science.gov (United States) Yu, You; Li, Yinan; Zhang, Yan 2016-04-01 Alzheimer's disease (AD) is a neurodegenerative disorder in which amyloid β plaques are a pathological characteristic. Little is known about the physiological functions of amyloid β precursor protein (APP). Based on its structure as a type I transmembrane protein, it has been proposed that APP might be a receptor, but so far, no ligand has been reported. In the present study, 9 proteins binding to the extracellular domain of APP were identified using a yeast two-hybrid system. After confirming the interactions in the mammalian system, mutated PLP1, members of the FLRT protein family, and KCTD16 were shown to interact with APP. These proteins have been reported to be involved in Pelizaeus-Merzbacher disease (PMD) and axon guidance. Therefore, our results shed light on the mechanisms of physiological function of APP in AD, PMD, and axon guidance. 17. Estrogen stimulates release of secreted amyloid precursor protein from primary rat cortical neurons via protein kinase C pathway Institute of Scientific and Technical Information of China (English) Sun ZHANG; Ying HUANG; Yi-chun ZHU; Tai YAO 2005-01-01 Aim: To investigate the mechanism of the action of estrogen, which stimulates the release of secreted amyloid precursor protein α (sAPPα) and decreases the gen eration of amyloidprotein (Aβ), a dominant component in senile plaques in the brains of Alzheimer's disease patients. Methods: Experiments were carried out inprimary rat cortical neurons, and Western blot was used to detect sAPPα in aculture medium and the total amount of cellular amyloid precursor protein (APP) in neurons. Results: 17β-Estradiol (but not 17α-estradiol) and β-estradiol 6-(Ocarboxymethyl) oxime: BSA increased the secretion of sAPPα and this effect was blocked by protein kinase C (PKC) inhibitor calphostin C, but not by the classical estrogen receptor antagonist ICI 182,780. Meanwhile, 17β-estradiol did not alter the synthesis of cellular APP. Conclusion: The effect of 17β-estradiol on sAPPα secretion is likely mediated through the membrane binding sites, and needs molecular configuration specificity of the ligand. Furthermore, the action of the PKC dependent pathway might be involved in estrogen-induced sAPPα secretion. 18. LINGO-1 promotes lysosomal degradation of amyloidprotein precursor. Science.gov (United States) de Laat, Rian; Meabon, James S; Wiley, Jesse C; Hudson, Mark P; Montine, Thomas J; Bothwell, Mark 2015-01-01 Sequential proteolytic cleavages of amyloidprotein precursor (AβPP) by β-secretase and γ-secretase generate amyloid β (Aβ) peptides, which are thought to contribute to Alzheimer's disease (AD). Much of this processing occurs in endosomes following endocytosis of AβPP from the plasma membrane. However, this pathogenic mode of processing AβPP may occur in competition with lysosomal degradation of AβPP, a common fate of membrane proteins trafficking through the endosomal system. Following up on published reports that LINGO-1 binds and promotes the amyloidogenic processing of AβPP we have examined the consequences of LINGO-1/AβPP interactions. We report that LINGO-1 and its paralogs, LINGO-2 and LINGO-3, decrease processing of AβPP in the amyloidogenic pathway by promoting lysosomal degradation of AβPP. We also report that LINGO-1 levels are reduced in AD brain, representing a possible pathogenic mechanism stimulating the generation of Aβ peptides in AD. 19. LINGO-1 promotes lysosomal degradation of amyloidprotein precursor Directory of Open Access Journals (Sweden) Rian de Laat 2015-03-01 Full Text Available Sequential proteolytic cleavages of amyloidprotein precursor (AβPP by β-secretase and γ-secretase generate amyloid β (Aβ peptides, which are thought to contribute to Alzheimer's disease (AD. Much of this processing occurs in endosomes following endocytosis of AβPP from the plasma membrane. However, this pathogenic mode of processing AβPP may occur in competition with lysosomal degradation of AβPP, a common fate of membrane proteins trafficking through the endosomal system. Following up on published reports that LINGO-1 binds and promotes the amyloidogenic processing of AβPP we have examined the consequences of LINGO-1/AβPP interactions. We report that LINGO-1 and its paralogs, LINGO-2 and LINGO-3, decrease processing of AβPP in the amyloidogenic pathway by promoting lysosomal degradation of AβPP. We also report that LINGO-1 levels are reduced in AD brain, representing a possible pathogenic mechanism stimulating the generation of Aβ peptides in AD. 20. The coding sequence of amyloid-beta precursor protein APP contains a neural-specific promoter element. NARCIS (Netherlands) Collin, R.W.J.; Martens, G.J.M. 2006-01-01 The amyloid-beta precursor protein APP is generally accepted to be involved in the pathology of Alzheimer's disease. Since its physiological role is still unclear, we decided to study the function of APP via stable transgenesis in the amphibian Xenopus laevis. However, the application of constructs 1. A Synthetic Peptide with the Putative Iron Binding Motif of Amyloid Precursor Protein (APP) Does Not Catalytically Oxidize Iron NARCIS (Netherlands) Honarmand Ebrahimi, K.; Hagedoorn, P.L.; Hagen, W.R. 2012-01-01 The β-amyloid precursor protein (APP), which is a key player in Alzheimer's disease, was recently reported to possess an Fe(II) binding site within its E2 domain which exhibits ferroxidase activity [Duce et al. 2010, Cell 142: 857]. The putative ligands of this site were compared to those in the fer 2. Lost region in amyloid precursor protein (APP) through TALEN-mediated genome editing alters mitochondrial morphology. Science.gov (United States) Wang, Yajie; Wu, Fengyi; Pan, Haining; Zheng, Wenzhong; Feng, Chi; Wang, Yunfu; Deng, Zixin; Wang, Lianrong; Luo, Jie; Chen, Shi 2016-02-29 Alzheimer's disease (AD) is characterized by amyloid-β (Aβ) deposition in the brain. Aβ plaques are produced through sequential β/γ cleavage of amyloid precursor protein (APP), of which there are three main APP isoforms: APP695, APP751 and APP770. KPI-APPs (APP751 and APP770) are known to be elevated in AD, but the reason remains unclear. Transcription activator-like (TAL) effector nucleases (TALENs) induce mutations with high efficiency at specific genomic loci, and it is thus possible to knock out specific regions using TALENs. In this study, we designed and expressed TALENs specific for the C-terminus of APP in HeLa cells, in which KPI-APPs are predominantly expressed. The KPI-APP mutants lack a 12-aa region that encompasses a 5-aa trans-membrane (TM) region and 7-aa juxta-membrane (JM) region. The mutated KPI-APPs exhibited decreased mitochondrial localization. In addition, mitochondrial morphology was altered, resulting in an increase in spherical mitochondria in the mutant cells through the disruption of the balance between fission and fusion. Mitochondrial dysfunction, including decreased ATP levels, disrupted mitochondrial membrane potential, increased ROS generation and impaired mitochondrial dehydrogenase activity, was also found. These results suggest that specific regions of KPI-APPs are important for mitochondrial localization and function. 3. IFN-gamma promotes complement expression and attenuates amyloid plaque deposition in amyloid beta precursor protein transgenic mice. Science.gov (United States) Chakrabarty, Paramita; Ceballos-Diaz, Carolina; Beccard, Amanda; Janus, Christopher; Dickson, Dennis; Golde, Todd E; Das, Pritam 2010-05-01 Reactive gliosis surrounding amyloid beta (Abeta) plaques is an early feature of Alzheimer's disease pathogenesis and has been postulated to represent activation of the innate immune system in an apparently ineffective attempt to clear or neutralize Abeta aggregates. To evaluate the role of IFN-gamma-mediated neuroinflammation on the evolution of Abeta pathology in transgenic (Tg) mice, we have expressed murine IFN-gamma (mIFN-gamma) in the brains of Abeta precursor protein (APP) Tg mice using recombinant adeno-associated virus serotype 1. Expression of mIFN-gamma in brains of APP TgCRND8 mice results in robust noncell autonomous activation of microglia and astrocytes, and a concomitant significant suppression of Abeta deposition. In these mice, mIFN-gamma expression upregulated multiple glial activation markers, early components of the complement cascade as well as led to infiltration of Ly-6c positive peripheral monocytes but no significant effects on APP levels, APP processing or steady-state Abeta levels were noticed in vivo. Taken together, these results suggest that mIFN-gamma expression in the brain suppresses Abeta accumulation through synergistic effects of activated glia and components of the innate immune system that enhance Abeta aggregate phagocytosis. 4. AChE and the amyloid precursor protein (APP) - Cross-talk in Alzheimer's disease. Science.gov (United States) Nalivaeva, Natalia N; Turner, Anthony J 2016-11-25 The amyloid precursor protein (APP) and acetylcholinesterase (AChE) are multi-faceted proteins with a wide range of vital functions, both crucially linked with the pathogenesis of Alzheimer's disease (AD). APP is the precursor of the Aβ peptide, the pathological agent in AD, while AChE is linked to its pathogenesis either by increasing cholinergic deficit or exacerbating Aβ fibril formation and toxicity. As such, both proteins are the main targets in AD therapeutics with AChE inhibitors being currently the only clinically available AD drugs. In our studies we have demonstrated an important inter-relation in functioning of these proteins. Both can be released from the cell membrane and we have shown that AChE shedding involves a metalloproteinase-mediated mechanism which, like the α-secretase dependent cleavage of APP, is stimulated by cholinergic agonists. Overexpression of the neuronal specific isoform APP695 in neuronal cells substantially decreased levels of the AChE mRNA, protein and catalytic activity accompanied by a similar decrease in mRNA levels of the AChE membrane anchor, PRiMA (proline rich membrane anchor). We further established that this regulation does not involve APP processing and its intracellular domain (AICD) but requires the E1 region of APP, specifically its copper-binding domain. On the contrary, siRNA knock-down of APP in cholinergic SN56 cells resulted in a significant upregulation of AChE mRNA levels. Hence APP may influence AChE physiology while released AChE may regulate amyloidogenesis through multiple mechanisms suggesting novel therapeutic targets. 5. Amyloid precursor protein regulates migration and metalloproteinase gene expression in prostate cancer cells Energy Technology Data Exchange (ETDEWEB) Miyazaki, Toshiaki; Ikeda, Kazuhiro; Horie-Inoue, Kuniko [Division of Gene Regulation and Signal Transduction, Research Center for Genomic Medicine, Saitama Medical University, Saitama 350-1241 (Japan); Inoue, Satoshi, E-mail: INOUE-GER@h.u-tokyo.ac.jp [Division of Gene Regulation and Signal Transduction, Research Center for Genomic Medicine, Saitama Medical University, Saitama 350-1241 (Japan); Department of Geriatric Medicine, Graduate School of Medicine, The University of Tokyo, Tokyo 113-8655 (Japan); Department of Anti-Aging Medicine, Graduate School of Medicine, The University of Tokyo, Tokyo 113-8655 (Japan) 2014-09-26 Highlights: • APP knockdown reduced proliferation and migration of prostate cancer cells. • APP knockdown reduced expression of metalloproteinase and EMT-related genes. • APP overexpression promoted LNCaP cell migration. • APP overexpression increased expression of metalloproteinase and EMT-related genes. - Abstract: Amyloid precursor protein (APP) is a type I transmembrane protein, and one of its processed forms, β-amyloid, is considered to play a central role in the development of Alzheimer’s disease. We previously showed that APP is a primary androgen-responsive gene in prostate cancer and that its increased expression is correlated with poor prognosis for patients with prostate cancer. APP has also been implicated in several human malignancies. Nevertheless, the mechanism underlying the pro-proliferative effects of APP on cancers is still not well-understood. In the present study, we explored a pathophysiological role for APP in prostate cancer cells using siRNA targeting APP (siAPP). The proliferation and migration of LNCaP and DU145 prostate cancer cells were significantly suppressed by siAPP. Differentially expressed genes in siAPP-treated cells compared to control siRNA-treated cells were identified by microarray analysis. Notably, several metalloproteinase genes, such as ADAM10 and ADAM17, and epithelial–mesenchymal transition (EMT)-related genes, such as VIM, and SNAI2, were downregulated in siAPP-treated cells as compared to control cells. The expression of these genes was upregulated in LNCaP cells stably expressing APP when compared with control cells. APP-overexpressing LNCaP cells exhibited enhanced migration in comparison to control cells. These results suggest that APP may contribute to the proliferation and migration of prostate cancer cells by modulating the expression of metalloproteinase and EMT-related genes. 6. Amyloidprecursor protein: Multiple fragments, numerous transport routes and mechanisms. Science.gov (United States) 2015-05-15 This review provides insight into the intraneuronal transport of the AmyloidPrecursor Protein (APP), the prototype of an extensively posttranslationally modified and proteolytically cleaved transmembrane protein. Uncovering the intricacies of APP transport proves to be a challenging endeavor of cell biology research, deserving increased priority, since APP is at the core of the pathogenic process in Alzheimer's disease. After being synthesized in the endoplasmic reticulum in the neuronal soma, APP enters the intracellular transport along the secretory, endocytic, and recycling routes. Along these routes, APP undergoes cleavage into defined sets of fragments, which themselves are transported - mostly independently - to distinct sites in neurons, where they exert their functions. We review the currently known routes and mechanisms of transport of full-length APP, and of APP fragments, commenting largely on the experimental challenges posed by studying transport of extensively cleaved proteins. The review emphasizes the interrelationships between the proteolytic and posttranslational modifications, the intracellular transport, and the functions of the APP species. A goal remaining to be addressed in the future is the incorporation of the various views on APP transport into a coherent picture. In this review, the disease context is only marginally addressed; the focus is on the basic biology of APP transport under normal conditions. As shown, the studies of APP transport uncovered numerous mechanisms of transport, some of them conventional, and others, novel, awaiting exploration. 7. Inflammatory Eicosanoids Increase Amyloid Precursor Protein Expression via Activation of Multiple Neuronal Receptors. Science.gov (United States) Herbst-Robinson, Katie J; Liu, Li; James, Michael; Yao, Yuemang; Xie, Sharon X; Brunden, Kurt R 2015-12-17 Senile plaques comprised of Aβ peptides are a hallmark of Alzheimer's disease (AD) brain, as are activated glia that release inflammatory molecules, including eicosanoids. Previous studies have demonstrated that amyloid precursor protein (APP) and Aβ levels can be increased through activation of thromboxane A2-prostanoid (TP) receptors on neurons. We demonstrate that TP receptor regulation of APP expression depends on Gαq-signaling and conventional protein kinase C isoforms. Importantly, we discovered that Gαq-linked prostaglandin E2 and leukotriene D4 receptors also regulate APP expression. Prostaglandin E2 and thromboxane A2, as well as total APP levels, were found to be elevated in the brains of aged 5XFAD transgenic mice harboring Aβ plaques and activated glia, suggesting that increased APP expression resulted from eicosanoid binding to Gαq-linked neuronal receptors. Notably, inhibition of eicosanoid synthesis significantly lowered brain APP protein levels in aged 5XFAD mice. These results provide new insights into potential AD therapeutic strategies. 8. Expression Characterization and Preparation of Human Amyloid Precursor Protein in Escherichia coli Institute of Scientific and Technical Information of China (English) XU Guang-wei; WANG Jia-peng; HUANG Xue-mei; ZHANG Ying-jiu 2009-01-01 To analyze whether expressed amyloid precursor protein(APP) existed in hydrophilic(cytoplasmid) or hy-drophobic(lipid bilayer) environment in E. coli and to obtain intact APP for study on its function, we investigated the expression characterization and preparation of the three intact isoforms APP770, APP751, and APP695 in E. coli. The results show that these expressed APPs existed both in hydrophilic cytoplasm region as inclusion bodies and hy-drophobic membrane region as membrane-bound state in E. coll. APPs in inclusion bodies were purified on an NTA-Ni2. agarose column after dissolving in the urea buffer and APPs in membrane-bound state were obtained by ultracentrifugation. The activity analysis indicates that APP770 and APP751 exhibited strong trypsin-inhibitory activity like the natural ones. These results indicate that E. coil cells can be used as host cells for the expression of human integral membrane protein like APP in either soluble or membrane-bound state unless the interest protein undergone post-translational modification is required. 9. The Drosophila homologue of the amyloid precursor protein is a conserved modulator of Wnt PCP signaling. Directory of Open Access Journals (Sweden) Alessia Soldano Full Text Available Wnt Planar Cell Polarity (PCP signaling is a universal regulator of polarity in epithelial cells, but it regulates axon outgrowth in neurons, suggesting the existence of axonal modulators of Wnt-PCP activity. The Amyloid precursor proteins (APPs are intensely investigated because of their link to Alzheimer's disease (AD. APP's in vivo function in the brain and the mechanisms underlying it remain unclear and controversial. Drosophila possesses a single APP homologue called APP Like, or APPL. APPL is expressed in all neurons throughout development, but has no established function in neuronal development. We therefore investigated the role of Drosophila APPL during brain development. We find that APPL is involved in the development of the Mushroom Body αβ neurons and, in particular, is required cell-autonomously for the β-axons and non-cell autonomously for the α-axons growth. Moreover, we find that APPL is a modulator of the Wnt-PCP pathway required for axonal outgrowth, but not cell polarity. Molecularly, both human APP and fly APPL form complexes with PCP receptors, thus suggesting that APPs are part of the membrane protein complex upstream of PCP signaling. Moreover, we show that APPL regulates PCP pathway activation by modulating the phosphorylation of the Wnt adaptor protein Dishevelled (Dsh by Abelson kinase (Abl. Taken together our data suggest that APPL is the first example of a modulator of the Wnt-PCP pathway specifically required for axon outgrowth. 10. Amyloid Precursor Proteins Are Dynamically Trafficked and Processed During Neuronal Development Directory of Open Access Journals (Sweden) Jenna M. Ramaker 2016-11-01 Full Text Available Proteolytic processing of the Amyloid Precursor Protein (APP produces beta-amyloid (Aβ peptide fragments that accumulate in Alzheimer’s Disease (AD, but APP may also regulate multiple aspects of neuronal development, albeit via mechanisms that are not well understood. APP is a member of a family of transmembrane glycoproteins expressed by all higher organisms, including two mammalian orthologs (APLP1 and APLP2 that have complicated investigations into the specific activities of APP. By comparison, insects express only a single APP-related protein (APP-Like, or APPL that contains the same protein interaction domains identified in APP. However, unlike its mammalian orthologs, APPL is only expressed by neurons, greatly simplifying an analysis of its functions in vivo. Like APP, APPL is processed by secretases to generate a similar array of extracellular and intracellular cleavage fragments, as well as an Aβ-like fragment that can induce neurotoxic responses in the brain. Exploiting the complementary advantages of two insect models (Drosophila melanogaster and Manduca sexta, we have investigated the regulation of APPL trafficking and processing with respect to different aspects of neuronal development. By comparing the behavior of endogenously expressed APPL with fluorescently tagged versions of APPL and APP, we have shown that some full-length protein is consistently trafficked into the most motile regions of developing neurons both in vitro and in vivo. Concurrently, much of the holoprotein is rapidly processed into N- and C-terminal fragments that undergo bi-directional transport within distinct vesicle populations. Unexpectedly, we also discovered that APPL can be transiently sequestered into an amphisome-like compartment in developing neurons, while manipulations targeting APPL cleavage altered their motile behavior in cultured embryos. These data suggest that multiple mechanisms restrict the bioavailability of the holoprotein to regulate 11. Synaptotrophic effects of human amyloid beta protein precursors in the cortex of transgenic mice. Science.gov (United States) Mucke, L; Masliah, E; Johnson, W B; Ruppe, M D; Alford, M; Rockenstein, E M; Forss-Petter, S; Pietropaolo, M; Mallory, M; Abraham, C R 1994-12-15 The amyloid precursor protein (APP) is involved in Alzheimer's disease (AD) because its degradation products accumulate abnormally in AD brains and APP mutations are associated with early onset AD. However, its role in health and disease appears to be complex, with different APP derivatives showing either neurotoxic or neurotrophic effects in vitro. To elucidate the effects APP has on the brain in vivo, cDNAs encoding different forms of human APP (hAPP) were placed downstream of the neuron-specific enolase (NSE) promoter. In multiple lines of NSE-hAPP transgenic mice neuronal overexpression of hAPP was accompanied by an increase in the number of synaptophysin immunoreactive (SYN-IR) presynaptic terminals and in the expression of the growth-associated marker GAP-43. In lines expressing moderate levels of hAPP751 or hAPP695, this effect was more prominent in homozygous than in heterozygous transgenic mice. In contrast, a line with several-fold higher levels of hAPP695 expression showed less increase in SYN-IR presynaptic terminals per amount of hAPP expressed than the lower expressor lines and a decrease in synaptotrophic effects in homozygous compared with heterozygous offspring. Transgenic mice (2-24 months of age) showed no evidence for amyloid deposits or neurodegeneration. These findings suggest that APP may be important for the formation/maintenance of synapses in vivo and that its synaptotrophic effects may be critically dependent on the expression levels of different APP isoforms. Alterations in APP expression, processing or function could contribute to the synaptic pathology seen in AD. 12. Lactic acid induces aberrant amyloid precursor protein processing by promoting its interaction with endoplasmic reticulum chaperone proteins. Directory of Open Access Journals (Sweden) Yiwen Xiang Full Text Available BACKGROUND: Lactic acid, a natural by-product of glycolysis, is produced at excess levels in response to impaired mitochondrial function, high-energy demand, and low oxygen availability. The enzyme involved in the production of β-amyloid peptide (Aβ of Alzheimer's disease, BACE1, functions optimally at lower pH, which led us to investigate a potential role of lactic acid in the processing of amyloid precursor protein (APP. METHODOLOGY/PRINCIPAL FINDINGS: Lactic acid increased levels of Aβ40 and 42, as measured by ELISA, in culture medium of human neuroblastoma cells (SH-SY5Y, whereas it decreased APP metabolites, such as sAPPα. In cell lysates, APP levels were increased and APP was found to interact with ER-chaperones in a perinuclear region, as determined by co-immunoprecipitation and fluorescence microscopy studies. Lactic acid had only a very modest effect on cellular pH, did increase the levels of ER chaperones Grp78 and Grp94 and led to APP aggregate formation reminiscent of aggresomes. CONCLUSIONS/SIGNIFICANCE: These findings suggest that sustained elevations in lactic acid levels could be a risk factor in amyloidogenesis related to Alzheimer's disease through enhanced APP interaction with ER chaperone proteins and aberrant APP processing leading to increased generation of amyloid peptides and APP aggregates. 13. Ablation of Prion Protein in Wild Type Human Amyloid Precursor Protein (APP Transgenic Mice Does Not Alter The Proteolysis of APP, Levels of Amyloid-β or Pathologic Phenotype. Directory of Open Access Journals (Sweden) Isobel J Whitehouse Full Text Available The cellular prion protein (PrPC has been proposed to play an important role in the pathogenesis of Alzheimer's disease. In cellular models PrPC inhibited the action of the β-secretase BACE1 on wild type amyloid precursor protein resulting in a reduction in amyloid-β (Aβ peptides. Here we have assessed the effect of genetic ablation of PrPC in transgenic mice expressing human wild type amyloid precursor protein (line I5. Deletion of PrPC had no effect on the α- and β-secretase proteolysis of the amyloid precursor protein (APP nor on the amount of Aβ38, Aβ40 or Aβ42 in the brains of the mice. In addition, ablation of PrPC did not alter Aβ deposition or histopathology phenotype in this transgenic model. Thus using this transgenic model we could not provide evidence to support the hypothesis that PrPC regulates Aβ production. 14. Cerebral microvascular amyloid beta protein deposition induces vascular degeneration and neuroinflammation in transgenic mice expressing human vasculotropic mutant amyloid beta precursor protein. NARCIS (Netherlands) Miao, J.; Xu, F.; Davis, J.; Otte-Holler, I.; Verbeek, M.M.; Nostrand, W.E. van 2005-01-01 Cerebral vascular amyloid beta-protein (Abeta) deposition, also known as cerebral amyloid angiopathy, is a common pathological feature of Alzheimer's disease. Additionally, several familial forms of cerebral amyloid angiopathy exist including the Dutch (E22Q) and Iowa (D23N) mutations of Abeta. Incr 15. Emerging roles for the amyloid precursor protein and derived peptides in the regulation of cellular and systemic metabolism. Science.gov (United States) Czeczor, Juliane K; McGee, Sean L 2017-03-28 The amyloid precursor protein (APP) is a transmembrane protein that can be cleaved by proteases through two different pathways to yield a number of small peptides, each with distinct physiological properties and functions. It has been extensively studied in the context of Alzheimer's disease, with the APP-derived amyloid beta (Aβ) peptide being a major constituent of the amyloid plaques observed in this disease. It has been known for some time that APP can regulate neuronal metabolism, however this review will examine evidence that APP and its peptides can also regulate key metabolic processes such as insulin action, lipid synthesis and storage and mitochondrial function in peripheral tissues. This review will present a hypothesis that amyloidogenic processing of APP in peripheral tissues plays a key role in the response to nutrient excess and that this could contribute to the pathogenesis of metabolic diseases such as obesity and type 2 diabetes (T2D). This article is protected by copyright. All rights reserved. 16. Amyloid precursor protein-mediated endocytic pathway disruption induces axonal dysfunction and neurodegeneration. Science.gov (United States) Xu, Wei; Weissmiller, April M; White, Joseph A; Fang, Fang; Wang, Xinyi; Wu, Yiwen; Pearn, Matthew L; Zhao, Xiaobei; Sawa, Mariko; Chen, Shengdi; Gunawardena, Shermali; Ding, Jianqing; Mobley, William C; Wu, Chengbiao 2016-05-02 The endosome/lysosome pathway is disrupted early in the course of both Alzheimer's disease (AD) and Down syndrome (DS); however, it is not clear how dysfunction in this pathway influences the development of these diseases. Herein, we explored the cellular and molecular mechanisms by which endosomal dysfunction contributes to the pathogenesis of AD and DS. We determined that full-length amyloid precursor protein (APP) and its β-C-terminal fragment (β-CTF) act though increased activation of Rab5 to cause enlargement of early endosomes and to disrupt retrograde axonal trafficking of nerve growth factor (NGF) signals. The functional impacts of APP and its various products were investigated in PC12 cells, cultured rat basal forebrain cholinergic neurons (BFCNs), and BFCNs from a mouse model of DS. We found that the full-length wild-type APP (APPWT) and β-CTF both induced endosomal enlargement and disrupted NGF signaling and axonal trafficking. β-CTF alone induced atrophy of BFCNs that was rescued by the dominant-negative Rab5 mutant, Rab5S34N. Moreover, expression of a dominant-negative Rab5 construct markedly reduced APP-induced axonal blockage in Drosophila. Therefore, increased APP and/or β-CTF impact the endocytic pathway to disrupt NGF trafficking and signaling, resulting in trophic deficits in BFCNs. Our data strongly support the emerging concept that dysregulation of Rab5 activity contributes importantly to early pathogenesis of AD and DS. 17. Dimerization of the transmembrane domain of amyloid precursor proteins and familial Alzheimer's disease mutants Directory of Open Access Journals (Sweden) Fraser Paul E 2008-01-01 Full Text Available Abstract Background Amyloid precursor protein (APP is enzymatically cleaved by γ-secretase to form two peptide products, either Aβ40 or the more neurotoxic Aβ42. The Aβ42/40 ratio is increased in many cases of familial Alzheimer's disease (FAD. The transmembrane domain (TM of APP contains the known dimerization motif GXXXA. We have investigated the dimerization of both wild type and FAD mutant APP transmembrane domains. Results Using synthetic peptides derived from the APP-TM domain, we show that this segment is capable of forming stable transmembrane dimers. A model of a dimeric APP-TM domain reveals a putative dimerization interface, and interestingly, majority of FAD mutations in APP are localized to this interface region. We find that FAD-APP mutations destabilize the APP-TM dimer and increase the population of APP peptide monomers. Conclusion The dissociation constants are correlated to both the Aβ42/Aβ40 ratio and the mean age of disease onset in AD patients. We also show that these TM-peptides reduce Aβ production and Aβ42/Aβ40 ratios when added to HEK293 cells overexpressing the Swedish FAD mutation and γ-secretase components, potentially revealing a new class of γ-secretase inhibitors. 18. Overexpression of amyloid precursor protein increases copper content in HEK293 cells Energy Technology Data Exchange (ETDEWEB) Suazo, Miriam; Hodar, Christian; Morgan, Carlos [INTA, Laboratorio de Bioinformatica y Expresion Genica, Universidad de Chile, El Libano 5524, Macul, Santiago (Chile); Cerpa, Waldo [Centro de Envejecimiento y Regeneracion (CARE), Centro de Regulacion Celular y Patologia ' Joaquin V. Luco' (CRCP), MIFAB, Departamento de Biologia Celular y Molecular, Facultad de Ciencias Biologicas, Pontificia Universidad Catolica de Chile, Santiago (Chile); Cambiazo, Veronica [INTA, Laboratorio de Bioinformatica y Expresion Genica, Universidad de Chile, El Libano 5524, Macul, Santiago (Chile); Millenium Nucleus CGC, Universidad de Chile (Chile); Inestrosa, Nibaldo C. [Centro de Envejecimiento y Regeneracion (CARE), Centro de Regulacion Celular y Patologia ' Joaquin V. Luco' (CRCP), MIFAB, Departamento de Biologia Celular y Molecular, Facultad de Ciencias Biologicas, Pontificia Universidad Catolica de Chile, Santiago (Chile); Gonzalez, Mauricio, E-mail: mgonzale@inta.cl [INTA, Laboratorio de Bioinformatica y Expresion Genica, Universidad de Chile, El Libano 5524, Macul, Santiago (Chile) 2009-05-15 Amyloid precursor protein (APP) is a transmembrane glycoprotein widely expressed in mammalian tissues and plays a central role in Alzheimer's disease. However, its physiological function remains elusive. Cu{sup 2+} binding and reduction activities have been described in the extracellular APP135-156 region, which might be relevant for cellular copper uptake and homeostasis. Here, we assessed Cu{sup 2+} reduction and {sup 64}Cu uptake in two human HEK293 cell lines overexpressing APP. Our results indicate that Cu{sup 2+} reduction increased and cells accumulated larger levels of copper, maintaining cell viability at supra-physiological levels of Cu{sup 2+} ions. Moreover, wild-type cells exposed to both Cu{sup 2+} ions and APP135-155 synthetic peptides increased copper reduction and uptake. Complementation of function studies in human APP751 transformed Fre1 defective Saccharomyces cerevisiae cells rescued low Cu{sup 2+} reductase activity and increased {sup 64}Cu uptake. We conclude that Cu{sup 2+} reduction activity of APP facilitates copper uptake and may represent an early step in cellular copper homeostasis. 19. Regulation of amyloid precursor protein processing by the Beclin 1 complex. Directory of Open Access Journals (Sweden) Philipp A Jaeger Full Text Available Autophagy is an intracellular degradation pathway that functions in protein and organelle turnover in response to starvation and cellular stress. Autophagy is initiated by the formation of a complex containing Beclin 1 (BECN1 and its binding partner Phosphoinositide-3-kinase, class 3 (PIK3C3. Recently, BECN1 deficiency was shown to enhance the pathology of a mouse model of Alzheimer Disease (AD. However, the mechanism by which BECN1 or autophagy mediate these effects are unknown. Here, we report that the levels of Amyloid precursor protein (APP and its metabolites can be reduced through autophagy activation, indicating that they are a substrate for autophagy. Furthermore, we find that knockdown of Becn1 in cell culture increases the levels of APP and its metabolites. Accumulation of APP and APP C-terminal fragments (APP-CTF are accompanied by impaired autophagosomal clearance. Pharmacological inhibition of autophagosomal-lysosomal degradation causes a comparable accumulation of APP and APP-metabolites in autophagosomes. Becn1 reduction in cell culture leads to lower levels of its binding partner Pik3c3 and increased presence of Microtubule-associated protein 1, light chain 3 (LC3. Overexpression of Becn1, on the other hand, reduces cellular APP levels. In line with these observations, we detected less BECN1 and PIK3C3 but more LC3 protein in brains of AD patients. We conclude that BECN1 regulates APP processing and turnover. BECN1 is involved in autophagy initiation and autophagosome clearance. Accordingly, BECN1 deficiency disrupts cellular autophagy and autophagosomal-lysosomal degradation and alters APP metabolism. Together, our findings suggest that autophagy and the BECN1-PIK3C3 complex regulate APP processing and play an important role in AD pathology. 20. Protective effects of ferulic acid in amyloid precursor protein plus presenilin-1 transgenic mouse model of Alzheimer disease. Science.gov (United States) Yan, Ji-Jing; Jung, Jun-Sub; Kim, Taek-Keun; Hasan, Ashraful; Hong, Chang-Won; Nam, Ju-Suk; Song, Dong-Keun 2013-01-01 We previously reported the protective effects of long-term administration of ferulic acid against the in vivo toxicity of β-amyloid peptide administered intracerebroventricularly in mice. In the present study, we investigated the effects of ferulic acid in transgenic amyloid precursor protein (APP)swe/presenilin 1 (PS1)dE9 (APP/PS1) mouse model of Alzheimer disease (AD). Chronic (for 6 months from the age of 6 to 12 months) oral administration of ferulic acid at a dose of 5.3 mg/kg/day significantly enhanced the performance in novel-object recognition task, and reduced amyloid deposition and interleukin-1 beta (IL-1β) levels in the frontal cortex. These results suggest that ferulic acid at a certain dosage could be useful for prevention and treatment of AD. 1. Glial expression of the {beta}-Amyloid Precursor Protein (APP) in global ischemia Energy Technology Data Exchange (ETDEWEB) Banati, R.B.; Gehrmann, J.; Kreutzberg, G.W. [Max Planck Institute of Psychiarty, Martinsried (Germany)]\|[Max Planck Institute for Neurological Research, Koeln (Germany)]\|[Univ. Hospital, Zurich (Switzerland) 1995-07-01 The {beta}-amyloid precursor protein (APP) bears characteristics of an acute-phase protein and therefore is likely to be involved in the glial response to brain injury. In the brain, APP is rapidly synthesized by activated glial cells in response to comparatively mild neuronal lesions, e.g., a remote peripheral nerve injury. Perfusion deficits in the brain result largely in neuronal necrosis and are a common condition in elderly patients. This neuronal necrosis is accompanied by a pronounced reaction of astrocytes and microglia, which can also be observed in animal models. We have therefore studied in the rat, immunocytochemically, the induction of APP after 30 min of global ischemia caused by four-vessel occlusion. The postischemic brain injuries were examined at survival times from 12 h to 7 days. From day 3 onward, APP immunoreactivity was strongly induced in the CA{sub 1} and CA{sub 4} regions of the rat dorsal hippocampus as well as in the dorsolateral striatum. In these areas, the majority of APP-immunoreactive cells were reactive glial fibrillary acidic protein (GFAP)-positive astrocytes, as shown by double-immunofluorescence labeling for GFAP and APP. Additionally, small ramified cells, most likely activated microglia, expressed APP immunoreactivity. In contrast, in the parietal cortex, APP immunoreactivity occurred focally in clusters of activated microglia rather than in astrocytes, as demonstrated by double-immunofluorescence labeling for APP and the microglia-binding lectin Griffonia simplicifolia isolectin B{sub 4}. In conclusion, following global ischemia, APP is induced in reactive glial cells with spatial differences in the distribution pattern of APP induction in actrocytes and microglia. 51 refs., 4 figs. 2. Mutation analysis of presenilin-1 gene in Alzheimer’s disease patients and the effects of its mutation on expression of presenilin-1 and amyloid precursor protein Institute of Scientific and Technical Information of China (English) 刘晓雄 2013-01-01 Objective To analyze the presenilin-1(PS-1) gene mutations in Alzheimer’s disease(AD) patients and investigate the influence of the initiation codon mutation on the mRNA expression of PS-1 and amyloid precursor protein 3. Effect of catalpol on senile plaques and spatial learning and memory ability in amyloidprotein precursor/presenilin 1 double transgenic mice Institute of Scientific and Technical Information of China (English) 宋冲 2013-01-01 Objective To investigate whether catalpol affects senile plaque formation and spatial learning and memory ability in the amyloid-βprotein precursor/presenilin 1(APP/PS1)double transgenic mice.Methods 4. Inhibiting p38 mitogen-activated protein kinase attenuates cerebral ischemic injury in Swedish mutant amyloid precursor protein transgenic mice Institute of Scientific and Technical Information of China (English) Liangyu Zou; Haiyan Qin; Yitao He; Heming Huang; Yi Lu; Xiaofan Chu 2012-01-01 Cerebral ischemia was induced using photothrombosis 1 hour after intraperitoneal injection of the p38 mitogen-activated protein kinase (MAPK) inhibitor SB239063 into Swedish mutant amyloid precursor protein (APP/SWE) transgenic and non-transgenic mice. The number of surviving neurons in the penumbra was quantified using Nissl staining, and the activity of p38 MAPKs was measured by western blotting. The number of surviving neurons in the penumbra was significantly reduced in APP/SWE transgenic mice compared with non-transgenic controls 7 days after cerebral ischemia, but the activity of p38 MAPKs was significantly elevated compared with the non-ischemic hemisphere in the APP/SWE transgenic mice. SB239063 prevented these changes. The APP/SWE mutation exacerbated ischemic brain injury, and this could be alleviated by inhibiting p38 MAPK activity. 5. Calcium ionophore A23187 specifically decreases the secretion of beta-secretase cleaved amyloid precursor protein during apoptosis in primary rat cortical cultures DEFF Research Database (Denmark) Sennvik, K; Benedikz, Eirikur; Fastbom, J; 2001-01-01 Alzheimer's disease (AD) is characterized by the degeneration and loss of neurons, intracellular neurofibrillary tangles and the accumulation of extracellular senile plaques consisting mainly of beta-amyloid (A beta). A beta is generated from the amyloid precursor protein (APP) by sequential beta... 6. Soluble beta-amyloid precursor protein is related to disease progression in amyotrophic lateral sclerosis. Directory of Open Access Journals (Sweden) Petra Steinacker Full Text Available BACKGROUND: Biomarkers of disease progression in amyotrophic lateral sclerosis (ALS could support the identification of beneficial drugs in clinical trials. We aimed to test whether soluble fragments of beta-amyloid precursor protein (sAPPα and sAPPß correlated with clinical subtypes of ALS and were of prognostic value. METHODOLOGY/PRINCIPAL FINDINGS: In a cross-sectional study including patients with ALS (N = 68 with clinical follow-up data over 6 months, Parkinson's disease (PD, N = 20, and age-matched controls (N = 40, cerebrospinal fluid (CSF levels of sAPPα a, sAPPß and neurofilaments (NfH(SMI35 were measured by multiplex assay, Progranulin by ELISA. CSF sAPPα and sAPPß levels were lower in ALS with a rapidly-progressive disease course (p = 0.03, and p = 0.02 and with longer disease duration (p = 0.01 and p = 0.01, respectively. CSF NfH(SMI35 was elevated in ALS compared to PD and controls, with highest concentrations found in patients with rapid disease progression (p<0.01. High CSF NfH(SMI3 was linked to low CSF sAPPα and sAPPß (p = 0.001, and p = 0.007, respectively. The ratios CSF NfH(SMI35/CSF sAPPα,-ß were elevated in patients with fast progression of disease (p = 0.002 each. CSF Progranulin decreased with ongoing disease (p = 0.04. CONCLUSIONS: This study provides new CSF candidate markers associated with progression of disease in ALS. The data suggest that a deficiency of cellular neuroprotective mechanisms (decrease of sAPP is linked to progressive neuro-axonal damage (increase of NfH(SMI35 and to progression of disease. 7. Metabolic Characterization of Intact Cells Reveals Intracellular Amyloid Beta but Not Its Precursor Protein to Reduce Mitochondrial Respiration Science.gov (United States) Schaefer, Patrick M.; von Einem, Bjoern; Walther, Paul; Calzia, Enrico; von Arnim, Christine A. F. 2016-01-01 One hallmark of Alzheimer´s disease are senile plaques consisting of amyloid beta (Aβ), which derives from the processing of the amyloid precursor protein (APP). Mitochondrial dysfunction has been linked to the pathogenesis of Alzheimer´s disease and both Aβ and APP have been reported to affect mitochondrial function in isolated systems. However, in intact cells, considering a physiological localization of APP and Aβ, it is pending what triggers the mitochondrial defect. Thus, the aim of this study was to dissect the impact of APP versus Aβ in inducing mitochondrial alterations with respect to their subcellular localization. We performed an overexpression of APP or beta-site amyloid precursor protein cleaving enzyme 1 (BACE1), increasing APP and Aβ levels or Aβ alone, respectively. Conducting a comprehensive metabolic characterization we demonstrate that only APP overexpression reduced mitochondrial respiration, despite lower extracellular Aβ levels compared to BACE overexpression. Surprisingly, this could be rescued by a gamma secretase inhibitor, oppositionally indicating an Aβ-mediated mitochondrial toxicity. Analyzing Aβ localization revealed that intracellular levels of Aβ and an increased spatial association of APP/Aβ with mitochondria are associated with reduced mitochondrial respiration. Thus, our data provide marked evidence for a prominent role of intracellular Aβ accumulation in Alzheimer´s disease associated mitochondrial dysfunction. Thereby it highlights the importance of the localization of APP processing and intracellular transport as a decisive factor for mitochondrial function, linking two prominent hallmarks of neurodegenerative diseases. PMID:28005987 8. Iron-export ferroxidase activity of β-amyloid precursor protein is inhibited by zinc in Alzheimer's disease. Science.gov (United States) Duce, James A; Tsatsanis, Andrew; Cater, Michael A; James, Simon A; Robb, Elysia; Wikhe, Krutika; Leong, Su Ling; Perez, Keyla; Johanssen, Timothy; Greenough, Mark A; Cho, Hyun-Hee; Galatis, Denise; Moir, Robert D; Masters, Colin L; McLean, Catriona; Tanzi, Rudolph E; Cappai, Roberto; Barnham, Kevin J; Ciccotosto, Giuseppe D; Rogers, Jack T; Bush, Ashley I 2010-09-17 Alzheimer's Disease (AD) is complicated by pro-oxidant intraneuronal Fe(2+) elevation as well as extracellular Zn(2+) accumulation within amyloid plaque. We found that the AD β-amyloid protein precursor (APP) possesses ferroxidase activity mediated by a conserved H-ferritin-like active site, which is inhibited specifically by Zn(2+). Like ceruloplasmin, APP catalytically oxidizes Fe(2+), loads Fe(3+) into transferrin, and has a major interaction with ferroportin in HEK293T cells (that lack ceruloplasmin) and in human cortical tissue. Ablation of APP in HEK293T cells and primary neurons induces marked iron retention, whereas increasing APP695 promotes iron export. Unlike normal mice, APP(-/-) mice are vulnerable to dietary iron exposure, which causes Fe(2+) accumulation and oxidative stress in cortical neurons. Paralleling iron accumulation, APP ferroxidase activity in AD postmortem neocortex is inhibited by endogenous Zn(2+), which we demonstrate can originate from Zn(2+)-laden amyloid aggregates and correlates with Aβ burden. Abnormal exchange of cortical zinc may link amyloid pathology with neuronal iron accumulation in AD. 9. Influence of apolipoprotein E and its receptors on cerebral amyloid precursor protein metabolism following traumatic brain injury Institute of Scientific and Technical Information of China (English) ZHOU Shuai; SUN Xiao-chuan 2012-01-01 Traumatic brain injury (TBI) is the leading cause of mortality and disability among young individuals in our society,and globally the incidence of TBI is rising sharply.Mounting evidence has indicated that apolipoprotein E (apoE:protein; APOE:gene) genotype influences the outcome after TBI.The proposed mechanism by which APOE affects the clinicopathological consequences of TBI is multifactorial and includes amyloid deposition,disruption of lipid distribution,dysfunction of mitochondrial energy production,oxidative stress and increases intracellular calcium in response to injury.This paper reviews the current state of knowledge regarding the influence of apoE and its receptors on cerebral amyloid betaprotein precursor metabolism following TBI. 10. N-Acetyl-L-Cystein downregulates beta-amyloid precursor protein gene transcription in human neuroblastoma cells. Science.gov (United States) Studer, R; Baysang, G; Brack, C 2001-01-01 The causes for the sporadic form of Alzheimer's disease (AD) are still poorly understood, except from the fact that age is an important risk factor. The main component of the characteristic amyloid plaques in brains of AD patients are Abeta peptides, derivatives of the amyloid precursor protein APP. Oxidative stress may contribute to the aetiology of AD by dysregulation of APP metabolism. Overexpression of the APP gene could result in an increased secretion of neurotoxic Abeta peptides, while preventing the overexpression might be protective. We here report that the antioxidant N-Acetyl-L-Cystein (NAC) downregulates APP gene transcription in human neuroblastoma cells. The effect is reversible when cells are returned to NAC free medium. These results open up new possibilities for the development of therapeutic agents that intervene at the transcriptional level. 11. Alzheimer's disease therapeutics targeted to the control of amyloid precursor protein translation: maintenance of brain iron homeostasis. Science.gov (United States) 2014-04-15 The neurotoxicity of amyloid beta (Aβ), a major cleavage product of the amyloid precursor protein (APP), is enhanced by iron, as found in the amyloid plaques of Alzheimer's disease (AD) patients. By contrast, the long-known neuroprotective activity of APP is evident after α-secretase cleavage of the precursor to release sAPPα, and depends on the iron export actions of APP itself. The latter underlie its neurotrophic and protective effects in facilitating the homeostatic actions of ferroportin mediated-iron export. Thus APP-dependent iron export may alleviate oxidative stress by minimizing labile iron thus protecting neurons from iron overload during stroke and hemorrhage. Consistent with this, altered phosphorylation of iron-regulatory protein-1 (IRP1) and its signaling processes play a critical role in modulating APP translation via the 5' untranslated region (5'UTR) of its transcript. The APP 5'UTR region encodes a functional iron-responsive element (IRE) RNA stem loop that represents a potential target for modulating APP production. Targeted regulation of APP gene expression via the modulation of 5'UTR sequence function represents a novel approach for the potential treatment of AD since altering APP translation can be used to improve both the protective brain iron balance and provide anti-amyloid efficacy. Approved drugs including paroxetine and desferrioxamine and several novel compounds have been identified that suppress abnormal metal-promoted Aβ accumulation with a subset of these acting via APP 5'UTR-dependent mechanisms to modulate APP translation and cleavage to generate the non-toxic sAPPα. 12. Exercise is more effective than diet control in preventing high fat diet-induced β-amyloid deposition and memory deficit in amyloid precursor protein transgenic mice. Science.gov (United States) Maesako, Masato; Uemura, Kengo; Kubota, Masakazu; Kuzuya, Akira; Sasaki, Kazuki; Hayashida, Naoko; Asada-Utsugi, Megumi; Watanabe, Kiwamu; Uemura, Maiko; Kihara, Takeshi; Takahashi, Ryosuke; Shimohama, Shun; Kinoshita, Ayae 2012-06-29 Accumulating evidence suggests that some dietary patterns, specifically high fat diet (HFD), increase the risk of developing sporadic Alzheimer disease (AD). Thus, interventions targeting HFD-induced metabolic dysfunctions may be effective in preventing the development of AD. We previously demonstrated that amyloid precursor protein (APP)-overexpressing transgenic mice fed HFD showed worsening of cognitive function when compared with control APP mice on normal diet. Moreover, we reported that voluntary exercise ameliorates HFD-induced memory impairment and β-amyloid (Aβ) deposition. In the present study, we conducted diet control to ameliorate the metabolic abnormality caused by HFD on APP transgenic mice and compared the effect of diet control on cognitive function with that of voluntary exercise as well as that of combined (diet control plus exercise) treatment. Surprisingly, we found that exercise was more effective than diet control, although both exercise and diet control ameliorated HFD-induced memory deficit and Aβ deposition. The production of Aβ was not different between the exercise- and the diet control-treated mice. On the other hand, exercise specifically strengthened the activity of neprilysin, the Aβ-degrading enzyme, the level of which was significantly correlated with that of deposited Aβ in our mice. Notably, the effect of the combination treatment (exercise and diet control) on memory and amyloid pathology was not significantly different from that of exercise alone. These studies provide solid evidence that exercise is a useful intervention to rescue HFD-induced aggravation of cognitive decline in transgenic model mice of AD. 13. Complement C3 deficiency leads to accelerated amyloid beta plaque deposition and neurodegeneration and modulation of the microglia/macrophage phenotype in amyloid precursor protein transgenic mice. Science.gov (United States) Maier, Marcel; Peng, Ying; Jiang, Liying; Seabrook, Timothy J; Carroll, Michael C; Lemere, Cynthia A 2008-06-18 Complement factor C3 is the central component of the complement system and a key inflammatory protein activated in Alzheimer's disease (AD). Previous studies demonstrated that inhibition of C3 by overexpression of soluble complement receptor-related protein y in an AD mouse model led to reduced microgliosis, increased amyloid beta (Abeta) plaque burden, and neurodegeneration. To further address the role of C3 in AD pathology, we generated a complement C3-deficient amyloid precursor protein (APP) transgenic AD mouse model (APP;C3(-/-)). Brains were analyzed at 8, 12, and 17 months of age by immunohistochemical and biochemical methods and compared with age-matched APP transgenic mice. At younger ages (8-12 months), no significant neuropathological differences were observed between the two transgenic lines. In contrast, at 17 months of age, APP;C3(-/-) mice showed significant changes of up to twofold increased total Abeta and fibrillar amyloid plaque burden in midfrontal cortex and hippocampus, which correlated with (1) significantly increased Tris-buffered saline (TBS)-insoluble Abeta(42) levels and reduced TBS-soluble Abeta(42) and Abeta(40) levels in brain homogenates, (2) a trend for increased Abeta levels in the plasma, (3) a significant loss of neuronal-specific nuclear protein-positive neurons in the hippocampus, and (4) differential activation of microglia toward a more alternative phenotype (e.g., significantly increased CD45-positive microglia, increased brain levels of interleukins 4 and 10, and reduced levels of CD68, F4/80, inducible nitric oxide synthase, and tumor necrosis factor). Our results suggest a beneficial role for complement C3 in plaque clearance and neuronal health as well as in modulation of the microglia phenotype. 14. Schisandrin B protects PC12 cells by decreasing the expression of amyloid precursor protein and vacuolar protein sorting 35★ OpenAIRE Yan, Mingmin; Mao, Shanping; Dong, Huimin; Liu, Baohui; Zhang, Qian; PAN, GAOFENG; Fu, Zhiping 2012-01-01 PC12 cell injury was induced using 20 μM amyloid β-protein 25–35 to establish a model of Alzheimer's disease. The cells were then treated with 5, 10, and 25 μM Schisandrin B. Methylthiazolyldiphenyl-tetrazolium bromide assays and Hoechst 33342 staining results showed that with increasing Schisandrin B concentration, the survival rate of PC12 cells injured by amyloid β-protein 25–35 gradually increased and the rate of apoptosis gradually decreased. Reverse transcription-PCR, immunocytochemical... 15. Baicalein reduces β-amyloid and promotes nonamyloidogenic amyloid precursor protein processing in an Alzheimer’s disease transgenic mouse model Science.gov (United States) Zhang, She-Qing; Obregon, Demian; Ehrhart, Jared; Deng, Juan; Tian, Jun; Hou, Huayan; Giunta, Brian; Sawmiller, Darrell; Tan, Jun 2013-01-01 Baicalein, a flavonoid isolated from the roots of Scutellaria baicalensis, is known to modulate γ-aminobutyric acid (GABA) type A receptors. Given prior reports demonstrating benefits of GABAA modulation for Alzheimer’s disease (AD) treatment, we wished to determine whether this agent might be beneficial for AD. CHO cells engineered to overexpress wild-type amyloid precursor protein (APP), primary culture neuronal cells from AD mice (Tg2576) and AD mice were treated with baicalein. In the cell cultures, baicalein significantly reduced the production of β-amyloid (Aβ) by increasing APP α-processing. These effects were blocked by the GABAA antagonist bicuculline. Likewise, AD mice treated daily with i.p. baicalein for 8 weeks showed enhanced APP α-secretase processing, reduced Aβ production, and reduced AD-like pathology together with improved cognitive performance. Our findings suggest that baicalein promotes nonamyloidogenic processing of APP, thereby reducing Aβ production and improving cognitive performance, by activating GABAA receptors. © 2013 Wiley Periodicals, Inc. PMID:23686791 16. P-glycoprotein efflux and other factors limit brain amyloid beta reduction by beta-site amyloid precursor protein-cleaving enzyme 1 inhibitors in mice. Science.gov (United States) Meredith, Jere E; Thompson, Lorin A; Toyn, Jeremy H; Marcin, Lawrence; Barten, Donna M; Marcinkeviciene, Jovita; Kopcho, Lisa; Kim, Young; Lin, Alan; Guss, Valerie; Burton, Catherine; Iben, Lawrence; Polson, Craig; Cantone, Joe; Ford, Michael; Drexler, Dieter; Fiedler, Tracey; Lentz, Kimberley A; Grace, James E; Kolb, Janet; Corsa, Jason; Pierdomenico, Maria; Jones, Kelli; Olson, Richard E; Macor, John E; Albright, Charles F 2008-08-01 Alzheimer's disease (AD) is a progressive neurodegenerative disease. Amyloid beta (Abeta) peptides are hypothesized to cause the initiation and progression of AD based on pathologic data from AD patients, genetic analysis of mutations that cause early onset forms of AD, and preclinical studies. Based on this hypothesis, beta-site amyloid precursor protein (APP)-cleaving enzyme 1 (BACE1) inhibitors are an attractive therapeutic approach for AD because cleavage of the APP by BACE1 is required to form Abeta. In this study, three potent BACE1 inhibitors are characterized. All three inhibitors decrease Abeta formation in cultured cells with IC(50) values less than 10 nM. Analysis of APP C-terminal fragments by immunoblotting and Abeta peptides by mass spectrometry showed that these inhibitors decreased Abeta by inhibiting BACE1. An assay for Abeta1-40 in mice was developed and used to show that these BACE1 inhibitors decreased plasma Abeta1-40, but not brain Abeta1-40, in wild-type mice. Because these BACE1 inhibitors were substrates for P-glycoprotein (P-gp), a member of the ATP-binding cassette superfamily of efflux transporters, these inhibitors were administered to P-gp knockout (KO) mice. These studies showed that all three BACE1 inhibitors decreased brain Abeta1-40 in P-gp KO mice, demonstrating that P-gp is a major limitation for development of BACE1 inhibitors to test the amyloid hypothesis. A comparison of plasma Abeta1-40 and brain Abeta1-40 dose responses for these three compounds revealed differences in relative ED(50) values, indicating that factors other than P-gp can also contribute to poor brain activity by BACE1 inhibitors. 17. The purinergic receptor P2X7 triggers alpha-secretase-dependent processing of the amyloid precursor protein. Science.gov (United States) Delarasse, Cécile; Auger, Rodolphe; Gonnord, Pauline; Fontaine, Bertrand; Kanellopoulos, Jean M 2011-01-28 The amyloid precursor protein (APP) is cleaved by β- and γ-secretases to generate the β-amyloid (Aβ) peptides, which are present in large amounts in the amyloid plaques of Alzheimer disease (AD) patient brains. Non-amyloidogenic processing of APP by α-secretases leads to proteolytic cleavage within the Aβ peptide sequence and shedding of the soluble APP ectodomain (sAPPα), which has been reported to be endowed with neuroprotective properties. In this work, we have shown that activation of the purinergic receptor P2X7 (P2X7R) stimulates sAPPα release from mouse neuroblastoma cells expressing human APP, from human neuroblastoma cells and from mouse primary astrocytes or neural progenitor cells. sAPPα shedding is inhibited by P2X7R antagonists or knockdown of P2X7R with specific small interfering RNA (siRNA) and is not observed in neural cells from P2X7R-deficient mice. P2X7R-dependent APP-cleavage is independent of extracellular calcium and strongly inhibited by hydroxamate-based metalloprotease inhibitors, TAPI-2 and GM6001. However, knockdown of a disintegrin and metalloproteinase-9 (ADAM9), ADAM10 and ADAM17 by specific siRNA, known to have α-secretase activity, does not block the P2X7R-dependent non-amyloidogenic pathway. Using several specific pharmacological inhibitors, we demonstrate that the mitogen-activated protein kinase modules Erk1/2 and JNK are involved in P2X7R-dependent α-secretase activity. Our study suggests that P2X7R, which is expressed in hippocampal neurons and glial cells, is a potential therapeutic target in AD. 18. Two memory associated genes regulated by amyloid precursor protein intracellular domain ovel insights into the pathogenesis of learning and memory impairment in Alzheimer's disease Institute of Scientific and Technical Information of China (English) Chuandong Zheng; Xi Gu; Zhimei Zhong; Rui Zhu; Tianming Gao; Fang Wang 2012-01-01 In this study, we employed chromatin immunoprecipitation, a useful method for studying the locations of transcription factors bound to specific DNA regions in specific cells, to investigate amyloid precursor protein intracellular domain binding sites in chromatin DNA from hippocampal neurons of rats, and to screen out five putative genes associated with the learning and memory functions. The promoter regions of the calcium/calmodulin-dependent protein kinase II alpha and glutamate receptor-2 genes were amplified by PCR from DNA products immunoprecipitated by amyloid precursor protein intracellular domain. An electrophoretic mobility shift assay and western blot analysis suggested that the promoter regions of these two genes associated with learning and memory were bound by amyloid precursor protein intracellular domain (in complex form). Our experimental findings indicate that the amyloid precursor protein intracellular domain is involved in the transcriptional regulation of learning- and memory-associated genes in hippocampal neurons. These data may provide new insights into the molecular mechanism underlying the symptoms of progressive memory loss in Alzheimer's disease. 19. The Amyloid Precursor Protein of Alzheimer's Disease in the Reduction of Copper(II) to Copper(I) Science.gov (United States) Multhaup, Gerd; Schlicksupp, Andrea; Hesse, Lars; Beher, Dirk; Ruppert, Thomas; Masters, Colin L.; Beyreuther, Konrad 1996-03-01 The transition metal ion copper(II) has a critical role in chronic neurologic diseases. The amyloid precursor protein (APP) of Alzheimer's disease or a synthetic peptide representing its copper-binding site reduced bound copper(II) to copper(I). This copper ion-mediated redox reaction led to disulfide bond formation in APP, which indicated that free sulfhydryl groups of APP were involved. Neither superoxide nor hydrogen peroxide had an effect on the kinetics of copper(II) reduction. The reduction of copper(II) to copper(I) by APP involves an electron-transfer reaction and could enhance the production of hydroxyl radicals, which could then attack nearby sites. Thus, copper-mediated toxicity may contribute to neurodegeneration in Alzheimer's disease. 20. Caffeine, Through Adenosine A3 Receptor-Mediated Actions, Suppresses AmyloidProtein Precursor Internalization and Amyloid-β Generation. Science.gov (United States) Li, Shanshan; Geiger, Nicholas H; Soliman, Mahmoud L; Hui, Liang; Geiger, Jonathan D; Chen, Xuesong 2015-01-01 Intraneuronal accumulation and extracellular deposition of amyloid-β (Aβ) protein continues to be implicated in the pathogenesis of Alzheimer's disease (AD), be it familial in origin or sporadic in nature. Aβ is generated intracellularly following endocytosis of amyloidprotein precursor (AβPP), and, consequently, factors that suppress AβPP internalization may decrease amyloidogenic processing of AβPP. Here we tested the hypothesis that caffeine decreases Aβ generation by suppressing AβPP internalization in primary cultured neurons. Caffeine concentration-dependently blocked low-density lipoprotein (LDL) cholesterol internalization and a specific adenosine A3 receptor (A3R) antagonist as well as siRNA knockdown of A3Rs mimicked the effects of caffeine on neuronal internalization of LDL cholesterol. Further implicating A3Rs were findings that a specific A3R agonist increased neuronal internalization of LDL cholesterol. In addition, caffeine as well as siRNA knockdown of A3Rs blocked the ability of LDL cholesterol to increase Aβ levels. Furthermore, caffeine blocked LDL cholesterol-induced decreases in AβPP protein levels in neuronal plasma membranes, increased surface expression of AβPP on neurons, and the A3R antagonist as well as siRNA knockdown of A3Rs mimicked the effects of caffeine on AβPP surface expression. Moreover, the A3R agonist decreased neuronal surface expression of AβPP. Our findings suggest that caffeine exerts protective effects against amyloidogenic processing of AβPP at least in part by suppressing A3R-mediated internalization of AβPP. 1. Nerve Growth Factor Increases mRNA Levels for the Prion Protein and the β -amyloid Protein Precursor in Developing Hamster Brain Science.gov (United States) Mobley, William C.; Neve, Rachael L.; Prusiner, Stanley B.; McKinley, Michael P. 1988-12-01 Deposition of amyloid filaments serves as a pathologic hallmark for some neurodegenerative disorders. The prion protein (PrP) is found in amyloid of animals with scrapie and humans with Creutzfeldt-Jakob disease; the β protein is present in amyloid deposits in Alzheimer disease and Down syndrome patients. These two proteins are derived from precursors that in the brain are expressed primarily in neurons and are membrane bound. We found that gene expression for PrP and the β -protein precursor (β -PP) is regulated in developing hamster brain. Specific brain regions showed distinct patterns of ontogenesis for PrP and β -PP mRNAs. The increases in PrP and β -PP mRNAs in developing basal forebrain coincided with an increase in choline acetyltransferase activity, raising the possibility that these markers might be coordinately controlled in cholinergic neurons and regulated by nerve growth factor (NGF). Injections of NGF into the brains of neonatal hamsters increased both PrP and β -PP mRNA levels. Increased PrP and β -PP mRNA levels induced by NGF were confined to regions that contain NGF-responsive cholinergic neurons and were accompanied by elevations in choline acetyltransferase. It remains to be established whether or not exogenous NGF acts to increase PrP and β -PP gene expression selectively in forebrain cholinergic neurons in the developing hamster and endogenous NGF regulates expression of these genes. 2. Y682 mutation of amyloid precursor protein promotes endo-lysosomal dysfunction by disrupting APP-SorLA interaction Directory of Open Access Journals (Sweden) Luca Rosario La Rosa 2015-04-01 Full Text Available The intracellular transport and localization of amyloid precursor protein (APP are critical determinants of APP processing and β-amyloid peptide production, thus crucially important for the pathophysiology of Alzheimer’s disease (AD. Notably, the C-terminal Y682ENPTY687 domain of APP binds to specific adaptors controlling APP trafficking and sorting in neurons. Mutation on the Y682 residue to glycine (Y682G leads to altered APP sorting in hippocampal neurons that favors its accumulation in intracellular compartments and the release of soluble APPα. Such alterations induce premature aging and learning and cognitive deficits in APP Y682G mutant mice (APPYG/YG. Here, we report that Y682G mutation affects formation of the APP complex with sortilin-related receptor (SorLA, resulting in endo-lysosomal dysfunctions and neuronal degeneration. Moreover, disruption of the APP/SorLA complex changes the trafficking pathway of SorLA, with its consequent increase in secretion outside neurons. Mutations in the SorLA gene are a prognostic factor in AD, and increases in SorLA levels in cerebrospinal fluid are predictive of AD in humans. These results might open new possibilities in comprehending the role played by SorLA in its interaction with APP and in the progression of neuronal degeneration. In addition, they further underline the crucial role played by Y682 residue in controlling APP trafficking in neurons. 3. Tetrahydrohyperforin Inhibits the Proteolytic Processing of Amyloid Precursor Protein and Enhances Its Degradation by Atg5-Dependent Autophagy. Directory of Open Access Journals (Sweden) Viviana A Cavieres Full Text Available Alzheimer's disease (AD is a neurodegenerative disorder characterized by the accumulation of amyloid-β (Aβ peptide. We have previously shown that the compound tetrahydrohyperforin (IDN5706 prevents accumulation of Aβ species in an in vivo model of AD, however the mechanism that explains this reduction is not well understood. We show herein that IDN5706 decreases the levels of ER degradation enhancer, mannosidase alpha-like 1 (EDEM1, a key chaperone related to endoplasmic-reticulum-associated degradation (ERAD. Moreover, we observed that low levels of EDEM1 correlated with a strong activation of autophagy, suggesting a crosstalk between these two pathways. We observed that IDN5706 perturbs the glycosylation and proteolytic processing of the amyloid precursor protein (APP, resulting in the accumulation of immature APP (iAPP in the endoplasmic reticulum. To investigate the contribution of autophagy, we tested the effect of IDN5706 in Atg5-depleted cells. We found that depletion of Atg5 enhanced the accumulation of iAPP in response to IDN5706 by slowing down its degradation. Our findings reveal that IDN5706 promotes degradation of iAPP via the activation of Atg5-dependent autophagy, shedding light on the mechanism that may contribute to the reduction of Aβ production in vivo. 4. Tetrahydrohyperforin Inhibits the Proteolytic Processing of Amyloid Precursor Protein and Enhances Its Degradation by Atg5-Dependent Autophagy Science.gov (United States) Muñoz, Vanessa C.; Yefi, Claudia P.; Bustamante, Hianara A.; Barraza, Rafael R.; Tapia-Rojas, Cheril; Otth, Carola; Barrera, María José; González, Carlos; Mardones, Gonzalo A.; Inestrosa, Nibaldo C.; Burgos, Patricia V. 2015-01-01 Alzheimer's disease (AD) is a neurodegenerative disorder characterized by the accumulation of amyloid-β (Aβ) peptide. We have previously shown that the compound tetrahydrohyperforin (IDN5706) prevents accumulation of Aβ species in an in vivo model of AD, however the mechanism that explains this reduction is not well understood. We show herein that IDN5706 decreases the levels of ER degradation enhancer, mannosidase alpha-like 1 (EDEM1), a key chaperone related to endoplasmic-reticulum-associated degradation (ERAD). Moreover, we observed that low levels of EDEM1 correlated with a strong activation of autophagy, suggesting a crosstalk between these two pathways. We observed that IDN5706 perturbs the glycosylation and proteolytic processing of the amyloid precursor protein (APP), resulting in the accumulation of immature APP (iAPP) in the endoplasmic reticulum. To investigate the contribution of autophagy, we tested the effect of IDN5706 in Atg5-depleted cells. We found that depletion of Atg5 enhanced the accumulation of iAPP in response to IDN5706 by slowing down its degradation. Our findings reveal that IDN5706 promotes degradation of iAPP via the activation of Atg5-dependent autophagy, shedding light on the mechanism that may contribute to the reduction of Aβ production in vivo. PMID:26308941 5. Multiplex assay for live-cell monitoring of cellular fates of amyloidprecursor protein (APP. Directory of Open Access Journals (Sweden) Maria Merezhko Full Text Available Amyloidprecursor protein (APP plays a central role in pathogenesis of Alzheimer's disease. APP has a short half-life and undergoes complex proteolytic processing that is highly responsive to various stimuli such as changes in cellular lipid or energy homeostasis. Cellular trafficking of APP is controlled by its large protein interactome, including dozens of cytosolic adaptor proteins, and also by interactions with lipids. Currently, cellular regulation of APP is mostly studied based on appearance of APP-derived proteolytic fragments to conditioned media and cellular extracts. Here, we have developed a novel live-cell assay system based on several indirect measures that reflect altered APP trafficking and processing in cells. Protein-fragment complementation assay technology for detection of APP-BACE1 protein-protein interaction forms the core of the new assay. In a multiplex form, the assay can measure four endpoints: total cellular APP level, total secreted sAPP level in media, APP-BACE1 interaction in cells and in exosomes released by the cells. Functional validation of the assay with pharmacological and genetic tools revealed distinct patterns of cellular fates of APP, with immediate mechanistic implications. This new technology will facilitate functional genomics studies of late-onset Alzheimer's disease, drug discovery efforts targeting APP and characterization of the physiological functions of APP and its proteolytic fragments. 6. BECN1/Beclin 1 sorts cell-surface APP/amyloid β precursor protein for lysosomal degradation. Science.gov (United States) Swaminathan, Gayathri; Zhu, Wan; Plowey, Edward D 2016-12-01 The regulation of plasma membrane (PM)-localized transmembrane protein/receptor trafficking has critical implications for cell signaling, metabolism and survival. In this study, we investigated the role of BECN1 (Beclin 1) in the degradative trafficking of PM-associated APP (amyloid β precursor protein), whose metabolism to amyloid-β, an essential event in Alzheimer disease, is dependent on divergent PM trafficking pathways. We report a novel interaction between PM-associated APP and BECN1 that recruits macroautophagy/endosomal regulatory proteins PIK3C3 and UVRAG. We found that BECN1 promotes surface APP internalization and sorting predominantly to endosomes and endolysosomes. BECN1 also promotes the targeting of a smaller fraction of internalized APP to LC3-positive phagophores, suggesting a role for BECN1-dependent PM macroautophagy in APP degradation. Furthermore, BECN1 facilitates lysosomal degradation of surface APP and reduces the secretion of APP metabolites (soluble ectodomains, sAPP). The association between APP and BECN1 is dependent on the evolutionarily conserved domain (ECD) of BECN1 (amino acids 267-337). Deletion of a BECN1 ECD subregion (amino acids 285-299) did not impair BECN1- PIK3C3 interaction, PtdIns3K function or macroautophagy, but was sufficient to impair the APP-BECN1 interaction and BECN1's effects on surface APP internalization and degradation, resulting in increased secretion of sAPPs. Interestingly, both the BECN1-APP association and BECN1-dependent APP endocytosis and degradative trafficking were negatively regulated by active AKT. Our results further implicate phosphorylation of the BECN1 Ser295 residue in the inhibition of APP degradation by AKT. Our studies reveal a novel function for BECN1 in the sorting of a plasma membrane protein for endolysosomal and macroautophagic degradation. 7. Evidence supporting the role of calpain in the α-processing of amyloidprecursor protein. Science.gov (United States) Nguyen, Huey T; Sawmiller, Darrell R; Wu, Qi; Maleski, Jerome J; Chen, Ming 2012-04-13 Amyloid plaques are a hallmark of the aging and senile dementia brains, yet their mechanism of origins has remained elusive. A central issue is the regulatory mechanism and identity of α-secretase, a protease responsible for α-processing of amyloidprecursor protein (APP). A remarkable feature of this enzyme is its high sensitivity to a wide range of cellular stimulators, many of which are agonists for Ca(2+) signaling. This feature, together with previous work in our laboratory, has suggested that calpain, a Ca(2+)-dependent protease, plays a key role in APP α-processing. In this study we report that overexpression of the μ-calpain gene in HEK293 cells resulted in a 2.7-fold increase of the protein levels. Measurements of intracellular calpain enzymatic activity revealed that the calpain overexpressing cells displayed a prominent elevation of the activity compared to wild-type cells. When the cells were stimulated by nicotine, glutamate or phorbol 12,13-dibutylester, the activity increase was even more remarkable and sensitive to calpeptin, a calpain inhibitor. Meanwhile, APP secretion from the calpain overexpressing cells was robustly increased under both resting and stimulated conditions over wild-type cells. Furthermore, cell surface biotinylation experiments showed that μ-calpain was clearly detected among the cell surface proteins. These data together support our view that calpain should be a reasonable candidate for α-secretase for further study. This model is discussed with an interesting fact that three other deposited proteins (tau, spectrin and crystalline) are also the known substrates of calpain. Finally we discuss some current misconceptions in senile dementia research. 8. Statins reduce amyloid β-peptide production by modulating amyloid precursor protein maturation and phosphorylation through a cholesterol-independent mechanism in cultured neurons. Science.gov (United States) Hosaka, Ai; Araki, Wataru; Oda, Akiko; Tomidokoro, Yasushi; Tamaoka, Akira 2013-03-01 Statins, 3-hydroxy-3-methylglutaryl-coenzyme A (HMG-CoA) reductase inhibitors, have been reported to attenuate amyloid-β peptide (Aβ) production in various cellular models. However, the mechanisms by which statins affect neuronal Aβ production have not yet been clarified. Here, we investigated this issue in rat primary cortical neurons using two statins, pitavastatin (PV) and atorvastatin (AV). Treatment of neurons with 0.2-2.5 μM PV or AV for 4 days induced a concentration- and time-dependent reduction in the secretion of both Aβ40 and Aβ42. Moreover, Western blot analyses of cell lysates showed that treatment with PV or AV significantly reduced expression levels of the mature form of amyloid precursor protein (APP) and Thr668-phosphorylated APP (P-APP), but not immature form of APP; the decreases in P-APP levels were more notable than those of mature APP levels. The statin treatment did not alter expression of BACE1 (β-site APP-cleaving enzyme 1) or γ-secretase complex proteins (presenilin 1, nicastrin, APH-1, and PEN-2). In neurons overexpressing APP via recombinant adenoviruses, PV or AV similarly reduced Aβ secretion and the levels of mature APP and P-APP. Statins also markedly reduced cellular cholesterol content in neurons in a concentration-dependent manner. Co-treatment with mevalonate reversed the statin-induced decreases in Aβ secretion and mature APP and P-APP levels, whereas co-treatment with cholesterol did not, despite recovery of cellular cholesterol levels. Finally, cell-surface biotinylation experiments revealed that both statins significantly reduced the levels of cell-surface P-APP without changing those of cell surface mature APP. These results suggest that statins reduce Aβ production by selectively modulating APP maturation and phosphorylation through a mechanism independent of cholesterol reduction in cultured neurons. 9. Model Hirano bodies protect against tau-independent and tau-dependent cell death initiated by the amyloid precursor protein intracellular domain. Directory of Open Access Journals (Sweden) Matthew Furgerson Full Text Available The main pathological hallmarks of Alzheimer's disease are amyloid-beta plaques and neurofibrillary tangles, which are primarily composed of amyloid precursor protein (APP and tau, respectively. These proteins and their role in the mechanism of neurodegeneration have been extensively studied. Hirano bodies are a frequently occurring pathology in Alzheimer's disease as well as other neurodegenerative diseases. However, the physiological role of Hirano bodies in neurodegenerative diseases has yet to be determined. We have established cell culture models to study the role of Hirano bodies in amyloid precursor protein and tau-induced cell death mechanisms. Exogenous expression of APP and either of its c-terminal fragments c31 or Amyloid Precursor Protein Intracellular Domain c58 (AICDc58 enhance cell death. The presence of tau is not required for this enhanced cell death. However, the addition of a hyperphosphorylated tau mimic 352PHPtau significantly increases cell death in the presence of both APP and c31 or AICDc58 alone. The mechanism of cell death induced by APP and its c-terminal fragments and tau was investigated. Fe65, Tip60, p53, and caspases play a role in tau-independent and tau-dependent cell death. In addition, apoptosis was determined to contribute to cell death. The presence of model Hirano bodies protected against cell death, indicating Hirano bodies may play a protective role in neurodegeneration. 10. Continuation of exercise is necessary to inhibit high fat diet-induced β-amyloid deposition and memory deficit in amyloid precursor protein transgenic mice. Science.gov (United States) Maesako, Masato; Uemura, Kengo; Iwata, Ayana; Kubota, Masakazu; Watanabe, Kiwamu; Uemura, Maiko; Noda, Yasuha; Asada-Utsugi, Megumi; Kihara, Takeshi; Takahashi, Ryosuke; Shimohama, Shun; Kinoshita, Ayae 2013-01-01 High fat diet (HFD) is prevalent in many modern societies and HFD-induced metabolic condition is a growing concern worldwide. It has been previously reported that HFD clearly worsens cognitive function in amyloid precursor protein (APP) transgenic mice. On the other hand, we have demonstrated that voluntary exercise in an enriched environment is an effective intervention to rescue HFD-induced β-amyloid (Aβ) deposition and memory deficit. However, it had been unclear whether consumption of HFD after exercising abolished the beneficial effect of exercise on the inhibition of Alzheimer's disease (AD) pathology. To examine this question, we exposed wild type (WT) and APP mice fed with HFD to exercise conditions at different time periods. In our previous experiment, we gave HFD to mice for 20 weeks and subjected them to exercise during weeks 10-20. In the present study, mice were subjected to exercise conditions during weeks 0-10 or weeks 5-15 while being on HFD. Interestingly, we found that the effect of exercise during weeks 0-10 or weeks 5-15 on memory function was not abolished in WT mice even if they kept having HFD after finishing exercise. However, in APP transgenic mice, HFD clearly disrupted the effect of exercise during weeks 0-10 or weeks 5-15 on memory function. Importantly, we observed that the level of Aβ oligomer was significantly elevated in the APP mice that exercised during weeks 0-10: this might have been caused by the up-regulation of Aβ production. These results provide solid evidence that continuation of exercise is necessary to rescue HFD-induced aggravation of cognitive decline in the pathological setting of AD. 11. Continuation of exercise is necessary to inhibit high fat diet-induced β-amyloid deposition and memory deficit in amyloid precursor protein transgenic mice. Directory of Open Access Journals (Sweden) Masato Maesako Full Text Available High fat diet (HFD is prevalent in many modern societies and HFD-induced metabolic condition is a growing concern worldwide. It has been previously reported that HFD clearly worsens cognitive function in amyloid precursor protein (APP transgenic mice. On the other hand, we have demonstrated that voluntary exercise in an enriched environment is an effective intervention to rescue HFD-induced β-amyloid (Aβ deposition and memory deficit. However, it had been unclear whether consumption of HFD after exercising abolished the beneficial effect of exercise on the inhibition of Alzheimer's disease (AD pathology. To examine this question, we exposed wild type (WT and APP mice fed with HFD to exercise conditions at different time periods. In our previous experiment, we gave HFD to mice for 20 weeks and subjected them to exercise during weeks 10-20. In the present study, mice were subjected to exercise conditions during weeks 0-10 or weeks 5-15 while being on HFD. Interestingly, we found that the effect of exercise during weeks 0-10 or weeks 5-15 on memory function was not abolished in WT mice even if they kept having HFD after finishing exercise. However, in APP transgenic mice, HFD clearly disrupted the effect of exercise during weeks 0-10 or weeks 5-15 on memory function. Importantly, we observed that the level of Aβ oligomer was significantly elevated in the APP mice that exercised during weeks 0-10: this might have been caused by the up-regulation of Aβ production. These results provide solid evidence that continuation of exercise is necessary to rescue HFD-induced aggravation of cognitive decline in the pathological setting of AD. 12. Transcriptional regulation of human FE65, a ligand of Alzheimer's disease amyloid precursor protein, by Sp1. LENUS (Irish Health Repository) Yu, Hoi-Tin 2010-03-01 FE65 is a neuronal-enriched adaptor protein that binds to the Alzheimer\\'s disease amyloid precursor protein (APP). FE65 forms a transcriptionally active complex with the APP intracellular domain (AICD). The precise gene targets for this complex are unclear but several Alzheimer\\'s disease-linked genes have been proposed. Additionally, evidence suggests that FE65 influences APP metabolism. The mechanism by which FE65 expression is regulated is as yet unknown. To gain insight into the regulatory mechanism, we cloned a 1.6 kb fragment upstream of the human FE65 gene and found that it possesses particularly strong promoter activity in neurones. To delineate essential regions in the human FE65 promoter, a series of deletion mutants were generated. The minimal FE65 promoter was located between -100 and +5, which contains a functional Sp1 site. Overexpression of the transcription factor Sp1 potentiates the FE65 promoter activity. Conversely, suppression of the FE65 promoter was observed in cells either treated with an Sp1 inhibitor or in which Sp1 was knocked down. Furthermore, reduced levels of Sp1 resulted in downregulation of endogenous FE65 mRNA and protein. These findings reveal that Sp1 plays a crucial role in transcriptional control of the human FE65 gene. 13. CHIP stabilizes amyloid precursor protein via proteasomal degradation and p53-mediated trans-repression of β-secretase. Science.gov (United States) Singh, Amir Kumar; Pati, Uttam 2015-08-01 In patient with Alzheimer's disease (AD), deposition of amyloid-beta Aβ, a proteolytic cleavage of amyloid precursor protein (APP) by β-secretase/BACE1, forms senile plaque in the brain. BACE1 activation is caused due to oxidative stresses and dysfunction of ubiquitin-proteasome system (UPS), which is linked to p53 inactivation. As partial suppression of BACE1 attenuates Aβ generation and AD-related pathology, it might be an ideal target for AD treatment. We have shown that both in neurons and in HEK-APP cells, BACE1 is a new substrate of E3-ligase CHIP and an inverse relation exists between CHIP and BACE1 level. CHIP inhibits ectopic BACE1 level by promoting its ubiquitination and proteasomal degradation, thus reducing APP processing; it stabilizes APP in neurons, thus reducing Aβ. CHIP(U) (box) domain physically interacts with BACE1; however, both U-box and TPR domain are essential for ubiquitination and degradation of BACE1. Further, BACE1 is a downstream target of p53 and overexpression of p53 decreases BACE1 level. In HEK-APP cells, CHIP is shown to negatively regulate BACE1 promoter through stabilization of p53's DNA-binding conformation and its binding upon 5' UTR element (+127 to +150). We have thus discovered that CHIP regulates p53-mediated trans-repression of BACE1 at both transcriptional and post-translational level. We propose that a CHIP-BACE1-p53 feedback loop might control APP stabilization, which could further be utilized for new therapeutic intervention in AD. 14. Enzyme specificity of proteinase inhibitor region in amyloid precursor protein of Alzheimer's disease: different properties compared with protease nexin I. Science.gov (United States) Kitaguchi, N; Takahashi, Y; Oishi, K; Shiojiri, S; Tokushima, Y; Utsunomiya, T; Ito, H 1990-03-29 Senile plaques, often surrounded by abnormally grown neurites, are characteristic of Alzheimer's diseased brain. The core of the plaque is mainly composed of amyloid beta protein (beta-AP), two of whose three precursors (APP) have serine proteinase inhibitor regions (APPI). APPI derivatives containing 60, 72 or 88 amino-acid fragments (APPI-60, APPI-72 and APPI-88, respectively) of the longest APP were produced in COS-1 cell culture medium, with the APPI cDNA ligated to the signal sequence of tissue plasminogen activator. The secreted APPIs were purified by sequential acetone precipitation followed by affinity chromatography using immobilized trypsin. These three APPIs and O-glycosylation-site-mutated APPI showed similar inhibitory activity against trypsin, chymotrypsin and plasmin. The purified APPI-72 was found to inhibit trypsin (Ki = 1.1 x 10(-10) M) and chymotrypsin (Ki = 5.8 x 10(-9) M) most strongly, and to inhibit leukocyte elastase (Ki = 7.9 x 10(-7) M) and several blood coagulation proteinases (Ki = 0.46-12 x 10(-7) M), but not urokinase or thrombin. The observed inhibition pattern was quite different from that of protease nexin I, one of serine proteinase inhibitors possessing neurite outgrowth activity. This suggests that the physiological roles of APPI are different from those of protease nexin I, and that APPI could not cause aberrant growth of neurite into the plaque. The presence of APPI having strong inhibitory activity in the brain might lead to the formation of amyloid deposits by preventing complete degradation of APPs. 15. Soluble amyloid precursor protein alpha (sAPPα) inhibits tau phosphorylation through modulation of GSK3β signaling pathway Science.gov (United States) Deng, Juan; Habib, Ahsan; Obregon, Demian F.; Barger, Steven W.; Giunta, Brian; Wang, Yan-Jiang; Hou, Huayan; Sawmiller, Darrell; Tan, Jun 2015-01-01 We recently found that sAPPα decreases Aβ generation by directly associating with β-site amyloid precursor protein (APP) converting enzyme 1 (BACE1), thereby modulating APP processing. Because inhibition of BACE1 decreases GSK3β-mediated Alzheimer’s disease (AD)-like tau phosphorylation in AD patient-derived neurons, we determined whether sAPPα also reduces GSK3β-mediated tau phosphorylation. We initially found increased levels of inhibitory phosphorylation of GSK3β in primary neurons from sAPPα over-expressing mice. Further, recombinant human sAPPα evoked the same phenomenon in SH-SY5Y cells. Further, in SH-SY5Y cells overexpressing BACE1, and HeLa cells overexpressing human tau, sAPPα reduced GSK3β activity and tau phosphorylation. Importantly, the reductions in GSK3β activity and tau phosphorylation elicited by sAPPα were prevented by BACE1 but not γ-secretase inhibition. In accord, AD mice overexpressing human sAPPα had less GSK3β activity and tau phosphorylation compared with controls. These results implicate a direct relationship between APP β-processing and GSK3β-mediated tau phosphorylation and further define the central role of sAPPα in APP autoregulation and AD pathogenesis. PMID:26342176 16. Amyloid precursor protein is required for normal function of the rod and cone pathways in the mouse retina. Directory of Open Access Journals (Sweden) Tracy Ho Full Text Available Amyloid precursor protein (APP is a transmembrane glycoprotein frequently studied for its role in Alzheimer's disease. Our recent study in APP knockout (KO mice identified an important role for APP in modulating normal neuronal development in the retina. However the role APP plays in the adult retina and whether it is required for vision is unknown. In this study we evaluated the role of APP in retinal function and morphology comparing adult wildtype (WT and APP-KO mice. APP was expressed on neuronal cells of the inner retina, including horizontal, cone bipolar, amacrine and ganglion cells in WT mice. The function of the retina was assessed using the electroretinogram and although the rod photoreceptor responses were similar in APP-KO and WT mice, the post-photoreceptor, inner retinal responses of both the rod and cone pathways were reduced in APP-KO mice. These changes in inner retinal function did not translate to a substantial change in visual acuity as assessed using the optokinetic response or to changes in the gross cellular structure of the retina. These findings indicate that APP is not required for basic visual function, but that it is involved in modulating inner retinal circuitry. 17. Peripheral biomarkers in Autism: secreted amyloid precursor protein-alpha as a probable key player in early diagnosis. Science.gov (United States) Bailey, Antoinette R; Giunta, Brian N; Obregon, Demian; Nikolic, William V; Tian, Jun; Sanberg, Cyndy D; Sutton, Danielle T; Tan, Jun 2008-01-01 Autism is a pervasive developmental disorder characterized by impairments in socialization and communication. There is currently no single molecular marker or laboratory tool capable of diagnosing autism at an early age. The purpose of this study is to explore the plausible use of peripheral biomarkers in the early diagnosis of autism via a sensitive ELISA. Here, we measured plasma secreted amyloid precursor protein alpha (sAPP-alpha) levels in autistic and aged-matched control blood samples and found a significantly increased level of sAPP-alpha in 60% of the known autistic children. We then tested 150 human umbilical cord blood (HUCB) samples and found significantly elevated levels of plasma sAPP-alpha in 10 of 150 samples. As an additional confirmatory measure, we performed Western blot analysis on these samples which consistently showed increased sAPP-alpha levels in autistic children and 10 of 150 HUCB samples; suggesting a group of autistic patients which could be identified in early childhood by levels of sAPP-alpha. While there is need for further studies of this concept, the measurement of sAPP-alpha levels in serum and human umbilical cord blood by ELISA is a potential tool for early diagnosis of autism. 18. Amyloid precursor protein modulates Nav1.6 sodium channel currents through a Go-coupled JNK pathway Science.gov (United States) Li, Shao; Wang, Xi; Ma, Quan-Hong; Yang, Wu-lin; Zhang, Xiao-Gang; Dawe, Gavin S.; Xiao, Zhi-Cheng 2016-01-01 Amyloid precursor protein (APP), commonly associated with Alzheimer’s disease, also marks axonal degeneration. In the recent studies, we demonstrated that APP aggregated at nodes of Ranvier (NORs) in myelinated central nervous system (CNS) axons and interacted with Nav1.6. However, the physiological function of APP remains unknown. In this study, we described reduced sodium current densities in APP knockout hippocampal neurons. Coexpression of APP or its intracellular domains containing a VTPEER motif with Nav1.6 sodium channels in Xenopus oocytes resulted in an increase in peak sodium currents, which was enhanced by constitutively active Go mutant and blocked by a dominant negative mutant. JNK and CDK5 inhibitor attenuated increases in Nav1.6 sodium currents induced by overexpression of APP. Nav1.6 sodium currents were increased by APPT668E (mutant Thr to Glu) and decreased by T668A (mutant Thr to ALa) mutant, respectively. The cell surface expression of Nav1.6 sodium channels in the white matter of spinal cord and the spinal conduction velocity is decreased in APP, p35 and JNK3 knockout mice. Therefore, APP modulates Nav1.6 sodium channels through a Go-coupled JNK pathway, which is dependent on phosphorylation of APP at Thr668. PMID:28008944 19. Genomic mosaicism with increased amyloid precursor protein (APP) gene copy number in single neurons from sporadic Alzheimer's disease brains. Science.gov (United States) Bushman, Diane M; Kaeser, Gwendolyn E; Siddoway, Benjamin; Westra, Jurgen W; Rivera, Richard R; Rehen, Stevens K; Yung, Yun C; Chun, Jerold 2015-02-04 Previous reports have shown that individual neurons of the brain can display somatic genomic mosaicism of unknown function. In this study, we report altered genomic mosaicism in single, sporadic Alzheimer's disease (AD) neurons characterized by increases in DNA content and amyloid precursor protein (APP) gene copy number. AD cortical nuclei displayed large variability with average DNA content increases of ~8% over non-diseased controls that were unrelated to trisomy 21. Two independent single-cell copy number analyses identified amplifications at the APP locus. The use of single-cell qPCR identified up to 12 copies of APP in sampled neurons. Peptide nucleic acid (PNA) probes targeting APP, combined with super-resolution microscopy detected primarily single fluorescent signals of variable intensity that paralleled single-cell qPCR analyses. These data identify somatic genomic changes in single neurons, affecting known and unknown loci, which are increased in sporadic AD, and further indicate functionality for genomic mosaicism in the CNS. 20. Effects of ethanol on aggregation, serotonin release, and amyloid precursor protein processing in rat and human platelets. Science.gov (United States) Ehrlich, Daniela; Humpel, Christian 2014-01-01 It is known that oxidative stress leads to amyloid precursor protein (APP) dysregulation in platelets. Ethanol (EtOH) is a vascular risk factor and induces oxidative stress. The aim of the present study was thus to investigate whether EtOH affects APP processing in rat and human platelets. Platelets were exposed to 50 mM EtOH with and without 2 mM calcium-chloride (CaCl₂) for 20 or 180 minutes at 37°C. Platelet aggregation, serotonin release and APP isoforms 130 and 106/110 kDa were analyzed. As a control, 100 mM H₂O₂ was tested in rat platelets. Our data show that EtOH alone did not affect any of the analyzed parameters, whereas CaCl₂ significantly increased aggregation of rat and human platelets. In addition, CaCl₂ alone enhanced serotonin release in rat platelets. EtOH counteracted CaCl₂-induced aggregation and serotonin release. In the presence of CaCl₂, EtOH reduced the 130 kDa APP isoform in rat and human platelets. In conclusion, this study shows that in the presence of CaCl₂, EtOH affects the platelet function and APP processing in rat and human platelets. 1. Two different immunostaining patterns of beta-amyloid precursor protein (APP) may distinguish traumatic from nontraumatic axonal injury. Science.gov (United States) Hayashi, Takahito; Ago, Kazutoshi; Nakamae, Takuma; Higo, Eri; Ogata, Mamoru 2015-09-01 Immunostaining for beta-amyloid precursor protein (APP) is recognized as an effective tool for detecting traumatic axonal injury, but it also detects axonal injury due to ischemic or other metabolic causes. Previously, we reported two different patterns of APP staining: labeled axons oriented along with white matter bundles (pattern 1) and labeled axons scattered irregularly (pattern 2) (Hayashi et al. (Leg Med (Tokyo) 11:S171-173, 2009). In this study, we investigated whether these two patterns are consistent with patterns of trauma and hypoxic brain damage, respectively. Sections of the corpus callosum from 44 cases of blunt head injury and equivalent control tissue were immunostained for APP. APP was detected in injured axons such as axonal bulbs and varicose axons in 24 of the 44 cases of head injuries that also survived for three or more hours after injury. In 21 of the 24 APP-positive cases, pattern 1 alone was observed in 14 cases, pattern 2 alone was not observed in any cases, and both patterns 1 and 2 were detected in 7 cases. APP-labeled injured axons were detected in 3 of the 44 control cases, all of which were pattern 2. These results suggest that pattern 1 indicates traumatic axonal injury, while pattern 2 results from hypoxic insult. These patterns may be useful to differentiate between traumatic and nontraumatic axonal injuries. 2. Conformational changes induced by the A21G Flemish mutation in the amyloid precursor protein lead to increased Aβ production. Science.gov (United States) Tang, Tzu-Chun; Hu, Yi; Kienlen-Campard, Pascal; El Haylani, Laetitia; Decock, Marie; Van Hees, Joanne; Fu, Ziao; Octave, Jean-Noel; Constantinescu, Stefan N; Smith, Steven O 2014-03-04 Proteolysis of the β C-terminal fragment (β-CTF) of the amyloid precursor protein generates the Aβ peptides associated with Alzheimer's disease. Familial mutations in the β-CTF, such as the A21G Flemish mutation, can increase Aβ secretion. We establish how the Flemish mutation alters the structure of C55, the first 55 residues of the β-CTF, using FTIR and solid-state NMR spectroscopy. We show that the A21G mutation reduces β sheet structure of C55 from Leu17 to Ala21, an inhibitory region near the site of the mutation, and increases α-helical structure from Gly25 to Gly29, in a region near the membrane surface and thought to interact with cholesterol. Cholesterol also increases Aβ peptide secretion, and we show that the incorporation of cholesterol into model membranes enhances the structural changes induced by the Flemish mutant, suggesting a common link between familial mutations and the cellular environment. 3. Compound Danshen tablets downregulate amyloid protein precursor mRNA expression in a transgenic cell model of Alzheimer's disease Effects and a comparison with donepezil Institute of Scientific and Technical Information of China (English) Ren'an Qin; Desheng Zhou; Jiajun Wang; Hua Hu; Yang Yang; Xiaoxuan Yao; Xiaopeng Sun 2012-01-01 After gene mutation, the pcDNA3.1/APP595/596 plasmid was transfected into HEK293 cells to establish a cell model of Alzheimer’s disease. The cell model was treated with donepezil or compound Danshen tablets after culture for 72 hours. Reverse transcription-PCR showed that the mRNA expression of amyloid protein precursor decreased in all groups following culture for 24 hours, and that there was no significant difference in the amount of decrease between donepezil and compound Danshen tablets. Our results suggest that compound Danshen tablets can reduce expression of the mRNA for amyloid protein precursor in a transgenic cell model of Alzheimer’s disease, with similar effects to donepezil. 4. Cerebrospinal fluid levels of amyloid precursor protein are associated with ventricular size in post-hemorrhagic hydrocephalus of prematurity. Directory of Open Access Journals (Sweden) Diego M Morales Full Text Available Neurological outcomes of preterm infants with post-hemorrhagic hydrocephalus (PHH remain among the worst in infancy, yet there remain few instruments to inform the treatment of PHH. We previously observed PHH-associated elevations in cerebrospinal fluid (CSF amyloid precursor protein (APP, neural cell adhesion molecule-L1 (L1CAM, neural cell adhesion molecule-1 (NCAM-1, and other protein mediators of neurodevelopment.The objective of this study was to examine the association of CSF APP, L1CAM, and NCAM-1 with ventricular size as an early step toward developing CSF markers of PHH.CSF levels of APP, L1CAM, NCAM-1, and total protein (TP were measured in 12 preterm infants undergoing PHH treatment. Ventricular size was determined using cranial ultrasounds. The relationships between CSF APP, L1CAM, and NCAM-1, occipitofrontal circumference (OFC, volume of CSF removed, and ventricular size were examined using correlation and regression analyses.CSF levels of APP, L1CAM, and NCAM-1 but not TP paralleled treatment-related changes in ventricular size. CSF APP demonstrated the strongest association with ventricular size, estimated by frontal-occipital horn ratio (FOR (Pearson R = 0.76, p = 0.004, followed by NCAM-1 (R = 0.66, p = 0.02 and L1CAM (R = 0.57,p = 0.055. TP was not correlated with FOR (R = 0.02, p = 0.95.Herein, we report the novel observation that CSF APP shows a robust association with ventricular size in preterm infants treated for PHH. The results from this study suggest that CSF APP and related proteins at once hold promise as biomarkers of PHH and provide insight into the neurological consequences of PHH in the preterm infant. 5. Quantification of gamma-secretase modulation differentiates inhibitor compound selectivity between two substrates Notch and amyloid precursor protein Directory of Open Access Journals (Sweden) Yang Ting 2008-11-01 Full Text Available Abstract Background Deposition of amyloidprotein (Aβ is a major pathological hallmark of Alzheimer's disease (AD. Aβ is generated from γ-secretase cleavage of amyloid precursor protein (APP. In addition to APP, γ-secretase also cleaves other type I integral membrane proteins, including the Notch receptor, a key molecule involved in embryonic development. Results To explore selective γ-secretase inhibitors, a combination of five methods was used to systematically determine these inhibitors' profiles on the γ-secretase cleavage of APP and Notch. When two potent γ-secretase inhibitors, compound E (cpd E and DAPT, were used in a conventional in vitro γ-secretase activity assay, cpd E completely blocked Aβ generation from the cleavage of substrate APP C100, but only had a minor effect on Notch cleavage and NICD generation. Next, cpd E and DAPT were applied to HEK293 cells expressing a truncated Notch substrate NotchΔE. Both cpd E and DAPT were more potent in blocking Aβ generation than NICD generation. Third, a reporter construct was created that carried the NICD targeting promoter with three Su(H binding sequences followed by the luciferase gene. We found that the inhibition of NICD generation by cpd E and DAPT was consistent with the reduced expression of luciferase gene driven by this Notch targeting promoter. Fourth, levels of "Notch-Aβ-like" (Nβ* peptide derived from two previously reported chimeric APP with its transmembrane domain or the juxtamembrane portion replaced by the Notch sequence were quantified. Measurement of Nβ* peptides by ELISA confirmed that EC50's of cpd E were much higher for Nβ* than Aβ. Finally, the expression levels of Notch target gene her6 in cpd E or DAPT-treated zebrafish were correlated with the degree of tail curvature due to defective somitogenesis, a well characterized Notch phenotype in zebrafish. Conclusion Our ELISA-based quantification of Aβ and Nβ* in combination with the test in 6. Characterization of amyloidprecursor protein intracellular domain-associated transcriptional complexes in SH-SY5Y neurocytes Institute of Scientific and Technical Information of China (English) Wulin Yang; Amy Yong Chen Lau; Shuizhong Luo; Qian Zhu3; Li Lu 2012-01-01 [Objective] Alzheimer's disease (AD) is one of the major disorders worldwide.Recent research suggests that the amyloidprecursor protein intracellular domain (AICD) is a potential contributor to AD development and progression.The small AICD is rapidly degraded after processing from the full-length protein.The present study aimed to apply a highly efficient biotinylation approach in vitro to study AICD-associated complexes in neurocytes.[Methods] By coexpressing Escherichia coli biotin ligase with biotinyl-tagged AICD in the SH-SY5Y neuronal cell line,the effects of AICD overexpression on cell proliferation and apoptosis were analyzed.Besides,AICD-associated nuclear transcriptional complexes were purified and then examined by mass spectrometry.[Results] Our data showed that AICD overexpression not only affected cell proliferation but also led to apoptosis in differentiated SH-SY5Y cells.Moreover,biotinylation allowed single-step purification of biotinylated AICD-associated complexes from total nuclear extract via high-affinity biotin-streptavidin binding.Following this by mass spectrometry,we identified physically associated proteins,some reported previously and other novel binding partners,CUX1 and SPT5.[Conclusion]Based on these [Results],a map of theAICD-associated nuclear interactome was depicted.Specifically,AICD can activate CUXI transcriptional activity,which may be associated with AICD-dependent neuronal cell death.This work helps to understand the AICD-associated biologicalevents in AD progression and provides novel insights into the development of AD. 7. Glucocorticoids increase impairments in learning and memory due to elevated amyloid precursor protein expression and neuronal apoptosis in 12-month old mice. Science.gov (United States) Li, Wei-Zu; Li, Wei-Ping; Yao, Yu-You; Zhang, Wen; Yin, Yan-Yan; Wu, Guo-Cui; Gong, Hui-Ling 2010-02-25 Alzheimer's disease is a chronic neurodegenerative disorder marked by a progressive loss of memory and cognitive function. Stress level glucocorticoids are correlated with dementia progression in patients with Alzheimer's disease. In this study, twelve month old male mice were chronically treated for 21 days with stress-level dexamethasone (5mg/kg). We investigated the pathological consequences of dexamethasone administration on learning and memory impairments, amyloid precursor protein processing and neuronal cell apoptosis in 12-month old male mice. Our results indicate that dexamethasone can induce learning and memory impairments, neuronal cell apoptosis, and mRNA levels of the amyloid precursor protein, beta-secretase and caspase-3 are selectively increased after dexamethasone administration. Immunohistochemistry demonstrated that amyloid precursor protein, caspase-3 and cytochrome c in the cortex and CA1, CA3 regions of the hippocampus are significantly increased in 12-month old male mice. Furthermore, dexamethasone treatment induced cortex and hippocampus neuron apoptosis as well as increasing the activity of caspase-9 and caspase-3. These findings suggest that high levels of glucocorticoids, found in Alzheimer's disease, are not merely a consequence of the disease process but rather play a central role in the development and progression of Alzheimer's disease. Stress management or pharmacological reduction of glucocorticoids warrant additional consideration of the regimen used in Alzheimer's disease therapies. 8. Neuroanatomical localization and quantification of amyloid precursor protein mRNA by in situ hybridization in the brains of normal, aneuploid, and lesioned mice Energy Technology Data Exchange (ETDEWEB) Bendotti, C.; Forloni, G.L.; Morgan, R.A.; O' Hara, B.F.; Oster-Granite, M.L.; Reeves, R.H.; Gearhart, J.D.; Coyle, J.T. (Johns Hopkins Univ. School of Medicine, Baltimore, MD (USA)) 1988-05-01 Amyloid precursor protein mRNA was localized in frozen sections from normal and experimentally lesioned adult mouse brain and from normal and aneuploid fetal mouse brain by in situ hybridization with a {sup 35}S-labeled mouse cDNA probe. The highest levels of hybridization in adult brain were associated with neurons, primarily in telencephalic structures. The dense labeling associated with hippocampal pyramidal cells was reduced significantly when the cells were eliminated by injection of the neurotoxin ibotenic acid but was not affected when electrolytic lesions were placed in the medial septum. Since the gene encoding amyloid precursor protein has been localized to mouse chromosome 16, the authors also examined the expression of this gene in the brains of mouse embryos with trisomy 16 and trisomy 19 at 15 days of gestation. RNA gel blot analysis and in situ hybridization showed a marked increase in amyloid precursor protein mRNA in the trisomy 16 mouse head and brain when compared with euploid littermates or with trisomy 19 mice. 9. Dual-specificity phosphatase 26 (DUSP26) stimulates Aβ42 generation by promoting amyloid precursor protein axonal transport during hypoxia. Science.gov (United States) Jung, Sunmin; Nah, Jihoon; Han, Jonghee; Choi, Seon-Guk; Kim, Hyunjoo; Park, Jaesang; Pyo, Ha-Kyung; Jung, Yong-Keun 2016-06-01 Amyloid beta peptide (Aβ) is a pathological hallmark of Alzheimer's disease (AD) and is generated through the sequential cleavage of amyloid precursor protein (APP) by β- and γ-secretases. Hypoxia is a known risk factor for AD and stimulates Aβ generation by γ-secretase; however, the underlying mechanisms remain unclear. In this study, we showed that dual-specificity phosphatase 26 (DUSP26) regulates Aβ generation through changes in subcellular localization of the γ-secretase complex and its substrate C99 under hypoxic conditions. DUSP26 was identified as a novel γ-secretase regulator from a genome-wide functional screen using a cDNA expression library. The phosphatase activity of DUSP26 was required for the increase in Aβ42 generation through γ-secretase, but this regulation did not affect the amount of the γ-secretase complex. Interestingly, DUSP26 induced the accumulation of C99 in the axons by stimulating anterograde transport of C99-positive vesicles. Additionally, DUSP26 induced c-Jun N-terminal kinase (JNK) activation for APP processing and axonal transport of C99. Under hypoxic conditions, DUSP26 expression levels were elevated together with JNK activation, and treatment with JNK inhibitor SP600125, or the DUSP26 inhibitor NSC-87877, reduced hypoxia-induced Aβ generation by diminishing vesicle trafficking of C99 to the axons. Finally, we observed enhanced DUSP26 expression and JNK activation in the hippocampus of AD patients. Our results suggest that DUSP26 mediates hypoxia-induced Aβ generation through JNK activation, revealing a new regulator of γ-secretase-mediated APP processing under hypoxic conditions. We propose the role of phosphatase dual-specificity phosphatase 26 (DUSP26) in the selective regulation of Aβ42 production in neuronal cells under hypoxic stress. Induction of DUSP26 causes JNK-dependent shift in the subcellular localization of γ-secretase and C99 from the cell body to axons for Aβ42 generation. These findings provide a 10. The Amyloid Precursor Protein (APP) Does Not Have a Ferroxidase Site in Its E2 Domain NARCIS (Netherlands) Honarmand Ebrahimi, K.; Dienemann, C.; Hoefgens, S.; Than, M.E.; Hagedoorn, P.L.; Hagen, W.R. 2013-01-01 The ubiquitous 24-meric iron-storage protein ferritin and multicopper oxidases such as ceruloplasmin or hephaestin catalyze oxidation of Fe(II) to Fe(III), using molecular oxygen as oxidant. The ferroxidase activity of these proteins is essential for cellular iron homeostasis. It has been reported t 11. A synthetic peptide with the putative iron binding motif of amyloid precursor protein (APP does not catalytically oxidize iron. Directory of Open Access Journals (Sweden) Kourosh Honarmand Ebrahimi Full Text Available The β-amyloid precursor protein (APP, which is a key player in Alzheimer's disease, was recently reported to possess an Fe(II binding site within its E2 domain which exhibits ferroxidase activity [Duce et al. 2010, Cell 142: 857]. The putative ligands of this site were compared to those in the ferroxidase site of ferritin. The activity was indirectly measured using transferrin, which scavenges the Fe(III product of the reaction. A 22-residue synthetic peptide, named FD1, with the putative ferroxidase site of APP, and the E2 domain of APP were each reported to exhibit 40% of the ferroxidase activity of APP and of ceruloplasmin. It was also claimed that the ferroxidase activity of APP is inhibited by Zn(II just as in ferritin. We measured the ferroxidase activity indirectly (i by the incorporation of the Fe(III product of the ferroxidase reaction into transferrin and directly (ii by monitoring consumption of the substrate molecular oxygen. The results with the FD1 peptide were compared to the established ferroxidase activities of human H-chain ferritin and of ceruloplasmin. For FD1 we observed no activity above the background of non-enzymatic Fe(II oxidation by molecular oxygen. Zn(II binds to transferrin and diminishes its Fe(III incorporation capacity and rate but it does not specifically bind to a putative ferroxidase site of FD1. Based on these results, and on comparison of the putative ligands of the ferroxidase site of APP with those of ferritin, we conclude that the previously reported results for ferroxidase activity of FD1 and - by implication - of APP should be re-evaluated. 12. A synthetic peptide with the putative iron binding motif of amyloid precursor protein (APP) does not catalytically oxidize iron. Science.gov (United States) Ebrahimi, Kourosh Honarmand; Hagedoorn, Peter-Leon; Hagen, Wilfred R 2012-01-01 The β-amyloid precursor protein (APP), which is a key player in Alzheimer's disease, was recently reported to possess an Fe(II) binding site within its E2 domain which exhibits ferroxidase activity [Duce et al. 2010, Cell 142: 857]. The putative ligands of this site were compared to those in the ferroxidase site of ferritin. The activity was indirectly measured using transferrin, which scavenges the Fe(III) product of the reaction. A 22-residue synthetic peptide, named FD1, with the putative ferroxidase site of APP, and the E2 domain of APP were each reported to exhibit 40% of the ferroxidase activity of APP and of ceruloplasmin. It was also claimed that the ferroxidase activity of APP is inhibited by Zn(II) just as in ferritin. We measured the ferroxidase activity indirectly (i) by the incorporation of the Fe(III) product of the ferroxidase reaction into transferrin and directly (ii) by monitoring consumption of the substrate molecular oxygen. The results with the FD1 peptide were compared to the established ferroxidase activities of human H-chain ferritin and of ceruloplasmin. For FD1 we observed no activity above the background of non-enzymatic Fe(II) oxidation by molecular oxygen. Zn(II) binds to transferrin and diminishes its Fe(III) incorporation capacity and rate but it does not specifically bind to a putative ferroxidase site of FD1. Based on these results, and on comparison of the putative ligands of the ferroxidase site of APP with those of ferritin, we conclude that the previously reported results for ferroxidase activity of FD1 and - by implication - of APP should be re-evaluated. 13. Structural basis for matrix metalloproteinase-2 (MMP-2)-selective inhibitory action of β-amyloid precursor protein-derived inhibitor. Science.gov (United States) Hashimoto, Hiroshi; Takeuchi, Tomoka; Komatsu, Kyoko; Miyazaki, Kaoru; Sato, Mamoru; Higashi, Shouichi 2011-09-23 Unlike other synthetic or physiological inhibitors for matrix metalloproteinases (MMPs), the β-amyloid precursor protein-derived inhibitory peptide (APP-IP) having an ISYGNDALMP sequence has a high selectivity toward MMP-2. Our previous study identified amino acid residues of MMP-2 essential for its selective inhibition by APP-IP and demonstrated that the N to C direction of the decapeptide inhibitor relative to the substrate-binding cleft of MMP-2 is opposite that of substrate. However, detailed interactions between the two molecules remained to be clarified. Here, we determined the crystal structure of the catalytic domain of MMP-2 in complex with APP-IP. We found that APP-IP in the complex is indeed embedded into the substrate-binding cleft of the catalytic domain in the N to C direction opposite that of substrate. With the crystal structure, it was first clarified that the aromatic side chain of Tyr(3) of the inhibitor is accommodated into the S1' pocket of the protease, and the carboxylate group of Asp(6) of APP-IP coordinates bidentately to the catalytic zinc of the enzyme. The Ala(7) to Pro(10) and Tyr(3) to Ile(1) strands of the inhibitor extend into the nonprime and the prime sides of the cleft, respectively. Therefore, the decapeptide inhibitor has long range contact with the substrate-binding cleft of the protease. This mode of interaction is probably essential for the high MMP-2 selectivity of the inhibitor because MMPs share a common architecture in the vicinity of the catalytic center, but whole structures of their substrate-binding clefts have sufficient variety for the inhibitor to distinguish MMP-2 from other MMPs. 14. Characterization of the beta amyloid precursor protein-like gene in the central nervous system of the crab Chasmagnathus. Expression during memory consolidation Directory of Open Access Journals (Sweden) Fustiñana Maria 2010-09-01 Full Text Available Abstract Background Human β-amyloid, the main component in the neuritic plaques found in patients with Alzheimer's disease, is generated by cleavage of the β-amyloid precursor protein. Beyond the role in pathology, members of this protein family are synaptic proteins and have been associated with synaptogenesis, neuronal plasticity and memory, both in vertebrates and in invertebrates. Consolidation is necessary to convert a short-term labile memory to a long-term and stable form. During consolidation, gene expression and de novo protein synthesis are regulated in order to produce key proteins for the maintenance of plastic changes produced during the acquisition of new information. Results Here we partially cloned and sequenced the beta-amyloid precursor protein like gene homologue in the crab Chasmagnathus (cappl, showing a 37% of identity with the fruit fly Drosophila melanogaster homologue and 23% with Homo sapiens but with much higher degree of sequence similarity in certain regions. We observed a wide distribution of cappl mRNA in the nervous system as well as in muscle and gills. The protein localized in all tissues analyzed with the exception of muscle. Immunofluorescence revealed localization of cAPPL in associative and sensory brain areas. We studied gene and protein expression during long-term memory consolidation using a well characterized memory model: the context-signal associative memory in this crab species. mRNA levels varied at different time points during long-term memory consolidation and correlated with cAPPL protein levels Conclusions cAPPL mRNA and protein is widely distributed in the central nervous system of the crab and the time course of expression suggests a role of cAPPL during long-term memory formation. 15. Using BAC transgenesis in zebrafish to identify regulatory sequences of the amyloid precursor protein gene in humans Directory of Open Access Journals (Sweden) Shakes Leighcraft A 2012-09-01 Full Text Available Abstract Background Non-coding DNA in and around the human Amyloid Precursor Protein (APP gene that is central to Alzheimer’s disease (AD shares little sequence similarity with that of appb in zebrafish. Identifying DNA domains regulating expression of the gene in such situations becomes a challenge. Taking advantage of the zebrafish system that allows rapid functional analyses of gene regulatory sequences, we previously showed that two discontinuous DNA domains in zebrafish appb are important for expression of the gene in neurons: an enhancer in intron 1 and sequences 28–31 kb upstream of the gene. Here we identify the putative transcription factor binding sites responsible for this distal cis-acting regulation, and use that information to identify a regulatory region of the human APP gene. Results Functional analyses of intron 1 enhancer mutations in enhancer-trap BACs expressed as transgenes in zebrafish identified putative binding sites of two known transcription factor proteins, E4BP4/ NFIL3 and Forkhead, to be required for expression of appb. A cluster of three E4BP4 sites at −31 kb is also shown to be essential for neuron-specific expression, suggesting that the dependence of expression on upstream sequences is mediated by these E4BP4 sites. E4BP4/ NFIL3 and XFD1 sites in the intron enhancer and E4BP4/ NFIL3 sites at −31 kb specifically and efficiently bind the corresponding zebrafish proteins in vitro. These sites are statistically over-represented in both the zebrafish appb and the human APP genes, although their locations are different. Remarkably, a cluster of four E4BP4 sites in intron 4 of human APP exists in actively transcribing chromatin in a human neuroblastoma cell-line, SHSY5Y, expressing APP as shown using chromatin immunoprecipitation (ChIP experiments. Thus although the two genes share little sequence conservation, they appear to share the same regulatory logic and are regulated by a similar set of transcription 16. Effects of Amyloid Precursor Protein 17 Peptide on the Protection of Diabetic Encephalopathy and Improvement of Glycol Metabolism in the Diabetic Rat Directory of Open Access Journals (Sweden) Heng Meng 2013-01-01 Full Text Available Researchers have proposed that amyloid precursor protein 17 peptide (APP17 peptide, an active fragment of amyloid precursor protein (APP in the nervous system, has therapeutic effects on neurodegeneration. Diabetic encephalopathy (DE is a neurological disease caused by diabetes. Here we use multiple experimental approaches to investigate the effect of APP17 peptide on changes in learning behavior and glycol metabolism in rats. It was found that rats with DE treated by APP17 peptide showed reversed behavioral alternation. The [18F]-FDG-PET images and other results all showed that the APP17 peptide could promote glucose metabolism in the brain of the DE rat model. Meanwhile, the insulin signaling was markedly increased as shown by increased phosphorylation of Akt and enhanced GLUT4 activation. Compared with the DE group, the activities of SOD, GSH-Px, and CAT in the rat hippocampal gyrus were increased, while MDA decreased markedly in the DE + APP17 peptide group. No amyloid plaques in the cortex and the hippocampus were detected in either group, indicating that the experimental animals in the current study were not suffering from Alzheimer’s disease. These results indicate that APP17 peptide could be used to treat DE effectively. 17. An Aberrant Phosphorylation of Amyloid Precursor Protein Tyrosine Regulates Its Trafficking and the Binding to the Clathrin Endocytic Complex in Neural Stem Cells of Alzheimer's Disease Patients Science.gov (United States) Poulsen, Ebbe T.; Iannuzzi, Filomena; Rasmussen, Helle F.; Maier, Thorsten J.; Enghild, Jan J.; Jørgensen, Arne L.; Matrone, Carmela 2017-01-01 Alzheimer's disease (AD) is the most common cause of dementia and is likely caused by defective amyloid precursor protein (APP) trafficking and processing in neurons leading to amyloid plaques containing the amyloid-β (Aβ) APP peptide byproducts. Understanding how APP is targeted to selected destinations inside neurons and identifying the mechanisms responsible for the generation of Aβ are thus the keys for the advancement of new therapies. We previously developed a mouse model with a mutation at tyrosine (Tyr) 682 in the C-terminus of APP. This residue is needed for APP to bind to the coating protein Clathrin and to the Clathrin adaptor protein AP2 as well as for the correct APP trafficking and sorting in neurons. By extending these findings to humans, we found that APP binding to Clathrin is decreased in neural stem cells from AD sufferers. Increased APP Tyr phosphorylation alters APP trafficking in AD neurons and it is associated to Fyn Tyr kinase activation. We show that compounds affecting Tyr kinase activity and counteracting defects in AD neurons can control APP location and compartmentalization. APP Tyr phosphorylation is thus a potential therapeutic target for AD. 18. Amyloid precursor protein and growth-associated protein 43 expression in brain white matter and spinal cord tissues in a rat model of experimental autoimmune encephalomyelitis Institute of Scientific and Technical Information of China (English) Yizhou Wang; Shuang Kou; Jingcheng Tang; Ping Zhang; Qiuxia Zhang; Yan Liu; Qi Zheng; Hui Zhao; Lei Wang 2011-01-01 Studies have demonstrated that amyloid precursor protein (APP) expression increases in multiple sclerosis tissues during acutely and chronically active stages.To determine the relationship between axonal injury and regeneration in multiple sclerosis, an animal model of experimental autoimmune encephalomyelitis was induced using different doses of myelin basic protein peptide.APP and growth-associated protein 43 (GAP-43), which is considered a specific marker of neural regeneration, were assessed by western blot analysis.Expression of APP and GAP-43, as well as the correlation between these two proteins, in brain white matter and spinal cord tissues of experimental autoimmune encephalomyelitis rats at different pathological stages was analyzed.Results showed that APP and GAP-43 expression increased during the acute stage and decreased during remission, with a positive correlation between APP and GAP-43 expression in brain white matter and spinal cord tissues.These results suggest that APP and GAP-43 could provide nutritional and protective effects on damaged neurons. 19. The histidine composition of the amyloid-β domain, but not the E1 copper binding domain, modulates β-secretase processing of amyloidprotein precursor in Alzheimer's disease. Science.gov (United States) Gough, Mallory; Blanthorn-Hazell, Sophee; Parkin, Edward T 2015-01-01 Amyloidprotein precursor (AβPP) proteolysis by β- and γ-secretases generates neurotoxic amyloid-β (Aβ)-peptides in Alzheimer's disease (AD). We have investigated the role of histidine residues within the extracellular E1 copper binding and Aβ domains of AβPP in its proteolysis. By stably expressing histidine to alanine AβPP mutant constructs in SH-SY5Y cells, we show that mutations in the E1 copper binding domain had no impact on α- or β-secretase processing. Mutation of histidine 14 within the Aβ-domain specifically down-regulated β-secretase processing without impacting on non-amyloidogenic proteolysis. Understanding how histidine 14 participates in AβPP proteolysis may reveal new intervention points for AD treatments. 20. Interaction of the amyloid precursor protein-like protein 1 (APLP1) E2 domain with heparan sulfate involves two distinct binding modes Energy Technology Data Exchange (ETDEWEB) Dahms, Sven O., E-mail: sdahms@fli-leibniz.de [Leibniz Institute for Age Research (FLI), Beutenbergstrasse 11, 07745 Jena (Germany); Mayer, Magnus C. [Freie Universität Berlin, Thielallee 63, 14195 Berlin (Germany); Miltenyi Biotec GmbH, Robert-Koch-Strasse 1, 17166 Teterow (Germany); Roeser, Dirk [Leibniz Institute for Age Research (FLI), Beutenbergstrasse 11, 07745 Jena (Germany); Multhaup, Gerd [McGill University Montreal, Montreal, Quebec H3G 1Y6 (Canada); Than, Manuel E., E-mail: sdahms@fli-leibniz.de [Leibniz Institute for Age Research (FLI), Beutenbergstrasse 11, 07745 Jena (Germany) 2015-03-01 Two X-ray structures of APLP1 E2 with and without a heparin dodecasaccharide are presented, revealing two distinct binding modes of the protein to heparan sulfate. The data provide a mechanistic explanation of how APP-like proteins bind to heparan sulfates and how they specifically recognize nonreducing structures of heparan sulfates. Beyond the pathology of Alzheimer’s disease, the members of the amyloid precursor protein (APP) family are essential for neuronal development and cell homeostasis in mammals. APP and its paralogues APP-like protein 1 (APLP1) and APP-like protein 2 (APLP2) contain the highly conserved heparan sulfate (HS) binding domain E2, which effects various (patho)physiological functions. Here, two crystal structures of the E2 domain of APLP1 are presented in the apo form and in complex with a heparin dodecasaccharide at 2.5 Å resolution. The apo structure of APLP1 E2 revealed an unfolded and hence flexible N-terminal helix αA. The (APLP1 E2){sub 2}–(heparin){sub 2} complex structure revealed two distinct binding modes, with APLP1 E2 explicitly recognizing the heparin terminus but also interacting with a continuous heparin chain. The latter only requires a certain register of the sugar moieties that fits to a positively charged surface patch and contributes to the general heparin-binding capability of APP-family proteins. Terminal binding of APLP1 E2 to heparin specifically involves a structure of the nonreducing end that is very similar to heparanase-processed HS chains. These data reveal a conserved mechanism for the binding of APP-family proteins to HS and imply a specific regulatory role of HS modifications in the biology of APP and APP-like proteins. 1. Beta-amyloid precursor protein cleavage enzyme-1 expression in adult rat retinal neurons in the early period after lead exposure Institute of Scientific and Technical Information of China (English) Jufang Huang; Kai Huang; Lei Shang; Hui Wang; Xiaoxin Yan; Kun Xiong 2011-01-01 Previous studies have reported that non-human primates and rodents exposed to lead during brain development may become dependent on the deposition of pre-determined β-amyloid protein (Aβ), and exhibit upregulation of β-site amyloid precursor protein expression in old age. However, further evidence is required to elucidate the precise relationship and molecular mechanisms underlying the effects of early lead exposure on excessive Aβ production in adult mammals. The present study investigated the effects of lead exposure on expression of β-amyloid precursor protein cleavage enzyme-1 (BACE-1) in the rat retina and the production of Aβ in early development, using the retina as a window for studying Alzheimer's disease. Adult rats were intraocularly injected with different doses of lead acetate (10 μmol/L, 100 μmol/L, 1 mmol/L, 10 mmol/L and 100 mmol/L). The results revealed that retinal lead concentration, BACE-1 and its cleavage products β-C-terminal fragment and retina Aβ1-40 were all significantly increased in almost all of the lead exposure groups 48 hours later in a dose-dependent manner. The only exception was the 10 μmol/L group. The distribution of BACE-1 in the retina did not exhibit obvious changes, and no distinctive increase in the activation of retinal microglia was apparent. Similarly, retinal synaptophysin expression did not exhibit any clear changes. These data suggest that lead exposure can result in the upregulation of retinal neuron BACE-1 expression in the early period of development and further increase the overproduction of Aβ1-40 in the retina. Our results provided novel insight into the molecular mechanisms underlying environmentally-induced Alzheimer's disease. 2. Differentiating the Influences of Aging and Adiposity on Brain Weights, Levels of Serum and Brain Cytokines, Gastrointestinal Hormones, and Amyloid Precursor Protein. Science.gov (United States) Banks, William A; Abrass, Christine K; Hansen, Kim M 2016-01-01 Aging and obesity exert important effects on disease. Differentiating these effects is difficult, however, because weight gain often accompanies aging. Here, we used a nested design of aged, calorically restricted, and refed rats to measure changes in brain and blood levels of cytokines and gastrointestinal hormones, brain amyloid precursor protein levels, and brain and body weights. By comparing groups and using path analysis, we found divergent influences of chronological aging versus body weight, our main findings being (i) changes in whole brain weight and serum macrophage colony-stimulating factor levels correlated better with body weight than with chronological aging, (ii) a decrease in brain cytokines and brain plasminogen activator inhibitor levels correlated better with chronological aging than with body weight, (iii) serum erythropoietin levels were influenced by both body weight and aging, (iv) serum plasminogen activator inhibitor, serum cytokines, and brain tumor necrosis factor were not influenced by aging or body weight, and (v) brain amyloid precursor protein more closely related to body weight and serum levels of gastrointestinal hormones than to brain weight, chronological aging, or cytokines. These findings show that although aging and body weight interact, their influences are distinct not only among various cytokines and hormones but also between the central nervous system and the peripheral tissue compartments. 3. Data on amyloid precursor protein accumulation, spontaneous physical activity, and motor learning after traumatic brain injury in the triple-transgenic mouse model of Alzheimer׳s disease. Science.gov (United States) Kishimoto, Yasushi; Shishido, Hajime; Sawanishi, Mayumi; Toyota, Yasunori; Ueno, Masaki; Kubota, Takashi; Kirino, Yutaka; Tamiya, Takashi; Kawai, Nobuyuki 2016-12-01 This data article contains supporting information regarding the research article entitled "Traumatic brain injury accelerates amyloid-β deposition and impairs spatial learning in the triple-transgenic mouse model of Alzheimer׳s disease" (H. Shishido, Y. Kishimoto, N. Kawai, Y. Toyota, M. Ueno, T. Kubota, Y. Kirino, T. Tamiya, 2016) [1]. Triple-transgenic (3×Tg)-Alzheimer׳s disease (AD) model mice exhibited significantly poorer spatial learning than sham-treated 3×Tg-AD mice 28 days after traumatic brain injury (TBI). Correspondingly, amyloid-β (Aβ) deposition within the hippocampus was significantly greater in 3×Tg-AD mice 28 days after TBI. However, data regarding the short-term and long-term influences of TBI on amyloid precursor protein (APP) accumulation in AD model mice remain limited. Furthermore, there is little data showing whether physical activity and motor learning are affected by TBI in AD model mice. Here, we provide immunocytochemistry data confirming that TBI induces significant increases in APP accumulation in 3×Tg-AD mice at both 7 days and 28 days after TBI. Furthermore, 3×Tg-AD model mice exhibit a reduced ability to acquire conditioned responses (CRs) during delay eyeblink conditioning compared to sham-treated 3×Tg-AD model mice 28 days after TBI. However, physical activity and motor performance are not significantly changed in TBI-treated 3×Tg-AD model mice. 4. Transgenic expression of the amyloid-beta precursor protein-intracellular domain does not induce Alzheimer's Disease-like traits in vivo. Directory of Open Access Journals (Sweden) Luca Giliberto Full Text Available BACKGROUND: Regulated intramembranous proteolysis of the amyloid-beta precursor protein by the gamma-secretase yields amyloid-beta, which is the major component of the amyloid plaques found in Alzheimer's disease (AD, and the APP intracellular domain (AID. In vitro studies have involved AID in apoptosis and gene transcription. In vivo studies, which utilize transgenic mice expressing AID in the forebrain, only support a role for AID in apoptosis but not gene transcription. METHODOLOGY/PRINCIPAL FINDINGS: Here, we have further characterized several lines of AID transgenic mice by crossing them with human Tau-bearing mice, to determine whether over-expression of AID in the forebrain provokes AD-like pathologic features in this background. We have found no evidence that AID overexpression induces AD-like characteristics, such as activation of GSK-3beta, hyperphosphorylation of Tau and formation of neurofibrillary pathology. CONCLUSIONS/SIGNIFICANCE: Overall, these data suggest that AID transgenic mice do not represent a model that reproduces the overt biochemical and anatomo-pathologic lesions observed in AD patients. They can still be a valuable tool to understand the role of AID in enhancing the cell sensitivity to apoptotic stimuli, whose pathways still need to be characterized. 5. An Alzheimer Disease-linked Rare Mutation Potentiates Netrin Receptor Uncoordinated-5C-induced Signaling That Merges with Amyloid β Precursor Protein Signaling. Science.gov (United States) Hashimoto, Yuichi; Toyama, Yuka; Kusakari, Shinya; Nawa, Mikiro; Matsuoka, Masaaki 2016-06-03 6. Novel 5' untranslated region directed blockers of iron-regulatory protein-1 dependent amyloid precursor protein translation: implications for down syndrome and Alzheimer's disease. Directory of Open Access Journals (Sweden) Full Text Available We reported that iron influx drives the translational expression of the neuronal amyloid precursor protein (APP, which has a role in iron efflux. This is via a classic release of repressor interaction of APP mRNA with iron-regulatory protein-1 (IRP1 whereas IRP2 controls the mRNAs encoding the L- and H-subunits of the iron storage protein, ferritin. Here, we identified thirteen potent APP translation blockers that acted selectively towards the uniquely configured iron-responsive element (IRE RNA stem loop in the 5' untranslated region (UTR of APP mRNA. These agents were 10-fold less inhibitory of 5'UTR sequences of the related prion protein (PrP mRNA. Western blotting confirmed that the 'ninth' small molecule in the series selectively reduced neural APP production in SH-SY5Y cells at picomolar concentrations without affecting viability or the expression of α-synuclein and ferritin. APP blocker-9 (JTR-009, a benzimidazole, reduced the production of toxic Aβ in SH-SY5Y neuronal cells to a greater extent than other well tolerated APP 5'UTR-directed translation blockers, including posiphen, that were shown to limit amyloid burden in mouse models of Alzheimer's disease (AD. RNA binding assays demonstrated that JTR-009 operated by preventing IRP1 from binding to the IRE in APP mRNA, while maintaining IRP1 interaction with the H-ferritin IRE RNA stem loop. Thus, JTR-009 constitutively repressed translation driven by APP 5'UTR sequences. Calcein staining showed that JTR-009 did not indirectly change iron uptake in neuronal cells suggesting a direct interaction with the APP 5'UTR. These studies provide key data to develop small molecules that selectively reduce neural APP and Aβ production at 10-fold lower concentrations than related previously characterized translation blockers. Our data evidenced a novel therapeutic strategy of potential impact for people with trisomy of the APP gene on chromosome 21, which is a phenotype long associated with Down 7. Novel 5' untranslated region directed blockers of iron-regulatory protein-1 dependent amyloid precursor protein translation: implications for down syndrome and Alzheimer's disease. Science.gov (United States) Bandyopadhyay, Sanghamitra; Cahill, Catherine; Balleidier, Amelie; Huang, Conan; Lahiri, Debomoy K; Huang, Xudong; Rogers, Jack T 2013-01-01 We reported that iron influx drives the translational expression of the neuronal amyloid precursor protein (APP), which has a role in iron efflux. This is via a classic release of repressor interaction of APP mRNA with iron-regulatory protein-1 (IRP1) whereas IRP2 controls the mRNAs encoding the L- and H-subunits of the iron storage protein, ferritin. Here, we identified thirteen potent APP translation blockers that acted selectively towards the uniquely configured iron-responsive element (IRE) RNA stem loop in the 5' untranslated region (UTR) of APP mRNA. These agents were 10-fold less inhibitory of 5'UTR sequences of the related prion protein (PrP) mRNA. Western blotting confirmed that the 'ninth' small molecule in the series selectively reduced neural APP production in SH-SY5Y cells at picomolar concentrations without affecting viability or the expression of α-synuclein and ferritin. APP blocker-9 (JTR-009), a benzimidazole, reduced the production of toxic Aβ in SH-SY5Y neuronal cells to a greater extent than other well tolerated APP 5'UTR-directed translation blockers, including posiphen, that were shown to limit amyloid burden in mouse models of Alzheimer's disease (AD). RNA binding assays demonstrated that JTR-009 operated by preventing IRP1 from binding to the IRE in APP mRNA, while maintaining IRP1 interaction with the H-ferritin IRE RNA stem loop. Thus, JTR-009 constitutively repressed translation driven by APP 5'UTR sequences. Calcein staining showed that JTR-009 did not indirectly change iron uptake in neuronal cells suggesting a direct interaction with the APP 5'UTR. These studies provide key data to develop small molecules that selectively reduce neural APP and Aβ production at 10-fold lower concentrations than related previously characterized translation blockers. Our data evidenced a novel therapeutic strategy of potential impact for people with trisomy of the APP gene on chromosome 21, which is a phenotype long associated with Down syndrome (DS 8. Critical analysis of the use of β-site amyloid precursor protein-cleaving enzyme 1 inhibitors in the treatment of Alzheimer's disease Directory of Open Access Journals (Sweden) Evin G 2014-01-01 Full Text Available Genevieve Evin,1,2 Adel Barakat21Oxidation Biology Laboratory, Mental Health Research Institute, Florey Institute of Neuroscience and Mental Health, University of Melbourne, 2Department of Pathology, University of Melbourne, Parkville, VIC, AustraliaAbstract: Alzheimer's disease (AD is the major cause of dementia in the elderly and an unmet clinical challenge. A variety of therapies that are currently under development are directed to the amyloid cascade. Indeed, the accumulation and toxicity of amyloid-β (Aβ is believed to play a central role in the etiology of the disease, and thus rational interventions are aimed at reducing the levels of Aβ in the brain. Targeting β-site amyloid precursor protein-cleaving enzyme (BACE-1 represents an attractive strategy, as this enzyme catalyzes the initial and rate-limiting step in Aβ production. Observation of increased levels of BACE1 and enzymatic activity in the brain, cerebrospinal fluid, and platelets of patients with AD and mild cognitive impairment supports the potential benefits of BACE1 inhibition. Numerous potent inhibitors have been generated, and many of these have been proved to lower Aβ levels in the brain of animal models. Over 10 years of intensive research on BACE1 inhibitors has now culminated in advancing half a dozen of these drugs into human trials, yet translating the in vitro and cellular efficacy of BACE1 inhibitors into preclinical and clinical trials represents a challenge. This review addresses the promises and also the potential problems associated with BACE1 inhibitors for AD therapy, as the complex biological function of BACE1 in the brain is becoming unraveled.Keywords: amyloid, dementia, secretase, aspartyl protease, neuregulin 9. [Compensatory mechanisms to heal neuroplasticity impairment under Alzheiemer's disease neurodegeneration. I: The role of amyloid beta and its' precursor protein]. Science.gov (United States) Kudinov, A R; Kudinova, N V; Kezlia, E V; Kozyrev, K M; Medvedev, A E; Berezov, T T 2012-01-01 In-depth scholar literature analysis of Alzheimer's disease neurodegenerative features of amyloid beta protein neurochemistry modification and excessive phosphorylation of tau protein (and associated neuronal cytoskeleton rearrangements) are secondary phenomena. At early disease stage these neurobiochemical mechanisms are reversible and serve to heal an impairment of biophysical properties of neuronal membranes, neurotransmission, basic neuronal function and neuroplasticity, while preserving anatomical and functional brain fields. Abeta and tau could well serve to biochemically restore physico-chemical properties of neual membranes due to a role these proteins play in lipid metabolism. Under such scenario therapeutic block of aggregation and plaque formation of Abeta and inhibition of tau phosphorylation, as well as pharmaceutical modification of other secondary neurodegenerative features (such as a cascade of oxidative stress reactions) are unable to provide an effective cure of Alzheimer's disease and related pathologies of the Central and peripheral nervous systems, because they are not arraying primary pathagenetic cause. We review the role of Abeta in compensatory mechanisms of neuroplasticity restoration under normal physiological condition and Alzheimer's disease. 10. Molecular mechanism of the intramembrane cleavage of the β-carboxyl terminal fragment of amyloid precursor protein by γ-secretase Directory of Open Access Journals (Sweden) Maho eMorishima-Kawashima 2014-11-01 Full Text Available Amyloid β-protein (Aβ plays a central role in the pathogenesis of Alzheimer’s disease, the most common age-associated neurodegenerative disorder. Aβ is generated through intramembrane proteolysis of the β-carboxyl terminal fragment (βCTF of β-amyloid precursor protein (APP by γ-secretase. The initial cleavage by γ-secretase occurs in the membrane/cytoplasm boundary of the βCTF, liberating the APP intracellular domain (AICD. The remaining βCTFs, which are truncated at the C-terminus (longer Aβs, are then cropped sequentially in a stepwise manner, predominantly at three residue intervals, to generate Aβ. There are two major Aβ product lines which generate Aβ40 and Aβ42 with concomitant release of three and two tripeptides, respectively. Additionally, many alternative cleavages occur, releasing peptides with three to six residues. These modulate the Aβ product lines and define the species and quantity of Aβ generated. Here, we review our current understanding of the intramembrane cleavage of the βCTF by γ-secretase, which may contribute to the future goal of developing an efficient therapeutic strategy for Alzheimer’s disease. 11. Structural Studies of the Alzheimer's Amyloid Precursor Protein Copper-Binding Domain Reveal How It Binds Copper Ions Energy Technology Data Exchange (ETDEWEB) Kong, G.K.-W.; Adams, J.J.; Harris, H.H.; Boas, J.F.; Curtain, C.C.; Galatis, D.; Master, C.L.; Barnham, K.J.; McKinstry, W.J.; Cappai, R.; Parker, M.W.; /Sydney U. 2007-07-09 Alzheimer's disease (AD) is the major cause of dementia. Amyloid {beta} peptide (A {beta}), generated by proteolytic cleavage of the amyloid precursor protein (APP), is central to AD pathogenesis. APP can function as a metalloprotein and modulate copper (Cu) transport, presumably via its extracellular Cu-binding domain (CuBD). Cu binding to the CuBD reduces A{beta} levels, suggesting that a Cu mimetic may have therapeutic potential. We describe here the atomic structures of apo CuBD from three crystal forms and found they have identical Cu-binding sites despite the different crystal lattices. The structure of Cu[2+]-bound CuBD reveals that the metal ligands are His147, His151, Tyrl68 and two water molecules, which are arranged in a square pyramidal geometry. The site resembles a Type 2 non-blue Cu center and is supported by electron paramagnetic resonance and extended X-ray absorption fine structure studies. A previous study suggested that Met170 might be a ligand but we suggest that this residue plays a critical role as an electron donor in CuBDs ability to reduce Cu ions. The structure of Cu[+]-bound CuBD is almost identical to the Cu[2+]-bound structure except for the loss of one of the water ligands. The geometry of the site is unfavorable for Cu[+], thus providing a mechanism by which CuBD could readily transfer Cu ions to other proteins. 12. Sortilin-related receptor 1 interacts with amyloid precursor protein and is activated by 6-shogaol, leading to inhibition of the amyloidogenic pathway. Science.gov (United States) Na, Ji-Young; Song, Kibbeum; Lee, Ju-Woon; Kim, Sokho; Kwon, Jungkee 2017-03-18 Sortilin-related receptor 1 (SORL1) is a neuronal sorting protein that reduces amyloid precursor protein (APP) trafficking to secretases that generate amyloid beta (Aβ). Although 6-shogaol, a constituent of ginger, has been reported to have anti-inflammatory and anti-oxidant effects on neuronal cells, research regarding the activation of SORL1 has not yet been reported. Here, we aimed to investigate whether 6-shogaol contributes to the increases in SORL1 that are related to Alzheimer's disease (AD). To clarify the effect of 6-shogaol as a possible activator of SORL1, we used SORL1 siRNA as a blockade of SORL1 in hippocampal neuronal cells (HT22). We found that SORL1 siRNA treatment naturally inhibited SORL1 and led to increases in β-secretase APP cleaving enzyme (BACE), secreted APP-β (sAPPβ) and Aβ. In contrast, 6-shogaol-mediated activation of SORL1 significantly downregulated BACE, sAPPβ, and Aβ in both in vitro HT22 cells and in vivo APPSw/PS1-dE9 Tg mice. Therefore, SORL1 activation by 6-shogaol provides neuronal cell survival through the inhibition of Aβ production. These results indicate that 6-shogaol should be regarded as an SORL1 activator and a potential preventive agent for the treatment of AD. 13. Evidence that the amyloidprotein precursor intracellular domain, AICD, derives from β-secretase-generated C-terminal fragment. Science.gov (United States) Flammang, Brice; Pardossi-Piquard, Raphaëlle; Sevalle, Jean; Debayle, Delphine; Dabert-Gay, Anne-Sophie; Thévenet, Aurélie; Lauritzen, Inger; Checler, Frédéric 2012-01-01 One of the major pathological hallmarks of brains affected with Alzheimer's disease (AD) is the senile plaque, an extracellular deposit mainly composed of a set of highly insoluble peptides of various lengths (39-43 amino acids) referred to as amyloid-β (Aβ) peptides. Aβ peptides are derived from combined proteolytic cleavages undergone on the amyloidprotein precursor (AβPP) by a set of enzymes called secretases. Several lines of anatomical and biological evidence suggest that Aβ peptides would not account for all pathological stigmata and molecular dysfunctions taking place in AD. In amyloidogenic and non-amyloidogenic pathways, AβPP first undergoes β- or α-secretases-mediated cleavages yielding C99 and C83, respectively. These two membrane-embedded C-terminal fragments are both potential targets of subsequent γ-secretase-mediated proteolysis. The latter cleavage not only generates either p3 or Aβ peptides but similarly gives rise to an AβPP IntraCellular Domain (AICD fragment) that could modulate the transcription of several genes linked to AD pathology. It is therefore striking that AICD theoretically derives from both amyloidogenic and non-amyloidogenic AβPP processing pathways. Here we show that AICD predominantly derives from C99 by means of recombinant substrates and transiently transfected cells expressing C99. Our data suggest a preferred pathogenic pathway for AICD production and suggests that this fragment, in addition to C99 and Aβ peptides, could contribute to AD pathology. 14. β-Secretase inhibitor increases amyloidprecursor protein level in rat brain cortical primary neurons induced by okadaic acid Institute of Scientific and Technical Information of China (English) YU Chun-Jiang; WANG Wei-zhi; LIU Wei 2008-01-01 Background Senile plaques and neurofibrillary tangles (NFTs) represent two of the major histopathological hallmarks of Alzheimer's disease (AD). The plaques are primarily composed of aggregated amyloid β (Aβ) peptides. The processing of amyloidprecursor protein (AβPP) in okadaic acid (OA)-induced tau phosphorylation primary neurons was studied.Methods Primary cultures of rat brain cortical neurons were treated with OA and β-secretase inhibitor. Neurons' viability was measured. AβPP processing was examined by immunocytochemistry and Western blotting with specific antibodies against the AβPP-N-terminus (NT) and AβPP-C-terminus (CT).Results Ten nrnol/L OA had a time-dependent suppression effect on primary neurons' viability. The suppression effect was alleviated markedly by pretreatment with β-secretase inhibitor. After OA treatment, both AβPP and β-C-terminal fragment (βCTF) were significantly increased in neurons. AβPP level was increased further in neurons pretreated with β-secretase inhibitor.Conclusions In OA-induced tau phosphorylation cell model, inhibition of β-secretase may protect neurons from death induced by OA. Because of increased accumulation of AβPP in neurons after OA treatment, more AβPP turns to be cleaved by β-secretase, producing neurotoxic βCTF. As a potential effective therapeutic target, β-secretase is worth investigating further. 15. Iron and the translation of the amyloid precursor protein (APP) and ferritin mRNAs: riboregulation against neural oxidative damage in Alzheimer's disease. Science.gov (United States) Rogers, Jack T; Bush, Ashley I; Cho, Hyan-Hee; Smith, Deborah H; Thomson, Andrew M; Friedlich, Avi L; Lahiri, Debomoy K; Leedman, Peter J; Huang, Xudong; Cahill, Catherine M 2008-12-01 The essential metals iron, zinc and copper deposit near the Abeta (amyloid beta-peptide) plaques in the brain cortex of AD (Alzheimer's disease) patients. Plaque-associated iron and zinc are in neurotoxic excess at 1 mM concentrations. APP (amyloid precursor protein) is a single transmembrane metalloprotein cleaved to generate the 40-42-amino-acid Abetas, which exhibit metal-catalysed neurotoxicity. In health, ubiquitous APP is cleaved in a non-amyloidogenic pathway within its Abeta domain to release the neuroprotective APP ectodomain, APP(s). To adapt and counteract metal-catalysed oxidative stress, as during reperfusion from stroke, iron and cytokines induce the translation of both APP and ferritin (an iron storage protein) by similar mechanisms. We reported that APP was regulated at the translational level by active IL (interleukin)-1 (IL-1-responsive acute box) and IRE (iron-responsive element) RNA stem-loops in the 5' untranslated region of APP mRNA. The APP IRE is homologous with the canonical IRE RNA stem-loop that binds the iron regulatory proteins (IRP1 and IRP2) to control intracellular iron homoeostasis by modulating ferritin mRNA translation and transferrin receptor mRNA stability. The APP IRE interacts with IRP1 (cytoplasmic cis-aconitase), whereas the canonical H-ferritin IRE RNA stem-loop binds to IRP2 in neural cell lines, and in human brain cortex tissue and in human blood lysates. The same constellation of RNA-binding proteins [IRP1/IRP2/poly(C) binding protein] control ferritin and APP translation with implications for the biology of metals in AD. 16. Mild oxidative stress induces redistribution of BACE1 in non-apoptotic conditions and promotes the amyloidogenic processing of Alzheimer's disease amyloid precursor protein. Directory of Open Access Journals (Sweden) Jiang-Li Tan Full Text Available BACE1 is responsible for β-secretase cleavage of the amyloid precursor protein (APP, which represents the first step in the production of amyloid β (Aβ peptides. Previous reports, by us and others, have indicated that the levels of BACE1 protein and activity are increased in the brain cortex of patients with Alzheimer's disease (AD. The association between oxidative stress (OS and AD has prompted investigations that support the potentiation of BACE1 expression and enzymatic activity by OS. Here, we have established conditions to analyse the effects of mild, non-lethal OS on BACE1 in primary neuronal cultures, independently from apoptotic mechanisms that were shown to impair BACE1 turnover. Six-hour treatment of mouse primary cortical cells with 10-40 µM hydrogen peroxide did not significantly compromise cell viability but it did produce mild oxidative stress (mOS, as shown by the increased levels of reactive radical species and activation of p38 stress kinase. The endogenous levels of BACE1 mRNA and protein were not significantly altered in these conditions, whereas a toxic H2O2 concentration (100 µM caused an increase in BACE1 protein levels. Notably, mOS conditions resulted in increased levels of the BACE1 C-terminal cleavage product of APP, β-CTF. Subcellular fractionation techniques showed that mOS caused a major rearrangement of BACE1 localization from light to denser fractions, resulting in an increased distribution of BACE1 in fractions containing APP and markers for trans-Golgi network and early endosomes. Collectively, these data demonstrate that mOS does not modify BACE1 expression but alters BACE1 subcellular compartmentalization to favour the amyloidogenic processing of APP, and thus offer new insight in the early molecular events of AD pathogenesis. 17. The E1 copper binding domain of full-length amyloid precursor protein mitigates copper-induced growth inhibition in brain metastatic prostate cancer DU145 cells. Science.gov (United States) Gough, Mallory; Blanthorn-Hazell, Sophee; Delury, Craig; Parkin, Edward 2014-10-31 Copper plays an important role in the aetiology and growth of tumours and levels of the metal are increased in the serum and tumour tissue of patients affected by a range of cancers including prostate cancer (PCa). The molecular mechanisms that enable cancer cells to proliferate in the presence of elevated copper levels are, therefore, of key importance in our understanding of tumour growth progression. In the current study, we have examined the role played by the amyloid precursor protein (APP) in mitigating copper-induced growth inhibition of the PCa cell line, DU145. A range of APP molecular constructs were stably over-expressed in DU145 cells and their effects on cell proliferation in the presence of copper were monitored. Our results show that endogenous APP expression was induced by sub-toxic copper concentrations in DU145 cells and over-expression of the wild-type protein was able to mitigate copper-induced growth inhibition via a mechanism involving the cytosolic and E1 copper binding domains of the full-length protein. APP likely represents one of a range of copper binding proteins that PCa cells employ in order to ensure efficient proliferation despite elevated concentrations of the metal within the tumour microenvironment. Targeting the expression of such proteins may contribute to therapeutic strategies for the treatment of cancers. 18. A lentiviral sponge for miR-101 regulates RanBP9 expression and amyloid precursor protein metabolism in hippocampal neurons Directory of Open Access Journals (Sweden) Christian eBarbato 2014-02-01 Full Text Available Neurodegeneration associated with amyloid β (Aβ peptide accumulation, synaptic loss, and memory impairment are pathophysiological features of Alzheimer's disease (AD. Numerous microRNAs regulate amyloid precursor protein (APP expression and metabolism. We previously reported that miR-101 is a negative regulator of APP expression in cultured hippocampal neurons. In this study, a search for predicted APP metabolism-associated miR-101 targets led to the identification of a conserved miR-101 binding site within the 3’ untranslated region (UTR of the mRNA encoding Ran-binding protein 9 (RanBP9. RanBP9 increases APP processing by β-amyloid converting enzyme 1 (BACE1, secretion of soluble APPβ (sAPPβ, and generation of Aβ. MiR-101 significantly reduced reporter gene expression when co-transfected with a RanBP9 3'-UTR reporter construct, while site-directed mutagenesis of the predicted miR-101 target site eliminated the reporter response. To investigate the effect of stable inhibition of miR-101 both in vitro and in vivo, a microRNA sponge was developed to bind miR-101 and derepress its targets. Four tandem bulged miR-101 responsive elements (REs, located downstream of the enhanced green fluorescence protein (EGFP open reading frame and driven by the synapsin promoter, were placed in a lentiviral vector to create the pLSyn-miR-101 sponge. Delivery of the sponge to primary hippocampal neurons significantly increased both APP and RanBP9 expression, as well as sAPPβ levels in the conditioned medium. Importantly, silencing of endogenous RanBP9 reduced sAPPβ levels in miR-101 sponge-containing hippocampal cultures, indicating that miR-101 inhibition may increase amyloidogenic processing of APP by RanBP9. Lastly, the impact of miR-101 on its targets was demonstrated in vivo by intrahippocampal injection of the pLSyn-miR-101 sponge into C57BL6 mice. This study thus provides the basis for studying the consequences of long-term miR-101 inhibition on 19. The leucine-rich repeats of LINGO-1 are not required for self-interaction or interaction with the amyloid precursor protein. Science.gov (United States) 2012-02-10 LINGO-1 (leucine rich repeat and Ig domain containing Nogo receptor interacting protein-1) is a central nervous system transmembrane protein which simultaneously interacts with the Nogo-66 receptor and p75(NTR) or TROY on neurons to form a receptor complex responsible for myelin-mediated neurite outgrowth inhibition. On oligodendroglial cells, LINGO-1 interacts with p75(NTR) to constitutively inhibit multiple aspects of oligodendrocyte differentiation. Recently, LINGO-1 was identified as an in vivo interacting partner of the amyloid precursor protein (APP) and, correspondingly, cellular LINGO-1 expression was found to augment the release of the Abeta peptide, the potential causative agent of Alzheimer's disease. In addition, the recombinant LINGO-1 ectodomain has been shown to self-interact in solution and after crystallisation. Here, we have used deletional mutagenesis to identify the regions on LINGO-1 that are involved in homo- and heterotypic interactions. We have found that the N-terminal region containing the leucine-rich repeats along with the transmembrane and cytoplasmic domains of LINGO-1 are not required for self-interaction or interaction with APP. 20. Differential interaction of Apolipoprotein-E isoforms with insulin receptors modulates brain insulin signaling in mutant human amyloid precursor protein transgenic mice. Science.gov (United States) Chan, Elizabeth S; Chen, Christopher; Cole, Gregory M; Wong, Boon-Seng 2015-09-08 It is unclear how human apolipoprotein E4 (ApoE4) increases the risk for Alzheimer's disease (AD). Although Aβ levels can lead to insulin signaling impairment, these experiments were done in the absence of human ApoE. To examine ApoE role, we crossed the human ApoE-targeted replacement mice with mutant human amyloid precursor protein (APP) mice. In 26 week old mice with lower Aβ levels, the expression and phosphorylation of insulin signaling proteins remained comparable among APP, ApoE3xAPP and ApoE4xAPP mouse brains. When the mice aged to 78 weeks, these proteins were markedly reduced in APP and ApoE4xAPP mouse brains. While Aβ can bind to insulin receptor, how ApoE isoforms modulate this interaction remains unknown. Here, we showed that ApoE3 had greater association with insulin receptor as compared to ApoE4, regardless of Aβ42 concentration. In contrast, ApoE4 bound more Aβ42 with increasing peptide levels. Using primary hippocampal neurons, we showed that ApoE3 and ApoE4 neurons are equally sensitive to physiological levels of insulin. However, in the presence of Aβ42, insulin failed to elicit a downstream response only in ApoE4 hippocampal neurons. Taken together, our data show that ApoE genotypes can modulate this Aβ-mediated insulin signaling impairment. 1. Potential Natural Products for Alzheimer’s Disease: Targeted Search Using the Internal Ribosome Entry Site of Tau and AmyloidPrecursor Protein Directory of Open Access Journals (Sweden) Yun-Chieh Tasi 2015-04-01 Full Text Available Overexpression of the amyloid precursor protein (APP and the hyperphosphorylation of the tau protein are vital in the understanding of the cause of Alzheimer’s disease (AD. As a consequence, regulation of the expression of both APP and tau proteins is one important approach in combating AD. The APP and tau proteins can be targeted at the levels of transcription, translation and protein structural integrity. This paper reports the utilization of a bi-cistronic vector containing either APP or tau internal ribosome entry site (IRES elements flanked by β-galactosidase gene (cap-dependent and secreted alkaline phosphatase (SEAP (cap-independent to discern the mechanism of action of memantine, an N-methyl-d-aspartate (NMDA receptor antagonist. Results indicate that memantine could reduce the activity of both the APP and tau IRES at a concentration of ~10 μM (monitored by SEAP activity without interfering with the cap-dependent translation as monitored by the β-galactosidase assay. Western blot analysis of the tau protein in neuroblastoma (N2A and rat hippocampal cells confirmed the halting of the expression of the tau proteins. We also employed this approach to identify a preparation named NB34, extracts of Boussingaultia baselloides (madeira-vine fermented with Lactobacillus spp., which can function similarly to memantine in both IRES of APP and Tau. The water maze test demonstrated that NB34 could improve the spatial memory of a high fat diet induced neurodegeneration in apolipoprotein E-knockout (ApoE−/− mice. These results revealed that the bi-cistronic vector provided a simple, and effective platform in screening and establishing the mechanistic action of potential compounds for the treatment and management of AD. 2. Early in vivo Effects of the Human Mutant AmyloidProtein Precursor (hAβPPSwInd) on the Mouse Olfactory Bulb. Science.gov (United States) Rusznák, Zoltán; Kim, Woojin Scott; Hsiao, Jen-Hsiang T; Halliday, Glenda M; Paxinos, George; Fu, YuHong 2016-01-01 The amyloidprotein precursor (AβPP) has long been linked to Alzheimer's disease (AD). Using J20 mice, which express human AβPP with Swedish and Indiana mutations, we studied early pathological changes in the olfactory bulb. The presence of AβPP/amyloid-β (Aβ) was examined in mice aged 3 months (before the onset of hippocampal Aβ deposition) and over 5 months (when hippocampal Aβ deposits are present). The number of neurons, non-neurons, and proliferating cells was assessed using the isotropic fractionator method. Our results demonstrate that although AβPP is overexpressed in some of the mitral cells, widespread Aβ deposition and microglia aggregates are not prevalent in the olfactory bulb. The olfactory bulbs of the younger J20 group harbored significantly fewer neurons than those of the age-matched wild-type mice (5.57±0.13 million versus 6.59±0.36 million neurons; p = 0.011). In contrast, the number of proliferating cells was higher in the young J20 than in the wild-type group (i.e., 6617±425 versus 4455±623 cells; p = 0.011). A significant increase in neurogenic activity was also observed in the younger J20 olfactory bulb. In conclusion, our results indicate that (1) neurons participating in the mouse olfactory function overexpress AβPP; (2) the cellular composition of the young J20 olfactory bulb is different from that of wild-type littermates; (3) these differences may reflect altered neurogenic activity and/or delayed development of the J20 olfactory system; and (4) AβPP/Aβ-associated pathological changes that take place in the J20 hippocampus and olfactory bulb are not identical. 3. Differential effects of 24-hydroxycholesterol and 27-hydroxycholesterol on β-amyloid precursor protein levels and processing in human neuroblastoma SH-SY5Y cells Directory of Open Access Journals (Sweden) Schommer Eric 2009-01-01 Full Text Available Abstract Background Activation of the liver × receptors (LXRs by exogenous ligands stimulates the degradation of β-amyloid 1–42 (Aβ42, a peptide that plays a central role in the pathogenesis of Alzheimer's disease (AD. The oxidized cholesterol products (oxysterols, 24-hydroxycholesterol (24-OHC and 27-hydroxycholesterol (27-OHC, are endogenous activators of LXRs. However, the mechanisms by which these oxysterols may modulate Aβ42 levels are not well known. Results We determined the effect of 24-OHC and/or 27-OHC on Aβ generation in SH-SY5Y cells. We found that while 27-OHC increases levels of Aβ42, 24-OHC did not affect levels of this peptide. Increased Aβ42 levels with 27-OHC are associated with increased levels of β-amyloid precursor protein (APP as well as β-secretase (BACE1, the enzyme that cleaves APP to yield Aβ. Unchanged Aβ42 levels with 24-OHC are associated with increased levels of sAPPα, suggesting that 24-OHC favors the processing of APP to the non-amyloidogenic pathway. Interestingly, 24-OHC, but not 27-OHC, increases levels of the ATP-binding cassette transporters, ABCA1 and ABCG1, which regulate cholesterol transport within and between cells. Conclusion These results suggest that cholesterol metabolites are linked to Aβ42 production. 24-OHC may favor the non-amyloidogenic pathway and 27-OHC may enhance production of Aβ42 by upregulating APP and BACE1. Regulation of 24-OHC: 27-OHC ratio could be an important strategy in controlling Aβ42 levels in AD. 4. The amyloid precursor protein (APP) intracellular domain regulates translation of p44, a short isoform of p53, through an IRES-dependent mechanism. Science.gov (United States) Li, Mi; Pehar, Mariana; Liu, Yan; Bhattacharyya, Anita; Zhang, Su-Chun; O'Riordan, Kenneth J; Burger, Corinna; D'Adamio, Luciano; Puglielli, Luigi 2015-10-01 p44 is a short isoform of the tumor suppressor protein p53 that is regulated in an age-dependent manner. When overexpressed in the mouse, it causes a progeroid phenotype that includes premature cognitive decline, synaptic defects, and hyperphosphorylation of tau. The hyperphosphorylation of tau has recently been linked to the ability of p44 to regulate transcription of relevant tau kinases. Here, we report that the amyloid precursor protein (APP) intracellular domain (AICD), which results from the processing of the APP, regulates translation of p44 through a cap-independent mechanism that requires direct binding to the second internal ribosome entry site (IRES) of the p53 mRNA. We also report that AICD associates with nucleolin, an already known IRES-specific trans-acting factor that binds with p53 IRES elements and regulates translation of p53 isoforms. The potential biological impact of our findings was assessed in a mouse model of Alzheimer's disease. In conclusion, our study reveals a novel aspect of AICD and p53/p44 biology and provides a possible molecular link between APP, p44, and tau. 5. Intracellular domains of amyloid precursor-like protein 2 interact with CP2 transcription factor in the nucleus and induce glycogen synthase kinase-3beta expression. Science.gov (United States) Xu, Y; Kim, H-S; Joo, Y; Choi, Y; Chang, K-A; Park, C H; Shin, K-Y; Kim, S; Cheon, Y-H; Baik, T-K; Kim, J-H; Suh, Y-H 2007-01-01 Amyloid precursor protein (APP) is a member of a gene family that includes two APP-like proteins, APLP1 and 2. Recently, it has been reported that APLP1 and 2 undergo presenilin-dependent gamma-secretase cleavage, as does APP, resulting in the release of an approximately 6 kDa intracellular C-terminal domain (ICD), which can translocate into the nucleus. In this study, we demonstrate that the APLP2-ICDs interact with CP2/LSF/LBP1 (CP2) transcription factor in the nucleus and induce the expression of glycogen synthase kinase 3beta (GSK-3beta), which has broad-ranged substrates such as tau- and beta-catenin. The significance of this finding is substantiated by the in vivo evidence of the increase in the immunoreactivities for the nuclear C-terminal fragments of APLP2, and for GSK-3beta in the AD patients' brain. Taken together, these results suggest that APLP2-ICDs contribute to the AD pathogenesis, by inducing GSK-3beta expression through the interaction with CP2 transcription factor in the nucleus. 6. The Na+/H+ exchanger NHE6 modulates endosomal pH to control processing of amyloid precursor protein in a cell culture model of Alzheimer disease. Science.gov (United States) 2015-02-27 Early intervention may be key to safe and effective therapies in patients with Alzheimer disease. Endosomal dysfunction is an early step in neurodegeneration. Endosomes are a major site of production of Aβ peptide from the processing of amyloid precursor protein (APP) by clipping enzymes (β- and γ-secretases). The β-secretase enzyme BACE1 requires acidic lumen pH for optimum function, and acid pH promotes Aβ aggregation. The Na(+)/H(+) exchanger NHE6 provides a leak pathway for protons, limiting luminal acidification by proton pumps. Like APP, NHE6 expression was induced upon differentiation of SH-SY5Y neuroblastoma cells and localized to an endosomal compartment. Therefore, we investigated whether NHE6 expression altered APP localization and processing in a stably transfected cell culture model of human APP expression. We show that co-expression with NHE6 or treatment with the Na(+)/H(+) ionophore monensin shifted APP away from the trans-Golgi network into early and recycling endosomes in HEK293 cells. NHE6 alkalinized the endosomal lumen, similar to monensin, and significantly attenuated APP processing and Aβ secretion. In contrast, Aβ production was elevated upon NHE6 knockdown. We show that NHE6 transcript and protein levels are lowered in Alzheimer brains relative to control. These findings, taken together with emerging genetic evidence linking endosomal Na(+)/H(+) exchangers with Alzheimer disease, suggest that proton leak pathways may regulate Aβ generation and contribute to disease etiology. 7. β-site amyloid precursor protein cleaving enzyme 1(BACE1) regulates Notch signaling by controlling the cleavage of Jagged 1 (Jag1) and Jagged 2 (Jag2) proteins. Science.gov (United States) He, Wanxia; Hu, Jinxuan; Xia, Yuxing; Yan, Riqiang 2014-07-25 BACE1 is a type I transmembrane aspartyl protease that cleaves amyloid precursor protein at the β-secretase site to initiate the release of β-amyloid peptide. As a secretase, BACE1 also cleaves additional membrane-bound molecules by exerting various cellular functions. In this study, we showed that BACE1 can effectively shed the membrane-anchored signaling molecule Jagged 1 (Jag1).Wealso mapped the cleavage sites of Jag1 by ADAM10 and ADAM17. Although Jag1 shares a high degree of homology with Jag2 in the ectodomain region, BACE1 fails to cleave Jag2 effectively, indicating a selective cleavage of Jag1. Abolished cleavage of Jag1 in BACE1-null mice leads to enhanced astrogenesis and, concomitantly, reduced neurogenesis. This characterization provides biochemical evidence that the Jag1-Notch pathway is under the control of BACE1 activity 8. The E1 copper binding domain of full-length amyloid precursor protein mitigates copper-induced growth inhibition in brain metastatic prostate cancer DU145 cells Energy Technology Data Exchange (ETDEWEB) Gough, Mallory, E-mail: m.gough1@lancaster.ac.uk; Blanthorn-Hazell, Sophee, E-mail: s.blanthorn-hazell@lancaster.ac.uk; Delury, Craig, E-mail: c.delury@lancaster.ac.uk; Parkin, Edward, E-mail: e.parkin@lancaster.ac.uk 2014-10-31 Highlights: • Copper levels are elevated in the tumour microenvironment. • APP mitigates copper-induced growth inhibition of DU145 prostate cancer (PCa) cells. • The APP intracellular domain is a prerequisite; soluble forms have no effect. • The E1 CuBD of APP is also a prerequisite. • APP copper binding potentially mitigates copper-induced PCa cell growth inhibition. - Abstract: Copper plays an important role in the aetiology and growth of tumours and levels of the metal are increased in the serum and tumour tissue of patients affected by a range of cancers including prostate cancer (PCa). The molecular mechanisms that enable cancer cells to proliferate in the presence of elevated copper levels are, therefore, of key importance in our understanding of tumour growth progression. In the current study, we have examined the role played by the amyloid precursor protein (APP) in mitigating copper-induced growth inhibition of the PCa cell line, DU145. A range of APP molecular constructs were stably over-expressed in DU145 cells and their effects on cell proliferation in the presence of copper were monitored. Our results show that endogenous APP expression was induced by sub-toxic copper concentrations in DU145 cells and over-expression of the wild-type protein was able to mitigate copper-induced growth inhibition via a mechanism involving the cytosolic and E1 copper binding domains of the full-length protein. APP likely represents one of a range of copper binding proteins that PCa cells employ in order to ensure efficient proliferation despite elevated concentrations of the metal within the tumour microenvironment. Targeting the expression of such proteins may contribute to therapeutic strategies for the treatment of cancers. 9. Presenilin 2 deficiency causes a mild pulmonary phenotype and no changes in amyloid precursor protein processing but enhances the embryonic lethal phenotype of presenilin 1 deficiency. Science.gov (United States) Herreman, A; Hartmann, D; Annaert, W; Saftig, P; Craessaerts, K; Serneels, L; Umans, L; Schrijvers, V; Checler, F; Vanderstichele, H; Baekelandt, V; Dressel, R; Cupers, P; Huylebroeck, D; Zwijsen, A; Van Leuven, F; De Strooper, B 1999-10-12 Mutations in the homologous presenilin 1 (PS1) and presenilin 2 (PS2) genes cause the most common and aggressive form of familial Alzheimer's disease. Although PS1 function and dysfunction have been extensively studied, little is known about the function of PS2 in vivo. To delineate the relationships of PS2 and PS1 activities and whether PS2 mutations involve gain or loss of function, we generated PS2 homozygous deficient (-/-) and PS1/PS2 double homozygous deficient mice. In contrast to PS1(-/-) mice, PS2(-/-) mice are viable and fertile and develop only mild pulmonary fibrosis and hemorrhage with age. Absence of PS2 does not detectably alter processing of amyloid precursor protein and has little or no effect on physiologically important apoptotic processes, indicating that Alzheimer's disease-causing mutations in PS2, as in PS1, result in gain of function. Although PS1(+/-) PS2( -/-) mice survive in relatively good health, complete deletion of both PS2 and PS1 genes causes a phenotype closely resembling full Notch-1 deficiency. These results demonstrate in vivo that PS1 and PS2 have partially overlapping functions and that PS1 is essential and PS2 is redundant for normal Notch signaling during mammalian embryological development. 10. Structural Characterization of the E2 Domain of APL-1, a C. Elegans Homolog of Human Amyloid Precursor Protein, and its Heparin Binding Site Energy Technology Data Exchange (ETDEWEB) Hoopes, J.; Liu, X; Xu, X; Demeler, B; Folta-Stogniew, E; Li, C; Ha, Y 2010-01-01 The amyloid {beta}-peptide deposit found in the brain tissue of patients with Alzheimer disease is derived from a large heparin-binding protein precursor APP. The biological function of APP and its homologs is not precisely known. Here we report the x-ray structure of the E2 domain of APL-1, an APP homolog in Caenorhabditis elegans, and compare it to the human APP structure. We also describe the structure of APL-1 E2 in complex with sucrose octasulfate, a highly negatively charged disaccharide, which reveals an unexpected binding pocket between the two halves of E2. Based on the crystal structure, we are able to map, using site-directed mutagenesis, a surface groove on E2 to which heparin may bind. Our biochemical data also indicate that the affinity of E2 for heparin is influenced by pH: at pH 5, the binding appears to be much stronger than that at neutral pH. This property is likely caused by histidine residues in the vicinity of the mapped heparin binding site and could be important for the proposed adhesive function of APL-1. 11. β-Amyloid precursor protein-b is essential for Mauthner cell development in the zebrafish in a Notch-dependent manner. Science.gov (United States) Banote, Rakesh Kumar; Edling, Malin; Eliassen, Fredrik; Kettunen, Petronella; Zetterberg, Henrik; Abramsson, Alexandra 2016-05-01 Amyloid precursor protein (APP) is a transmembrane glycoprotein that has been the subject of intense research because of its implication in Alzheimer's disease. However, the physiological function of APP in the development and maintenance of the central nervous system remains largely unknown. We have previously shown that the APP homologue in zebrafish (Danio rerio), Appb, is required for motor neuron patterning and formation. Here we study the function of Appb during neurogenesis in the zebrafish hindbrain. Partial knockdown of Appb using antisense morpholino oligonucleotides blocked the formation of the Mauthner neurons, uni- or bilaterally, with an aberrant behavior as a consequence of this cellular change. The Appb morphants had decreased neurogenesis, increased notch signaling and notch1a expression at the expense of deltaA/D expression. The Mauthner cell development could be restored either by a general decrease in Notch signaling through γ-secretase inhibition or by a partial knock down of Notch1a. Together, this demonstrates the importance of Appb in neurogenesis and for the first time shows the essential requirement of Appb in the formation of a specific cell type, the Mauthner cell, in the hindbrain during development. Our results suggest that Appb-regulated neurogenesis is mediated through balancing the Notch1a signaling pathway and provide new insights into the development of the Mauthner cell. 12. The spinal muscular atrophy with pontocerebellar hypoplasia gene VRK1 regulates neuronal migration through an amyloidprecursor protein-dependent mechanism. Science.gov (United States) Vinograd-Byk, Hadar; Sapir, Tamar; Cantarero, Lara; Lazo, Pedro A; Zeligson, Sharon; Lev, Dorit; Lerman-Sagie, Tally; Renbaum, Paul; Reiner, Orly; Levy-Lahad, Ephrat 2015-01-21 Spinal muscular atrophy with pontocerebellar hypoplasia (SMA-PCH) is an infantile SMA variant with additional manifestations, particularly severe microcephaly. We previously identified a nonsense mutation in Vaccinia-related kinase 1 (VRK1), R358X, as a cause of SMA-PCH. VRK1-R358X is a rare founder mutation in Ashkenazi Jews, and additional mutations in patients of different origins have recently been identified. VRK1 is a nuclear serine/threonine protein kinase known to play multiple roles in cellular proliferation, cell cycle regulation, and carcinogenesis. However, VRK1 was not known to have neuronal functions before its identification as a gene mutated in SMA-PCH. Here we show that VRK1-R358X homozygosity results in lack of VRK1 protein, and demonstrate a role for VRK1 in neuronal migration and neuronal stem cell proliferation. Using shRNA in utero electroporation in mice, we show that Vrk1 knockdown significantly impairs cortical neuronal migration, and affects the cell cycle of neuronal progenitors. Expression of wild-type human VRK1 rescues both proliferation and migration phenotypes. However, kinase-dead human VRK1 rescues only the migration impairment, suggesting the role of VRK1 in neuronal migration is partly noncatalytic. Furthermore, we found that VRK1 deficiency in human and mouse leads to downregulation of amyloidprecursor protein (APP), a known neuronal migration gene. APP overexpression rescues the phenotype caused by Vrk1 knockdown, suggesting that VRK1 affects neuronal migration through an APP-dependent mechanism. 13. O-GlcNAcylation promotes non-amyloidogenic processing of amyloidprotein precursor via inhibition of endocytosis from the plasma membrane. Science.gov (United States) Chun, Yoon Sun; Park, Yurim; Oh, Hyun Geun; Kim, Tae-Wan; Yang, Hyun Ok; Park, Myoung Kyu; Chung, Sungkwon 2015-01-01 Amyloidprotein precursor (AβPP) is transported to the plasma membrane, where it is sequentially cleaved by α-secretase and γ-secretase. This is called non-amyloidogenic pathway since it precludes the production of amyloid-β (Aβ), the main culprit of Alzheimer's disease (AD). Alternatively, once AβPP undergoes clathrin-dependent endocytosis, it can be sequentially cleaved by β-secretase and γ-secretase at endosomes, producing Aβ (amyloidogenic pathway). β-N-acetylglucosamine (GlcNAc) can be attached to serine/threonine residues of the target proteins. This novel type of O-linked glycosylation is called O-GlcNAcylation mediated by O-GlcNAc transferase (OGT). The removal of GlcNAc is mediated by O-GlcNAcase (OGN). Recently, it is shown that O-GlcNAcylation of AβPP increases the non-amyloidogenic pathway. To investigate the regulatory role for O-GlcNAcylation in AβPP processing, we first tested the effects of inhibitor for OGN, PUGNAc, on AβPP metabolism in HeLa cells stably transfected with Swedish mutant form of AβPP. Increasing O-GlcNAcylated AβPP level increased α-secretase product while decreased β-secretase products. We found that PUGNAc increased the trafficking rate of AβPP from the trans-Golgi network to the plasma membrane, and selectively decreased the endocytosis rate of AβPP. These events may contribute to the increased AβPP level in the plasma membrane by PUGNAc. Inhibiting clathrin-dependent endocytosis prevented the effect of PUGNAc on Aβ, suggesting that the effect of PUGNAc was mainly mediated by decreasing AβPP endocytosis. These results strongly indicate that O-GlcNAcylation promotes the plasma membrane localization of AβPP, which enhances the non-amyloidogenic processing of AβPP. Thus, O-GlcNAcylation of AβPP can be a potential therapeutic strategy for AD. 14. Development of transgenic rats producing human β-amyloid precursor protein as a model for Alzheimer's disease: Transgene and endogenous APP genes are regulated tissue-specifically Directory of Open Access Journals (Sweden) Chan Anthony WS 2008-02-01 15. Altered cell cycle-related gene expression in brain and lymphocytes from a transgenic mouse model of Alzheimer's disease [amyloid precursor protein/presenilin 1 (PS1)]. Science.gov (United States) Esteras, Noemí; Bartolomé, Fernando; Alquézar, Carolina; Antequera, Desireé; Muñoz, Úrsula; Carro, Eva; Martín-Requero, Ángeles 2012-09-01 Cumulative evidence indicates that aberrant re-expression of many cell cycle-related proteins and inappropriate neuronal cell cycle control are critical events in Alzheimer's disease (AD) pathogenesis. Evidence of cell cycle activation in post-mitotic neurons has also been observed in murine models of AD, despite the fact that most of these mice do not show massive loss of neuronal bodies. Dysfunction of the cell cycle appears to affect cells other than neurons, as peripheral cells, such as lymphocytes and fibroblasts from patients with AD, show an altered response to mitogenic stimulation. We sought to determine whether cell cycle disturbances are present simultaneously in both brain and peripheral cells from the amyloid precursor protein (APP)/presenilin 1 (PS1) mouse model of AD, in order to validate the use of peripheral cells from patients not only to study cell cycle abnormalities as a pathogenic feature of AD, but also as a means to test novel therapeutic approaches. By using cell cycle pathway-specific RT(2)Profiler™ PCR Arrays, we detected changes in a number of cell cycle-related genes in brain as well as in lymphocytes from APP/PS1 mice. Moreover, we found enhanced 5'-bromo-2'-deoxyuridine incorporation into DNA in lymphocytes from APP/PS1 mice, and increased expression of the cell proliferation marker proliferating cell nuclear antigen (PCNA), and the cyclin-dependent kinase (CDK) inhibitor Cdkn2a, as detected by immunohistochemistry in cortical neurons of the APP/PS1 mice. Taken together, the cell cycle-related changes in brain and blood cells reported here support the mitosis failure hypothesis in AD and validate the use of peripheral cells as surrogate tissue to study the molecular basis of AD pathogenesis. 16. Sequential NMR resonance assignment and structure determination of the Kunitz-type inhibitor domain of the Alzheimer's beta-amyloid precursor protein. Science.gov (United States) Heald, S L; Tilton, R F; Hammond, L J; Lee, A; Bayney, R M; Kamarck, M E; Ramabhadran, T V; Dreyer, R N; Davis, G; Unterbeck, A 1991-10-29 Certain precursor proteins (APP751 and APP770) of the amyloid beta-protein (AP) present in Alzheimer's disease contain a Kunitz-type serine protease inhibitor domain (APPI). In this study, the domain is obtained as a functional inhibitor through both recombinant (APPIr) and synthetic (APPIs) methodologies, and the solution structure of APPI is determined by 1H 2D NMR techniques. Complete sequence-specific resonance assignments (except for P13 and G37 NH) for both APPIr and APPIs are achieved using standard procedures. Ambiguities arising from degeneracies in the NMR resonances are resolved by varying sample conditions. Qualitative interpretation of short- and long-range NOEs reveals secondary structural features similar to those extensively documented by NMR for bovine pancreatic trypsin inhibitor (BPTI). A more rigorous interpretation of the NOESY spectra yields NOE-derived interresidue distance restraints which are used in conjunction with dynamic simulated annealing to generate a family of APPI structures. Within this family, the beta-sheet and helical regions are in good agreement with the crystal structure of BPTI, whereas portions of the protease-binding loops deviate from those in BPTI. These deviations are consistent with those recently described in the crystal structure of APPI (Hynes et al., 1990). Also supported in the NMR study is the hydrophobic patch in the protease-binding domain created by side chain-side chain NOE contacts between M17 and F34. In addition, the NMR spectra indicate that the rotation of the W21 ring in APPI is hindered, unlike Y21 in BPTI, showing a greater than 90% preference for one orientation in the hydrophobic groove. 17. Effects of long-term estrogen replacement therapy on beta-amyloid precursor protein and mRNA expression in ovariectomized rat hippocampus Institute of Scientific and Technical Information of China (English) Bo Jiang; Eryuan Liao; Liming Tan; Ruchun Dai; Zhijie Xiao 2009-01-01 BACKGROUND: In vitro cultures of neural stem cells have shown that estrogen can regulate beta-amyloid precursor protein (β-APP) metabolism and reduce amyloid-beta production.OBJECTIVE: To investigate the effects of long-term oral administration of compound nylestriol or low-dose 17beta-estradiol on β-APP and mRNA expression in the hippocampus of ovariectomized (OVX) rats. DESIGN, TIME AND SETTING: This randomized and controlled experiment was performed at the Animal Laboratory and Laboratory of Endocrine and Metabolic Disease, Xiangya Second Hospital of Central South University between April 2003 and May 2004.MATERIALS: According to body mass, 50 six-month-old female Sprague-Dawley rats were randomly divided into five groups (n = 10 per group): normal control, sham operation, OVX model, 17beta-estradiol (Sigma, USA), and compound nylestriol tablet (Laboratory of Endocrine and Metabolic Disease, Xiangya Second Hospital of Central South University) groups.METHODS: Rats in OVX plus 17beta-estradiol and OVX plus compound nylestriol tablet groups underwent ovariectomy. On the second day after surgery, rats were intragastrically given 17beta-estradiol (100 μg/kg), once per day or compound nylestriol tablet (0.5 mg/kg) and levonorgestrel (0.15 mg/kg) every 2 days.MAIN OUTCOME MEASURES: β-APP expression in the hippocampus of OVX rats was determined using immunohistochemistry (SABC method) and β-APP mRNA expression was analyzed by in situ hybridization. The results were quantitatively analyzed using cell counting and average optical density. RESULTS: The number and optical density of β-APP-positive neurons in every subregion of the hippocampus of OVX rats was dramatically increased compared with normal and sham operation groups following 35 weeks of administration (P < 0.05). Levels of β-APP were decreased following oral administration of compound nylestriol or 17beta-estradiol. In situ hybridization showed that long-term estrogen deficiency and oral administration 18. Mechanistic pharmacokinetic-pharmacodynamic modeling of BACE1 inhibition in monkeys: development of a predictive model for amyloid precursor protein processing. Science.gov (United States) Liu, Xingrong; Wong, Harvey; Scearce-Levie, Kimberly; Watts, Ryan J; Coraggio, Melis; Shin, Young G; Peng, Kun; Wildsmith, Kristin R; Atwal, Jasvinder K; Mango, Jason; Schauer, Stephen P; Regal, Kelly; Hunt, Kevin W; Thomas, Allen A; Siu, Michael; Lyssikatos, Joseph; Deshmukh, Gauri; Hop, Cornelis E C A 2013-07-01 This study was conducted to determine the pharmacokinetics (PK) and pharmacodynamics (PD) of two novel inhibitors of β-site amyloid precursor protein (APP)-cleaving enzyme (BACE1), GNE-629 [(4S,4a'S,10a'S)-2-amino-8'-(2-fluoropyridin-3-yl)-1-methyl-3',4',4a',10a'-tetrahydro-1'H-spiro[imidazole-4,10'-pyrano[4,3-b]chromen]-5(1H)-one] and GNE-892 [(R)-2-amino-1,3',3'-trimethyl-7'-(pyrimidin-5-yl)-3',4'-dihydro-2'H-spiro[imidazole-4,1'-naphthalen]-5(1H)-one], and to develop a PK-PD model to predict in vivo effects based solely on in vitro activity and PK. GNE-629 and GNE-892 concentrations and PD biomarkers including amyloid β (Aβ) in the plasma and cerebrospinal fluid (CSF), and secreted APPβ (sAPPβ) and secreted APPα (sAPPα) in the CSF were measured after a single oral administration of GNE-629 (100 mg/kg) or GNE-892 (30 or 100 mg/kg) in cynomolgus monkeys. A mechanistic PK-PD model was developed to simultaneously characterize the plasma Aβ and CSF Aβ, sAPPα, and sAPPβ using GNE-629 in vivo data. This model was used to predict the in vivo effects of GNE-892 after adjustments based on differences in in vitro cellular activity and PK. The PK-PD model estimated GNE-629 CSF and free plasma IC₅₀ of 0.0033 μM and 0.065 μM, respectively. These differences in CSF and free plasma IC₅₀ suggest that different mechanisms are involved in Aβ formation in these two compartments. The predicted in vivo effects for GNE-892 using the PK-PD model were consistent with the observed data. In conclusion, a PK-PD model was developed to mechanistically describe the effects of BACE1 inhibition on Aβ, sAPPβ, and sAPPα in the CSF, and Aβ in the plasma. This model can be used to prospectively predict in vivo effects of new BACE1 inhibitors using just their in vitro activity and PK data. 19. Phosphorylation of amyloid precursor protein at threonine 668 is essential for its copper-responsive trafficking in SH-SY5Y neuroblastoma cells. Science.gov (United States) Acevedo, Karla M; Opazo, Carlos M; Norrish, David; Challis, Leesa M; Li, Qiao-Xin; White, Anthony R; Bush, Ashley I; Camakaris, James 2014-04-18 Amyloid precursor protein (APP) undergoes post-translational modification, including O- and N-glycosylation, ubiquitination, and phosphorylation as it traffics through the secretory pathway. We have previously reported that copper promotes a change in the cellular localization of APP. We now report that copper increases the phosphorylation of endogenous APP at threonine 668 (Thr-668) in SH-SY5Y neuronal cells. The level of APPT668-p (detected using a phospho-site-specific antibody) exhibited a copper-dependent increase. Using confocal microscopy imaging we demonstrate that the phospho-deficient mutant, Thr-668 to alanine (T668A), does not exhibit detectable copper-responsive APP trafficking. In contrast, mutating a serine to an alanine at residue 655 does not affect copper-responsive trafficking. We further investigated the importance of the Thr-668 residue in copper-responsive trafficking by treating SH-SY5Y cells with inhibitors for glycogen synthase kinase 3-β (GSK3β) and cyclin-dependent kinases (Cdk), the main kinases that phosphorylate APP at Thr-668 in neurons. Our results show that the GSK3β kinase inhibitors LiCl, SB 216763, and SB 415286 prevent copper-responsive APP trafficking. In contrast, the Cdk inhibitors Purvalanol A and B had no significant effect on copper-responsive trafficking in SH-SY5Y cells. In cultured primary hippocampal neurons, copper promoted APP re-localization to the axon, and this effect was inhibited by the addition of LiCl, indicating that a lithium-sensitive kinase(s) is involved in copper-responsive trafficking in hippocampal neurons. This is consistent with APP axonal transport to the synapse, where APP is involved in a number of functions. We conclude that copper promotes APP trafficking by promoting a GSK3β-dependent phosphorylation in SH-SY5Y cells. 20. Increased secreted amyloid precursor protein-α (sAPPα in severe autism: proposal of a specific, anabolic pathway and putative biomarker. Directory of Open Access Journals (Sweden) Balmiki Ray Full Text Available Autism is a neurodevelopmental disorder characterized by deficits in verbal communication, social interactions, and the presence of repetitive, stereotyped and compulsive behaviors. Excessive early brain growth is found commonly in some patients and may contribute to disease phenotype. Reports of increased levels of brain-derived neurotrophic factor (BDNF and other neurotrophic-like factors in autistic neonates suggest that enhanced anabolic activity in CNS mediates this overgrowth effect. We have shown previously that in a subset of patients with severe autism and aggression, plasma levels of the secreted amyloid-β (Aβ precursor protein-alpha form (sAPPα were significantly elevated relative to controls and patients with mild-to-moderate autism. Here we further tested the hypothesis that levels of sAPPα and sAPPβ (proteolytic cleavage products of APP by α- and β-secretase, respectively are deranged in autism and may contribute to an anabolic environment leading to brain overgrowth. We measured plasma levels of sAPPα, sAPPβ, Aβ peptides and BDNF by corresponding ELISA in a well characterized set of subjects. We included for analysis 18 control, 6 mild-to-moderate, and 15 severely autistic patient plasma samples. We have observed that sAPPα levels are increased and BDNF levels decreased in the plasma of patients with severe autism as compared to controls. Further, we show that Aβ1-40, Aβ1-42, and sAPPβ levels are significantly decreased in the plasma of patients with severe autism. These findings do not extend to patients with mild-to-moderate autism, providing a biochemical correlate of phenotypic severity. Taken together, this study provides evidence that sAPPα levels are generally elevated in severe autism and suggests that these patients may have aberrant non-amyloidogenic processing of APP. 1. Retromer Binds the FANSHY Sorting Motif in SorLA to Regulate Amyloid Precursor Protein Sorting and Processing DEFF Research Database (Denmark) Fjorback, Anja W; Seaman, Matthew; Gustafsen, Camilla; 2012-01-01 and levels of retromer proteins are altered in AD. Here we report that sorLA and retromer functionally interact in neurons to control trafficking and amyloidogenic processing of APP. We have identified a sequence (FANSHY) in the cytoplasmic domain of sorLA that is recognized by the VPS26 subunit... 2. Porcine prion protein amyloid. Science.gov (United States) Hammarström, Per; Nyström, Sofie 2015-01-01 Mammalian prions are composed of misfolded aggregated prion protein (PrP) with amyloid-like features. Prions are zoonotic disease agents that infect a wide variety of mammalian species including humans. Mammals and by-products thereof which are frequently encountered in daily life are most important for human health. It is established that bovine prions (BSE) can infect humans while there is no such evidence for any other prion susceptible species in the human food chain (sheep, goat, elk, deer) and largely prion resistant species (pig) or susceptible and resistant pets (cat and dogs, respectively). PrPs from these species have been characterized using biochemistry, biophysics and neurobiology. Recently we studied PrPs from several mammals in vitro and found evidence for generic amyloidogenicity as well as cross-seeding fibril formation activity of all PrPs on the human PrP sequence regardless if the original species was resistant or susceptible to prion disease. Porcine PrP amyloidogenicity was among the studied. Experimentally inoculated pigs as well as transgenic mouse lines overexpressing porcine PrP have, in the past, been used to investigate the possibility of prion transmission in pigs. The pig is a species with extraordinarily wide use within human daily life with over a billion pigs harvested for human consumption each year. Here we discuss the possibility that the largely prion disease resistant pig can be a clinically silent carrier of replicating prions. 3. The Golgi-Localized γ-Ear-Containing ARF-Binding (GGA Proteins Alter AmyloidPrecursor Protein (APP Processing through Interaction of Their GAE Domain with the Beta-Site APP Cleaving Enzyme 1 (BACE1. Directory of Open Access Journals (Sweden) Bjoern von Einem Full Text Available Proteolytic processing of amyloidprecursor protein (APP by beta-site APP cleaving enzyme 1 (BACE1 is the initial step in the production of amyloid beta (Aβ, which accumulates in senile plaques in Alzheimer's disease (AD. Essential for this cleavage is the transport and sorting of both proteins through endosomal/Golgi compartments. Golgi-localized γ-ear-containing ARF-binding (GGA proteins have striking cargo-sorting functions in these pathways. Recently, GGA1 and GGA3 were shown to interact with BACE1, to be expressed in neurons, and to be decreased in AD brain, whereas little is known about GGA2. Since GGA1 impacts Aβ generation by confining APP to the Golgi and perinuclear compartments, we tested whether all GGAs modulate BACE1 and APP transport and processing. We observed decreased levels of secreted APP alpha (sAPPα, sAPPβ, and Aβ upon GGA overexpression, which could be reverted by knockdown. GGA-BACE1 co-immunoprecipitation was impaired upon GGA-GAE but not VHS domain deletion. Autoinhibition of the GGA1-VHS domain was irrelevant for BACE1 interaction. Our data suggest that all three GGAs affect APP processing via the GGA-GAE domain. 4. Repeated administration of the noradrenergic neurotoxin N-(2-chloroethyl-N-ethyl-2-bromobenzylamine (DSP-4 modulates neuroinflammation and amyloid plaque load in mice bearing amyloid precursor protein and presenilin-1 mutant transgenes Directory of Open Access Journals (Sweden) Richardson Jill C 2007-02-01 Full Text Available Abstract Background Data indicates anti-oxidant, anti-inflammatory and pro-cognitive properties of noradrenaline and analyses of post-mortem brain of Alzheimer's disease (AD patients reveal major neuronal loss in the noradrenergic locus coeruleus (LC, the main source of CNS noradrenaline (NA. The LC has projections to brain regions vulnerable to amyloid deposition and lack of LC derived NA could play a role in the progression of neuroinflammation in AD. Previous studies reveal that intraperitoneal (IP injection of the noradrenergic neurotoxin N-(2-chloroethyl-N-ethyl-2-bromobenzylamine (DSP-4 can modulate neuroinflammation in amyloid over-expressing mice and in one study, DSP-4 exacerbated existing neurodegeneration. Methods TASTPM mice over-express human APP and beta amyloid protein and show age related cognitive decline and neuroinflammation. In the present studies, 5 month old C57/BL6 and TASTPM mice were injected once monthly for 6 months with a low dose of DSP-4 (5 mg kg-1 or vehicle. At 8 and 11 months of age, mice were tested for cognitive ability and brains were examined for amyloid load and neuroinflammation. Results At 8 months of age there was no difference in LC tyrosine hydroxylase (TH across all groups and cortical NA levels of TASTPM/DSP-4, WT/Vehicle and WT/DSP-4 were similar. NA levels were lowest in TASTPM/Vehicle. Messenger ribonucleic acid (mRNA for various inflammatory markers were significantly increased in TASTPM/Vehicle compared with WT/Vehicle and by 8 months of age DSP-4 treatment modified this by reducing the levels of some of these markers in TASTPM. TASTPM/Vehicle showed increased astrocytosis and a significantly larger area of cortical amyloid plaque compared with TASTPM/DSP-4. However, by 11 months, NA levels were lowest in TASTPM/DSP-4 and there was a significant reduction in LC TH of TASTPM/DSP-4 only. Both TASTPM groups had comparable levels of amyloid, microglial activation and astrocytosis and mRNA for 5. Amyloid Precursor Protein (APP) May Act as a Substrate and a Recognition Unit for CRL4CRBN and Stub1 E3 Ligases Facilitating Ubiquitination of Proteins Involved in Presynaptic Functions and Neurodegeneration. Science.gov (United States) 2016-08-12 The amyloid precursor protein (APP), whose mutations cause Alzheimer disease, plays an important in vivo role and facilitates transmitter release. Because the APP cytosolic region (ACR) is essential for these functions, we have characterized its brain interactome. We found that the ACR interacts with proteins that regulate the ubiquitin-proteasome system, predominantly with the E3 ubiquitin-protein ligases Stub1, which binds the NH2 terminus of the ACR, and CRL4(CRBN), which is formed by Cul4a/b, Ddb1, and Crbn, and interacts with the COOH terminus of the ACR via Crbn. APP shares essential functions with APP-like protein-2 (APLP2) but not APP-like protein-1 (APLP1). Noteworthy, APLP2, but not APLP1, interacts with Stub1 and CRL4(CRBN), pointing to a functional pathway shared only by APP and APLP2. In vitro ubiquitination/ubiquitome analysis indicates that these E3 ligases are enzymatically active and ubiquitinate the ACR residues Lys(649/650/651/676/688) Deletion of Crbn reduces ubiquitination of Lys(676) suggesting that Lys(676) is physiologically ubiquitinated by CRL4(CRBN) The ACR facilitated in vitro ubiquitination of presynaptic proteins that regulate exocytosis, suggesting a mechanism by which APP tunes transmitter release. Other dementia-related proteins, namely Tau and apoE, interact with and are ubiquitinated via the ACR in vitro This, and the evidence that CRBN and CUL4B are linked to intellectual disability, prompts us to hypothesize a pathogenic mechanism, in which APP acts as a modulator of E3 ubiquitin-protein ligase(s), shared by distinct neuronal disorders. The well described accumulation of ubiquitinated protein inclusions in neurodegenerative diseases and the link between the ubiquitin-proteasome system and neurodegeneration make this concept plausible. 6. 外源性H2S通过调节β-位淀粉样前体蛋白裂解酶1表达对PC12细胞APP/Ap代谢的影响%Effect of Exogenous Hydrogen Sulfide on Amyloid Precursor Protein/β-amyloid Processing Through Regulating Expression of β-site Amyloid Precursor Protein Cleaving Enzyme 1 in Pheochromocytoma Cells Institute of Scientific and Technical Information of China (English) 代政伟; 孟涛; 晏勇 2011-01-01 目的观察外源性硫化氮对啥格细胞瘤细胞p一位淀粉样前体蛋白裂解酶1(BACE1)的调节作用,进而探讨其对淀粉样前体蛋白/β-位淀粉样蛋白代谢途径的影响.方法用硫氮化钠作外源性HZS供体,实脸设空白对照组、NaHS 50 μmol/L组、NaHS 100μmol/L组和NaHS 200 μmol/L组,按分组浓度处理PC12细胞24 h后,RT-PCR和Western blot法检测细胞内BACEI mRNA及蛋白表达,并用Western blot法继而检测APP代谢过程中关健蛋白APP,C99,C83表达变化,ELISA法检浏细胞培养液中Aβ40和Aβ42水平.结果 NaHS在实脸浓度范围内从基因与蛋白两个水平上呈剂量依赖性下调BACEI表达,并下调C99,Aβ40和Aβ42蛋白表达,上调C83蛋白,各NaHS组分别与对照组比校,差别均有统计学意义(P0.05).结论外源性HZS具有通过调节PC12细胞BACEI表达下调APP/Ap代谢的作用.%Objective To observe the effect of exogenous hydrogen sulfide on β-site amyioid precursor protein cleaving enzyme 1 ( BACE1 ) and the amyloid precursor protein/β-amyloid (APP/Aβ) processing in pheochromocytoma (PC12) cells. Methods PC12 cells were divided into 4 groups:blank control group,NaHS 50 μmol/L group, NaHS100 μmol/L group and NaHS 200 .μmol/L group. Four groups were treated with 0,50,100 or 200 μmol/L sodium hydrosulfide( NaHS, the homer of exogenous hydrogen sulfide ), respectively. RT-PCR and Western blot were used to detect the levels of BACE1 mRNA and protein expression. Western blot was also used to detect the levels of key proteins in the metabolic process of APP,including APP,C99 and C83. ELISA method was used to analyze the levels of Aβ40 and Aβ42 in cellular culture medium. Results Compared with blank control group, NaHS significantly and dose-dependently decreased BACE1 mRNA and protein expression within experimental concentration rages in NaHS groups. So did the C99, Aβ40 and Aβ42 proteins( all P ＜ 0. 05 ). On the contrary, C83 protein significantly increased 7. Activation of the Wnt/β-catenin pathway represses the transcription of the β-amyloid precursor protein cleaving enzyme (BACE1) via binding of T-cell factor-4 to BACE1 promoter. Science.gov (United States) Parr, Callum; Mirzaei, Nazanin; Christian, Mark; Sastre, Magdalena 2015-02-01 Alterations in the Wnt signaling pathway have been implicated in Alzheimer's disease; however, its role in the processing of the amyloid precursor protein remains unknown. In this study, activation of the Wnt pathway by overexpression of the agonist Wnt3a or β-catenin or by inhibition of glycogen kinase synthase-3 in N2a cells resulted in a reduction in Aβ levels and in the activity and expression of BACE1 (β-APP cleaving enzyme). Conversely, inhibition of the pathway by transfection of the antagonists secreted frizzled receptor protein-1 or dickkopf-1 produced the opposite effects. Chromatin immunoprecipitation analysis demonstrated that β-catenin binds specifically to regions within the promoter of BACE1 containing putative T-cell factor/lymphoid enhancer binding factor-1 (TCF/LEF) motifs, consistent with canonical Wnt target regulation. Furthermore, cells transfected with β-catenin mutants incapable of binding to TCF/LEF increased BACE1 gene promoter activity. Interestingly, TCF4 knockdown reversed the effects of Wnt3a activation on BACE1 transcription. We found that TCF4 binds to the same region on BACE1 promoter following Wnt3a stimulation, indicating that TCF4 functions as a transcriptional repressor of BACE1 gene. In conclusion, Wnt/β-catenin stimulation may repress BACE1 transcription via binding of TCF4 to BACE1 gene, and therefore, activation of the Wnt pathway may hold the key to new treatments of Alzheimer disease.-Parr, C., Mirzaei, N., Christian, M., and Sastre, M. Activation of the Wnt/β-catenin pathway represses the transcription of the β-amyloid precursor protein cleaving enzyme (BACE1) via binding of T-cell factor-4 to BACE1 promoter. 8. Effects of Gingko biloba leaf extract on learning, memory, and hippocampal amyloid precursor protein mRNA expressions in diabetic rats Institute of Scientific and Technical Information of China (English) Xiaofan Zhang; Bo Liang; Zhifeng Liang; Jun Lin 2008-01-01 BACKGROUND: The mechanisms of brain injury Following diabetes could be related to amyloid precursor protein (APP) mRNA overexpression. Studies have shown that Gingko biloba leaf extract (Egb) is effective in promoting functional recovery of the brain after traumatic injury. Egb is also effective in improving central nervous system plasticity and learning and memory functions of the elderly.OBJECTIVE: To study the effects of Egb on learning and memory, as well as hippocampal APP mRNA expression in the brains of diabetic rats, using Morris water maze behavioral testing and reverse transcription polymerase chain reaction (RT-PCR), respectively.DESIGN: Complete random design, controlled experimental study.SETTING: Department of Pharmacology, Pharmaceutical School, Guangxi Medical University.MATERIALS: A total of 70 male Wistar rats (180-220 g), 8 weeks old and specific pathogen free, were used for this study. GbE (containing 24.8% flavone glycosides and 6.2% diterpene lactone) was purchased from Guilin Sitejia Natural Plants Pharmaceutical Factory (Guangxi Province, Lot NO. 200405). Streptozotocin was purchased from Sigma (USA). Protamine zinc insulin injection was purchased from WANBANG Biochemical Pharmaceutical Co., Ltd. (Xuzhou Jiangsu, China).METHODS: The experiment was performed in the Experimental Center of Guangxi Medical University from March to October 2005. ① Experimental intervention: 70 rats were divided randomly into normal control group, diabetic model group (DM group), diabetic model +10 μg/kg insulin group (DM + Ins group), diabetic model + 100 mg/kg ginkgo leaf extract group (DM + Egb high-dose group), and diabetic model + 50 mg/kg ginkgo leaf extract group (DM + Egb low-dose group); there were 14 rats in each group. Rats with an intraperitoneal (I.p.) injection of citrate buffer solution (pH 4.4) served as the control group. To establish the diabetes model, rats were treated with I.p. Injection of 55 mg/kg streptozotocin. Insulin (10 U/kg) was 9. PuF, an antimetastatic and developmental signaling protein, interacts with the Alzheimer’s amyloidprecursor protein via a tissue-specific proximal regulatory element (PRE Directory of Open Access Journals (Sweden) Lahiri Debomoy K 2013-01-01 Full Text Available Abstract Background Alzheimer’s disease (AD is intimately tied to amyloid-β (Aβ peptide. Extraneuronal brain plaques consisting primarily of Aβ aggregates are a hallmark of AD. Intraneuronal Aβ subunits are strongly implicated in disease progression. Protein sequence mutations of the Aβ precursor protein (APP account for a small proportion of AD cases, suggesting that regulation of the associated gene (APP may play a more important role in AD etiology. The APP promoter possesses a novel 30 nucleotide sequence, or “proximal regulatory element” (PRE, at −76/−47, from the +1 transcription start site that confers cell type specificity. This PRE contains sequences that make it vulnerable to epigenetic modification and may present a viable target for drug studies. We examined PRE-nuclear protein interaction by gel electrophoretic mobility shift assay (EMSA and PRE mutant EMSA. This was followed by functional studies of PRE mutant/reporter gene fusion clones. Results EMSA probed with the PRE showed DNA-protein interaction in multiple nuclear extracts and in human brain tissue nuclear extract in a tissue-type specific manner. We identified transcription factors that are likely to bind the PRE, using competition gel shift and gel supershift: Activator protein 2 (AP2, nm23 nucleoside diphosphate kinase/metastatic inhibitory protein (PuF, and specificity protein 1 (SP1. These sites crossed a known single nucleotide polymorphism (SNP. EMSA with PRE mutants and promoter/reporter clone transfection analysis further implicated PuF in cells and extracts. Functional assays of mutant/reporter clone transfections were evaluated by ELISA of reporter protein levels. EMSA and ELISA results correlated by meta-analysis. Conclusions We propose that PuF may regulate the APP gene promoter and that AD risk may be increased by interference with PuF regulation at the PRE. PuF is targeted by calcium/calmodulin-dependent protein kinase II inhibitor 1, which also 10. Alcadein cleavages by amyloid beta-precursor protein (APP) alpha- and gamma-secretases generate small peptides, p3-Alcs, indicating Alzheimer disease-related gamma-secretase dysfunction. Science.gov (United States) Hata, Saori; Fujishige, Sayaka; Araki, Yoichi; Kato, Naoko; Araseki, Masahiko; Nishimura, Masaki; Hartmann, Dieter; Saftig, Paul; Fahrenholz, Falk; Taniguchi, Miyako; Urakami, Katsuya; Akatsu, Hiroyasu; Martins, Ralph N; Yamamoto, Kazuo; Maeda, Masahiro; Yamamoto, Tohru; Nakaya, Tadashi; Gandy, Sam; Suzuki, Toshiharu 2009-12-25 Alcadeins (Alcs) constitute a family of neuronal type I membrane proteins, designated Alc(alpha), Alc(beta), and Alc(gamma). The Alcs express in neurons dominantly and largely colocalize with the Alzheimer amyloid precursor protein (APP) in the brain. Alcs and APP show an identical function as a cargo receptor of kinesin-1. Moreover, proteolytic processing of Alc proteins appears highly similar to that of APP. We found that APP alpha-secretases ADAM 10 and ADAM 17 primarily cleave Alc proteins and trigger the subsequent secondary intramembranous cleavage of Alc C-terminal fragments by a presenilin-dependent gamma-secretase complex, thereby generating "APP p3-like" and non-aggregative Alc peptides (p3-Alcs). We determined the complete amino acid sequence of p3-Alc(alpha), p3-Alc(beta), and p3-Alc(gamma), whose major species comprise 35, 37, and 31 amino acids, respectively, in human cerebrospinal fluid. We demonstrate here that variant p3-Alc C termini are modulated by FAD-linked presenilin 1 mutations increasing minor beta-amyloid species Abeta42, and these mutations alter the level of minor p3-Alc species. However, the magnitudes of C-terminal alteration of p3-Alc(alpha), p3-Alc(beta), and p3-Alc(gamma) were not equivalent, suggesting that one type of gamma-secretase dysfunction does not appear in the phenotype equivalently in the cleavage of type I membrane proteins. Because these C-terminal alterations are detectable in human cerebrospinal fluid, the use of a substrate panel, including Alcs and APP, may be effective to detect gamma-secretase dysfunction in the prepathogenic state of Alzheimer disease subjects. 11. Protein Polymers and Amyloids DEFF Research Database (Denmark) Risør, Michael Wulff 2014-01-01 , underlining the importance of understanding this relationship. The monomeric C-36 peptide was investigated by liquid-state NMR spectroscopy and found to be intrinsically disordered with minor propensities towards β-sheet structure. The plasticity of such a peptide makes it suitable for a whole range......, is a general hallmark. They also include the α1-antitrypsin deficiency, where disease-causing mutations in the serine protease inhibitor, α1-antitrypsin (α1AT), leads to accumulation of the aberrant protein in the liver of these patients. The native metastable structure of α1AT constitutes a molecular trap...... of this mechanism were investigated through a series of interaction experiments. Despite a very buried location in the native structure, evidence here suggest that the C-terminal tail is labile under slightly destabilizing conditions, providing new detail to this matter. A small infectious polymer unit was also... 12. Janus faces of amyloid proteins in neuroinflammation. Science.gov (United States) Steinman, Lawrence; Rothbard, Jonathan B; Kurnellas, Michael P 2014-07-01 Amyloid forming molecules are generally considered harmful. In Alzheimer's Disease two amyloid molecules Aβ A4 and tau vie for consideration as the main pathogenic culprit. But molecules obey the laws of chemistry and defy the way we categorize them as humans with our well-known proclivities to bias in our reasoning. We have been exploring the brains of multiple sclerosis patients to identify molecules that are associated with protection from inflammation and degeneration. In 2001 we noted that aB crystallin (cryab) was the most abundant transcript found in MS lesions, but not in healthy brains. Cryab can reverse paralysis and attenuate inflammation in several models of inflammation including experimental autoimmune encephalomyelitis (EAE), and various models of ischemia. Cryab is an amyloid forming molecule. We have identified a core structure common to many amyloids including amyloid protein Aβ A4, tau, amylin, prion protein, serum amyloid protein P, and cryab. The core hexapeptide structure is highly immune suppressive and can reverse paralysis in EAE when administered systemically. Administration of this amyloid forming hexapeptide quickly lowers inflammatory cytokines in plasma like IL-6 and IL-2. The hexapeptide bind a set of proinflammatory mediators in plasma, including acute phase reactants and complement components. The beneficial properties of amyloid forming hexapeptides provide a potential new therapeutic direction. These experiments indicate that amyloid forming molecules have Janus faces, providing unexpected benefit for neuroinflammatory conditions. 13. ApoER2 expression increases Aβ production while decreasing Amyloid Precursor Protein (APP endocytosis: Possible role in the partitioning of APP into lipid rafts and in the regulation of γ-secretase activity Directory of Open Access Journals (Sweden) Bu Guojun 2007-07-01 Full Text Available Abstract Background The generation of the amyloid-β peptide (Aβ through the proteolytic processing of the amyloid precursor protein (APP is a central event in the pathogenesis of Alzheimer's disease (AD. Recent studies highlight APP endocytosis and localization to lipid rafts as important events favoring amyloidogenic processing. However, the precise mechanisms underlying these events are poorly understood. ApoER2 is a member of the low density lipoprotein receptor (LDL-R family exhibiting slow endocytosis rate and a significant association with lipid rafts. Despite the important neurophysiological roles described for ApoER2, little is known regarding how ApoER2 regulates APP trafficking and processing. Results Here, we demonstrate that ApoER2 physically interacts and co-localizes with APP. Remarkably, we found that ApoER2 increases cell surface APP levels and APP association with lipid rafts. The increase of cell surface APP requires the presence of ApoER2 cytoplasmic domain and is a result of decreased APP internalization rate. Unexpectedly, ApoER2 expression correlated with a significant increase in Aβ production and reduced levels of APP-CTFs. The increased Aβ production was dependent on the integrity of the NPxY endocytosis motif of ApoER2. We also found that expression of ApoER2 increased APP association with lipid rafts and increased γ-secretase activity, both of which might contribute to increased Aβ production. Conclusion These findings show that ApoER2 negatively affects APP internalization. However, ApoER2 expression stimulates Aβ production by shifting the proportion of APP from the non-rafts to the raft membrane domains, thereby promoting β-secretase and γ-secretase mediated amyloidogenic processing and also by incrementing the activity of γ-secretase. 14. Repeated administration of the noradrenergic neurotoxin N-(2-chloroethyl)-N-ethyl-2-bromobenzylamine (DSP-4) modulates neuroinflammation and amyloid plaque load in mice bearing amyloid precursor protein and presenilin-1 mutant transgenes OpenAIRE Richardson Jill C; Virley David J; Babin Anna; Bate Simon T; Joyce Flora; Perren Marion J; Seymour Zoe; Culbert Ainsley A; Ashmeade Tracey; Vidgeon-Hart Martin P; Pugh Perdita L; Upton Neil; Sunter David 2007-01-01 Abstract Background Data indicates anti-oxidant, anti-inflammatory and pro-cognitive properties of noradrenaline and analyses of post-mortem brain of Alzheimer's disease (AD) patients reveal major neuronal loss in the noradrenergic locus coeruleus (LC), the main source of CNS noradrenaline (NA). The LC has projections to brain regions vulnerable to amyloid deposition and lack of LC derived NA could play a role in the progression of neuroinflammation in AD. Previous studies reveal that intrape... 15. Luteolin Isolated from the Medicinal Plant Elsholtzia rugulosa (Labiatae Prevents Copper-Mediated Toxicity in β-Amyloid Precursor Protein Swedish Mutation Overexpressing SH-SY5Y Cells Directory of Open Access Journals (Sweden) Guanhua Du 2011-03-01 Full Text Available Luteolin, a 3’,4’,5,7-tetrahydroxyflavone, is a plant flavonoid and pharmacologically active agent that has been isolated from several plant species. In the present study, the effects of luteolin obtained from the medicinal plant Elsholtzia rugulosa and the related mechanisms were examined in an Alzheimer's disease (AD cell model. In this model, copper was used to exacerbate the neurotoxicity in β-amyloid precursor protein Swedish mutation stably overexpressed SH-SY5Y cells (named “APPsw cells” for short. Based on this model, we demonstrated that luteolin increased cell viability, reduced intracellular ROS generation, enhanced the activity of SOD and reversed mitochondrial membrane potential dissipation. Inhibition of caspase-related apoptosis was consistently involved in the neuroprotection afforded by luteolin. Furthermore, it down-regulated the expression of AβPP and lowered the secretion of Aβ1-42. These results indicated that luteolin from the Elsholtzia rugulosa exerted neroprotective effects through mechanisms that decrease AβPP expression, lower Aβ secretion, regulate the redox imbalance, preserve mitochondrial function, and depress the caspase family-related apoptosis. 16. Oncogene K-Ras Affects the Processing of Amyloid Precursor Protein (APP) Through Regulating Its Phosphorylation at Thr668%原癌基因K-Ras调控APPThr668位点磷酸化及APP的切割 Institute of Scientific and Technical Information of China (English) 刘杨; 杨龙雨; 谢勇壮; 张弦; 许华曦; 张云武 2012-01-01 The expression of Ras is elevated during early stages of Alzheimer's disease. Here we investigated the effect of K-Ras on the processing of amyloid precursor protein (APP). The results showed that overexpression of K-Ras and its constitutively active mutant K-RasG12V could activate ERK1/2 and JNK pathways and induced phosphorylation of APP at"ftr668. While inhibition of the JNK pathway blocked the phosphorylation of APP. In addition, overexpression of K-Ras reduced the levels of sAPPf) and increased the levels of sAPPa but had no effect on the levels of AD AMI 0 and BACE1. Through biptin labeling experiment, we demonstrated that overexpression of K-Ras increased cell surface levels of APP without affecting the levels of tptal APP. Together, these results suggest that K-Ras can regulate APP phosphorylation and APP trafficking for its processing through the JNK pathway, implying that K-Ras may be a new target/pathway for regulating AD pathologies.%在阿尔茨海默症(Alzheimer's disease,AD)发病的早期,Ras蛋白所在的信号通路被激活,但具体作用机制还不清楚.探讨了K-Ras及其突变体K-RasG12V对淀粉样前体蛋白(amyloid precursor protein,APP)的剪切的影响.Western blot结果显示,过量表达K-Ras能够激活细胞外调节蛋白激酶1/2(extracellular signal-regulated kinase,ERK 1/2)、c-Jun氨基末端激酶(c-Jun N-terminal kinase,JNK)通路,并增加APP在Thr668的磷酸化;抑制JNK通路则阻断了K-Ras过表达所引起的APP Thr668磷酸化.此外,过表达K-Ras造成分泌到细胞外的sAPPα增加,而sAPPβ减少.通过生物素标记实验发现,过表达K-Ras使得APP在细胞膜上的定位增加,而细胞内APP总量没有改变.这些结果表明,过量表达K-Ras可以通过调控JNK的通路,增加APP在Thr668位点的磷酸化,造成APP在细胞膜上水平升高,导致APP向sAPPβ的切割减少,而向sAPPα的切割增加.提示K-Ras对APP切割的影响可能在AD的发病过程中起着一定的应激作用. 17. Alternative Selection of β-Site APP-Cleaving Enzyme 1 (BACE1) Cleavage Sites in Amyloid β-Protein Precursor (APP) Harboring Protective and Pathogenic Mutations within the Aβ Sequence. Science.gov (United States) Kimura, Ayano; Hata, Saori; Suzuki, Toshiharu 2016-11-11 β-Site APP-cleaving enzyme 1 (BACE1) cleaves amyloid β-protein precursor (APP) at the bond between Met(671) and Asp(672) (β-site) to generate the carboxyl-terminal fragment (CTFβ/C99). BACE1 also cleaves APP at another bond between Thr(681) and Gln(682) (β'-site), yielding CTFβ'/C89. Cleavage of CTFβ/C99 by γ-secretase generates Aβ(1-XX), whereas cleavage of CTFβ'/C89 generates Aβ(11-XX). Thus, β'-site cleavage by BACE1 is amyloidolytic rather than amyloidogenic. β' cleavage of mouse APP is more common than the corresponding cleavage of human APP. We found that the H684R substitution within human Aβ, which replaces the histidine in the human protein with the arginine found at the corresponding position in mouse, facilitated β' cleavage irrespective of the species origin of BACE1, thereby significantly increasing the level of Aβ(11-XX) and decreasing the level of Aβ(1-XX). Thus, amino acid substitutions within the Aβ sequence influenced the selectivity of alternative β- or β'-site cleavage of APP by BACE1. In familial Alzheimer's disease (FAD), the APP gene harbors pathogenic variations such as the Swedish (K670N/M671L), Leuven (E682K), and A673V mutations, all of which decrease Aβ(11-40) generation, whereas the protective Icelandic mutation (A673T) increases generation of Aβ(11-40). Thus, A673T promotes β' cleavage of APP and protects subjects against AD. In addition, CTFβ/C99 was cleaved by excess BACE1 activity to generate CTFβ'/C89, followed by Aβ(11-40), even if APP harbored pathogenic mutations. The resultant Aβ(11-40) was more metabolically labile in vivo than Aβ(1-40). Our analysis suggests that some FAD mutations in APP are amyloidogenic and/or amyloidolytic via selection of alternative BACE1 cleavage sites. 18. Serum amyloid A: an acute phase apolipoprotein and precursor of AA amyloid. Science.gov (United States) Marhaug, G; Dowton, S B 1994-08-01 Serum amyloid A is an acute phase protein complexed to HDL as an apoprotein. The molecular weight is 11.4-12.5 kDa in different species and the protein has from 104 to 112 amino acids, without or with an insertion of eight amino acids at position 72. The protein is very well conserved throughout evolution, indicating an important biological function. The N-terminal part of the molecule is hydrophobic and probably responsible for the lipid binding properties. The most conserved part is from position 38 to 52 and this part is therefore believed to be responsible for the until now unknown biological function. The protein is coded on chromosome 11p in man, and chromosome 7 in mice, and found in all mammals until now investigated, and also in the Peking duck. In the rat a truncated SAA mRNA has been demonstrated, but no equivalent serum protein has been reported. Acute phase SAA is first of all produced in hepatocytes after induction by cytokines, but extrahepatic expression of both acute phase and constitutive SAA proteins have been demonstrated. Several cytokines, first of all IL-1, IL-6 and TNF are involved in the induction of SAA synthesis, but the mutual importance of these cytokines seems to be cell-type specific and to vary in various experimental settings. The role of corticosteroids in SAA induction is somewhat confusing. In most in vitro studies corticosteroids show an enhancing or synergistic effect with cytokines on SAA production in cultured cell. However, in clinical studies and in vivo studies in animals an inhibitory effect of corticosteroids is evident, probably due to the all over anti-inflammatory effect of the drug. Until now no drug has been found that selectively inhibits SAA production by hepatocytes. Effective anti-inflammatory or antibacterial treatment is the only tool for reducing SAA concentration in serum and reducing the risk of developing secondary amyloidosis. The function of SAA is still unclear. Interesting theories, based on current 19. Protein misfolding, congophilia, oligomerization, and defective amyloid processing in preeclampsia. Science.gov (United States) Buhimschi, Irina A; Nayeri, Unzila A; Zhao, Guomao; Shook, Lydia L; Pensalfini, Anna; Funai, Edmund F; Bernstein, Ira M; Glabe, Charles G; Buhimschi, Catalin S 2014-07-16 Preeclampsia is a pregnancy-specific disorder of unknown etiology and a leading contributor to maternal and perinatal morbidity and mortality worldwide. Because there is no cure other than delivery, preeclampsia is the leading cause of iatrogenic preterm birth. We show that preeclampsia shares pathophysiologic features with recognized protein misfolding disorders. These features include urine congophilia (affinity for the amyloidophilic dye Congo red), affinity for conformational state-dependent antibodies, and dysregulation of prototype proteolytic enzymes involved in amyloid precursor protein (APP) processing. Assessment of global protein misfolding load in pregnancy based on urine congophilia (Congo red dot test) carries diagnostic and prognostic potential for preeclampsia. We used conformational state-dependent antibodies to demonstrate the presence of generic supramolecular assemblies (prefibrillar oligomers and annular protofibrils), which vary in quantitative and qualitative representation with preeclampsia severity. In the first attempt to characterize the preeclampsia misfoldome, we report that the urine congophilic material includes proteoforms of ceruloplasmin, immunoglobulin free light chains, SERPINA1, albumin, interferon-inducible protein 6-16, and Alzheimer's β-amyloid. The human placenta abundantly expresses APP along with prototype APP-processing enzymes, of which the α-secretase ADAM10, the β-secretases BACE1 and BACE2, and the γ-secretase presenilin-1 were all up-regulated in preeclampsia. The presence of β-amyloid aggregates in placentas of women with preeclampsia and fetal growth restriction further supports the notion that this condition should join the growing list of protein conformational disorders. If these aggregates play a pathophysiologic role, our findings may lead to treatment for preeclampsia. 20. Contrasting effects of nanoparticle-protein attraction on amyloid aggregation. Science.gov (United States) Radic, Slaven; Davis, Thomas P; Ke, Pu Chun; Ding, Feng 2015-01-01 Nanoparticles (NPs) have been experimentally found to either promote or inhibit amyloid aggregation of proteins, but the molecular mechanisms for such complex behaviors remain unknown. Using coarse-grained molecular dynamics simulations, we investigated the effects of varying the strength of nonspecific NP-protein attraction on amyloid aggregation of a model protein, the amyloid-beta peptide implicated in Alzheimer's disease. Specifically, with increasing NP-peptide attraction, amyloid aggregation on the NP surface was initially promoted due to increased local protein concentration on the surface and destabilization of the folded state. However, further increase of NP-peptide attraction decreased the stability of amyloid fibrils and reduced their lateral diffusion on the NP surface necessary for peptide conformational changes and self-association, thus prohibiting amyloid aggregation. Moreover, we found that the relative concentration between protein and NPs also played an important role in amyloid aggregation. With a high NP/protein ratio, NPs that intrinsically promote protein aggregation may display an inhibitive effect by depleting the proteins in solution while having a low concentration of the proteins on each NP's surface. Our coarse-grained molecular dynamics simulation study offers a molecular mechanism for delineating the contrasting and seemingly conflicting effects of NP-protein attraction on amyloid aggregation and highlights the potential of tailoring anti-aggregation nanomedicine against amyloid diseases. 1. Amyloid β-sheet mimics that antagonize protein aggregation and reduce amyloid toxicity Science.gov (United States) Cheng, Pin-Nan; Liu, Cong; Zhao, Minglei; Eisenberg, David; Nowick, James S. 2012-11-01 The amyloid protein aggregation associated with diseases such as Alzheimer's, Parkinson's and type II diabetes (among many others) features a bewildering variety of β-sheet-rich structures in transition from native proteins to ordered oligomers and fibres. The variation in the amino-acid sequences of the β-structures presents a challenge to developing a model system of β-sheets for the study of various amyloid aggregates. Here, we introduce a family of robust β-sheet macrocycles that can serve as a platform to display a variety of heptapeptide sequences from different amyloid proteins. We have tailored these amyloid β-sheet mimics (ABSMs) to antagonize the aggregation of various amyloid proteins, thereby reducing the toxicity of amyloid aggregates. We describe the structures and inhibitory properties of ABSMs containing amyloidogenic peptides from the amyloid-β peptide associated with Alzheimer's disease, β2-microglobulin associated with dialysis-related amyloidosis, α-synuclein associated with Parkinson's disease, islet amyloid polypeptide associated with type II diabetes, human and yeast prion proteins, and Tau, which forms neurofibrillary tangles. 2. Evaluación de la expresión de la proteína precursora de amiloide en células sanguíneas de pacientes con la mutación E280A en el gen de la presenilina 1 Alzheimer disease amyloid precursor protein e280a mutation flow cytometry presenilin Directory of Open Access Journals (Sweden) Francisco Lopera Restrepo 2005-01-01 development of an aggressive form of familial Alzheimer's disease. In order to define the role of such mutation on the expression of Amyloid Precursor Protein in peripheral blood mononuclear cells and B lymphocytes we carried out a study in three groups of people, namely: healthy carriers of the mutation, affected carriers and healthy non-carriers as controls. Flow cytometry was used for the detection of Amyloid Presursor Protein in cell membranes and intracellulary; HeLa and CHO cells were used as positive controls. Expression level of Amyloid Precursor Protein was higher in the intracellular compartment than in the cell membrane. The levels of expression in the intracellular compartment of HeLa and CHO cells were variable in contrast with those of peripheral blood mononuclear cells in which they were lower but stable. Contrariwise to the results of other authors, who have detected higher levels of Amyloid Precursor Protein in Alzheimer's disease patients, our results revealed no difference between healthy controls and carriers of the E280A mutation in the presenilin-1 gene, either diseased or healthy. Our results show that this mutation does not directly change the expression of Amyloid Precursor Protein in peripheral blood mononuclear cells. 3. Unraveling the mystery of protein-amyloid binding mechanisms NARCIS (Netherlands) Beringer, D. 2013-01-01 There are several diseases which are caused by amyloid, a deposit of aggregated protein. Examples of these diseases are Alzheimer’s disease, caused by the aggregation of the peptide Aβ, and Diabetes type 2, caused by hIAPP aggregates. A large number of proteins interact with these amyloid fibrils, s 4. The amyloid stretch hypothesis: Recruiting proteins toward the dark side Science.gov (United States) Esteras-Chopo, Alexandra; Serrano, Luis; de la Paz, Manuela López 2005-01-01 A detailed understanding of the molecular events underlying the conversion and self-association of normally soluble proteins into amyloid fibrils is fundamental to the identification of therapeutic strategies to prevent or cure amyloid-related disorders. Recent investigations indicate that amyloid fibril formation is not just a general property of the polypeptide backbone depending on external factors, but that it is strongly modulated by amino acid side chains. Here, we propose and address the validation of the premise that the amyloidogenicity of a protein is indeed localized in short protein stretches (amyloid stretch hypothesis). We demonstrate that the conversion of a soluble nonamyloidogenic protein into an amyloidogenic prone molecule can be triggered by a nondestabilizing six-residue amyloidogenic insertion in a particular structural environment. Interestingly enough, although the inserted amyloid sequences clearly cause the process, the protease-resistant core of the fiber also includes short adjacent sequences from the otherwise soluble globular domain. Thus, short amyloid stretches accessible for intermolecular interactions trigger the self-assembly reaction and pull the rest of the protein into the fibrillar aggregate. The reliable identification of such amyloidogenic stretches in proteins opens the possibility of using them as targets for the inhibition of the amyloid fibril formation process. PMID:16263932 5. Amyloid-like protein inclusions in tobacco transgenic plants. Directory of Open Access Journals (Sweden) Anna Villar-Piqué Full Text Available The formation of insoluble protein deposits in human tissues is linked to the onset of more than 40 different disorders, ranging from dementia to diabetes. In these diseases, the proteins usually self-assemble into ordered β-sheet enriched aggregates known as amyloid fibrils. Here we study the structure of the inclusions formed by maize transglutaminase (TGZ in the chloroplasts of tobacco transplastomic plants and demonstrate that they have an amyloid-like nature. Together with the evidence of amyloid structures in bacteria and fungi our data argue that amyloid formation is likely a ubiquitous process occurring across the different kingdoms of life. The discovery of amyloid conformations inside inclusions of genetically modified plants might have implications regarding their use for human applications. 6. SERF Protein Is a Direct Modifier of Amyloid Fiber Assembly Directory of Open Access Journals (Sweden) S. Fabio Falsone 2012-08-01 Full Text Available The inherent cytotoxicity of aberrantly folded protein aggregates contributes substantially to the pathogenesis of amyloid diseases. It was recently shown that a class of evolutionary conserved proteins, called MOAG-4/SERF, profoundly alter amyloid toxicity via an autonomous but yet unexplained mode. We show that the biological function of human SERF1a originates from its atypical ability to specifically distinguish between amyloid and nonamyloid aggregation. This inherently unstructured protein directly affected the aggregation kinetics of a broad range of amyloidogenic proteins in vitro, while being inactive against nonamyloid aggregation. A representative biophysical analysis of the SERF1a:α-synuclein (aSyn complex revealed that the amyloid-promoting activity resulted from an early and transient interaction, which was sufficient to provoke a massive increase of soluble aSyn amyloid nucleation templates. Therefore, the autonomous amyloid-modifying activity of SERF1a observed in living organisms relies on a direct and dedicated manipulation of the early stages in the amyloid aggregation pathway. 7. Hitchhiking vesicular transport routes to the vacuole: amyloid recruitment to the Insoluble Protein Deposit (IPOD). Science.gov (United States) Kumar, Rajesh; Neuser, Nicole; Tyedmers, Jens 2017-03-09 Sequestration of aggregates into specialized deposition sites occurs in many species across all kingdoms of life ranging from bacteria to mammals and is commonly believed to have a cytoprotective function. Yeast cells possess at least three different spatially separated deposition sites, one of which is termed "Insoluble Protein Deposit (IPOD)" and harbors amyloid aggregates. We have recently discovered that recruitment of amyloid aggregates to the IPOD employs an actin cable based recruitment machinery that also involves vesicular transport (1) . Here we discuss how different proteins known to be involved in vesicular transport processes to the vacuole might act to guide amyloid aggregates to the IPOD. These factors include the Myosin V motor protein Myo2 involved in transporting vacuolar vesicles along actin cables, the transmembrane protein Atg9 involved in the recruitment of large precursor hydrolase complexes to the vacuole, the phosphatidylinositol/ phosphatidylcholine (PI/PC) transfer protein Sec 14 and the SNARE chaperone Sec 18. Furthermore, we present new data suggesting that the yeast dynamin homolog Vps1 is also crucial for faithful delivery of the amyloid model protein PrD-GFP to the IPOD. This is in agreement with a previously identified role for Vps1 in recruitment of heat-denatured aggregates to a perivacuolar deposition site (2) . 8. A comparison of immunohistochemistry and mass spectrometry for determining the amyloid fibril protein from formalin-fixed biopsy tissue. Science.gov (United States) Gilbertson, Janet A; Theis, Jason D; Vrana, Julie A; Lachmann, Helen; Wechalekar, Ashutosh; Whelan, Carol; Hawkins, Philip N; Dogan, Ahmet; Gillmore, Julian D 2015-04-01 Amyloidosis is caused by deposition in tissues of abnormal protein in a characteristic fibrillar form. There are many types of amyloidosis, classified according to the soluble protein precursor from which the amyloid fibrils are derived. Accurate identification of amyloid type is critical in every case since therapy for systemic amyloidosis is type specific. In ∼20-25% cases, however, immunohistochemistry (IHC) fails to prove the amyloid type and further tests are required. Laser microdissection and mass spectrometry (LDMS) is a powerful tool for identifying proteins from formalin-fixed paraffin-embedded tissues. We undertook a blinded comparison of IHC, performed at the UK National Amyloidosis Centre, and LDMS, performed at the Mayo Clinic, in 142 consecutive biopsy specimens from 38 different tissue types. There was 100% concordance between positive IHC and LDMS, and the latter increased diagnostic accuracy from 76% to 94%. LDMS in expert hands is a valuable tool for amyloid diagnosis. 9. Amyloid diseases of yeast: prions are proteins acting as genes. Science.gov (United States) Wickner, Reed B; Edskes, Herman K; Bateman, David A; Kelly, Amy C; Gorkovskiy, Anton; Dayani, Yaron; Zhou, Albert 2014-01-01 The unusual genetic properties of the non-chromosomal genetic elements [URE3] and [PSI+] led to them being identified as prions (infectious proteins) of Ure2p and Sup35p respectively. Ure2p and Sup35p, and now several other proteins, can form amyloid, a linear ordered polymer of protein monomers, with a part of each molecule, the prion domain, forming the core of this β-sheet structure. Amyloid filaments passed to a new cell seed the conversion of the normal form of the protein into the same amyloid form. The cell's phenotype is affected, usually from the deficiency of the normal form of the protein. Solid-state NMR studies indicate that the yeast prion amyloids are in-register parallel β-sheet structures, in which each residue (e.g. Asn35) forms a row along the filament long axis. The favourable interactions possible for aligned identical hydrophilic and hydrophobic residues are believed to be the mechanism for propagation of amyloid conformation. Thus, just as DNA mediates inheritance by templating its own sequence, these proteins act as genes by templating their conformation. Distinct isolates of a given prion have different biological properties, presumably determined by differences between the amyloid structures. Many lines of evidence indicate that the Saccharomyces cerevisiae prions are pathological disease agents, although the example of the [Het-s] prion of Podospora anserina shows that a prion can have beneficial aspects. 10. MicroRNA-339-5p down-regulates protein expression of β-site amyloid precursor protein-cleaving enzyme 1 (BACE1) in human primary brain cultures and is reduced in brain tissue specimens of Alzheimer disease subjects. Science.gov (United States) Long, Justin M; Ray, Balmiki; Lahiri, Debomoy K 2014-02-21 Alzheimer disease (AD) results, in part, from the excess accumulation of the amyloid-β (Aβ) peptide as neuritic plaques in the brain. The short Aβ peptide is derived from the large transmembrane Aβ precursor protein (APP). The rate-limiting step in the production of Aβ from APP is mediated by the β-site APP-cleaving enzyme 1 (BACE1). Dysregulation of BACE1 levels leading to excess Aβ deposition is implicated in sporadic AD. Thus, elucidating the full complement of regulatory pathways that control BACE1 expression is key to identifying novel drug targets central to the Aβ-generating process. MicroRNAs (miRNAs) are expected to participate in this molecular network. Here, we identified a known miRNA, miR-339-5p, as a key contributor to this regulatory network. Two distinct miR-339-5p target sites were predicted in the BACE1 3'-UTR by in silico analyses. Co-transfection of miR-339-5p with a BACE1 3'-UTR reporter construct resulted in significant reduction in reporter expression. Mutation of both target sites eliminated this effect. Delivery of the miR-339-5p mimic also significantly inhibited expression of BACE1 protein in human glioblastoma cells and human primary brain cultures. Delivery of target protectors designed against the miR-339-5p BACE1 3'-UTR target sites in primary human brain cultures significantly elevated BACE1 expression. Finally, miR-339-5p levels were found to be significantly reduced in brain specimens isolated from AD patients as compared with age-matched controls. Therefore, miR-339-5p regulates BACE1 expression in human brain cells and is most likely dysregulated in at least a subset of AD patients making this miRNA a novel drug target. 11. Milk proteins as precursors of bioactive peptides Directory of Open Access Journals (Sweden) Marta Dziuba 2009-03-01 Full Text Available Milk proteins, a source of bioactive peptides, are the subject of numerous research studies aiming to, among others, evaluate their properties as precursors of biologically active peptides. Physiologically active peptides released from their precursors may interact with selected receptors and affect the overall condition and health of humans. By relying on the BIOPEP database of proteins and bioactive peptides, developed by the Department of Food Biochemistry at the University of Warmia and Mazury in Olsztyn (www.uwm.edu.pl/biochemia, the profiles of potential activity of milk proteins were determined and the function of those proteins as bioactive peptide precursors was evaluated based on a quantitative criterion, i.e. the occurrence frequency of bioactive fragments (A. The study revealed that milk proteins are mainly a source of peptides with the following types of activity: antihypertensive (Amax = 0.225, immunomodulating (0.024, smooth muscle contracting (0.011, antioxidative (0.029, dipeptidyl peptidase IV inhibitors (0.148, opioid (0.073, opioid antagonistic (0.053, bonding and transporting metals and metal ions (0.024, antibacterial and antiviral (0.024, and antithrombotic (0.029. The enzymes capable of releasing bioactive peptides from precursor proteins were determined for every type of activity. The results of the experiment indicate that milk proteins such as lactoferrin, α-lactalbumin, β-casein and κ-casein hydrolysed by trypsin can be a relatively abundant source of biologically active peptides. 12. Analysis of the role of the gene coding the Amyloid-Precursor Protein Binding Protein 1 (APP-BP1) in the radio-sensitivity of epidermoid carcinomas of the upper aero-digestive tract infected by the human papillomavirus; Analyse du role du gene codant l'Amyloid-Precursor Protein Binding Protein 1 (APP-BP1) dans la radiosensibilite des carcinomes epidermoides des voies aero-digestives superieures infectees par le papillomavirus humain Energy Technology Data Exchange (ETDEWEB) Guihard, S.; Altmeyer, A.; Ramolu, L.; Macabre, C.; Abecassis, J.; Noel, G.; Jung, A.C. [Centre de lutte contre le cancer Paul-Strauss, 67 - Strasbourg (France) 2010-10-15 As the human papillomavirus (HPV) is at the origin of 25% of upper aero-digestive tract cancers, and as these tumours present an increased radio-sensitivity compared to other tumours, probably due to a greater transcriptional activity of p53, the authors report the study on the influence of a decrease of the expression of the APP-BP1 in these tumours which could favour a radio-induced apoptosis. By using a reverse transcriptase polymerase chain reaction (RT-PCR), they assessed the APP-BP1 expression levels as well as expression levels of transcriptions coding onco-proteins known to be over-expressed in HPV+ tumours. They compared the radio-sensitivities of HPV+ and HPV- cells, the first one appearing to be greater than the second one. Short communication 13. Amyloid beta-protein and lipid rafts: focused on biogenesis and catabolism. Science.gov (United States) Araki, Wataru; Tamaoka, Akira 2015-01-01 Cerebral accumulation of amyloid β-protein (Aβ) is thought to play a key role in the molecular pathology of Alzheimer's disease (AD). Three secretases (β-, γ-, and α-secretase) are proteases that control the production of Aβ from amyloid precursor protein. Increasing evidence suggests that cholesterol-rich membrane microdomains termed 'lipid rafts' are involved in the biogenesis and accumulation of Aβ as well as Aβ-mediated neurotoxicity. γ-Secretase is enriched in lipid rafts, which are considered an important site for Aβ generation. Additionally, Aβ-degrading peptidases located in lipid rafts, such as neprilysin, appear to play a role in Aβ catabolism. This mini-review focuses on the roles of lipid rafts in the biogenesis and catabolism of Aβ, covering recent research on the relationship between lipid rafts and the three secretases or Aβ-degrading peptidases. Furthermore, the significance of lipid rafts in Aβ aggregation and neurotoxicity is briefly summarized. 14. The Components of Flemingia macrophylla Attenuate Amyloid β-Protein Accumulation by Regulating Amyloid β-Protein Metabolic Pathway Directory of Open Access Journals (Sweden) Yun-Lian Lin 2012-01-01 Full Text Available Flemingia macrophylla (Leguminosae is a popular traditional remedy used in Taiwan as anti-inflammatory, promoting blood circulation and antidiabetes agent. Recent study also suggested its neuroprotective activity against Alzheimer's disease. Therefore, the effects of F. macrophylla on Aβ production and degradation were studied. The effect of F. macrophylla on Aβ metabolism was detected using the cultured mouse neuroblastoma cells N2a transfected with human Swedish mutant APP (swAPP-N2a cells. The effects on Aβ degradation were evaluated on a cell-free system. An ELISA assay was applied to detect the level of Aβ1-40 and Aβ1-42. Western blots assay was employed to measure the levels of soluble amyloid precursor protein and insulin degrading enzyme (IDE. Three fractions of F. macrophylla modified Aβ accumulation by both inhibiting β-secretase and activating IDE. Three flavonoids modified Aβ accumulation by activating IDE. The activated IDE pool by the flavonoids was distinctly regulated by bacitracin (an IDE inhibitor. Furthermore, flavonoid 94-18-13 also modulates Aβ accumulation by enhancing IDE expression. In conclusion, the components of F. macrophylla possess the potential for developing new therapeutic drugs for Alzheimer's disease. 15. Structural properties of Gerstmann-Straussler-Scheinker disease amyloid protein. Science.gov (United States) Salmona, Mario; Morbin, Michela; Massignan, Tania; Colombo, Laura; Mazzoleni, Giulia; Capobianco, Raffaella; Diomede, Luisa; Thaler, Florian; Mollica, Luca; Musco, Giovanna; Kourie, Joseph J; Bugiani, Orso; Sharma, Deepak; Inouye, Hideyo; Kirschner, Daniel A; Forloni, Gianluigi; Tagliavini, Fabrizio 2003-11-28 Prion protein (PrP) amyloid formation is a central feature of genetic and acquired forms of prion disease such as Gerstmann-Sträussler-Scheinker disease (GSS) and variant Creutzfeldt-Jakob disease. The major component of GSS amyloid is a PrP fragment spanning residues approximately 82-146. To investigate the determinants of the physicochemical properties of this fragment, we synthesized PrP-(82-146) and variants thereof, including entirely and partially scrambled peptides. PrP-(82-146) readily formed aggregates that were partially resistant to protease digestion. Peptide assemblies consisted of 9.8-nm-diameter fibrils having a parallel cross-beta-structure. Second derivative of infrared spectra indicated that PrP-(82-146) aggregates are primarily composed of beta-sheet (54%) and turn (24%) which is consistent with their amyloid-like properties. The peptide induced a remarkable increase in plasma membrane microviscosity of primary neurons. Modification of the amino acid sequence 106-126 caused a striking increase in aggregation rate, with formation of large amount of protease-resistant amorphous material and relatively few amyloid fibrils. Alteration of the 127-146 region had even more profound effects, with the inability to generate amyloid fibrils. These data indicate that the intrinsic properties of PrP-(82-146) are dependent upon the integrity of the C-terminal region and account for the massive deposition of PrP amyloid in GSS. 16. Prediction of Peptide and Protein Propensity for Amyloid Formation. Directory of Open Access Journals (Sweden) Carlos Família Full Text Available Understanding which peptides and proteins have the potential to undergo amyloid formation and what driving forces are responsible for amyloid-like fiber formation and stabilization remains limited. This is mainly because proteins that can undergo structural changes, which lead to amyloid formation, are quite diverse and share no obvious sequence or structural homology, despite the structural similarity found in the fibrils. To address these issues, a novel approach based on recursive feature selection and feed-forward neural networks was undertaken to identify key features highly correlated with the self-assembly problem. This approach allowed the identification of seven physicochemical and biochemical properties of the amino acids highly associated with the self-assembly of peptides and proteins into amyloid-like fibrils (normalized frequency of β-sheet, normalized frequency of β-sheet from LG, weights for β-sheet at the window position of 1, isoelectric point, atom-based hydrophobic moment, helix termination parameter at position j+1 and ΔG° values for peptides extrapolated in 0 M urea. Moreover, these features enabled the development of a new predictor (available at http://cran.r-project.org/web/packages/appnn/index.html capable of accurately and reliably predicting the amyloidogenic propensity from the polypeptide sequence alone with a prediction accuracy of 84.9 % against an external validation dataset of sequences with experimental in vitro, evidence of amyloid formation. 17. Eugenol prevents amyloid formation of proteins and inhibits amyloid-induced hemolysis Science.gov (United States) Dubey, Kriti; Anand, Bibin G.; Shekhawat, Dolat Singh; Kar, Karunakar 2017-02-01 Eugenol has attracted considerable attention because of its potential for many pharmaceutical applications including anti-inflammatory, anti-tumorigenic and anti-oxidant properties. Here, we have investigated the effect of eugenol on amyloid formation of selected globular proteins. We find that both spontaneous and seed-induced aggregation processes of insulin and serum albumin (BSA) are significantly suppressed in the presence of eugenol. Isothermal titration calorimetric data predict a single binding site for eugenol-insulin complex confirming the affinity of eugenol for native soluble insulin species. We also find that eugenol suppresses amyloid-induced hemolysis. Our findings reveal the inherent ability of eugenol to stabilize native proteins and to delay the conversion of protein species of native conformation into β-sheet assembled mature fibrils, which seems to be crucial for its inhibitory effect. 18. Tensile deformation and failure of amyloid and amyloid-like protein fibrils Science.gov (United States) Solar, Max; Buehler, Markus J. 2014-03-01 Here we report a series of full atomistic molecular dynamics simulations of six amyloid or amyloid-like protein fibrils in order to systematically understand the effect of different secondary structure motifs on the mechanical tensile and failure response of cross-\\beta protein fibrils. We find a similar failure behavior across the six structures; an initial failure event occurs at small strains involving cooperative rupture of a group of hydrogen bonds, followed by a slow one-by-one hydrogen bond rupture process as the remaining \\beta -sheets peel off with very low applied stress. We also find that the ultimate tensile strength of the protein fibrils investigated scales directly with the number of hydrogen bonds per unit area which break in the initial rupture event. Our results provide insights into structure-property relationships in protein fibrils important for disease and engineering applications and lay the groundwork for the development of materials selection criteria for the design of de novo amyloid-based functional biomaterials. 19. Rabbit serum amyloid protein A: expression and primary structure deduced from cDNA sequences. Science.gov (United States) Rygg, M; Marhaug, G; Husby, G; Dowton, S B 1991-12-01 Serum amyloid A protein (SAA), the precursor of amyloid protein A (AA) in deposits of secondary amyloidosis, is an acute phase plasma apolipoprotein produced by hepatocytes. The primary structure of SAA demonstrates high interspecies homology. Several isoforms exist in individual species, probably with different amyloidogenic potential. The nucleotide sequences of two different rabbit serum amyloid A cDNA clones have been analysed, one (corresponding to SAA1) 569 base pairs (bp) long and the other (corresponding to SAA2) 513 bp long. Their deduced amino acid sequences differ at five amino acid positions, four of which are located in the NH2-terminal region of the protein. The deduced amino acid sequence of SAA2 corresponds to rabbit protein AA previously described except for one amino acid in position 22. Eighteen hours after turpentine stimulation, rabbit SAA mRNA is abundant in liver, while lower levels are present in spleen. None of the other extrahepatic organs studied showed any SAA mRNA expression. A third mRNA species (1.9 kb) hybridizing with a single-stranded RNA probe transcribed from the rabbit SAA cDNA, was identified. SAA1 and SAA2 mRNA were found in approximately equal amounts in turpentine-stimulated rabbit liver, but seem to be coordinately decreased after repeated inflammatory stimulation. 20. Interaction of amyloid inhibitor proteins with amyloid beta peptides: insight from molecular dynamics simulations. Directory of Open Access Journals (Sweden) Payel Das Full Text Available Knowledge of the detailed mechanism by which proteins such as human αB- crystallin and human lysozyme inhibit amyloid beta (Aβ peptide aggregation is crucial for designing treatment for Alzheimer's disease. Thus, unconstrained, atomistic molecular dynamics simulations in explicit solvent have been performed to characterize the Aβ17-42 assembly in presence of the αB-crystallin core domain and of lysozyme. Simulations reveal that both inhibitor proteins compete with inter-peptide interaction by binding to the peptides during the early stage of aggregation, which is consistent with their inhibitory action reported in experiments. However, the Aβ binding dynamics appear different for each inhibitor. The binding between crystallin and the peptide monomer, dominated by electrostatics, is relatively weak and transient due to the heterogeneous amino acid distribution of the inhibitor surface. The crystallin-bound Aβ oligomers are relatively long-lived, as they form more extensive contact surface with the inhibitor protein. In contrast, a high local density of arginines from lysozyme allows strong binding with Aβ peptide monomers, resulting in stable complexes. Our findings not only illustrate, in atomic detail, how the amyloid inhibitory mechanism of human αB-crystallin, a natural chaperone, is different from that of human lysozyme, but also may aid de novo design of amyloid inhibitors. 1. Nucleation Process of a Fibril Precursor in the C-Terminal Segment of Amyloid Science.gov (United States) Baftizadeh, Fahimeh; Pietrucci, Fabio; Biarnés, Xevi; Laio, Alessandro 2013-04-01 By extended atomistic simulations in explicit solvent and bias-exchange metadynamics, we study the aggregation process of 18 chains of the C-terminal segment of amyloid-β, an intrinsically disordered protein involved in Alzheimer’s disease and prone to form fibrils. Starting from a disordered aggregate, we are able to observe the formation of an ordered nucleus rich in beta sheets. The rate limiting step in the nucleation pathway involves crossing a barrier of approximately 40kcal/mol and is associated with the formation of a very specific interdigitation of the side chains belonging to different sheets. This structural pattern is different from the one observed experimentally in a microcrystal of the same system, indicating that the structure of a “nascent” fibril may differ from the one of an “extended” fibril. 2. The formation of bioactive amyloid species by prion proteins in vitro and in cells. Science.gov (United States) Liu, Yuanbin; Ritter, Christiane; Riek, Roland; Schubert, David 2006-10-09 Amyloid proteins are a group of proteins that can polymerize into cross beta-sheeted amyloid species. We have found that enhancing cellular 3-(4,5-dimethylthiazol-2-yl)-2,5-diphenyltetrazolium bromide (MTT) formazan exocytosis is a common property of bioactive amyloid species formed from all of the amyloid proteins tested to date. In this report, we show that the infectious amyloid species of the prion protein HET-s of the filamentous fungus Podospora anserina, like other amyloidogenic proteins, also enhances MTT formazan exocytosis. More strikingly, cellular MTT formazan exocytosis revealed the formation of bioactive amyloid species in prion-infected mouse N2a neuroblastoma cells. These findings suggest that cellular MTT formazan exocytosis can be useful for studying the roles of bioactive amyloid species in prion infectivity and prion-induced neurodegeneration. 3. Salt anions promote the conversion of HypF-N into amyloid-like oligomers and modulate the structure of the oligomers and the monomeric precursor state. Science.gov (United States) Campioni, Silvia; Mannini, Benedetta; López-Alonso, Jorge P; Shalova, Irina N; Penco, Amanda; Mulvihill, Estefania; Laurents, Douglas V; Relini, Annalisa; Chiti, Fabrizio 2012-12-07 An understanding of the solution factors contributing to the rate of aggregation of a protein into amyloid oligomers, to the modulation of the conformational state populated prior to aggregation and to the structure/morphology of the resulting oligomers is one of the goals of present research in this field. We have studied the influence of six different salts on the conversion of the N-terminal domain of Escherichiacoli HypF (HypF-N) into amyloid-like oligomers under conditions of acidic pH. Our results show that salts having different anions (NaCl, NaClO(4), NaI, Na(2)SO(4)) accelerate oligomerization with an efficacy that follows the electroselectivity series of the anions (SO(4)(2-)≥ ClO(4)(-)>I(-)>Cl(-)). By contrast, salts with different cations (NaCl, LiCl, KCl) have similar effects. We also investigated the effect of salts on the structure of the final and initial states of HypF-N aggregation. The electroselectivity series does not apply to the effect of anions on the structure of the oligomers. By contrast, it applies to their effect on the content of secondary structure and on the exposure of hydrophobic clusters of the monomeric precursor state. The results therefore indicate that the binding of anions to the positively charged residues of HypF-N at low pH is the mechanism by which salts modulate the rate of oligomerization and the structure of the monomeric precursor state but not the structure of the resulting oligomers. Overall, the data contribute to rationalize the effect of salts on amyloid-like oligomer formation and to explain the role of charged biological macromolecules in protein aggregation processes. 4. The proteome response to amyloid protein expression in vivo. Directory of Open Access Journals (Sweden) Ricardo A Gomes Full Text Available Protein misfolding disorders such as Alzheimer, Parkinson and transthyretin amyloidosis are characterized by the formation of protein amyloid deposits. Although the nature and location of the aggregated proteins varies between different diseases, they all share similar molecular pathways of protein unfolding, aggregation and amyloid deposition. Most effects of these proteins are likely to occur at the proteome level, a virtually unexplored reality. To investigate the effects of an amyloid protein expression on the cellular proteome, we created a yeast expression system using human transthyretin (TTR as a model amyloidogenic protein. We used Saccharomyces cerevisiae, a living test tube, to express native TTR (non-amyloidogenic and the amyloidogenic TTR variant L55P, the later forming aggregates when expressed in yeast. Differential proteome changes were quantitatively analyzed by 2D-differential in gel electrophoresis (2D-DIGE. We show that the expression of the amyloidogenic TTR-L55P causes a metabolic shift towards energy production, increased superoxide dismutase expression as well as of several molecular chaperones involved in protein refolding. Among these chaperones, members of the HSP70 family and the peptidyl-prolyl-cis-trans isomerase (PPIase were identified. The latter is highly relevant considering that it was previously found to be a TTR interacting partner in the plasma of ATTR patients but not in healthy or asymptomatic subjects. The small ubiquitin-like modifier (SUMO expression is also increased. Our findings suggest that refolding and degradation pathways are activated, causing an increased demand of energetic resources, thus the metabolic shift. Additionally, oxidative stress appears to be a consequence of the amyloidogenic process, posing an enhanced threat to cell survival. 5. Amyloid-clearing proteins and their epigenetic regulation as a therapeutic target in Alzheimer’s disease Directory of Open Access Journals (Sweden) Natalia N Nalivaeva 2014-09-01 Full Text Available Abnormal elevation of amyloid β-peptide (Aβ levels in the brain is the primary trigger for neuronal cell death specific to Alzheimer’s disease (AD. It is now evident that Aβ levels in the brain are manipulable due to a dynamic equilibrium between its production from the amyloid precursor protein (APP and removal by amyloid clearance proteins. Clearance can be either enzymic or non-enzymic (binding/transport proteins. Intriguingly several of the main amyloid-degrading enzymes (ADEs are members of the M13 peptidase family (neprilysin (NEP, NEP2 and the endothelin converting enzymes (ECE-1 and -2. A distinct metallopeptidase, insulin-degrading enzyme (IDE, also contributes to Aβ degradation in the brain. The ADE family currently embraces more than 20 members, both membrane-bound and soluble, and of differing cellular locations. NEP plays an important role in brain function terminating neuropeptide signals. Its decrease in specific brain areas with age or after hypoxia, ischaemia or stroke contribute significantly to the development of AD pathology. The recently discovered mechanism of epigenetic regulation of NEP (and other genes by the APP intracellular domain (AICD and its dependence on the cell type and APP isoform expression suggest possibilities for selective manipulation of NEP gene expression in neuronal cells. We have also observed that another amyloid-clearing protein, namely transthyretin (TTR, is also regulated in the neuronal cell by a mechanism similar to NEP. Dependence of amyloid clearance proteins on histone deacetylases and the ability of HDAC inhibitors to up-regulate their expression in the brain opens new avenues for developing preventive strategies in AD. 6. Neurotrophic and Neurotoxic Effects of Amyloid \|beta Protein: Reversal by Tachykinin Neuropeptides Science.gov (United States) Yankner, Bruce A.; Duffy, Lawrence K.; Kirschner, Daniel A. 1990-10-01 The amyloid β protein is deposited in the brains of patients with Alzheimer's disease but its pathogenic role is unknown. In culture, the amyloid β protein was neurotrophic to undifferentiated hippocampal neurons at low concentrations and neurotoxic to mature neurons at higher concentrations. In differentiated neurons, amyloid β protein caused dendritic and axonal retraction followed by neuronal death. A portion of the amyloid β protein (amino acids 25 to 35) mediated both the trophic and toxic effects and was homologous to the tachykinin neuropeptide family. The effects of the amyloid β protein were mimicked by tachykinin antagonists and completely reversed by specific tachykinin agonists. Thus, the amyloid β protein could function as a neurotrophic factor for differentiating neurons, but at high concentrations in mature neurons, as in Alzheimer's disease, could cause neuronal degeneration. 7. Cholesterol-induced astrocyte activation is associated with increased amyloid precursor protein expression and processing%胆固醇介导的星形胶质细胞活化与淀粉样前体蛋白表达升高和进展相关 Institute of Scientific and Technical Information of China (English) Evangelina Avila-Muñoz; Clorinda Arias 2015-01-01 Cholesterol is essential for maintaining lipid raft integrity and has been regarded as a crucial regulatory factor for amyloidogenesis in Alzheimer's disease (AD). The vast majority of studies on amyloid precursor protein (APP) metabolism and amyloid β-protein (Aβ) production have focused on neurons. The role of astrocytes re-mains largely unexplored, despite the presence of activated astrocytes in the brains of most patients with AD and in transgenic models of the disease. The role of cholesterol in Aβ production has been thoroughly studied in neu-rons and attributed to the participation of lipid rafts in APP metabolism. Thus, in this study, we analyzed the effect of cholesterol loading in astrocytes and analyzed the expression and processing of APP. We found that cholesterol exposure induced astrocyte activation, increased APP content, and enhanced the interaction of APP with BACE-1. These effects were associated with an enrichment of ganglioside GM1-cholesterol patches in the astro-cyte membrane and with increased ROS production.%胆固醇对于保持脂筏的完整性起必要作用，其被认为是阿尔茨海默病（AD）中淀粉样蛋白生成的关键调节因子。大多数关于淀粉样前体蛋白（APP）代谢和β淀粉样蛋白（Aβ）生成的研究都聚焦于神经元。虽然在大多数 AD 患者和 AD 转基因模型脑内发现活化的星形胶质细胞，但星形胶质细胞在 AD 中的作用尚未得到充分探索。在神经元 Aβ生成中胆固醇的作用已得到充分研究，并归因于 APP 代谢中脂筏的参与。因此，本研究分析星形胶质细胞中胆固醇的作用，以及 APP 的表达和进展。本研究发现，胆固醇的表达导致星形胶质细胞活化，提高 APP 水平，增强 APP 和 BACE-1的交互作用。这些作用与星形胶质细胞细胞膜的神经节苷脂 GM1-胆固醇斑块和增高的 ROS 相关。 8. Observation of amyloid precursor protein cleavage and Aβ generation in living cells by using multiphoton laser scanning microscopy%多光子激光扫描成像技术对活细胞内淀粉样前体蛋白裂解和β-淀粉样蛋白生成的观察 Institute of Scientific and Technical Information of China (English) 李晓晴; 张苏明; 杨华静; 张智红 2007-01-01 Objective To investigate the proteolytic mechanism of amyloid precursor protein (APP) and to explore amyloidbeta (Aβ) generation in living neurons. Methods DNA fragments were amplified by PCR or synthesized. The four fragments- CFP- 54bp- YFP and C99 were ligated into pcDNAS.O vector to construct the recombinant plasmids pcDNA3.0-CFP-54bp-YFP and pcDNA3.0-CFP-54bp-YFP-C99. The SH-SY5Y cells were transiently transfected with pcDNA3.0-CFP-54bp-YFP or pcDNA3.0-CFP-54bp-YFP-C99.The SH-SY5Y cells were transiently transfected with pcDNA3.0-CFP-54bp-YFP or pcDNA3.0-CFP-54bp-YFP-C99.The expression of fusion gene was examined under a multiphoton laser scanning microscope.Fluorescence resonance energy transfer (FRET) was used to measure the p cleavage and y cleavage of APP.Aβ generation was confirmed by immunocytochemistry and multiphoton laser scanning microscopy.Cell viability was tested by MTT assay at different time points.Results (1) The double restriction endonuclease digestion and sequencing analysis confirmed the authenticity of the recombinant plasmids pcDNA3.0-CFP-54bp-YFP and pcDNA3.0-CFP-54bp-YFP-C99.(2) Blue and yellow fluorescences were detected in the transfected cells.(3) FRET occurred in pcDNA3.0-CFP-54bp-YFP-transfected cells but not in pcDNA3.0-CFP-54bp-YFP-C99-transfected cells.(4) Aβ was produced in the pcDNA3.0-CFP-54bp-YFP-C99 transfected cells.(5) Aβ-deposition was widespread in the cell.(6) Cell viability decreased along with the intracellular Aβ deposition.Conclusion C99 is important for the APP β cleavage.Aβ may be generated and deposited in cells at the early stage of Alzheimer's disease.Intracellular Aβ accumulation brings deleterious effects on cells.%目的在活细胞内探究淀粉样前体蛋白(amyloid precursor protein,APP)的裂解和β-淀粉样蛋白(amyloid beta,Aβ)的生成机制.方法利用PCR扩增CFP(编码蓝色荧光蛋白),YFP(编码黄色荧光蛋白)和C99(编码APP最后99个氨基酸)三片段.含有54 9. Minocycline alleviates beta-amyloid protein and tau pathology via restraining neuroinflammation induced by diabetic metabolic disorder Directory of Open Access Journals (Sweden) Cai Z 2013-08-01 Full Text Available Zhiyou Cai,1 Yong Yan,2 Yonglong Wang2 1Department of Neurology, the Lu’an Affiliated Hospital of Anhui Medical University, Lu’an People’s Hospital, Lu’an, Anhui Province, People’s Republic of China; 2Department of Neurology, the First Affiliated Hospital of Chongqing Medical University, Chongqing Key Laboratory of Neurology, Chongqing, People’s Republic of China Background: Compelling evidence has shown that diabetic metabolic disorder plays a critical role in the pathogenesis of Alzheimer’s disease, including increased expression of β-amyloid protein (Aβ and tau protein. Evidence has supported that minocycline, a tetracycline derivative, protects against neuroinflammation induced by neurodegenerative disorders or cerebral ischemia. This study has evaluated minocycline influence on expression of Aβ protein, tau phosphorylation, and inflammatory cytokines (interleukin-1β and tumor necrosis factor-α in the brain of diabetic rats to clarify neuroprotection by minocycline under diabetic metabolic disorder. Method: An animal model of diabetes was established by high fat diet and intraperitoneal injection of streptozocin. In this study, we investigated the effect of minocycline on expression of Aβ protein, tau phosphorylation, and inflammatory cytokines (interleukin-1β and tumor necrosis factor-α in the hippocampus of diabetic rats via immunohistochemistry, western blotting, and enzyme-linked immunosorbent assay. Results: These results showed that minocycline decreased expression of Aβ protein and lowered the phosphorylation of tau protein, and retarded the proinflammatory cytokines, but not amyloid precursor protein. Conclusion: On the basis of the finding that minocycline had no influence on amyloid precursor protein and beta-site amyloid precursor protein cleaving enzyme 1 which determines the speed of Aβ generation, the decreases in Aβ production and tau hyperphosphorylation by minocycline are through inhibiting 10. Non-targeted identification of prions and amyloid-forming proteins from yeast and mammalian cells. Science.gov (United States) Kryndushkin, Dmitry; Pripuzova, Natalia; Burnett, Barrington G; Shewmaker, Frank 2013-09-20 The formation of amyloid aggregates is implicated both as a primary cause of cellular degeneration in multiple human diseases and as a functional mechanism for providing extraordinary strength to large protein assemblies. The recent identification and characterization of several amyloid proteins from diverse organisms argues that the amyloid phenomenon is widespread in nature. Yet identifying new amyloid-forming proteins usually requires a priori knowledge of specific candidates. Amyloid fibers can resist heat, pressure, proteolysis, and denaturation by reagents such as urea or sodium dodecyl sulfate. Here we show that these properties can be exploited to identify naturally occurring amyloid-forming proteins directly from cell lysates. This proteomic-based approach utilizes a novel purification of amyloid aggregates followed by identification by mass spectrometry without the requirement for special genetic tools. We have validated this technique by blind identification of three amyloid-based yeast prions from laboratory and wild strains and disease-related polyglutamine proteins expressed in both yeast and mammalian cells. Furthermore, we found that polyglutamine aggregates specifically recruit some stress granule components, revealing a possible mechanism of toxicity. Therefore, core amyloid-forming proteins as well as strongly associated proteins can be identified directly from cells of diverse origin. 11. Amyloid protein unfolding and insertion kinetics on neuronal membrane mimics Science.gov (United States) Qiu, Liming; Buie, Creighton; Vaughn, Mark; Cheng, Kwan 2010-03-01 Atomistic details of beta-amyloid (Aβ ) protein unfolding and lipid interaction kinetics mediated by the neuronal membrane surface are important for developing new therapeutic strategies to prevent and cure Alzheimer's disease. Using all-atom MD simulations, we explored the early unfolding and insertion kinetics of 40 and 42 residue long Aβ in binary lipid mixtures with and without cholesterol that mimic the cholesterol-depleted and cholesterol-enriched lipid nanodomains of neurons. The protein conformational transition kinetics was evaluated from the secondary structure profile versus simulation time plot. The extent of membrane disruption was examined by the calculated order parameters of lipid acyl chains and cholesterol fused rings as well as the density profiles of water and lipid headgroups at defined regions across the lipid bilayer from our simulations. Our results revealed that both the cholesterol content and the length of the protein affect the protein-insertion and membrane stability in our model lipid bilayer systems. 12. Modeling the Aggregation Propensity and Toxicity of Amyloid-β Variants DEFF Research Database (Denmark) Tiwari, Manish Kumar; Kepp, Kasper Planeta 2015-01-01 Protein aggregation is a hallmark of many neurodegenerative disorders. Alzheimer’s disease (AD) is directly linked to deposits of amyloid-β (Aβ) derived from the amyloidprotein precursor (AβPP), and multiple experimental studies have investigated the aggregation behavior of these amyloids... 13. Native human serum amyloid P component is a single pentamer DEFF Research Database (Denmark) Sørensen, Inge Juul; Andersen, Ove; Nielsen, EH; 1995-01-01 Serum amyloid P component (SAP) and C-reactive protein (CRP) are members of the pentraxin protein family. SAP is the precursor protein to amyloid P component present in all forms of amyloidosis. The prevailing notion is that SAP in circulation has the form of a double pentameric molecule (decamer... 14. Effect of Metal Chelators on γ-Secretase Indicates That Calcium and Magnesium Ions Facilitate Cleavage of Alzheimer Amyloid Precursor Substrate Directory of Open Access Journals (Sweden) Michael Ho 2011-01-01 Full Text Available Gamma-secretase is involved in the production of Aβ amyloid peptides. It cleaves the transmembrane domain of the amyloid precursor protein (APP at alternative sites to produce Aβ and the APP intracellular domain (AICD. Metal ions play an important role in Aβ aggregation and metabolism, thus metal chelators and ligands represent potential therapeutic agents for AD treatment. A direct effect of metal chelators on γ-secretase has not yet been investigated. The authors used an in vitro γ-secretase assay consisting of cleavage of APP C100-3XFLAG by endogenous γ-secretase from rodent brains and human neuroblastoma SH-SY5Y, and detected AICD production by western blotting. Adding metalloprotease inhibitors to the reaction showed that clioquinol, phosphoramidon, and zinc metalloprotease inhibitors had no significant effect on γ-secretase activity. In contrast, phenanthroline, EDTA, and EGTA markedly decreased γ-secretase activity that could be restored by adding back calcium and magnesium ions. Mg2+ stabilized a 1,000 kDa presenilin 1 complex through blue native gel electrophoresis and size-exclusion chromatography. Data suggest that Ca2+ and Mg2+ stabilize γ-secretase and enhance its activity. 15. The coarse-grained OPEP force field for non-amyloid and amyloid proteins. Science.gov (United States) Chebaro, Yassmine; Pasquali, Samuela; Derreumaux, Philippe 2012-08-02 Coarse-grained protein models with various levels of granularity and degrees of freedom offer the possibility to explore many phenomena including folding, assembly, and recognition in terms of dynamics and thermodynamics that are inaccessible to all-atom representations in explicit aqueous solution. Here, we present a refined version of the coarse-grained optimized potential for efficient protein structure prediction (OPEP) based on a six-bead representation. The OPEP version 4.0 parameter set, which uses a new analytical formulation for the nonbonded interactions and adds specific side-chain-side-chain interactions for α-helix, is subjected to three tests. First, we show that molecular dynamics simulations at 300 K preserve the experimental rigid conformations of 17 proteins with 37-152 amino acids within a root-mean-square deviation (RMSD) of 3.1 Å after 30 ns. Extending the simulation time to 100 ns for five proteins does not change the RMSDs. Second, replica exchange molecular dynamics (REMD) simulations recover the NMR structures of three prototypical β-hairpin and α-helix peptides and the NMR three-stranded β-sheet topology of a 37-residue WW domain, starting from randomly chosen states. Third, REMD simulations on the ccβ peptide show a temperature transition from a three-stranded coiled coil to amyloid-like aggregates consistent with experiments, while simulations on low molecular weight aggregates of the prion protein helix 1 do not. Overall, these studies indicate the effectiveness of our OPEP4 coarse-grained model for protein folding and aggregation, and report two future directions for improvement. 16. Immunohistochemical identification and crossreactions of amyloid-A fibril protein in man and eleven other species OpenAIRE Gruys, E.; Linke, R.P.; Hol, P.R.; Geisel, O.; Nathrath, W.B.J.; Trautwein, G 1984-01-01 Antisera were prepared in rabbits, sheep or chicken against purified amyloid fibril protein AA from man, mouse, stone marten, dog, cow and hamster. These antisera were tested by immunodiffusion against all purified antigens and applied to tissue sections containing amyloid from man, mouse, hamster, guinea pig, rabbit, cat, dog, mink, stone marten, pine marten, cow and horse. The binding of the antibodies to amyloid in tissue sections was assessed by the indirect immunoperoxidase method. The s... 17. Oxidative stress up-regulates the expression of β-Amyloid precursor protein cleavage enzyme 1 in SH-SY5Y human neuroblastoma cells%氧化应激上调人神经母细胞瘤细胞内β-裂解酶的表达 Institute of Scientific and Technical Information of China (English) 谷心灵; 孟斐; 李良 2012-01-01 Objective To investigate the role of oxidative stress in the expression of p-Amyloid precursor protein cleavage enzyme 1 ( BACE1) and the changes DNA methylation and histone acetylation. Methods Cultured SH-SY5Y cells treated with H2O2 were used to test the expressions of BACE1, DNA methyltransferases 1, 3A (DN-MT1,DNMT3A) and histone deacetyltranferase (HDAC) by were examined by Western blot. The level of mRNA of BACE1 was assessed by RT-PCR. Acetylation level of histone H3 and H4 was examined by optical density assay. Results Both BACE1 mRNA and protein levels were up-regulated significantly after H2O2 treatment for 1 and 72 h; DNMT1 and DNMT3A expressions were decreased to 75% and 65% of control respectively after H2O2 treatment for 72 h; HD AC3 level was increased by 1.6 folds as compared with control; While the level of histone H3 acetylation was decreased and there was no change with histone H4 acetylation. Conclusions Oxidative stress may regulate BACE1 expression in SH-SY5 Y through alteration of DNA methylation and histone acetylation which play a role in Alzheimer's disease (AD) pathogenesis.%目的研究氧化应激对人神经母细胞瘤细胞(SH-SY5Y)β-裂解酶(BACE1)表达的影响及组蛋白乙酰化、DNA甲基化的改变.方法采用H2O2处理体外培养的SH-SY5Y,Westem blot法检测细胞的BACE1表达及DNA甲基转移酶(DNMTs)和组蛋白去乙酰化酶(HDAC)的表达；实时定量PCR检测BACE1 mRNA的表达；吸光度值法检测组蛋白3(H3)和组蛋白4(H4)整体乙酰化水平.结果 SH-SY5Y细胞经H2O2处理1和72 h后BACE1 mRNA和蛋白表达均明显增多；H2O2处理72 h后DNMT1、DNMT3A表达均下降,分别是对照组的75％和65％(P＜0.01)；而组蛋白去乙酰化酶HDAC3的表达增高至对照组的1.6倍(P＜0.01)；同时,组蛋白H3整体乙酰化水平下降,但H4乙酰化水平无明显改变.结论氧化应激可能通过改变SH-SY5Y细胞内DNA甲基化水平及组蛋白乙酰化状态调节BACE1的 18. Positive evolutionary selection of an HD motif on Alzheimer precursor protein orthologues suggests a functional role. Directory of Open Access Journals (Sweden) István Miklós 2012-02-01 Full Text Available HD amino acid duplex has been found in the active center of many different enzymes. The dyad plays remarkably different roles in their catalytic processes that usually involve metal coordination. An HD motif is positioned directly on the amyloid beta fragment (Aβ and on the carboxy-terminal region of the extracellular domain (CAED of the human amyloid precursor protein (APP and a taxonomically well defined group of APP orthologues (APPOs. In human Aβ HD is part of a presumed, RGD-like integrin-binding motif RHD; however, neither RHD nor RXD demonstrates reasonable conservation in APPOs. The sequences of CAEDs and the position of the HD are not particularly conserved either, yet we show with a novel statistical method using evolutionary modeling that the presence of HD on CAEDs cannot be the result of neutral evolutionary forces (p<0.0001. The motif is positively selected along the evolutionary process in the majority of APPOs, despite the fact that HD motif is underrepresented in the proteomes of all species of the animal kingdom. Position migration can be explained by high probability occurrence of multiple copies of HD on intermediate sequences, from which only one is kept by selective evolutionary forces, in a similar way as in the case of the "transcription binding site turnover." CAED of all APP orthologues and homologues are predicted to bind metal ions including Amyloid-like protein 1 (APLP1 and Amyloid-like protein 2 (APLP2. Our results suggest that HDs on the CAEDs are most probably key components of metal-binding domains, which facilitate and/or regulate inter- or intra-molecular interactions in a metal ion-dependent or metal ion concentration-dependent manner. The involvement of naturally occurring mutations of HD (Tottori (D7N and English (H6R mutations in early onset Alzheimer's disease gives additional support to our finding that HD has an evolutionary preserved function on APPOs. 19. Small heat shock proteins potentiate amyloid dissolution by protein disaggregases from yeast and humans. Directory of Open Access Journals (Sweden) Martin L Duennwald Full Text Available How small heat shock proteins (sHsps might empower proteostasis networks to control beneficial prions or disassemble pathological amyloid is unknown. Here, we establish that yeast sHsps, Hsp26 and Hsp42, inhibit prionogenesis by the [PSI+] prion protein, Sup35, via distinct and synergistic mechanisms. Hsp42 prevents conformational rearrangements within molten oligomers that enable de novo prionogenesis and collaborates with Hsp70 to attenuate self-templating. By contrast, Hsp26 inhibits self-templating upon binding assembled prions. sHsp binding destabilizes Sup35 prions and promotes their disaggregation by Hsp104, Hsp70, and Hsp40. In yeast, Hsp26 or Hsp42 overexpression prevents [PSI+] induction, cures [PSI+], and potentiates [PSI+]-curing by Hsp104 overexpression. In vitro, sHsps enhance Hsp104-catalyzed disaggregation of pathological amyloid forms of α-synuclein and polyglutamine. Unexpectedly, in the absence of Hsp104, sHsps promote an unprecedented, gradual depolymerization of Sup35 prions by Hsp110, Hsp70, and Hsp40. This unanticipated amyloid-depolymerase activity is conserved from yeast to humans, which lack Hsp104 orthologues. A human sHsp, HspB5, stimulates depolymerization of α-synuclein amyloid by human Hsp110, Hsp70, and Hsp40. Thus, we elucidate a heretofore-unrecognized human amyloid-depolymerase system that could have applications in various neurodegenerative disorders. 20. Functional Amyloid Formation within Mammalian Tissue. Directory of Open Access Journals (Sweden) 2005-11-01 Full Text Available Amyloid is a generally insoluble, fibrous cross-beta sheet protein aggregate. The process of amyloidogenesis is associated with a variety of neurodegenerative diseases including Alzheimer, Parkinson, and Huntington disease. We report the discovery of an unprecedented functional mammalian amyloid structure generated by the protein Pmel17. This discovery demonstrates that amyloid is a fundamental nonpathological protein fold utilized by organisms from bacteria to humans. We have found that Pmel17 amyloid templates and accelerates the covalent polymerization of reactive small molecules into melanin-a critically important biopolymer that protects against a broad range of cytotoxic insults including UV and oxidative damage. Pmel17 amyloid also appears to play a role in mitigating the toxicity associated with melanin formation by sequestering and minimizing diffusion of highly reactive, toxic melanin precursors out of the melanosome. Intracellular Pmel17 amyloidogenesis is carefully orchestrated by the secretory pathway, utilizing membrane sequestration and proteolytic steps to protect the cell from amyloid and amyloidogenic intermediates that can be toxic. While functional and pathological amyloid share similar structural features, critical differences in packaging and kinetics of assembly enable the usage of Pmel17 amyloid for normal function. The discovery of native Pmel17 amyloid in mammals provides key insight into the molecular basis of both melanin formation and amyloid pathology, and demonstrates that native amyloid (amyloidin may be an ancient, evolutionarily conserved protein quaternary structure underpinning diverse pathways contributing to normal cell and tissue physiology. 1. Functional amyloid formation within mammalian tissue. Directory of Open Access Journals (Sweden) Douglas M Fowler 2006-01-01 Full Text Available Amyloid is a generally insoluble, fibrous cross-beta sheet protein aggregate. The process of amyloidogenesis is associated with a variety of neurodegenerative diseases including Alzheimer, Parkinson, and Huntington disease. We report the discovery of an unprecedented functional mammalian amyloid structure generated by the protein Pmel17. This discovery demonstrates that amyloid is a fundamental nonpathological protein fold utilized by organisms from bacteria to humans. We have found that Pmel17 amyloid templates and accelerates the covalent polymerization of reactive small molecules into melanin-a critically important biopolymer that protects against a broad range of cytotoxic insults including UV and oxidative damage. Pmel17 amyloid also appears to play a role in mitigating the toxicity associated with melanin formation by sequestering and minimizing diffusion of highly reactive, toxic melanin precursors out of the melanosome. Intracellular Pmel17 amyloidogenesis is carefully orchestrated by the secretory pathway, utilizing membrane sequestration and proteolytic steps to protect the cell from amyloid and amyloidogenic intermediates that can be toxic. While functional and pathological amyloid share similar structural features, critical differences in packaging and kinetics of assembly enable the usage of Pmel17 amyloid for normal function. The discovery of native Pmel17 amyloid in mammals provides key insight into the molecular basis of both melanin formation and amyloid pathology, and demonstrates that native amyloid (amyloidin may be an ancient, evolutionarily conserved protein quaternary structure underpinning diverse pathways contributing to normal cell and tissue physiology. 2. 同型半胱氨酸对大鼠学习记忆及海马APP代谢影响%Influence of hyperhomocysteinemia on learning and memory ability and expression of β-amyloid precursor protein of hippocampus and intervention effect of folic acid in rats Institute of Scientific and Technical Information of China (English) 王健; 张永泽; 康美玉; 潘丽兰; 史玉; 高玉梅; 李凤铭 2012-01-01 Objective To explore the influence of hyperhotnocysteinemia( HHcy) on learning and memory ability and expression of β-amyloid precursor protein of hippocampus and the intervention effect of folic acid (FA) in rats. Methods Forty Wislar rats were randomly divided into normal control group, HHcy group, and two FA intervention groups(low and high dose) . Methionine( 1 g/kg·d) was dissolved in drinking water to make HHcy model. Treatment with FA(0.7 and 3.4 mg/kg·d) via intragastric intubation was administered in FA groups for 8 weeks. Plasma concentrations of homocysteinemia(Hcy) and FA before and after the experiment were measured. The rats' learning and memory abilities were tested by Morris water maze test. At the end of 8 weeks experiment, immunohistochemistry was used to observe the expression of p-amyloid precusor protein ( APP) in hippocampus. Results Compared with the normal control and FA groups,the escape latency in HHcy group was significantly longer;the numbers of passing the platform region was significantly less;the staying time in the platform region was significantly shorter( P <0.05 -0.01) ; and the mean values of APP and its metabolic secretase in region of hippocampus was significantly higher( P < 0. 01 ) . The results of all tests were not significantly different between the normal control group and FA groups. Conclusion HHcy can induce learning and memory impairment and decreased the expression of APP in hippocampus in rats. FA supplementation could attenuate the adverse effects.%目的探讨高同型半胱氨酸血症(HHcy)对大鼠学习记忆能力和海马β-淀粉样前体蛋白(APP)代谢影响及叶酸干预作用.方法将40只Wistar大鼠随机分为对照组、HHcy组和叶酸干预组,每组10只,在大鼠饮水中添加蛋氨酸(1.0g/kg)制作HHcy模型,叶酸低、高剂量干预组大鼠同时分别给予叶酸0.7和3.4mg/kg灌胃,持续8周.在实验前后测定各组血浆同型半胱氨酸(Hcy)、叶酸浓度,采用Morris水 3. Immunohistochemical identification and crossreactions of amyloid-A fibril protein in man and eleven other species NARCIS (Netherlands) Gruys, E.; Linke, R.P.; Hol, P.R.; Geisel, O.; Nathrath, W.B.J.; Trautwein, G. 1984-01-01 Antisera were prepared in rabbits, sheep or chicken against purified amyloid fibril protein AA from man, mouse, stone marten, dog, cow and hamster. These antisera were tested by immunodiffusion against all purified antigens and applied to tissue sections containing amyloid from man, mouse, hamster, 4. Islet amyloid polypeptide forms rigid lipid-protein amyloid fibrils on supported phospholipid bilayers. Science.gov (United States) Domanov, Yegor A; Kinnunen, Paavo K J 2008-02-08 Islet amyloid polypeptide (IAPP) forms fibrillar amyloid deposits in the pancreatic islets of Langerhans of patients with type 2 diabetes mellitus, and its misfolding and aggregation are thought to contribute to beta-cell death. Increasing evidence suggests that IAPP fibrillization is strongly influenced by lipid membranes and, vice versa, that the membrane architecture and integrity are severely affected by amyloid growth. Here, we report direct fluorescence microscopic observations of the morphological transformations accompanying IAPP fibrillization on the surface of supported lipid membranes. Within minutes of application in submicromolar concentrations, IAPP caused extensive remodeling of the membrane including formation of defects, vesiculation, and tubulation. The effects of IAPP concentration, ionic strength, and the presence of amyloid seeds on the bilayer perturbation and peptide aggregation were examined. Growth of amyloid fibrils was visualized using fluorescently labeled IAPP or thioflavin T staining. Two-color imaging of the peptide and membranes revealed that the fibrils were initially composed of the peptide only, and vesiculation occurred in the points where growing fibers touched the lipid membrane. Interestingly, after 2-5 h of incubation, IAPP fibers became "wrapped" by lipid membranes derived from the supported membrane. Progressive increase in molecular-level association between amyloid and membranes in the maturing fibers was confirmed by Förster resonance energy transfer spectroscopy. 5. Effects of Exogenous Hydrogen Sulfide on β-site Amyloid Precursor Protein Cleaving Enzyme 1 in Pheochromocytoma Cells%外源性硫化氢对嗜铬细胞瘤细胞β位淀粉样前体蛋白裂解酶1表达的影响 Institute of Scientific and Technical Information of China (English) 代政伟; 张华; 孟涛; 晏宁; 李洁颖; 晏勇 2011-01-01 Abstract Objective To observe the effects of exogenous hydrogen sulfide (H2S) on the expression of β-site amyloid precursor protein cleaving enzyme 1 (BACE1) and explore the possible ceDular signaling mechanism in pheochromocytoma (PC12) cells. Methods PC12 cells were exposed to different concentrations of sodium hydrosulfide (NaHS, the honor of H2S) for 24 hours. The levels of BACE1 mRNA and protein were detected by RT-PCR and Western blot,respectively. Western blot was also performed to detect the changes in the expressions of phosphorylated Akt-1 (pAkt1) and ERK1/2 (pERK1/2) proteins,which were key downstream proteins of PI3-K/Akt and MAPK/ ERK1/2 pathways,and BACE1 protein,which was affected by LY294002 and PD98059,the specific inhibitors of PD-K/Akt and MAPK/ ERK1/2 signaling pathways. The levels of AB42 in cellular culture medium was detected by ELBA. Results NaHS within the experimental concentration range decreased BACE1 expression in a dose-dependent manner, and the BACE1 expression reached the minimum level in PC12 cells exposed to 200 μmol/L NaHS. There were singificant differences in BACE1 expression between PC12 cells exposed to different concentrations of NaHS and control group (P 0.05). The expression of Aβ42 showed the same trend as BACE1 whether the inhibitors were used or not. Conclusion The PI3-K/Akt signaling pathway,not the MAPK/ERK1/2 signaling pathway, may be involved in the down-regulated expression of BACE1 induced by exogenous hydrogen sulfide in PC12 cells.%目的观察外源性硫化氢(H2S)对嗜铬细胞瘤细胞(PC12)β位淀粉样前体蛋白裂解酶1( BACE1)表达的影响,并探讨可能涉及的细胞信号机制.方法用不同浓度的硫氢化钠(NaHS)处理体外培养的PC12细胞,利用RT-PCR和Western blot法检测细胞内BACE1 mRNA及蛋白表达；继以LY294002和PD98059分别阻断磷脂酰肌醇3-激酶/丝氨酸苏氨酸蛋白激酶(PI3-K/Akt)及丝裂酶原活化蛋白激酶/细胞外信号调节激酶1/2( MAPK 6. Insulin-like growth factor-1 reduces β-amyloid precursor protein expression after ischemic white matter damage in near-term fetal sheep%胰岛素样生长因子-1减少胎羊缺血性脑白质损伤后淀粉样前体蛋白表达 Institute of Scientific and Technical Information of China (English) 曹云; Alistair Jan GUAN; Laura BENNET; David WU; Sherly GEORGE; Peter GLUCKMAN; 邵肖梅; Jian GUAN 2004-01-01 目的淀粉样前体蛋白(β-APP)是脑白质损伤早期敏感的指标,并参与缺氧缺血性脑损伤机制.本研究观察胎羊缺血性脑白质损伤及胰岛素样生长因子-1(IGF-1)治疗对淀粉样前体蛋白(β-APP)表达的影响.方法胎羊于胎龄117-124天(足月为147天)时通过双侧颈动脉阻塞30 min造成双侧脑缺血损伤,损伤后胎羊随机分为损伤组(n=8)和重组人IGF-1(rhIGF-1)治疗组(n=9);另设正常对照组(n=5),为假手术动物.治疗组缺血后90 min经侧脑室注射3μgrhIGF-1;损伤组经侧脑室注射等量人工脑脊液.缺血损伤后96 h结束实验,处死动物,取出胎羊,固定脑组织.免疫组化法检测脑白质胶质原纤维酸性蛋白(GFAP)、β-APP阳性细胞及白质内髓鞘碱性蛋白(MBP)密度.应用免疫荧光双标记观察APP表达阳性细胞.结果与正常对照组(27.8±4.8)比较,缺血损伤组MBP密度(4.7±7.1,P＜0.001)明显减少.正常对照组未见β-APP阳性细胞,损伤后阳性细胞数明显增加(49.6±23.7,P＜0.001),rhIGF-1治疗可减少β-APP阳性细胞数(17.9±16.5,P＜0.01).免疫荧光双标记显示部分细胞为β-APP-GFAP双标阳性细胞.结论胎羊缺血性脑白质损伤可导致星形胶质细胞表达β-APP,β-APP表达增加可能与脑损伤有关.IGF-1可减少β-APP表达,可能是减轻脑白质损伤的机制之一.%Objective β-amyloid precursor protein (β-APP) is thought to be a sensitive marker for brain white matter damage (WMD) and participates in the mechanisms of hypoxic-ischemic brain damage. This paper aims to study the influence of ischemia and IGF-1 treatment on the expression of β-APP in white matter of near-term fetal sheep.Methods Romney-Suffolk fetal sheep were instrumented at 117 to 124 days of gestation (term= 147 days). Reversible cerebral ischemia was induced by occlusion of bilateral carotid arteries for 30 mins. After damage the sheep were randomly divided into two groups: the Ischemic group ( n =8) and 7. Goodpasture Antigen-binding Protein/Ceramide Transporter Binds to Human Serum Amyloid P-Component and Is Present in Brain Amyloid Plaques NARCIS (Netherlands) Mencarelli, Chiara; Bode, Gerard H.; Losen, Mario; Kulharia, Mahesh; Molenaar, Peter C.; Veerhuis, Robert; Steinbusch, Harry W. M.; De Baets, Marc H.; Nicolaes, Gerry A. F.; Martinez-Martinez, Pilar 2012-01-01 Serum amyloid P component (SAP) is a non-fibrillar glycoprotein belonging to the pentraxin family of the innate immune system. SAP is present in plasma, basement membranes, and amyloid deposits. This study demonstrates, for the first time, that the Goodpasture antigen-binding protein (GPBP) binds to 8. Neuroprotective Approaches in Experimental Models of β-Amyloid Neurotoxicity : Relevance to Alzheimer's Disease NARCIS (Netherlands) Harkany, Tibor; Hortobágyi, Tibor; Sasvári, Maria; Kónya, Csaba; Penke, Botond; Luiten, Paul G.M.; Nyakas, Csaba 1999-01-01 1. β-Amyloid peptides (Aβs) accumulate abundantly in the Alzheimer’s disease (AD) brain in areas subserving information acquisition and processing, and memory formation. Aβ fragments are produced in a process of abnormal proteolytic cleavage of their precursor, the amyloid precursor protein (APP). W 9. THE EOSINOPHILIC MATERIAL IN ADENOMATOID ODONTOGENIC TUMOR ASSOCIATED WITH AMYLOID PROTEIN COMPONENT Institute of Scientific and Technical Information of China (English) SONG Bao-ping; LI Yong-mei; Haruo Okabe 1999-01-01 Objective: To investigate the relation between eosinophilic materials and amyloid P (AP) component in adenomatoid odontogenic tumor (AOT). Methods: The expression of amyloid proteins and basement membrane proteins, including type Ⅳ collagen, laminin and heparin sulfate proteoglycan (HSPG), in AOT were analyzed by immunohistochemical method. Results:Most eosinophilic droplets among tumor cells and some epithelial cells showed positive stain for AP component.The immunoreactions of type Ⅳ collagen and laminin were only found in blood vessels of this tumor. The tumor cells and eosinophilic materials in duct-like structures were constantly unstained for both amyloid and basement membrane proteins. Present results suggest that the nature and composition of eosinophilic droplets may differ from the eosinophilic layer in ductlike structures. This study first demonstrated that the amyloid-like deposition in AOT is associated with AP component by immunohistochemical method. It supported that AP component may be epithelial origin since the AP immunolocalization was found in tumor cells. 10. Effect of catalpol on senile plaques and spatial learning and memory ability in amyloidprotein precursor/presenilin 1 double transgenic mice%梓醇对淀粉样蛋白前体/早老素1双转基因小鼠老年斑和学习记忆的影响 Institute of Scientific and Technical Information of China (English) 宋冲; 楚亚楠; 贺桂琼; 刘刚; 王凌唏; 周泽芬; 姚秋会 2013-01-01 目的观察梓醇对淀粉样蛋白前体、早老素1(APP/PSI)双转基因小鼠老年斑和学习记忆能力的影响.方法将3个月龄的APP/PS1双转基因小鼠按照随机数字表法分为梓醇治疗组和生理盐水对照组,每组10只,并以10只同月龄的相同遗传背景的C57小鼠作为正常对照组.用梓醇(每天5 mg/kg)和等量生理盐水腹腔注射阿尔茨海默病(AD)模型小鼠3周,应用免疫组织化学检测各组小鼠老年斑数量的变化；应用Morris水迷宫检测小鼠空间学习记忆能力的变化.结果免疫组织化学结果显示:与生理盐水对照组(6.0±0.6)比较,梓醇治疗组小鼠老年斑数量(个)明显减少(2.3±0.7,t=3.500,P=0.025).行为学结果显示:(1)在可视平台实验中,3组小鼠找到平台的平均潜伏期和搜索的平均路径差异无统计学意义.(2)隐蔽平台下,梓醇治疗组小鼠找到平台的时间及搜索的路径较生理盐水对照组小鼠明显缩短；与正常对照组比较,差异无统计学意义.(3)在探索实验中,60 s内梓醇治疗组(6.4±0.5)小鼠穿越平台次数(次)明显高于生理盐水对照组(2.9±0.4,t=5.592,P=0.001),而与正常对照组(6.8±0.6)比较差异无统计学意义(t=0.418,P=0.682).结论梓醇治疗能显著减少AD模型小鼠脑内老年斑数量,改善小鼠的空间学习记忆能力.%Objective To investigate whether catalpol affects senile plaque formation and spatial learning and memory ability in the amyloidprotein precursor/presenilin 1 (APP/PSI) double transgenic mice.Methods Three month-old APP/PS1 double transgenic mice were randomly divided into catalpoltreated and saline-treated groups (n =10),with C57 mice of the same age and genetic background as normal control group (n =10).The catalpol (in a dose of 5 mg · kg-1 · d-1) and the same amount of saline were peritoneally injected into Alzheimer' s disease (AD) model mice for 3 weeks.Immunohistochemical staining was performed to examine senile 11. Amyloid Beta-Protein and Neural Network Dysfunction Directory of Open Access Journals (Sweden) Fernando Peña-Ortega 2013-01-01 Full Text Available Understanding the neural mechanisms underlying brain dysfunction induced by amyloid beta-protein (Aβ represents one of the major challenges for Alzheimer’s disease (AD research. The most evident symptom of AD is a severe decline in cognition. Cognitive processes, as any other brain function, arise from the activity of specific cell assemblies of interconnected neurons that generate neural network dynamics based on their intrinsic and synaptic properties. Thus, the origin of Aβ-induced cognitive dysfunction, and possibly AD-related cognitive decline, must be found in specific alterations in properties of these cells and their consequences in neural network dynamics. The well-known relationship between AD and alterations in the activity of several neural networks is reflected in the slowing of the electroencephalographic (EEG activity. Some features of the EEG slowing observed in AD, such as the diminished generation of different network oscillations, can be induced in vivo and in vitro upon Aβ application or by Aβ overproduction in transgenic models. This experimental approach offers the possibility to study the mechanisms involved in cognitive dysfunction produced by Aβ. This type of research may yield not only basic knowledge of neural network dysfunction associated with AD, but also novel options to treat this modern epidemic. 12. Deposition of mouse amyloid beta in human APP/PS1 double and single AD model transgenic mice. NARCIS (Netherlands) Groen, T. van; Kiliaan, A.J.; Kadish, I. 2006-01-01 The deposition of amyloid beta (Abeta) peptides and neurofibrillary tangles are the two characteristic pathological features of Alzheimer's disease (AD). To investigate the relation between amyloid precursor protein (APP) production, amyloid beta deposition and the type of Abeta in deposits, i.e., h 13. Specific Triazine Herbicides Induce Amyloid-beta(42) Production NARCIS (Netherlands) Portelius, Erik; Durieu, Emilie; Bodin, Marion; Cam, Morgane; Pannee, Josef; Leuxe, Charlotte; Mabondzo, Aloise; Oumata, Nassima; Galons, Herve; Lee, Jung Yeol; Chang, Young-Tae; Stuber, Kathrin; Koch, Philipp; Fontaine, Gaelle; Potier, Marie-Claude; Manousopoulou, Antigoni; Garbis, Spiros D.; Covaci, Adrian; Van Dam, Debby; De Deyn, Peter; Karg, Frank; Flajolet, Marc; Omori, Chiori; Hata, Saori; Suzuki, Toshiharu; Blennow, Kaj; Zetterberg, Henrik; Meijer, Laurent 2016-01-01 Proteolytic cleavage of the amyloid-beta protein precursor (A beta PP) ecretases leads to extracellular release of amyloid-beta (A beta) peptides. Increased production of A beta(42) over A beta(40) and aggregation into oligomers and plaques constitute an Alzheimer's disease (AD) hallmark. Identifyin 14. Comparison of the aggregation of homologous β2-microglobulin variants reveals protein solubility as a key determinant of amyloid formation. Science.gov (United States) Pashley, Clare L; Hewitt, Eric W; Radford, Sheena E 2016-02-13 The mouse and human β2-microglobulin protein orthologs are 70% identical in sequence and share 88% sequence similarity. These proteins are predicted by various algorithms to have similar aggregation and amyloid propensities. However, whilst human β2m (hβ2m) forms amyloid-like fibrils in denaturing conditions (e.g. pH2.5) in the absence of NaCl, mouse β2m (mβ2m) requires the addition of 0.3M NaCl to cause fibrillation. Here, the factors which give rise to this difference in amyloid propensity are investigated. We utilise structural and mutational analyses, fibril growth kinetics and solubility measurements under a range of pH and salt conditions, to determine why these two proteins have different amyloid propensities. The results show that, although other factors influence the fibril growth kinetics, a striking difference in the solubility of the proteins is a key determinant of the different amyloidogenicity of hβ2m and mβ2m. The relationship between protein solubility and lag time of amyloid formation is not captured by current aggregation or amyloid prediction algorithms, indicating a need to better understand the role of solubility on the lag time of amyloid formation. The results demonstrate the key contribution of protein solubility in determining amyloid propensity and lag time of amyloid formation, highlighting how small differences in protein sequence can have dramatic effects on amyloid formation. 15. Transmembrane amyloid-related proteins in CSF as potential biomarkers for Alzheimer’s disease Directory of Open Access Journals (Sweden) 2015-06-01 Full Text Available In the continuing search for new cerebrospinal fluid (CSF biomarkers for Alzheimer’s disease (AD, reasonable candidates are the secretase enzymes involved in the processing of the amyloid precursor protein (APP, as well as the large proteolytic cleavage fragments sAPPα and sAPPβ. The enzymatic activities of some of these secretases, such as BACE1 and TACE, have been investigated as potential AD biomarkers, and it has been assumed that these activities present in human CSF result from the soluble truncated forms of the membrane-bound enzymes. However, we and others recently identified soluble forms of BACE1 and APP in CSF containing the intracellular domains, as well as the multi-pass transmembrane presenilin-1 (PS1 and other subunits of γ-secretase. We also review recent findings that suggest that most of these soluble transmembrane proteins could display self-association properties based on hydrophobic and/or ionic interactions leading to the formation of heteromeric complexes. The oligomerization state of these potential new biomarkers needs to be taken into consideration for assessing their real potential as CSF biomarkers for AD by adequate molecular tools. 16. Constant region of a kappa III immunoglobulin light chain as a major AL-amyloid protein DEFF Research Database (Denmark) Engvig, J P; Olsen, K E; Gislefoss, R E 1998-01-01 and the corresponding AL protein as a kappa III immunoglobulin light chain from material of a patient with systemic AL-amyloidosis presenting as a local inguinal tumour. The two proteins showed some unique features. The major part of the AL amyloid fibril protein consisted of C-terminal fragments of the Bence... 17. Insights into the variability of nucleated amyloid polymerization by a minimalistic model of stochastic protein assembly Science.gov (United States) Eugène, Sarah; Xue, Wei-Feng; Robert, Philippe; Doumic, Marie 2016-05-01 Self-assembly of proteins into amyloid aggregates is an important biological phenomenon associated with human diseases such as Alzheimer's disease. Amyloid fibrils also have potential applications in nano-engineering of biomaterials. The kinetics of amyloid assembly show an exponential growth phase preceded by a lag phase, variable in duration as seen in bulk experiments and experiments that mimic the small volumes of cells. Here, to investigate the origins and the properties of the observed variability in the lag phase of amyloid assembly currently not accounted for by deterministic nucleation dependent mechanisms, we formulate a new stochastic minimal model that is capable of describing the characteristics of amyloid growth curves despite its simplicity. We then solve the stochastic differential equations of our model and give mathematical proof of a central limit theorem for the sample growth trajectories of the nucleated aggregation process. These results give an asymptotic description for our simple model, from which closed form analytical results capable of describing and predicting the variability of nucleated amyloid assembly were derived. We also demonstrate the application of our results to inform experiments in a conceptually friendly and clear fashion. Our model offers a new perspective and paves the way for a new and efficient approach on extracting vital information regarding the key initial events of amyloid formation. 18. Self-assembling of amyloid-like proteins Energy Technology Data Exchange (ETDEWEB) Sales, E.M.; Barbosa, L.R.S.; Itri, R. [Universidade de Sao Paulo (USP), SP (Brazil); Damalio, J.C.P.; Araujo, A.P.U. [Universidade de Sao Paulo (USP-SC), Sao Carlos, SP (Brazil); Spinozzi, F.; Mariani, P. [Universita Politecnica delle Marche, Ancona (Italy) 2012-07-01 Full text: Septins are proteins from the GTP-binding family and participate in cell division cycle performing functions such as secretion and cytoskeletal division. They can also be found in neurodegenerative conditions as Alzheimers and Parkinson's diseases, forming highly organized fiber-like aggregates known as amyloids. In this work, we used small angle x-ray scattering (SAXS) to investigate the formation and time evolution of septins aggregates under the influence of temperature and concentration. The SAXS measurements were performed with the GTPase domain of human Septin 2 (SEPT2G) at 0.5 and 1 mg/mL and temperatures between 4 and 45 deg C. At 0.5 mg/mL and 4 deg C, the protein self-aggregates as a dimer, being stable over one hour of observation. When the temperature was increased to 15 deg C, the results demonstrate that cylinder-like aggregates are formed and coexist with some dimer population and a small amount of larger aggregates. However, the number of very large aggregates increases with time concomitantly with the decrease of cylinder amount in the solution. At 37 deg C cylinder-like aggregates are not longer present in solution, whereas a significant amount of dimers decreases from 50% to 20% in less than 1 hour. At 45 deg C such an effect is even more accentuated: the percentage of dimers is only 6% in solution into a favor of 94% of very larger aggregates. When we analyze the protein at 1 mg/mL, at 4 deg C cylinder-like aggregates (36 nm-long and 12 nm-cross section) are already formed, coexisting with dimers and, as occurred for lower concentration, the two populations remained unchanged over one hour of observation. Out results also indicate that the dimensions of these cylinders increase with the concentration and the percentage of cylinders and larger aggregates are higher than those found for 0.5 mg/mL. In conclusion, our results showed the coexistence of dimers of SEPT2G with small fibers and larger aggregates in solution that evolve 19. HIV Tat protein and amyloid-β peptide form multifibrillar structures that cause neurotoxicity. Science.gov (United States) Hategan, Alina; Bianchet, Mario A; Steiner, Joseph; Karnaukhova, Elena; Masliah, Eliezer; Fields, Adam; Lee, Myoung-Hwa; Dickens, Alex M; Haughey, Norman; Dimitriadis, Emilios K; Nath, Avindra 2017-02-20 Deposition of amyloid-β plaques is increased in the brains of HIV-infected individuals, and the HIV transactivator of transcription (Tat) protein affects amyloidogenesis through several indirect mechanisms. Here, we investigated direct interactions between Tat and amyloid-β peptide. Our in vitro studies showed that in the presence of Tat, uniform amyloid fibrils become double twisted fibrils and further form populations of thick unstructured filaments and aggregates. Specifically, Tat binding to the exterior surfaces of the Aβ fibrils increases β-sheet formation and lateral aggregation into thick multifibrillar structures, thus producing fibers with increased rigidity and mechanical resistance. Furthermore, Tat and Aβ aggregates in complex synergistically induced neurotoxicity both in vitro and in animal models. Increased rigidity and mechanical resistance of the amyloid-β-Tat complexes coupled with stronger adhesion due to the presence of Tat in the fibrils may account for increased damage, potentially through pore formation in membranes. 20. Serum amyloid A and protein AA: molecular mechanisms of a transmissible amyloidosis. Science.gov (United States) Westermark, Gunilla T; Westermark, Per 2009-08-20 Systemic AA-amyloidosis is a complication of chronic inflammatory diseases and the fibril protein AA derives from the acute phase reactant serum AA. AA-amyloidosis can be induced in mice by an inflammatory challenge. The lag phase before amyloid develops can be dramatically shortened by administration of a small amount of amyloid fibrils. Systemic AA-amyloidosis is transmissible in mice and may be so in humans. Since transmission can cross species barriers it is possible that AA-amyloidosis can be induced by amyloid in food, e.g. foie gras. In mice, development of AA-amyloidosis can also be accelerated by other components with amyloid-like properties. A new possible risk factor may appear with synthetically made fibrils from short peptides, constructed for tissue repair. 1. AMYLOID-β PEPTIDE BINDS TO MICROTUBULE-ASSOCIATED PROTEIN 1B (MAP1B) Science.gov (United States) Gevorkian, Goar; Gonzalez-Noriega, Alfonso; Acero, Gonzalo; Ordoñez, Jorge; Michalak, Colette; Munguia, Maria Elena; Govezensky, Tzipe; Cribbs, David H.; Manoutcharian, Karen 2008-01-01 Extracellular and intraneuronal formation of amyloid-beta aggregates have been demonstrated to be involved in the pathogenesis of Alzheimer’s disease. However, the precise mechanism of amyloid-beta neurotoxicity is not completely understood. Previous studies suggest that binding of amyloid-beta to a number of targets have deleterious effects on cellular functions. In the present study we have shown for the first time that amyloid-beta 1-42 bound to a peptide comprising the microtubule binding domain of the heavy chain of microtubule-associated protein 1B by the screening of a human brain cDNA library expressed on M13 phage. This interaction may explain, in part, the loss of neuronal cytoskeletal integrity, impairment of microtubule-dependent transport and synaptic dysfunction observed previously in Alzheimer’s disease. PMID:18079022 2. Biotechnologically engineered protein binders for applications in amyloid diseases. Science.gov (United States) Haupt, Christian; Fändrich, Marcus 2014-10-01 The aberrant self-assembly of polypeptide chains into amyloid structures is a common phenomenon in several neurodegenerative diseases, systemic amyloidosis, and 'normal' aging. Improvements in laboratory-scale detection of these structures, their clinical diagnosis, and the treatment of disease likely depend on the advent of new molecules that recognize particular states or induce their clearance in vivo. This review will describe what biotechnology can do to generate proteinaceous amyloid-binders, explain their molecular recognition mechanisms, and summarize possibilities to functionalize further these ligands for specific applications. 3. Influence of Adsorption on Proteins and Amyloid Detection by Silicon Nitride Nanopore. Science.gov (United States) Balme, Sébastien; Coulon, Pierre Eugène; Lepoitevin, Mathilde; Charlot, Benoît; Yandrapalli, Naresh; Favard, Cyril; Muriaux, Delphine; Bechelany, Mikhael; Janot, Jean-Marc 2016-09-01 For the past 2 decades, emerging single-nanopore technologies have opened the route to multiple sensing applications. Besides DNA sensing, the identification of proteins and amyloids is a promising field for early diagnosis. However, the influence of the interactions between the nanopore surface and proteins should be taken into account. In this work, we have selected three proteins (avidin, lysozyme, and IgG) that exhibit different affinities with the SiNx surface, and we have also examined lysozyme amyloid. Our results show that the piranha treatment of SiNx significantly decreases protein adsorption. Moreover, we have successfully detected all proteins (pore diameter 17 nm) and shown the possibility of discriminating between denatured lysozyme and its amyloid. For all proteins, the capture rates are lower than expected, and we evidence that they are correlated with the affinity of proteins to the surface. Our result confirms that proteins interacting only with the nanopore surface wall stay long enough to be detected. For lysozyme amyloid, we show that the use of the nanopore is suitable for determining the number of monomer units even if only the proteins interacting with the nanopore are detected. 4. Extended analysis of AL-amyloid protein from abdominal wall subcutaneous fat biopsy DEFF Research Database (Denmark) Olsen, K E; Sletten, K; Westermark, Per 1998-01-01 a subcutaneous fat tissue biopsy and submitted to extended protein separation, typing and amino acid sequence analyses. The AL-protein belonged to the rare immunoglobulin light chain kappa, subtype kappa IV and contained unique amino acid substitutions, mostly in the highly preserved framework regions. The study...... shows that subcutaneous fat biopsies are useful sources of amyloid material for biochemical studies.... 5. Comparative investigation of B-Protein and its probable precursor Energy Technology Data Exchange (ETDEWEB) Schweikert, A.; Bucovaz, E. 1987-05-01 B-Protein, discovered in 1976 by Bucovaz, appears to be a general biological marker for the detection of cancer. An assay procedure was developed to detect B-Protein which involves the interaction of B-Protein with a specific radiolabeled protein named binding protein, a substructure of the coenzyme A-synthesizing protein complex (CoA-SPC) of Bakers' yeast. A protein which may be the precursor of B-Protein is present normally in serum, whereas, a modified or altered protein, designated B-Protein, is present in the serum of cancer patients. Analysis of B-Protein and its relationship with the normal serum protein demonstrates a difference in solubility between B-Protein and the normal counterpart. Although physiochemical characteristics between both are very similar, i.e., electrophoretic mobility, molecular weight, pI, immunological recognition, there appears to be minor differences in the carbohydrate moiety of B-Protein as demonstrated by periodic acid-Schiff base staining and the binding of Wheat Germ Lectin. Lipid content has also been examined but has not been associated with the difference in solubility. Currently, the difference in B-Protein and its normal protein counterpart appears to be related to conformational differences in the tertiary structures. 6. Metabolism of β-amyloid precursor protein, expressions of its related enzymes and effect of pioglitazone intervention in the brain of insulin resistance rats%胰岛素抵抗大鼠脑组织APP代谢及其相关酶的表达及吡格列酮的干预效果 Institute of Scientific and Technical Information of China (English) 袁树华; 高顺宗; 刘雪平; 郝跃伟; 赵婷婷; 侯亮 2009-01-01 目的观察胰岛素抵抗(IR)大鼠脑组织β-淀粉样蛋白(Aβ)、淀粉样前体蛋白(APP)及其代谢相关酶的表达及吡格列酮(PIO)的干预效果.方法从45只Wistar大鼠中随机选取10只作为对照组(NC组),35只给予10%果糖水诱发胰岛素抵抗,4周后根据胰岛素抵抗指数(IRI),将制作成功的胰岛素抵抗模型26只大鼠随机分为IR组、PIO组.PIO组灌服吡格列酮(10 mg·kg~(-1)·d~(-1))12周,IR组和NC组给予相同体积的生理盐水.免疫组化法观察大鼠海马Aβ42的表达;免疫印迹法检测大鼠脑APP、β-分泌酶(BACE1)、γ-分泌酶(PSI)的变化.结果IR组和PIO组大鼠海马Aβ42的表达明显高于NC组,与IR组相比,PIO组表达明显减低(P<0.01);与NC组相比,IR组和PIO组大鼠脑组织APP、BACE1及PS1的表达增高,PIO组表达较IR组减少(P<0.05).结论胰岛素抵抗大鼠脑组织通过上调BACE1、PS1活性,使Aβ42生成增加;吡格列酮能抑制BACE1、PS1的表达,减少Aβ42生成.%Objective To investigate the expressions of β-amyloid (Aβ), amyloid precmsor protein (APP) and its metabohsm-related enzymes, and to explore the effect of pioglitazone (PIO) intervention in the brain of insulin resistance rats. Methods Of 45 Wistar male rats, 10 were randomly chosen as the control group (NC group), and the others were given 10% fructose for 4 weeks to develop the insulin resistance (IR) model. 26 IR rats were randomly divided into the IR group(n = 13) and the PIO group (n= 13). The PIO group was given pioglitazone(10 mg·kg~(-1)·d~(-1) by gavage for 12 weeks, and the IR and NC groups were given an identical volume of physiological saline. Immunohistochemistry and Western blotting were employed to examine the level of Aβ42 in the hippoeampus and the changes of APP, β-secretase (BACE1) and γ-secretase (PSI) in the brain tissue, Re-suits Immunohistoehemistry results indicated that the optical density of Aβ42 in the hippocampus of the IR and PIO groups was 7. Staphylococcal Bap Proteins Build Amyloid Scaffold Biofilm Matrices in Response to Environmental Signals. Science.gov (United States) Taglialegna, Agustina; Navarro, Susanna; Ventura, Salvador; Garnett, James A; Matthews, Steve; Penades, José R; Lasa, Iñigo; Valle, Jaione 2016-06-01 Biofilms are communities of bacteria that grow encased in an extracellular matrix that often contains proteins. The spatial organization and the molecular interactions between matrix scaffold proteins remain in most cases largely unknown. Here, we report that Bap protein of Staphylococcus aureus self-assembles into functional amyloid aggregates to build the biofilm matrix in response to environmental conditions. Specifically, Bap is processed and fragments containing at least the N-terminus of the protein become aggregation-prone and self-assemble into amyloid-like structures under acidic pHs and low concentrations of calcium. The molten globule-like state of Bap fragments is stabilized upon binding of the cation, hindering its self-assembly into amyloid fibers. These findings define a dual function for Bap, first as a sensor and then as a scaffold protein to promote biofilm development under specific environmental conditions. Since the pH-driven multicellular behavior mediated by Bap occurs in coagulase-negative staphylococci and many other bacteria exploit Bap-like proteins to build a biofilm matrix, the mechanism of amyloid-like aggregation described here may be widespread among pathogenic bacteria. 8. Staphylococcal Bap Proteins Build Amyloid Scaffold Biofilm Matrices in Response to Environmental Signals Science.gov (United States) Taglialegna, Agustina; Navarro, Susanna; Ventura, Salvador; Garnett, James A.; Matthews, Steve; Penades, José R.; Lasa, Iñigo; Valle, Jaione 2016-01-01 Biofilms are communities of bacteria that grow encased in an extracellular matrix that often contains proteins. The spatial organization and the molecular interactions between matrix scaffold proteins remain in most cases largely unknown. Here, we report that Bap protein of Staphylococcus aureus self-assembles into functional amyloid aggregates to build the biofilm matrix in response to environmental conditions. Specifically, Bap is processed and fragments containing at least the N-terminus of the protein become aggregation-prone and self-assemble into amyloid-like structures under acidic pHs and low concentrations of calcium. The molten globule-like state of Bap fragments is stabilized upon binding of the cation, hindering its self-assembly into amyloid fibers. These findings define a dual function for Bap, first as a sensor and then as a scaffold protein to promote biofilm development under specific environmental conditions. Since the pH-driven multicellular behavior mediated by Bap occurs in coagulase-negative staphylococci and many other bacteria exploit Bap-like proteins to build a biofilm matrix, the mechanism of amyloid-like aggregation described here may be widespread among pathogenic bacteria. PMID:27327765 9. Effects of phosphatidylinositol-3 kinase/serine threonine kinase pathway on expression of beta-site amyloid precursor protein cleaving enzyme-1 in the hippocampus neurons%胰岛素信号通路磷脂酰肌醇-3激酶/丝氨酸苏氨酸蛋白激酶对海马神经元β-淀粉样前体蛋白裂解酶1表达的影响 Institute of Scientific and Technical Information of China (English) 李洁颖; 晏勇; 蔡志友; 冯占辉; 张华; 吴芳; 孟涛; 代政伟 2009-01-01 目的通过胰岛素和磷脂酰肌醇-3激酶(PDK)抑制剂渥曼青霉素(wortmannin,WORT)对PI3K/丝氨酸苏氨酸蛋白激酶(PDK/Akt)信号通路的激活和抑制作用,观察PI3K/Akt信号通路对海马神经元B-淀粉样前体蛋白裂解酶1(BACE1)表达的影响.方法 40只SD大鼠随机分为空白对照组、假手术组、胰岛素组和WORT组(每组10只),海马立体定向注射胰岛素和PI3K抑制剂WORT.免疫组织化学和Western blot法检测PI3K/Akt信号传导相关蛋白以及BACE1的表达水平.结果注射胰岛素的海马PI3K信号通路下游信号分子较对照组:Akt表达增加(0.952±0.060与0.835±0.029,t=4.9150,P=0.0001),Akt set473位点磷酸化(pAkt)水平上调(0.800±0.075与0.657±0.025,t=4.5598,P=0.0002),糖原合成激酶-3α(GSK-3α)磷酸化水平降低(0.604±0.062与0.726±0. 041,t=3.5871,P=0.0018),而成熟的BACE1及其裂解产物β分泌酶C末端(β-CTF)表达下调.WORT组的PI3K下游信号分子Akt、pAkt表达明显被抑制,磷酸化GSK-3α表达增加,同时成熟的BACE1(1.004±0.096)和β-CTF(1.031±0.048)的表达较对照组(分别0.498±0.064,0.786±0.101)上调(分别t=11.5980,P=0.0000;t=4.2194,P=0.0004).结论胰岛素信号通路PI3K/AKt可以调节BACE1的表达和活性并参与阿尔茨海默病的发病机制.%Objective To investigate the effect of phosphatidylinesitol-3 kinase/serine threonine kinase (PI3K/Akt) signaling pathway on expression of beta-site amyloid precursor protein cleaving enzyme-1 (BACE1) in the hippocampus neurons of rat brain. Methods Forty SD rats were randomly divided into 4 groups: blank control group, sham-operated group, insulin group and wortmannin group. Insulin or the specific inhibitor of PI3K, wortmannin was injected into hippocampus neurons to activate or inhibit the signaling pathway in insulin group or wortmannin group, respectively. Immunoprecipitation and Western blot were used to analyze the proteins levels of PI3K/Akt and BACE1. Results In insulin 10. [Amyloid typing from formalin-fixed paraffin-embedded tissues using LMD-LC-MS/MS system]. Science.gov (United States) Tasaki, Masayoshi; Obayashi, Konen; Ueda, Mitsuharu; Ando, Yukio 2014-03-01 Amyloidosis is one of the protein conformational disorders in which normally soluble proteins accumulate insoluble amyloid fibrils, leading to severe organ dysfunction. To date, 30 different amyloidogenic proteins have been reported. Immunohistochemistry (IHC) is usually used to identify the amyloid precursor protein, but the results may be inconclusive owing to a loss of epitopes or small amounts of amyloid deposits, comprising unknown amyloidogenic protein. Recently, laser microdissection (LMD)-liquid chromatography tandem mass spectrometry (LC-MS/MS) has been used in a novel method to identify amyloid precursor protein from amyloid-laden formalin-fixed paraffin embedded (FFPE) tissues. We describe the usefulness of the system for amyloid typing in this report. 11. Elongation of mouse prion protein amyloid-like fibrils: effect of temperature and denaturant concentration. Directory of Open Access Journals (Sweden) Katazyna Milto Full Text Available Prion protein is known to have the ability to adopt a pathogenic conformation, which seems to be the basis for protein-only infectivity. The infectivity is based on self-replication of this pathogenic prion structure. One of possible mechanisms for such replication is the elongation of amyloid-like fibrils. We measured elongation kinetics and thermodynamics of mouse prion amyloid-like fibrils at different guanidine hydrochloride (GuHCl concentrations. Our data show that both increases in temperature and GuHCl concentration help unfold monomeric protein and thus accelerate elongation. Once the monomers are unfolded, further increases in temperature raise the rate of elongation, whereas the addition of GuHCl decreases it. We demonstrated a possible way to determine different activation energies of amyloid-like fibril elongation by using folded and unfolded protein molecules. This approach separates thermodynamic data for fibril-assisted monomer unfolding and for refolding and formation of amyloid-like structure. 12. Diagnostic performance of amyloid A protein quantification in fat tissue of patients with clinical AA amyloidosis NARCIS (Netherlands) Hazenberg, Bouke P. C.; Bijzet, Johannes; Limburg, Pieter C.; Skinner, Martha; Hawkins, Philip N.; Butrimiene, Irena; Livneh, Avi; Lesnyak, Olga; Nasonov, Evgeney L.; Filipowicz-Sosnowska, Anna; Guel, Ahmet; Merlini, Giampaolo; Wiland, Piotr; Oezdogan, Huri; Gorevic, Peter D.; Ben Maiz, Hedi; Benson, Merrill D.; Direskeneli, Haner; Kaarela, Kalevi; Garceau, Denis; Hauck, Wendy; van Rijswijk, Martin 2007-01-01 Objective. Amyloid A protein quantification in fat tissue is a new immunochemical method for detecting AA amyloidosis, a rare but serious disease. The objective was to assess diagnostic performance in clinical AA amyloidosis. Methods. Abdominal subcutaneous fat tissue of patients with AA amyloidosis 13. Structural basis for precursor protein-directed ribosomal peptide macrocyclization Energy Technology Data Exchange (ETDEWEB) Li, Kunhua; Condurso, Heather L.; Li, Gengnan; Ding, Yousong; Bruner, Steven D. (Florida) 2016-11-11 Macrocyclization is a common feature of natural product biosynthetic pathways including the diverse family of ribosomal peptides. Microviridins are architecturally complex cyanobacterial ribosomal peptides that target proteases with potent reversible inhibition. The product structure is constructed via three macrocyclizations catalyzed sequentially by two members of the ATP-grasp family, a unique strategy for ribosomal peptide macrocyclization. Here we describe in detail the structural basis for the enzyme-catalyzed macrocyclizations in the microviridin J pathway of Microcystis aeruginosa. The macrocyclases MdnC and MdnB interact with a conserved α-helix of the precursor peptide using a novel precursor-peptide recognition mechanism. The results provide insight into the unique protein–protein interactions that are key to the chemistry, suggest an origin for the natural combinatorial synthesis of microviridin peptides, and provide a framework for future engineering efforts to generate designed compounds. 14. Microglia, neuroinflammation, and beta-amyloid protein in Alzheimer's disease. Science.gov (United States) Cai, Zhiyou; Hussain, M Delwar; Yan, Liang-Jun 2014-05-01 Compelling evidence from basic molecular biology has demonstrated the dual roles of microglia in the pathogenesis of Alzheimer's disease (AD). On one hand, microglia are involved in AD pathogenesis by releasing inflammatory mediators such as inflammatory cytokines, complement components, chemokines, and free radicals that are all known to contribute to beta-amyloid (Aβ) production and accumulation. On the other hand, microglia are also known to play a beneficial role in generating anti-Aβ antibodies and stimulating clearance of amyloid plaques. Aβ itself, an inducer of microglia activation and neuroinflammation, has been considered as an underlying and unifying factor in the development of AD. A vicious cycle of inflammation has been formed between Aβ accumulation, activated microglia, and microglial inflammatory mediators, which enhance Aβ deposition and neuroinflammation. Thus, inhibiting the vicious cycle seems to be a promising treatment to restrain further development of AD. With increasing research efforts on microglia in AD, intervention of microglia activation and neuroinflammation in AD may provide a potential target for AD therapy in spite of the provisional failure of nonsteroidal antiinflammatory drugs in clinical trials. 15. Membrane Incorporation, Channel Formation, and Disruption of Calcium Homeostasis by Alzheimer's β-Amyloid Protein Directory of Open Access Journals (Sweden) Masahiro Kawahara 2011-01-01 Full Text Available Oligomerization, conformational changes, and the consequent neurodegeneration of Alzheimer's β-amyloid protein (AβP play crucial roles in the pathogenesis of Alzheimer's disease (AD. Mounting evidence suggests that oligomeric AβPs cause the disruption of calcium homeostasis, eventually leading to neuronal death. We have demonstrated that oligomeric AβPs directly incorporate into neuronal membranes, form cation-sensitive ion channels (“amyloid channels”, and cause the disruption of calcium homeostasis via the amyloid channels. Other disease-related amyloidogenic proteins, such as prion protein in prion diseases or α-synuclein in dementia with Lewy bodies, exhibit similarities in the incorporation into membranes and the formation of calcium-permeable channels. Here, based on our experimental results and those of numerous other studies, we review the current understanding of the direct binding of AβP into membrane surfaces and the formation of calcium-permeable channels. The implication of composition of membrane lipids and the possible development of new drugs by influencing membrane properties and attenuating amyloid channels for the treatment and prevention of AD is also discussed. 16. Endogenously generated amyloid β increases membrane fluidity in neural 2a cells Institute of Scientific and Technical Information of China (English) NIU Ying; SHENG BaiYang; SONG Bo; LIU LingLing; ZHANG XiuFang; ZHAO NanMing; GONG YanDao 2009-01-01 The effect of endogenously generated amyloid β on membrane fluidity was investigated in Neural 2a cells stably expressing Swedish mutant amyloid precursor protein (APPswe). Membrane fluidity was studied by fluorescence polarizability using 1,6-Diphenyl-1,3,5-Hexatriene (DPH) as the fluorescence probe. It was found that the membrane fluidity in APPswe cells was significantly higher than that in its wild type counterparts. Alleviating the effect of amyloid β either by y secretase activity inhibition or by amyloid antibody treatment decreased membrane fluidity, which indicated an important role of amyloid β in increasing membrane fluidity. Treatment using amyloid β channel blocker, tromethamine and NA4 suggested that channel formed by amyloid β on the cell membrane is a way through which amyloid β takes its membrane fluidizing effect. 17. Neuroinflammation in Lyme neuroborreliosis affects amyloid metabolism Directory of Open Access Journals (Sweden) Anckarsäter Henrik 2010-06-01 Full Text Available Abstract Background The metabolism of amyloid precursor protein (APP and β-amyloid (Aβ is widely studied in Alzheimer's disease, where Aβ deposition and plaque development are essential components of the pathogenesis. However, the physiological role of amyloid in the adult nervous system remains largely unknown. We have previously found altered cerebral amyloid metabolism in other neuroinflammatory conditions. To further elucidate this, we investigated amyloid metabolism in patients with Lyme neuroborreliosis (LNB. Methods The first part of the study was a cross-sectional cohort study in 61 patients with acute facial palsy (19 with LNB and 42 with idiopathic facial paresis, Bell's palsy and 22 healthy controls. CSF was analysed for the β-amyloid peptides Aβ38, Aβ40 and Aβ42, and the amyloid precursor protein (APP isoforms α-sAPP and β-sAPP. CSF total-tau (T-tau, phosphorylated tau (P-tau and neurofilament protein (NFL were measured to monitor neural cell damage. The second part of the study was a prospective cohort-study in 26 LNB patients undergoing consecutive lumbar punctures before and after antibiotic treatment to study time-dependent dynamics of the biomarkers. Results In the cross-sectional study, LNB patients had lower levels of CSF α-sAPP, β-sAPP and P-tau, and higher levels of CSF NFL than healthy controls and patients with Bell's palsy. In the prospective study, LNB patients had low levels of CSF α-sAPP, β-sAPP and P-tau at baseline, which all increased towards normal at follow-up. Conclusions Amyloid metabolism is altered in LNB. CSF levels of α-sAPP, β-sAPP and P-tau are decreased in acute infection and increase after treatment. In combination with earlier findings in multiple sclerosis, cerebral SLE and HIV with cerebral engagement, this points to an influence of neuroinflammation on amyloid metabolism. 18. Mink serum amyloid A protein. Expression and primary structure based on cDNA sequences. Science.gov (United States) Marhaug, G; Husby, G; Dowton, S B 1990-06-15 The nucleotide sequences of two mink serum amyloid A (SAA) cDNA clones have been analyzed, one (SAA1) 776 base pairs long and the other (SAA2) 552 base pairs long. Significant differences were discovered when derived amino acid sequences were compared with data for apoSAA isolated from high density lipoprotein. Previous studies of mink protein SAA and amyloid protein A (AA) suggest that only one SAA isotype is amyloidogenic. The cDNA clone for SAA2 defines the "amyloid prone" isotype while SAA1 is found only in serum. Mink SAA1 has alanine in position 10, isoleucine in positions 24, 67, and 71, lysine in position 27, and proline in position 105. Residue 10 in mink SAA2 is valine while arginine and asparagine are at positions 24 and 27, respectively, all characteristics of protein AA isolated from mink amyloid fibrils. Mink SAA2 also has valine in position 67, phenylalanine in position 71, and amino acid 105 is serine. It remains unknown why these six amino acid substitutions render SAA2 more amyloidogenic than SAA1. Eighteen hours after lipopolysaccharide stimulation, mink SAA mRNA is abundant in liver with relatively minor accumulations in brain and lung. Genes encoding both SAA isotypes are expressed in all three organs while no SAA mRNA was detectable in amyloid prone organs, including spleen and intestine, indicating that deposition of AA from locally synthesized SAA is unlikely. A third mRNA species (2.2 kilobases) was identified and hybridizes with cDNA probes for mink SAA1 and SAA2. In addition to a major primary translation product (molecular mass 14,400 Da) an additional product with molecular mass 28,000 Da was immunoprecipitable. 19. Plasma beta amyloid and the risk of Alzheimer's disease in Down syndrome. NARCIS (Netherlands) Coppus, A.M.W.; Schuur, M.; Vergeer, J.; Janssens, A.C.; Oostra, B.A.; Verbeek, M.M.; Duijn, C.M. van 2012-01-01 Extracellular deposition of amyloid beta peptide (Abeta) has been implicated as a critical step in the pathogenesis of Alzheimer's disease (AD). In Down syndrome (DS), Alzheimer's disease is assumed to be caused by the triplication and overexpression of the gene for amyloid precursor protein (APP), 20. The Acute-Phase Proteins Serum Amyloid A and C Reactive Protein in Transudates and Exudates Science.gov (United States) Okino, Alessandra M.; Bürger, Cristiani; Cardoso, Jefferson R.; Lavado, Edson L.; Lotufo, Paulo A.; Campa, Ana 2006-01-01 The distinction between exudates and transudates is very important in the patient management. Here we evaluate whether the acute-phase protein serum amyloid A (SAA), in comparison with C reactive protein (CRP) and total protein (TP), can be useful in this discrimination. CRP, SAA, and TP were determined in 36 exudate samples (27 pleural and 9 ascitic) and in 12 transudates (9 pleural and 3 ascitic). CRP, SAA, and TP were measured. SAA present in the exudate corresponded to 10% of the amount found in serum, that is, the exudate/serum ratio (E/S) was 0.10 ± 0.13. For comparison, the exudate/serum ratio for CRP and TP was 0.39 ± 0.37 and 0.68 ± 0.15, respectively. There was a strong positive correlation between serum and exudate SAA concentration (r = 0.764;p < 0.0001). The concentration of SAA in transudates was low and did not overlap with that found in exudates (0.02-0.21 versus 0.8–360.5 g/mL). SAA in pleural and ascitic exudates results mainly from leakage of the serum protein via the inflamed membrane. A comparison of the E/S ratio of SAA and CRP points SAA as a very good marker in discriminating between exudates and transudates. PMID:16864904 1. Aβ42 Is Essential for Parenchymal and Vascular Amyloid Deposition in Mice OpenAIRE McGowan, Eileen; Pickford, Fiona; Kim, Jungsu; Onstead, Luisa; Eriksen, Jason; Yu, Cindy; Skipper, Lisa; Murphy, M. Paul; Beard, Jenny; Das, Pritam; Jansen,Karen; DeLucia, Michael; Lin, Wen-Lang; Dolios, Georgia; Wang, Rong 2005-01-01 Considerable circumstantial evidence suggests that Aβ42 is the initiating molecule in Alzheimer's disease (AD) pathogenesis. However, the absolute requirement for Aβ42 for amyloid deposition has never been demonstrated in vivo. We have addressed this by developing transgenic models that express Aβ1-40 or Aβ1-42 in the absence of human amyloid β protein precursor (APP) overexpression. Mice expressing high levels of Aβ1-40 do not develop overt amyloid pathology. In contrast, mice expressing low... 2. Conformational landscape of an amyloid intra-cellular domain and Landau-Ginzburg-Wilson paradigm in protein dynamics. Science.gov (United States) Dai, Jin; Niemi, Antti J; He, Jianfeng 2016-07-28 The Landau-Ginzburg-Wilson paradigm is proposed as a framework, to investigate the conformational landscape of intrinsically unstructured proteins. A universal Cα-trace Landau free energy is deduced from general symmetry considerations, with the ensuing all-atom structure modeled using publicly available reconstruction programs Pulchra and Scwrl. As an example, the conformational stability of an amyloid precursor protein intra-cellular domain (AICD) is inspected; the reference conformation is the crystallographic structure with code 3DXC in Protein Data Bank (PDB) that describes a heterodimer of AICD and a nuclear multi-domain adaptor protein Fe65. Those conformations of AICD that correspond to local or near-local minima of the Landau free energy are identified. For this, the response of the original 3DXC conformation to variations in the ambient temperature is investigated, using the Glauber algorithm. The conclusion is that in isolation the AICD conformation in 3DXC must be unstable. A family of degenerate conformations that minimise the Landau free energy is identified, and it is proposed that the native state of an isolated AICD is a superposition of these conformations. The results are fully in line with the presumed intrinsically unstructured character of isolated AICD and should provide a basis for a systematic analysis of AICD structure in future NMR experiments. 3. Conformational landscape of an amyloid intra-cellular domain and Landau-Ginzburg-Wilson paradigm in protein dynamics Science.gov (United States) Dai, Jin; Niemi, Antti J.; He, Jianfeng 2016-07-01 The Landau-Ginzburg-Wilson paradigm is proposed as a framework, to investigate the conformational landscape of intrinsically unstructured proteins. A universal Cα-trace Landau free energy is deduced from general symmetry considerations, with the ensuing all-atom structure modeled using publicly available reconstruction programs Pulchra and Scwrl. As an example, the conformational stability of an amyloid precursor protein intra-cellular domain (AICD) is inspected; the reference conformation is the crystallographic structure with code 3DXC in Protein Data Bank (PDB) that describes a heterodimer of AICD and a nuclear multi-domain adaptor protein Fe65. Those conformations of AICD that correspond to local or near-local minima of the Landau free energy are identified. For this, the response of the original 3DXC conformation to variations in the ambient temperature is investigated, using the Glauber algorithm. The conclusion is that in isolation the AICD conformation in 3DXC must be unstable. A family of degenerate conformations that minimise the Landau free energy is identified, and it is proposed that the native state of an isolated AICD is a superposition of these conformations. The results are fully in line with the presumed intrinsically unstructured character of isolated AICD and should provide a basis for a systematic analysis of AICD structure in future NMR experiments. 4. Estrogen protects neuronal cells from amyloid beta-induced apoptosis via regulation of mitochondrial proteins and function Directory of Open Access Journals (Sweden) Iwamoto Sean 2006-11-01 Full Text Available Abstract Background Neurodegeneration in Alzheimer's disease is associated with increased apoptosis and parallels increased levels of amyloid beta, which can induce neuronal apoptosis. Estrogen exposure prior to neurotoxic insult of hippocampal neurons promotes neuronal defence and survival against neurodegenerative insults including amyloid beta. Although all underlying molecular mechanisms of amyloid beta neurotoxicity remain undetermined, mitochondrial dysfunction, including altered calcium homeostasis and Bcl-2 expression, are involved in neurodegenerative vulnerability. Results In this study, we investigated the mechanism of 17β-estradiol-induced prevention of amyloid beta-induced apoptosis of rat hippocampal neuronal cultures. Estradiol treatment prior to amyloid beta exposure significantly reduced the number of apoptotic neurons and the associated rise in resting intracellular calcium levels. Amyloid beta exposure provoked down regulation of a key antiapoptotic protein, Bcl-2, and resulted in mitochondrial translocation of Bax, a protein known to promote cell death, and subsequent release of cytochrome c. E2 pretreatment inhibited the amyloid beta-induced decrease in Bcl-2 expression, translocation of Bax to the mitochondria and subsequent release of cytochrome c. Further implicating the mitochondria as a target of estradiol action, in vivo estradiol treatment enhanced the respiratory function of whole brain mitochondria. In addition, estradiol pretreatment protected isolated mitochondria against calcium-induced loss of respiratory function. Conclusion Therefore, we propose that estradiol pretreatment protects against amyloid beta neurotoxicity by limiting mitochondrial dysfunction via activation of antiapoptotic mechanisms. 5. Molecular simulations of beta-amyloid protein near hydrated lipids (PECASE). Energy Technology Data Exchange (ETDEWEB) Thompson, Aidan Patrick; Han, Kunwoo (Texas A& M University, College Station, TX); Ford, David M. (Texas A& M University, College Station, TX) 2005-12-01 We performed molecular dynamics simulations of beta-amyloid (A{beta}) protein and A{beta} fragment(31-42) in bulk water and near hydrated lipids to study the mechanism of neurotoxicity associated with the aggregation of the protein. We constructed full atomistic models using Cerius2 and ran simulations using LAMMPS. MD simulations with different conformations and positions of the protein fragment were performed. Thermodynamic properties were compared with previous literature and the results were analyzed. Longer simulations and data analyses based on the free energy profiles along the distance between the protein and the interface are ongoing. 6. Protein corona composition of gold nanoparticles/nanorods affects amyloid beta fibrillation process Science.gov (United States) 2015-03-01 Protein fibrillation process (e.g., from amyloid beta (Aβ) and α-synuclein) is the main cause of several catastrophic neurodegenerative diseases such as Alzheimer's and Parkinson diseases. During the past few decades, nanoparticles (NPs) were recognized as one of the most promising tools for inhibiting the progress of the disease by controlling the fibrillation kinetic process; for instance, gold NPs have a strong capability to inhibit Aβ fibrillations. It is now well understood that a layer of biomolecules would cover the surface of NPs (so called protein corona'') upon the interaction of NPs with protein sources. Due to the fact that the biological species (e.g., cells and amyloidal proteins) see'' the protein corona coated NPs rather than the pristine coated particles, one should monitor the fibrillation process of amyloidal proteins in the presence of corona coated NPs (and not pristine coated ones). Therefore, the previously obtained data on NPs effects on the fibrillation process should be modified to achieve a more reliable and predictable in vivo results. Herein, we probed the effects of various gold NPs (with different sizes and shapes) on the fibrillation process of Aβ in the presence and absence of protein sources (i.e., serum and plasma). We found that the protein corona formed a shell at the surface of gold NPs, regardless of their size and shape, reducing the access of Aβ to the gold inhibitory surface and, therefore, affecting the rate of Aβ fibril formation. More specifically, the anti-fibrillation potencies of various corona coated gold NPs were strongly dependent on the protein source and their concentrations (10% serum/plasma (simulation of an in vitro milieu) and 100% serum/plasma (simulation of an in vivo milieu)).Protein fibrillation process (e.g., from amyloid beta (Aβ) and α-synuclein) is the main cause of several catastrophic neurodegenerative diseases such as Alzheimer's and Parkinson diseases. During the past few decades 7. Automated solid-state NMR resonance assignment of protein microcrystals and amyloids Energy Technology Data Exchange (ETDEWEB) Schmidt, Elena [Goethe University Frankfurt am Main, Center for Biomolecular Magnetic Resonance, Institute of Biophysical Chemistry (Germany); Gath, Julia [ETH Zurich, Physical Chemistry (Switzerland); Habenstein, Birgit [UMR 5086 CNRS/Universite de Lyon 1, Institut de Biologie et Chimie des Proteines (France); Ravotti, Francesco; Szekely, Kathrin; Huber, Matthias [ETH Zurich, Physical Chemistry (Switzerland); Buchner, Lena [Goethe University Frankfurt am Main, Center for Biomolecular Magnetic Resonance, Institute of Biophysical Chemistry (Germany); Boeckmann, Anja, E-mail: a.bockmann@ibcp.fr [UMR 5086 CNRS/Universite de Lyon 1, Institut de Biologie et Chimie des Proteines (France); Meier, Beat H., E-mail: beme@ethz.ch [ETH Zurich, Physical Chemistry (Switzerland); Guentert, Peter, E-mail: guentert@em.uni-frankfurt.de [Goethe University Frankfurt am Main, Center for Biomolecular Magnetic Resonance, Institute of Biophysical Chemistry (Germany) 2013-07-15 Solid-state NMR is an emerging structure determination technique for crystalline and non-crystalline protein assemblies, e.g., amyloids. Resonance assignment constitutes the first and often very time-consuming step to a structure. We present ssFLYA, a generally applicable algorithm for automatic assignment of protein solid-state NMR spectra. Application to microcrystals of ubiquitin and the Ure2 prion C-terminal domain, as well as amyloids of HET-s(218-289) and {alpha}-synuclein yielded 88-97 % correctness for the backbone and side-chain assignments that are classified as self-consistent by the algorithm, and 77-90 % correctness if also assignments classified as tentative by the algorithm are included. 8. Beta-amyloid overload does not directly correlate with SAPK/JNK activation and tau protein phosphorylation in the cerebellar cortex of Ts65Dn mice. Science.gov (United States) Lomoio, Selene; Scherini, Elda; Necchi, Daniela 2009-11-10 It is known that in the nervous tissue beta-amyloid overproduction and its extracellular or intracellular deposition can activate mitogen-activated protein kinases involved in tau protein phosphorylation. Hyperphosphorylated tau is not more able to bind neuron microtubules, leading to their disassembly and axon degeneration. We have previously described that at 10 months of age in the cerebellum of Ts65Dn mice, which are partially trisomic for the chromosome 16 and are considered a valuable model for Down syndrome, Purkinje cells undergo axon degeneration. Taking into consideration that Ts65Dn mice carry three copies of the gene encoding for the amyloid precursor protein, to characterize potential signaling events triggering the degenerative phenomenon, specific antibodies were used to examine the role of beta-amyloid overload in the activation of the stress activated kinase/c-jun N-terminal kinase (SAPK/JNK) and tau protein phosphorylation in the cerebellar cortex of 12-month-old Ts65Dn mice. We found small extracellular deposits of beta-amyloid at the borderline between the granule cell layer and the white matter, i.e., in the vicinity of the area where calbindin immunostaining of Purkinje cell axons revealed clusters of newly formed terminals of injured axons. Moreover, intracellular deposits were present in the somata of Purkinje cells. The level of activation of SAPK/JNK was greatly increased. The activation occurred in the "pinceaux" made by basket interneuron axons at the axon hillock of Purkinje cells. Antibody directed against tau protein phosphorylated at Ser-396/Ser-404 revealed positive NG2 cells and Bergman fibers in the molecular layer and oligodendrocytes in the white matter. Data indicate that beta-amyloid extracellular deposits could have exerted a local cytotoxic effect, leading to Purkinje cell axon degeneration. The activation of SAPK/JNK in basket cell "pinceaux" may be a consequence of altered functionality of Purkinje cells and may represent 9. Hydrolysis of the amyloid prion protein and nonpathogenic meat and bone meal by anaerobic thermophilic prokaryotes and streptomyces subspecies. Science.gov (United States) Tsiroulnikov, Kirill; Rezai, Human; Bonch-Osmolovskaya, Elisaveta; Nedkov, Peter; Gousterova, Adriana; Cueff, Valérie; Godfroy, Anne; Barbier, Georges; Métro, François; Chobert, Jean-Marc; Clayette, Pascal; Dormont, Dominique; Grosclaude, Jeanne; Haertlé, Thomas 2004-10-06 Transmissible spongiform encephalopathies are caused by accumulation of highly resistant misfolded amyloid prion protein PrPres and can be initiated by penetration of such pathogen molecules from infected tissue to intact organism. Decontamination of animal meal containing amyloid prion protein is proposed thanks to the use of proteolytic enzymes secreted by thermophilic bacteria Thermoanaerobacter, Thermosipho, and Thermococcus subsp. and mesophilic soil bacteria Streptomyces subsp. Keratins alpha and beta, which resemble amyloid structures, were used as the substrates for the screening for microorganisms able to grow on keratins and producing efficient proteases specific for hydrolysis of beta-sheeted proteic structures, hence amyloids. Secretion of keratin-degrading proteases was evidenced by a zymogram method. Enzymes from thermophilic strains VC13, VC15, and S290 and Streptomyces subsp. S6 were strongly active against amyloid recombinant ovine prion protein and animal meal proteins. The studied proteases displayed broad primary specificities hydrolyzing low molecular mass peptide model substrates. Strong amyloidolytic activity of detected proteases was confirmed by experiments of hydrolysis of PrPres in SAFs produced from brain homogenates of mice infected with the 6PB1 BSE strain. The proteases from Thermoanaerobacter subsp. S290 and Streptomyces subsp. S6 are the best candidates for neutralization/elimination of amyloids in meat and bone meal and other protein-containing substances and materials. 10. Review： Protein folding pathology in domestic animals Institute of Scientific and Technical Information of China (English) GRUYSErik 2004-01-01 Fibrillar proteins form structural elements of cells and the extracellular matrix. Pathological lesions of fibrillar microanatomical structures, or secondary fibrillar changes in globular proteins are well known. A special group concerns histologically amorphous deposits, amyloid. The major characteristics of amyloid are: apple green birefringence after Congo red staining of histological sections, and non-branching 7-10nm thick fibrils on electron microscopy revealing a high content of cross beta pleated sheets. About 25 different types of amyloid have been characterised. In animals, AA-amyloid is the most frequent type. Other types of amyloid in animals represent: AIAPP (in cats), AApoAⅠ, AApoAⅡ, localised AL-amyloid, amyloid in odontogenic or mammary tumors and amyloid in the brain. In old dogs Aβ and in sheep APrPsc-amyloid can be encountered. AA-amyloidosis is a systemic disorder with a precursor in blood, acute phase serum amyloid A (SAA). In chronic inflammatory processes AA-amyloid can be deposited. A rapid crystallization of SAA to amyloid fibrils on small beta-sheeted fragments, the ‘amyloid enhancing factor' (AEF), is known and the AEF has been shown to penetrate the enteric barrier. Amyloid fibrils can aggregate from various precursor proteins in vitro in particular at acidic pH and when proteolytic fragments are formed. Molecular chaperones influence this process. Tissue data point to amyloid fibrillogenesis in lysosomes and near cell surfaces. A comparison can be made of the fibrillogenesis in prion diseases and in enhanced AA-amyloidosis. In the reactive form, acute phase SAA is the supply of the precursor protein, whereas in the prion diseases, cell membrane proteins form a structural source. AI3-amyloid in brain tissue of aged dogs showing signs of dementia forms a canine counterpart of senile dementia of the Alzheimer type (ccSDAT) in man. Misfolded proteins remain potential food hazards. Developments concerning prevention of amyloidogenesis 11. Aβ42 Is Essential for Parenchymal and Vascular Amyloid Deposition in Mice Science.gov (United States) McGowan, Eileen; Onstead, Luisa; Eriksen, Jason; Yu, Cindy; Skipper, Lisa; Murphy, M. Paul; Beard, Jenny; Das, Pritam; Jansen, Karen; DeLucia, Michael; Lin, Wen-Lang; Dolios, Georgia; Wang, Rong; Eckman, Christopher B.; Dickson, Dennis W.; Hutton, Mike; Hardy, John; Golde, Todd 2005-01-01 Summary Considerable circumstantial evidence suggests that Aβ42 is the initiating molecule in Alzheimer's disease (AD) pathogenesis. However, the absolute requirement for Aβ42 for amyloid deposition has never been demonstrated in vivo. We have addressed this by developing transgenic models that express Aβ1-40 or Aβ1-42 in the absence of human amyloid β protein precursor (APP) overexpression. Mice expressing high levels of Aβ1-40 do not develop overt amyloid pathology. In contrast, mice expressing lower levels of Aβ1-42 accumulate insoluble Aβ1-42 and develop compact amyloid plaques, congophilic amyloid angiopathy (CAA), and diffuse Aβ deposits. When mice expressing Aβ1-42 are crossed with mutant APP (Tg2576) mice, there is also a massive increase in amyloid deposition. These data establish that Aβ1-42 is essential for amyloid deposition in the parenchyma and also in vessels. PMID:16039562 12. The Effect of Glycosaminoglycans (GAGs on Amyloid Aggregation and Toxicity Directory of Open Access Journals (Sweden) Clara Iannuzzi 2015-02-01 Full Text Available Amyloidosis is a protein folding disorder in which normally soluble proteins are deposited extracellularly as insoluble fibrils, impairing tissue structure and function. Charged polyelectrolytes such as glycosaminoglycans (GAGs are frequently found associated with the proteinaceous deposits in tissues of patients affected by amyloid diseases. Experimental evidence indicate that they can play an active role in favoring amyloid fibril formation and stabilization. Binding of GAGs to amyloid fibrils occurs mainly through electrostatic interactions involving the negative polyelectrolyte charges and positively charged side chains residues of aggregating protein. Similarly to catalyst for reactions, GAGs favor aggregation, nucleation and amyloid fibril formation functioning as a structural templates for the self-assembly of highly cytotoxic oligomeric precursors, rich in β-sheets, into harmless amyloid fibrils. Moreover, the GAGs amyloid promoting activity can be facilitated through specific interactions via consensus binding sites between amyloid polypeptide and GAGs molecules. We review the effect of GAGs on amyloid deposition as well as proteins not strictly related to diseases. In addition, we consider the potential of the GAGs therapy in amyloidosis. 13. Progress in the development of therapeutic antibodies targeting prion proteins and β-amyloid peptides Institute of Scientific and Technical Information of China (English) 2010-01-01 Prion diseases and Alzheimer’s disease (AD) are characterized by protein misfolding, and can lead to dementia. However, prion diseases are infectious and transmissible, while AD is not. The similarities and differences between these diseases have led researchers to perform comparative studies. In the last 2 decades, progress has been made in immunotherapy using anti-prion protein and anti-β-amyloid antibodies. In this study, we review new ideas and strategies for therapeutic antibodies targeting prion diseases and AD through conformation dependence. 14. Gc protein (vitamin D-binding protein): Gc genotyping and GcMAF precursor activity. Science.gov (United States) Nagasawa, Hideko; Uto, Yoshihiro; Sasaki, Hideyuki; Okamura, Natsuko; Murakami, Aya; Kubo, Shinichi; Kirk, Kenneth L; Hori, Hitoshi 2005-01-01 The Gc protein (human group-specific component (Gc), a vitamin D-binding protein or Gc globulin), has important physiological functions that include involvement in vitamin D transport and storage, scavenging of extracellular G-actin, enhancement of the chemotactic activity of C5a for neutrophils in inflammation and macrophage activation (mediated by a GalNAc-modified Gc protein (GcMAF)). In this review, the structure and function of the Gc protein is focused on especially with regard to Gc genotyping and GcMAF precursor activity. A discussion of the research strategy "GcMAF as a target for drug discovery" is included, based on our own research. 15. Targeting vascular amyloid in arterioles of Alzheimer disease transgenic mice with amyloid β protein antibody-coated nanoparticles. Science.gov (United States) Poduslo, Joseph F; Hultman, Kristi L; Curran, Geoffry L; Preboske, Gregory M; Chamberlain, Ryan; Marjańska, Małgorzata; Garwood, Michael; Jack, Clifford R; Wengenack, Thomas M 2011-08-01 The relevance of cerebral amyloid angiopathy (CAA) to the pathogenesis of Alzheimer disease (AD) and dementia in general emphasizes the importance of developing novel targeting approaches for detecting and treating cerebrovascular amyloid (CVA) deposits. We developed a nanoparticle-based technology that uses a monoclonal antibody against fibrillar human amyloid-β42 that is surface coated onto a functionalized phospholipid monolayer. We demonstrate that this conjugated nanoparticle binds to CVA deposits in arterioles of AD transgenic mice (Tg2576) after infusion into the external carotid artery using 3 different approaches. The first 2 approaches use a blood vessel enrichment of homogenized brain and a leptomeningeal vessel preparation from thin tangential brain slices from the surface of the cerebral cortex. Targeting of CVA by the antibody-coated nanoparticle was visualized using fluorescent lissamine rhodamine-labeled phospholipids in the nanoparticles, which were compared with fluorescent staining of the endothelial cells and amyloid deposits using confocal laser scanning microscopy. The third approach used high-field strength magnetic resonance imaging of antibody-coated iron oxide nanoparticles after infusion into the external carotid artery. Dark foci of contrast enhancement in cortical arterioles were observed in T2-weighted images of ex vivo AD mouse brains that correlated histologically with CVA deposits. The targeting ability of these nanoparticles to CVA provides opportunities for the prevention and treatment of CAA. 16. Conformational stability of mammalian prion protein amyloid fibrils is dictated by a packing polymorphism within the core region. Science.gov (United States) Cobb, Nathan J; Apostol, Marcin I; Chen, Shugui; Smirnovas, Vytautas; Surewicz, Witold K 2014-01-31 Mammalian prion strains are believed to arise from the propagation of distinct conformations of the misfolded prion protein PrP(Sc). One key operational parameter used to define differences between strains has been conformational stability of PrP(Sc) as defined by resistance to thermal and/or chemical denaturation. However, the structural basis of these stability differences is unknown. To bridge this gap, we have generated two strains of recombinant human prion protein amyloid fibrils that show dramatic differences in conformational stability and have characterized them by a number of biophysical methods. Backbone amide hydrogen/deuterium exchange experiments revealed that, in sharp contrast to previously studied strains of infectious amyloid formed from the yeast prion protein Sup35, differences in β-sheet core size do not underlie differences in conformational stability between strains of mammalian prion protein amyloid. Instead, these stability differences appear to be dictated by distinct packing arrangements (i.e. steric zipper interfaces) within the amyloid core, as indicated by distinct x-ray fiber diffraction patterns and large strain-dependent differences in hydrogen/deuterium exchange kinetics for histidine side chains within the core region. Although this study was limited to synthetic prion protein amyloid fibrils, a similar structural basis for strain-dependent conformational stability may apply to brain-derived PrP(Sc), especially because large strain-specific differences in PrP(Sc) stability are often observed despite a similar size of the PrP(Sc) core region. 17. Conformational Stability of Mammalian Prion Protein Amyloid Fibrils Is Dictated by a Packing Polymorphism within the Core Region Science.gov (United States) Cobb, Nathan J.; Apostol, Marcin I.; Chen, Shugui; Smirnovas, Vytautas; Surewicz, Witold K. 2014-01-01 Mammalian prion strains are believed to arise from the propagation of distinct conformations of the misfolded prion protein PrPSc. One key operational parameter used to define differences between strains has been conformational stability of PrPSc as defined by resistance to thermal and/or chemical denaturation. However, the structural basis of these stability differences is unknown. To bridge this gap, we have generated two strains of recombinant human prion protein amyloid fibrils that show dramatic differences in conformational stability and have characterized them by a number of biophysical methods. Backbone amide hydrogen/deuterium exchange experiments revealed that, in sharp contrast to previously studied strains of infectious amyloid formed from the yeast prion protein Sup35, differences in β-sheet core size do not underlie differences in conformational stability between strains of mammalian prion protein amyloid. Instead, these stability differences appear to be dictated by distinct packing arrangements (i.e. steric zipper interfaces) within the amyloid core, as indicated by distinct x-ray fiber diffraction patterns and large strain-dependent differences in hydrogen/deuterium exchange kinetics for histidine side chains within the core region. Although this study was limited to synthetic prion protein amyloid fibrils, a similar structural basis for strain-dependent conformational stability may apply to brain-derived PrPSc, especially because large strain-specific differences in PrPSc stability are often observed despite a similar size of the PrPSc core region. PMID:24338015 18. Vaccinium uliginosum L. Improves Amyloid β Protein-Induced Learning and Memory Impairment in Alzheimer's Disease in Mice. Science.gov (United States) Choi, Yoon-Hee; Kwon, Hyuck-Se; Shin, Se-Gye; Chung, Cha-Kwon 2014-12-01 The present study investigated the effects of Vaccinium uliginosum L. (bilberry) on the learning and memory impairments induced by amyloidprotein (AβP) 1-42. ICR Swiss mice were divided into 4 groups: the control (Aβ40-1A), control with 5% bilberry group (Aβ40-1B), amyloid β protein 1-42 treated group (Aβ1-42A), and Aβ1-42 with 5% bilberry group (Aβ1-42B). The control was treated with amyloid β-protein 40-1 for placebo effect, and Alzheimer's disease (AD) group was treated with amyloid β-protein 1-42. Amyloid β-protein 1-42 was intracerebroventricular (ICV) micro injected into the hippocampus in 35% acetonitrile and 0.1% trifluoroacetic acid. Although bilberry added groups tended to decrease the finding time of hidden platform, no statistical significance was found. On the other hand, escape latencies of AβP injected mice were extended compared to that of Aβ40-1. In the Probe test, bilberry added Aβ1-42B group showed a significant (Pmemory compared to Aβ40-1 control group. In passive avoidance test, bilberry significantly (Pimprove memory and learning capability in chemically induced Alzheimer's disease in experimental animal models. 19. Effects of Shouwu-Yizhi capsule on learning and memory and the expressions of presenilin 1,β-amyloid precursor protein mRNAs in the hippocampus following cerebral ischemia reperfusion in rats%首乌益智胶囊对脑缺血再灌注大鼠学习记忆和海马β淀粉样前体蛋白、早老素1 mRNA表达的影响 Institute of Scientific and Technical Information of China (English) 陈超; 李长生; 杨晓妮; 程广清 2014-01-01 目的：探讨首乌益智胶囊对脑缺血再灌注大鼠学习记忆和早老素1（PS1）、β淀粉样前体蛋白(APP)mRNA表达的影响。方法80只大鼠按体质量随机分为假手术组、模型组、首乌益智胶囊组、脑复康组，每组20只。采用大脑中动脉闭塞法制作脑缺血再灌模型。造模后7 d，首乌益智胶囊组和脑复康组分别给予首乌益智胶囊溶液(52 mg/ml)、脑复康溶液(28 mg/ml)灌胃，均为1 ml/(100 g•d)，共28 d，模型组和假手术组等体积生理盐水灌胃。采用Morris水迷宫评价学习和记忆；采用实时荧光定量PCR检测大鼠海马PS1和APP mRNA表达。结果水迷宫实验显示，模型组大鼠逃避潜伏期较假手术组[(12.98±0.70)s比(9.43±0.78)s]显著延长，穿越平台次数较假手术组[(5.08±0.39)次比(7.62±0.43)次]显著减少，首乌益智胶囊组逃避潜伏期较模型组[(9.77±0.58)s比(12.98±0.70)s]显著缩短(P均＜0.01)，穿越平台次数较模型组[(7.40±0.44)次比(5.08±0.39)次]显著增加(P均＜0.01)。首乌益智胶囊组海马PS1和APP mRNA 表达[(0.99±0.01)比(1.08±0.03)]均较模型组[(1.06±0.03)比(1.12±0.04)]显著降低(P＜0.05或0.01)。结论首乌益智胶囊可抑制脑缺血再灌大鼠海马PS1和APP mRNA表达，改善学习和记忆。%Objective To investigate the effects of Shouwu-Yizhi capsule on learning and memory, and the expressions of presenilin 1(PS1),β-amyloid precursor protein (APP) mRNAs in the hippocampus following cerebral ischemia reperfusion in rats. Methods Sprague–Dawley rats were randomly divided into a Shouwu-Yizhi group, a piracetam group, a model group, and a sham operation group with 20 rats in each group. Focal cerebral ischemia reperfusion model was induced by middle cerebral artery occlusion for 2 hours. Seven days after ischemia reperfusion, the rats in the Shouwu-Yizhi and piracetam groups were administered intragastrically Shouwu-Yizhi solution (52 mg/ml) and 20. Intermolecular alignment in Y145Stop human prion protein amyloid fibrils probed by solid-state NMR spectroscopy. Science.gov (United States) Helmus, Jonathan J; Surewicz, Krystyna; Apostol, Marcin I; Surewicz, Witold K; Jaroniec, Christopher P 2011-09-07 The Y145Stop mutant of human prion protein, huPrP23-144, has been linked to PrP cerebral amyloid angiopathy, an inherited amyloid disease, and also serves as a valuable in vitro model for investigating the molecular basis of amyloid strains. Prior studies of huPrP23-144 amyloid by magic-angle-spinning (MAS) solid-state NMR spectroscopy revealed a compact β-rich amyloid core region near the C-terminus and an unstructured N-terminal domain. Here, with the focus on understanding the higher-order architecture of huPrP23-144 fibrils, we probed the intermolecular alignment of β-strands within the amyloid core using MAS NMR techniques and fibrils formed from equimolar mixtures of (15)N-labeled protein and (13)C-huPrP23-144 prepared with [1,3-(13)C(2)] or [2-(13)C]glycerol. Numerous intermolecular correlations involving backbone atoms observed in 2D (15)N-(13)C spectra unequivocally suggest an overall parallel in-register alignment of the β-sheet core. Additional experiments that report on intermolecular (15)N-(13)CO and (15)N-(13)Cα dipolar couplings yielded an estimated strand spacing that is within ∼10% of the distances of 4.7-4.8 Å typical for parallel β-sheets. 1. Opioid precursor protein isoform is targeted to the cell nuclei in the human brain NARCIS (Netherlands) Kononenko, Olga; Bazov, Igor; Watanabe, Hiroyuki; Gerashchenko, Ganna; Dyachok, Oleg; Verbeek, Dineke S; Alkass, Kanar; Druid, Henrik; Andersson, Malin; Mulder, Jan; Svenningsen, Åsa Fex; Rajkowska, Grazyna; Stockmeier, Craig A; Krishtal, Oleg; Yakovleva, Tatiana; Bakalkin, Georgy 2017-01-01 BACKGROUND: Neuropeptide precursors are traditionally viewed as proteins giving rise to small neuropeptide molecules. Prodynorphin (PDYN) is the precursor protein to dynorphins, endogenous ligands for the κ-opioid receptor. Alternative mRNA splicing of neuropeptide genes may regulate cell- and tissu 2. OPIOID PRECURSOR PROTEIN ISOFORM IS TARGETED TO THE CELL NUCLEI IN THE HUMAN BRAIN DEFF Research Database (Denmark) Kononenko, Olga; Bazov, Igor; Watanabe, Hiroyuki; 2016-01-01 Neuropeptide precursors are traditionally viewed as proteins giving rise to small neuropeptide molecules. Prodynorphin (PDYN) is the precursor protein to dynorphins, endogenous ligands for the κ-opioid receptor. We here describe two novel splicing variants of human PDYN mRNA. Expression of one... 3. Oxidative stress induces macroautophagy of amyloid beta-protein and ensuing apoptosis DEFF Research Database (Denmark) Zheng, Lin; Kågedal, Katarina; Dehvari, Nodi; 2009-01-01 There is increasing evidence for the toxicity of intracellular amyloid beta-protein (Abeta) to neurons and the involvement of lysosomes in this process in Alzheimer disease (AD). We have recently shown that oxidative stress, a recognized determinant of AD, enhances macroautophagy and leads...... to intralysosomal accumulation of Abeta in cultured neuroblastoma cells. We hypothesized that oxidative stress promotes AD by stimulating macroautophagy of Abeta that further may induce cell death by destabilizing lysosomal membranes. To investigate such possibility, we compared the effects of hyperoxia (40... 4. A quantitative method for detecting deposits of amyloid A protein in aspirated fat tissue of patients with arthritis OpenAIRE Hazenberg, B.; Limburg, P; Bijzet, J.; VAN RIJSWIJK, M. H 1999-01-01 OBJECTIVE—To describe a new, quantitative, and reproducible method for detecting deposits of amyloid A protein in aspirated fat tissue and to compare it with smears stained with Congo red. METHODS—After extraction of at least 30 mg of abdominal fat tissue in guanidine, the amyloid A protein concentration was measured by a monoclonal antibody-based sandwich ELISA. RESULTS—The concentrations in 24 patients with arthritis and AA amyloidosis (median 236, range 1.1-8530 ng/mg tissue) were higher (... 5. Specific binding of DNA to aggregated forms of Alzheimer's disease amyloid peptides. Science.gov (United States) Camero, Sergio; Ayuso, Jose M; Barrantes, Alejandro; Benítez, María J; Jiménez, Juan S 2013-04-01 Anomalous protein aggregation is closely associated to age-related mental illness. Extraneuronal plaques, mainly composed of aggregated amyloid peptides, are considered as hallmarks of Alzheimer's disease. According to the amyloid cascade hypothesis, this disease starts as a consequence of an abnormal processing of the amyloid precursor protein resulting in an excess of amyloid peptides. Nuclear localization of amyloid peptide aggregates together with amyloid-DNA interaction, have been repeatedly reported. In this paper we have used surface plasmon resonance and electron microscopy to study the structure and behavior of different peptides and proteins, including β-lactoglobulin, bovine serum albumin, myoglobin, histone, casein and the amyloid-β peptides related to Alzheimer's disease Aβ25-35 and Aβ1-40. The main purpose of this study is to investigate whether proneness to DNA interaction is a general property displayed by aggregated forms of proteins, or it is an interaction specifically related to the aggregated forms of those particular proteins and peptides related to neurodegenerative diseases. Our results reveal that those aggregates formed by amyloid peptides show a particular proneness to interact with DNA. They are the only aggregated structures capable of binding DNA, and show more affinity for DNA than for other polyanions like heparin and polyglutamic acid, therefore strengthening the hypothesis that amyloid peptides may, by means of interaction with nuclear DNA, contribute to the onset of Alzheimer's disease. 6. Protein folding pathology in domestic animals Institute of Scientific and Technical Information of China (English) GRUYS Erik 2004-01-01 Fibrillar proteins form structural elements of cells and the extracellular matrix. Pathological lesions of fibrillar microanatomical structures, or secondary fibrillar changes in globular proteins are well known. A special group concerns histologically amorphous deposits, amyloid. The major characteristics of amyloid are: apple green birefringence after Congo red staining of histological sections, and non-branching 7-10 nm thick fibrils on electron microscopy revealing a high content of cross beta pleated sheets. About 25 different types of amyloid have been characterised. In animals,AA-amyloid is the most frequent type. Other types of amyloid in animals represent: AIAPP (in cats), AApoAⅠ, AApoAⅡ,localised AL-amyloid, amyloid in odontogenic or mammary tumors and amyloid in the brain. In old dogs Aβ and in sheep APrPsc-amyloid can be encountered. AA-amyloidosis is a systemic disorder with a precursor in blood, acute phase serum amyloid A (SAA). In chronic inflammatory processes AA-amyloid can be deposited. A rapid crystallization of SAA to shown to penetrate the enteric barrier. Amyloid fibrils can aggregate from various precursor proteins in vitro in particular at acidic pH and when proteolytic fragments are formed. Molecular chaperones influence this process. Tissue data point to amyloid fibrillogenesis in lysosomes and near cell surfaces. A comparison can be made of the fibrillogenesis in prion diseases and in enhanced AA-amyloidosis. In the reactive form, acute phase SAA is the supply of the precursor protein,whereas in tho prion diseases, cell membrane proteins form a structural source. Aβ-amyloid in brain tissue of aged dogs showing signs of dementia forms a canine counterpart of senile dementia of the Alzheimer type (ccSDAT) in man. Misfolded proteins remain potential food hazards. Developments concerning prevention of amyloidogenesis and therapy of amyloid deposits are shortly commented. 7. APP蛋白家族胞内段释放与神经干细胞向神经元细胞定向分化的关系研究%Study on the Relationship between the Release of Intracellular Domain of AmyloidPrecursor Protein and Directional Differentiation of Neural Stem Cells into Neuron Cells Institute of Scientific and Technical Information of China (English) 章建国; Amy Yong Chen Low; 杨武林 2012-01-01 [Objective] The research aimed to study the effects of the intracellular domain of APP family on the directional differentiation of neuron. [Method ] Neural stem cells were isolated and cultured in vitro, which were then transfected with plasmids containing the intracellular domains of APP family for overexpression. Their effects on the directional differentiation of neural stem cells into neurons were studied. [Result ] The over-expression of the intracellular domain of APP protein family can inhibit the differentiation of neural stem cells into neurons, and the effects of intracellular segments of APP and APLP2 were particularly significant. Mutagenesis experiments showed that it was necessary to release 31 amino acid terminal fragment through Capase hydrolysis in this process. The directional differentiation of neural stem cells into neuron cells was controlled through releasing APP-ICD31 by the intracellular domain of APP family. [Conclusion] This research further proved the relationship between APP protein and the incidence of Alzheimers disease,and provided new targets for the treatment of Alzheimers disease.%[目的]研究APP家族胞内段时神经细胞定向分化的影响.[方法]通过分离体外培养神经干细胞,转染导入APP蛋白家族胞内段以过表达后,研究其对神经干细胞向神经元定向分化的影响.[结果]APP家族蛋白胞内段的过表达可以抑制神经干细胞向神经元细胞的分化,其中APP和APLP2胞内段的影响尤为显著.突变试验表明,通过Capase水解释放末端31氧基酸片断是这个过程必需的.APP家族胞内段是通过释放APP-ICD31来抑制神经干细胞向神经元细胞的定向分化.[结论]该研究进一步证实了APP蛋白和老年痴呆病发生的联系,也为老年痴呆症的治疗提供新的靶点. 8. Proteomic study of amyloid beta (25-35) peptide exposure to neuronal cells: Impact on APE1/Ref-1's protein-protein interaction. Science.gov (United States) Mantha, Anil K; Dhiman, Monisha; Taglialatela, Giulio; Perez-Polo, Regino J; Mitra, Sankar 2012-06-01 The genotoxic, extracellular accumulation of amyloid β (Aβ) protein and subsequent neuronal cell death are associated with Alzheimer's disease (AD). APE1/Ref-1, the predominant apurinic/apyrimidinic (AP) endonuclease and essential in eukaryotic cells, plays a central role in the base excision repair (BER) pathway for repairing oxidized and alkylated bases and single-strand breaks (SSBs) in DNA. APE1/Ref-1 is also involved in the redox activation of several trans-acting factors (TFs) in various cell types, but little is known about its role in neuronal functions. There is emerging evidence for APE1/Ref-1's role in neuronal cells vulnerable in AD and other neurodegenerative disorders, as reflected in its nuclear accumulation in AD brains. An increase in APE1/Ref-1 has been shown to enhance neuronal survival after oxidative stress. To address whether APE1/Ref-1 level or its association with other proteins is responsible for this protective effect, we used 2-D proteomic analyses and identified cytoskeleton elements (i.e., tropomodulin 3, tropomyosin alpha-3 chain), enzymes involved in energy metabolism (i.e., pyruvate kinase M2, N-acetyl transferase, sulfotransferase 1c), proteins involved in stress response (i.e., leucine-rich and death domain, anti-NGF30), and heterogeneous nuclear ribonucleoprotien-H (hnRNP-H) as being associated with APE1/Ref-1 in Aβ(25-35)-treated rat pheochromocytoma PC12 and human neuroblastoma SH-SY5Y cell lines, two common neuronal precursor lines used in Aβ neurotoxicity studies. Because the levels of some of these proteins are affected in the brains of AD patients, our study suggests a neuroprotective role for APE1/Ref-1 via its association with those proteins and modulating their cellular functions during Aβ-mediated neurotoxicity. 9. Hybrid Amyloid Membranes for Continuous Flow Catalysis. Science.gov (United States) Bolisetty, Sreenath; Arcari, Mario; Adamcik, Jozef; Mezzenga, Raffaele 2015-12-29 Amyloid fibrils are promising nanomaterials for technological applications such as biosensors, tissue engineering, drug delivery, and optoelectronics. Here we show that amyloid-metal nanoparticle hybrids can be used both as efficient active materials for wet catalysis and as membranes for continuous flow catalysis applications. Initially, amyloid fibrils generated in vitro from the nontoxic β-lactoglobulin protein act as templates for the synthesis of gold and palladium metal nanoparticles from salt precursors. The resulting hybrids possess catalytic features as demonstrated by evaluating their activity in a model catalytic reaction in water, e.g., the reduction of 4-nitrophenol into 4-aminophenol, with the rate constant of the reduction increasing with the concentration of amyloid-nanoparticle hybrids. Importantly, the same nanoparticles adsorbed onto fibrils surface show improved catalytic efficiency compared to the same unattached particles, pointing at the important role played by the amyloid fibril templates. Then, filter membranes are prepared from the metal nanoparticle-decorated amyloid fibrils by vacuum filtration. The resulting membranes serve as efficient flow catalysis active materials, with a complete catalytic conversion achieved within a single flow passage of a feeding solution through the membrane. 10. Complement activation by the amyloid proteins A beta peptide and beta 2-microglobulin DEFF Research Database (Denmark) Nybo, Mads; Nielsen, E H; Svehag, S E 1999-01-01 Complement activation (CA) has been reported to play a role in the pathogenesis of Alzheimer's disease (AD). To investigate whether CA may contribute to amyloidogenesis in general, the CA potential of different amyloid fibril proteins was tested. CA induced by A beta preparations containing soluble...... protein, protofilaments and some fibrils or only fibrils in a solid phase system (ELISA) was modest with a slow kinetics compared to the positive delta IgG control. Soluble A beta induced no detectable CA in a liquid phase system (complement consumption assay) while fibrillar A beta caused CA at 200 mg....../ml and higher concentrations. Soluble beta 2-microglobulin (beta 2M) purified from peritoneal dialysates was found to be as potent a complement activator as A beta in both solid and liquid phase systems while beta 2M purified from urine exhibited lower activity, a difference which may be explained... 11. Native human serum amyloid P component is a single pentamer DEFF Research Database (Denmark) Sørensen, Inge Juul; Andersen, Ove; Nielsen, EH; 1995-01-01 Serum amyloid P component (SAP) and C-reactive protein (CRP) are members of the pentraxin protein family. SAP is the precursor protein to amyloid P component present in all forms of amyloidosis. The prevailing notion is that SAP in circulation has the form of a double pentameric molecule (decamer...... by rocket immunoelectrophoresis and electron microscopy. Thus, electron micrographs of purified SAP showed a predominance of decamers. However, the decamer form of SAP reversed to single pentamers when purified SAP was incorporated into SAP-depleted serum.... 12. Paradoxical Condensation of Copper with Elevated β-Amyloid in Lipid Rafts under Cellular Copper Deficiency Conditions: IMPLICATIONS FOR ALZHEIMER DISEASE* OpenAIRE Hung, Ya Hui; Robb, Elysia L.; Volitakis, Irene; Ho, Michael; Evin, Genevieve; Li, Qiao-Xin; Janetta G Culvenor; Masters, Colin L.; Cherny, Robert A.; Bush, Ashley I. 2009-01-01 Redox-active copper is implicated in the pathogenesis of Alzheimer disease (AD), β-amyloid peptide (Aβ) aggregation, and amyloid formation. Aβ·copper complexes have been identified in AD and catalytically oxidize cholesterol and lipid to generate H2O2 and lipid peroxides. The site and mechanism of this abnormality is not known. Growing evidence suggests that amyloidogenic processing of the β-amyloid precursor protein (APP) occurs in lipid rafts, membrane microdomains enriched in cholesterol. ... 13. Amyloid protein-mediated differential DNA methylation status regulates gene expression in Alzheimer's disease model cell line Energy Technology Data Exchange (ETDEWEB) Sung, Hye Youn; Choi, Eun Nam [Department of Biochemistry, School of Medicine, Ewha Womans University, 911-1 Mok-6-dong, Yangcheon-ku, Seoul 158-710 (Korea, Republic of); Ahn Jo, Sangmee [Department of Pharmacy, College of Pharmacy, Dankook University, San 29 Anseo-dong, Dongnam-gu, Cheonan-si, Chungnam 330-714 (Korea, Republic of); Oh, Seikwan [Department of Neuroscience and TIDRC, School of Medicine, Ewha Womans University, 911-1 Mok-6-dong, Yangcheon-ku, Seoul 158-710 (Korea, Republic of); Ahn, Jung-Hyuck, E-mail: ahnj@ewha.ac.kr [Department of Biochemistry, School of Medicine, Ewha Womans University, 911-1 Mok-6-dong, Yangcheon-ku, Seoul 158-710 (Korea, Republic of) 2011-11-04 Highlights: Black-Right-Pointing-Pointer Genome-wide DNA methylation pattern in Alzheimer's disease model cell line. Black-Right-Pointing-Pointer Integrated analysis of CpG methylation and mRNA expression profiles. Black-Right-Pointing-Pointer Identify three Swedish mutant target genes; CTIF, NXT2 and DDR2 gene. Black-Right-Pointing-Pointer The effect of Swedish mutation on alteration of DNA methylation and gene expression. -- Abstract: The Swedish mutation of amyloid precursor protein (APP-sw) has been reported to dramatically increase beta amyloid production through aberrant cleavage at the beta secretase site, causing early-onset Alzheimer's disease (AD). DNA methylation has been reported to be associated with AD pathogenesis, but the underlying molecular mechanism of APP-sw-mediated epigenetic alterations in AD pathogenesis remains largely unknown. We analyzed genome-wide interplay between promoter CpG DNA methylation and gene expression in an APP-sw-expressing AD model cell line. To identify genes whose expression was regulated by DNA methylation status, we performed integrated analysis of CpG methylation and mRNA expression profiles, and identified three target genes of the APP-sw mutant; hypomethylated CTIF (CBP80/CBP20-dependent translation initiation factor) and NXT2 (nuclear exporting factor 2), and hypermethylated DDR2 (discoidin domain receptor 2). Treatment with the demethylating agent 5-aza-2 Prime -deoxycytidine restored mRNA expression of these three genes, implying methylation-dependent transcriptional regulation. The profound alteration in the methylation status was detected at the -435, -295, and -271 CpG sites of CTIF, and at the -505 to -341 region in the promoter of DDR2. In the promoter region of NXT2, only one CpG site located at -432 was differentially unmethylated in APP-sw cells. Thus, we demonstrated the effect of the APP-sw mutation on alteration of DNA methylation and subsequent gene expression. This epigenetic regulatory 14. Tissue transglutaminase colocalizes with extracellular matrix proteins in cerebral amyloid angiopathy. Science.gov (United States) de Jager, Mieke; van der Wildt, Berend; Schul, Emma; Bol, John G J M; van Duinen, Sjoerd G; Drukarch, Benjamin; Wilhelmus, Micha M M 2013-04-01 Cerebral amyloid angiopathy (CAA) is a key histopathological hallmark of Alzheimer's disease (AD) and hereditary cerebral hemorrhage with amyloidosis of the Dutch type (HCHWA-D). CAA is characterized by amyloid-beta (Aβ) depositions and remodeling of the extracellular matrix (ECM) in brain vessels and plays an important role in the development and progression of both AD and HCHWA-D. Tissue transglutaminase (tTG) modulates the ECM by molecular cross-linking of ECM proteins. Here, we investigated the distribution pattern, cellular source, and activity of tTG in CAA in control, AD, and HCHWA-D cases. We observed increased tTG immunoreactivity and colocalization with Aβ in the vessel wall in early stage CAA, whereas in later CAA stages, tTG and its cross-links were present in halos enclosing the Aβ deposition. In CAA, tTG and its cross-links at the abluminal side of the vessel were demonstrated to be either of astrocytic origin in parenchymal vessels, of fibroblastic origin in leptomeningeal vessels, and of endothelial origin at the luminal side of the deposited Aβ. Furthermore, the ECM proteins fibronectin and laminin colocalized with the tTG-positive halos surrounding the deposited Aβ in CAA. However, we observed that in situ tTG activity was present throughout the vessel wall in late stage CAA. Together, our data suggest that tTG and its activity might play a differential role in the development and progression of CAA, possibly evolving from direct modulation of Aβ aggregation to cross-linking of ECM proteins resulting in ECM restructuring. 15. The β-amyloid protein induces S100β expression in rat hippocampus through a mechanism that involves IL-1 Institute of Scientific and Technical Information of China (English) 2007-01-01 Objective To explore the effect of β-amyloid protein (Aβ) on S100β expression in rat hippocampus and its mechanisms. Methods At 7 days after bilateral stereotaxis injection of different dose of fibrillar Aβ 25-35 and interluekin-1 receptor antagonist (IL-1ra) into the rat CA1 region, the learning and memory abilities of rats were tested with passive avoidance task. Amyloid deposition was detected by using Congo red staining technique. Nissl staining and immunohistochemical techniques were used to analyze th... 16. Chronic administration of R-flurbiprofen attenuates learning impairments in transgenic amyloid precursor protein mice Directory of Open Access Journals (Sweden) Koo Edward H 2007-07-01 Full Text Available Abstract Background Long-term use of non-steroidal anti-inflammatory drugs (NSAIDs is associated with a reduced incidence of Alzheimer's disease (AD. We and others have shown that certain NSAIDs reduce secretion of Aβ42 in cell culture and animal models, and that the effect of NSAIDs on Aβ42 is independent of the inhibition of cyclooxygenase by these compounds. Since Aβ42 is hypothesized to be the initiating pathologic molecule in AD, the ability of these compounds to lower Aβ42 selectively may be associated with their protective effect. We have previously identified R-flurbiprofen (tarenflurbil as a selective Aβ42 lowering agent with greatly reduced cyclooxygenase activity that shows promise for testing this hypothesis. In this study we report the effect of chronic R-flurbiprofen treatment on cognition and Aβ loads in Tg2576 APP mice. Results A four-month preventative treatment regimen with R-flurbiprofen (10 mg/kg/day was administered to young Tg2576 mice prior to robust plaque or Aβ pathology. This treatment regimen improved spatial learning as assessed by the Morris water maze, indicated by an increased spatial bias during the third probe trial and an increased utilization of a place strategy to solve the water maze. These results are consistent with an improvement in hippocampal- and medial temporal lobe-dependent memory function. A modest, though not statistically significant, reduction in formic acid-soluble levels of Aβ was also observed. To determine if R-flurbiprofen could reverse cognitive deficits in Tg2576 mice where plaque pathology was already robust, a two-week therapeutic treatment was given to older Tg2576 mice with the same dose of R-flurbiprofen. This approach resulted in a significant decrease in Aβ plaque burden but no significant improvement in spatial learning. Conclusion We have found that chronic administration of R-flurbiprofen is able to attenuate spatial learning deficits if given prior to plaque deposition in Tg2576 mice. Given its ability to selectively target Aβ42 production and improve cognitive impairments in transgenic APP mice, as well as promising data from a phase 2 human clinical trial, future studies are needed to investigate the utility of R-flurbiprofen as an AD therapeutic and its possible mechanisms of action. 17. The amyloid precursor protein controls adult hippocampal neurogenesis through GABAergic interneurons. Science.gov (United States) Wang, Baiping; Wang, Zilai; Sun, Lu; Yang, Li; Li, Hongmei; Cole, Allysa L; Rodriguez-Rivera, Jennifer; Lu, Hui-Chen; Zheng, Hui 2014-10-01 Impaired neurogenesis in the adult hippocampus has been implicated in AD pathogenesis. Here we reveal that the APP plays an important role in the neural progenitor proliferation and newborn neuron maturation in the mouse dentate gyrus. APP controls adult neurogenesis through a non cell-autonomous mechanism by GABAergic neurons, as selective deletion of GABAergic, but not glutamatergic, APP disrupts adult hippocampal neurogenesis. APP, highly expressed in the majority of GABAergic neurons in the dentate gyrus, enhances the inhibitory tone to granule cells. By regulating both tonic and phasic GABAergic inputs to dentate granule cells, APP maintains excitatory-inhibitory balance and preserves cognitive functions. Our studies uncover an indispensable role of APP in the GABAergic system for controlling adult hippocampal neurogenesis, and our findings indicate that APP dysfunction may contribute to impaired neurogenesis and cognitive decline associated with AD. 18. Chronic administration of R-flurbiprofen attenuates learning impairments in transgenic amyloid precursor protein mice Science.gov (United States) Kukar, Thomas; Prescott, Sonya; Eriksen, Jason L; Holloway, Vallie; Murphy, M Paul; Koo, Edward H; Golde, Todd E; Nicolle, Michelle M 2007-01-01 Background Long-term use of non-steroidal anti-inflammatory drugs (NSAIDs) is associated with a reduced incidence of Alzheimer's disease (AD). We and others have shown that certain NSAIDs reduce secretion of Aβ42 in cell culture and animal models, and that the effect of NSAIDs on Aβ42 is independent of the inhibition of cyclooxygenase by these compounds. Since Aβ42 is hypothesized to be the initiating pathologic molecule in AD, the ability of these compounds to lower Aβ42 selectively may be associated with their protective effect. We have previously identified R-flurbiprofen (tarenflurbil) as a selective Aβ42 lowering agent with greatly reduced cyclooxygenase activity that shows promise for testing this hypothesis. In this study we report the effect of chronic R-flurbiprofen treatment on cognition and Aβ loads in Tg2576 APP mice. Results A four-month preventative treatment regimen with R-flurbiprofen (10 mg/kg/day) was administered to young Tg2576 mice prior to robust plaque or Aβ pathology. This treatment regimen improved spatial learning as assessed by the Morris water maze, indicated by an increased spatial bias during the third probe trial and an increased utilization of a place strategy to solve the water maze. These results are consistent with an improvement in hippocampal- and medial temporal lobe-dependent memory function. A modest, though not statistically significant, reduction in formic acid-soluble levels of Aβ was also observed. To determine if R-flurbiprofen could reverse cognitive deficits in Tg2576 mice where plaque pathology was already robust, a two-week therapeutic treatment was given to older Tg2576 mice with the same dose of R-flurbiprofen. This approach resulted in a significant decrease in Aβ plaque burden but no significant improvement in spatial learning. Conclusion We have found that chronic administration of R-flurbiprofen is able to attenuate spatial learning deficits if given prior to plaque deposition in Tg2576 mice. Given its ability to selectively target Aβ42 production and improve cognitive impairments in transgenic APP mice, as well as promising data from a phase 2 human clinical trial, future studies are needed to investigate the utility of R-flurbiprofen as an AD therapeutic and its possible mechanisms of action. PMID:17650315 19. Activation of human microglia by fibrillar prion protein-related peptides is enhanced by amyloid-associated factors SAP and C1q NARCIS (Netherlands) Veerhuis, R.; Boshuizen, R.S.; Morbin, M.; Mazzoleni, G.; Hoozemans, J.J.; Langedijk, J.P.; Tagliavini, F.; Langeveld, J.P.M.; Eikelenboom, P. 2005-01-01 Complement activation products C1q and C3d, serum amyloid P component (SAP) and activated glial cells accumulate in amyloid deposits of conformationally changed prion protein (PrPSc) in Creutzfeldt¿Jakob disease, Gerstmann¿Sträussler¿Scheinker disease and scrapie-infected mouse brain. Biological pro 20. Amyloid-β peptides and tau protein as biomarkers in cerebrospinal and interstitial fluid following traumatic brain injury: A review of experimental and clinical studies Directory of Open Access Journals (Sweden) Parmenion P. Tsitsopoulos 2013-06-01 Full Text Available Traumatic brain injury (TBI survivors frequently suffer from life-long deficits in cognitive functions and a reduced quality of life. Axonal injury, observed in most severe TBI patients, results in accumulation of amyloid precursor protein (APP. Post-injury enzymatic cleavage of APP can generate amyloid-β (Aβ peptides, a hallmark finding in Alzheimer’s disease (AD. At autopsy, brains of AD and a subset of TBI victims display some similarities including accumulation of Aβ peptides and neurofibrillary tangles of hyperphosphorylated tau proteins. Most epidemiological evidence suggests a link between TBI and AD, implying that TBI has neurodegenerative sequelae. Aβ peptides and tau may be used as biomarkers in interstitial fluid (ISF using cerebral microdialysis and/or cerebrospinal fluid (CSF following clinical TBI. In the present review, the available clinical and experimental literature on Aβ peptides and tau as potential biomarkers following TBI is comprehensively analyzed. Elevated CSF and ISF tau protein levels have been observed following severe TBI and suggested to correlate with clinical outcome. Although Aβ peptides are produced by normal neuronal metabolism, high levels of long and/or fibrillary Aβ peptides may be neurotoxic. Increased CSF and/or ISF Aβ levels post-injury may be related to neuronal activity and/or the presence of axonal injury. The heterogeneity of animal models, clinical cohorts, analytical techniques and the complexity of TBI in available studies make the clinical value of tau and Aβ as biomarkers uncertain at present. Additionally, the link between early post-injury changes in tau and Aβ peptides and the future risk of developing AD remains unclear. Future studies using e.g. rapid biomarker sampling combined with enhanced analytical techniques and/or novel pharmacological tools could provide additional information on the importance of Aβ peptides and tau protein in both the acute pathophysiology and long 1. Evidence of a Novel Mechanism for Partial γ-Secretase Inhibition Induced Paradoxical Increase in Secreted Amyloid β Protein Science.gov (United States) Baranello, Robert; Pacheco-Quinto, Javier; Crosson, Craig; Ablonczy, Zsolt; Eckman, Elizabeth; Eckman, Christopher B.; Ramakrishnan, Viswanathan; Greig, Nigel H.; Pappolla, Miguel A.; Sambamurti, Kumar 2014-01-01 BACE1 (β-secretase) and α-secretase cleave the Alzheimer's amyloid β protein (Aβ) precursor (APP) to C-terminal fragments of 99 aa (CTFβ) and 83 aa (CTFα), respectively, which are further cleaved by γ-secretase to eventually secrete Aβ and Aα (a.k.a. P3) that terminate predominantly at residues 40 and 42. A number of γ-secretase inhibitors (GSIs), such as N-[N-(3,5-Difluorophenacetyl-L-alanyl)]-S-phenylglycine t-butyl ester (DAPT), have been developed with the goal of reducing Aβ to treat Alzheimer's disease (AD). Although most studies show that DAPT inhibits Aβ in a dose-dependent manner several studies have also detected a biphasic effect with an unexpected increase at low doses of DAPT in cell cultures, animal models and clinical trials. In this article, we confirm the increase in Aβ40 and Aβ42 in SH-SY5Y human neuroblastoma cells treated with low doses of DAPT and identify one of the mechanisms for this paradox. We studied the pathway by first demonstrating that stimulation of Aβ, a product of γ-secretase, was accompanied by a parallel increase of its substrate CTFβ, thereby demonstrating that the inhibitor was not anomalously stimulating enzyme activity at low levels. Secondly, we have demonstrated that inhibition of an Aβ degrading activity, endothelin converting enzyme (ECE), yielded more Aβ, but abolished the DAPT-induced stimulation. Finally, we have demonstrated that Aα, which is generated in the secretory pathway before endocytosis, is not subject to the DAPT-mediated stimulation. We therefore conclude that impairment of γ-secretase can paradoxically increase Aβ by transiently skirting Aβ degradation in the endosome. This study adds to the growing body of literature suggesting that preserving γ-secretase activity, rather than inhibiting it, is important for prevention of neurodegeneration. PMID:24658363 2. Evidence of a novel mechanism for partial γ-secretase inhibition induced paradoxical increase in secreted amyloid β protein. Directory of Open Access Journals (Sweden) Eliza Barnwell Full Text Available BACE1 (β-secretase and α-secretase cleave the Alzheimer's amyloid β protein (Aβ precursor (APP to C-terminal fragments of 99 aa (CTFβ and 83 aa (CTFα, respectively, which are further cleaved by γ-secretase to eventually secrete Aβ and Aα (a.k.a. P3 that terminate predominantly at residues 40 and 42. A number of γ-secretase inhibitors (GSIs, such as N-[N-(3,5-Difluorophenacetyl-L-alanyl]-S-phenylglycine t-butyl ester (DAPT, have been developed with the goal of reducing Aβ to treat Alzheimer's disease (AD. Although most studies show that DAPT inhibits Aβ in a dose-dependent manner several studies have also detected a biphasic effect with an unexpected increase at low doses of DAPT in cell cultures, animal models and clinical trials. In this article, we confirm the increase in Aβ40 and Aβ42 in SH-SY5Y human neuroblastoma cells treated with low doses of DAPT and identify one of the mechanisms for this paradox. We studied the pathway by first demonstrating that stimulation of Aβ, a product of γ-secretase, was accompanied by a parallel increase of its substrate CTFβ, thereby demonstrating that the inhibitor was not anomalously stimulating enzyme activity at low levels. Secondly, we have demonstrated that inhibition of an Aβ degrading activity, endothelin converting enzyme (ECE, yielded more Aβ, but abolished the DAPT-induced stimulation. Finally, we have demonstrated that Aα, which is generated in the secretory pathway before endocytosis, is not subject to the DAPT-mediated stimulation. We therefore conclude that impairment of γ-secretase can paradoxically increase Aβ by transiently skirting Aβ degradation in the endosome. This study adds to the growing body of literature suggesting that preserving γ-secretase activity, rather than inhibiting it, is important for prevention of neurodegeneration. 3. Increased plasma amyloid beta protein 1-42 levels in Down syndrome. Science.gov (United States) Mehta, P D; Dalton, A J; Mehta, S P; Kim, K S; Sersen, E A; Wisniewski, H M 1998-01-23 Amyloid beta protein 1-40 (A beta40) and A beta42 levels were quantitated in plasma from 43 persons with Down syndrome (DS; 26-68 years of age), 43 age-matched normal controls, and 19 non-DS mentally retarded (MR) persons (26-91 years of age) by using a sandwich enzyme linked immunosorbent assay. A beta40 levels were higher in DS and MR than controls, but were similar between DS and MR groups. A beta42 levels were higher in DS than controls or MR persons. The ratios of A beta42/A beta40 were higher in DS than controls or MR persons. The findings are consistent with those seen in DS brains. 4. Alzheimer's disease amyloid peptides interact with DNA, as proved by surface plasmon resonance. Science.gov (United States) Barrantes, Alejandro; Camero, Sergio; Garcia-Lucas, Angel; Navarro, Pedro J; Benitez, María J; Jiménez, Juan S 2012-10-01 According to the amyloid hypothesis, abnormal processing of the β-amyloid precursor protein in Alzheimer's disease patients increases the production of β-amyloid toxic peptides, which, after forming highly aggregated fibrillar structures, lead to extracellular plaques formation, neuronal loss and dementia. However, a great deal of evidence has point to intracellular small oligomers of amyloid peptides, probably transient intermediates in the process of fibrillar structures formation, as the most toxic species. In order to study the amyloid-DNA interaction, we have selected here three different forms of the amyloid peptide: Aβ1-40, Aβ25-35 and a scrambled form of Aβ25-35. Surface Plasmon Resonance was used together with UV-visible spectroscopy, Electrophoresis and Electronic Microscopy to carry out this study. Our results prove that, similarly to the full length Aβ1-42, all conformations of toxic amyloid peptides, Aβ1-40 and Aβ25-35, may bind DNA. In contrast, the scrambled form of Aβ25-35, a non-aggregating and nontoxic form of this peptide, could not bind DNA. We conclude that although the amyloid-DNA interaction is closely related to the amyloid aggregation proneness, this cannot be the only factor which determines the interaction, since small oligomers of amyloid peptides may also bind DNA if their predominant negatively charged amino acid residues are previously neutralized. 5. Mechanism of neuronal versus endothelial cell uptake of Alzheimer's disease amyloid beta protein. Directory of Open Access Journals (Sweden) Karunya K Kandimalla Full Text Available Alzheimer's disease (AD is characterized by significant neurodegeneration in the cortex and hippocampus; intraneuronal tangles of hyperphosphorylated tau protein; and accumulation of beta-amyloid (Abeta proteins 40 and 42 in the brain parenchyma as well as in the cerebral vasculature. The current understanding that AD is initiated by the neuronal accumulation of Abeta proteins due to their inefficient clearance at the blood-brain-barrier (BBB, places the neurovascular unit at the epicenter of AD pathophysiology. The objective of this study is to investigate cellular mechanisms mediating the internalization of Abeta proteins in the principle constituents of the neurovascular unit, neurons and BBB endothelial cells. Laser confocal micrographs of wild type (WT mouse brain slices treated with fluorescein labeled Abeta40 (F-Abeta40 demonstrated selective accumulation of the protein in a subpopulation of cortical and hippocampal neurons via nonsaturable, energy independent, and nonendocytotic pathways. This groundbreaking finding, which challenges the conventional belief that Abeta proteins are internalized by neurons via receptor mediated endocytosis, was verified in differentiated PC12 cells and rat primary hippocampal (RPH neurons through laser confocal microscopy and flow cytometry studies. Microscopy studies have demonstrated that a significant proportion of F-Abeta40 or F-Abeta42 internalized by differentiated PC12 cells or RPH neurons is located outside of the endosomal or lysosomal compartments, which may accumulate without degradation. In contrast, BBME cells exhibit energy dependent uptake of F-Abeta40, and accumulate the protein in acidic cell organelle, indicative of endocytotic uptake. Such a phenomenal difference in the internalization of Abeta40 between neurons and BBB endothelial cells may provide essential clues to understanding how various cells can differentially regulate Abeta proteins and help explain the vulnerability of cortical 6. Binding of an oxindole alkaloid from Uncaria tomentosa to amyloid protein (Abeta1-40). Science.gov (United States) Frackowiak, Teresa; Baczek, Tomasz; Roman, Kaliszana; Zbikowska, Beata; Gleńsk, Michał; Fecka, Izabela; Cisowski, Wojciech 2006-01-01 The primary aim of this work was to determine the interactions of an oxindole alkaloid (mitraphylline) isolated from Uncaria tomentosa with beta-amyloid 1-40 (Abeta1-40 protein) applying the capillary electrophoresis (CE) method. Specifically the Hummel-Dreyer method and Scatchard analysis were performed to study the binding of oxindole alkaloids with Abeta1-40 protein. Prior to these studies extraction of the alkaloid of interest was carried out. Identification of the isolated alkaloid was performed by the use of thin-layer chromatography (TLC) and high-performance liquid chromatography (HPLC) combined with electrospray ionization mass spectrometry (ESI-MS). The proposed approach was proved to be an efficient and accurate method for specific compound isolation and identification purposes. Moreover, analytical information from the CE approach can be considered as the valuable tool for binding constant determination. The binding constant of mitraphylline with Abeta1-40 protein determined by the Hummel-Dreyer method and Scatchard analysis equals K = 9.95 x 10(5) M(-1). The results obtained showed the significant binding of the tested compound with Abeta1-40 protein. These results are discussed and interpreted in the view of developing a strategy for identification of novel compounds of great importance in Alzheimer disease therapy. 7. MD-simulations of Beta-Amyloid Protein Insertion Efficiency and Kinetics into Neuronal Membrane Mimics Science.gov (United States) Qiu, Liming; Buie, Creighton; Vaughn, Mark; Cheng, Kwan 2011-03-01 Early interaction events of beta-amyloid (A β) peptides with the neuronal membranes play a key role in the pathogenesis of Alzheimer's disease. We have used all-atom MD simulations to study the protein insertion efficiency and kinetics of monomeric A β40 and A β42 into phosphatidylcholine lipid bilayers (PC) with and without 40 mole% cholesterol (CHOL) that mimic the cholesterol-enriched and depleted lipid nanodomains of the neuronal plasma membranes. Independent replicates of 200-ns simulations of each protein pre-inserted in the upper lipid layer were generated. In PC bilayers, only 25% of A β40 and 50% of A β42 in the replicates showed complete insertion into the lower lipid layer, whereas the percentages increased to 50% and 100%, respectively, in PC/CHOL bilayers, providing evidence that cholesterol improves the protein insertion efficiency into the bilayers. The rate of protein insertion was proportional to the hydrophobic, transmembrane helix length of the inserted peptide and depended on the cholesterol content. We propose that the lysine snorkeling and C-terminus anchoring of A β to the PC headgroups at the upper and lower lipid/water interfaces represent the dual-transmembrane stabilization mechanisms of A β in the neuronal membrane domains. 8. Control the aggregation of model amyloid insulin protein under ac-electric fields Science.gov (United States) Zheng, Zhongli; Jing, Benxin; Zhu, Y. Elaine 2013-03-01 In vitro experiments have been widely used to characterize the misfolding/unfolding pathway characteristic of amylodogenic proteins. Conversion from natively folded amyloidogenic proteins to oligomers via nucleation is the accepted path to fibril formation upon heating over a certain lag time period. In an alternative engineering approach to manipulate and control protein aggregation, we have investigated the aggregation kinetics of insulin, a well-established amyloid model protein, under applied ac-electric fields of varied ac-frequency and voltage at room temperature. Using fluorescence correlation spectroscopy and fluorescence imaging, we have observed that the insulin aggregation can occur at much shortened lag time under applied ac-electric fields, when a critical ac-voltage is exceeded. The strong dependence of lag time on ac-frequency over a narrow range of 500 Hz-5 kHz indicates the effect of ac-electroosmosis on the diffusion controlled process of insulin nucleation. Yet, no difference of conformational structure is detected with insulin under applied ac-fields, suggesting the equivalence of ac-polarization to the conventional thermal activation process for insulin aggregation. 9. Processing Pisum sativum seed storage protein precursors in vitro Institute of Scientific and Technical Information of China (English) YANGLIJUN; CDOMONEY; 等 1990-01-01 The profile of polypeptides separated by SDS-PAGE from seed of major crop species such as pea(Pisum sativum) is complex,resulting from cleavage (processing) of precursors expressed from multiple copies of genes encoding vicilin and legumin,the major storage globulins.Translation in vitro of mRNAs hybridselected from mid-maturation pea seed RNAs by defined vicilin and legumin cDNA clones provided precursor molecules that were cleaved in vitro by a cell-free protease extract obtained from similar stage seed;the derived polypeptides were of comparable sizes to those observed in vivo.The feasibility of transcribing mRNA in vitro from a cDNA clone and cleavage in vitro of the derived translation products was established for a legumin clone,providing a method for determining polypeptide products of an expressed sequence.This approach will also be useful for characterising cleavage site requirements since modifications an readily be introduced at the DNA level. 10. Precision biopolymers from protein precursors for biomedical applications. Science.gov (United States) Kuan, Seah Ling; Wu, Yuzhou; Weil, Tanja 2013-03-12 The synthesis of biohybrid materials with tailored functional properties represents a topic of emerging interest. Combining proteins as natural, macromolecular building blocks, and synthetic polymers opens access to giant brush-like biopolymers of high structural definition. The properties of these precision polypeptide copolymers can be tailored through various chemical modifications along their polypeptide backbone, which expands the repertoire of known protein-based materials to address biomedical applications. In this article, the synthetic strategies for the design of precision biopolymers from proteins through amino acid specific conjugation reagents are highlighted and the different functionalization strategies, their characterization, and applications are discussed. 11. Differential gene expression in human brain pericytes induced by amyloid-beta protein. NARCIS (Netherlands) Rensink, A.A.M.; Otte-Holler, I.; Donkelaar, H.J. ten; Waal, R.M.W. de; Kremer, H.P.H.; Verbeek, M.M. 2004-01-01 Cerebral amyloid angiopathy is one of the characteristics of Alzheimer's disease (AD) and this accumulation of fibrillar amyloid-beta (Alphabeta) in the vascular wall is accompanied by marked vascular damage. In vitro, Abeta1-40 carrying the 'Dutch' mutation (DAbeta1-40) induces degeneration of cult 12. Fatal transmissible amyloid encephalopathy: a new type of prion disease associated with lack of prion protein membrane anchoring. Directory of Open Access Journals (Sweden) Bruce Chesebro 2010-03-01 Full Text Available Prion diseases are fatal neurodegenerative diseases of humans and animals characterized by gray matter spongiosis and accumulation of aggregated, misfolded, protease-resistant prion protein (PrPres. PrPres can be deposited in brain in an amyloid-form and/or non-amyloid form, and is derived from host-encoded protease-sensitive PrP (PrPsen, a protein normally anchored to the plasma membrane by glycosylphosphatidylinositol (GPI. Previously, using heterozygous transgenic mice expressing only anchorless PrP, we found that PrP anchoring to the cell membrane was required for typical clinical scrapie. However, in the present experiments, using homozygous transgenic mice expressing two-fold more anchorless PrP, scrapie infection induced a new fatal disease with unique clinical signs and altered neuropathology, compared to non-transgenic mice expressing only anchored PrP. Brain tissue of transgenic mice had high amounts of infectivity, and histopathology showed dense amyloid PrPres plaque deposits without gray matter spongiosis. In contrast, infected non-transgenic mice had diffuse non-amyloid PrPres deposits with significant gray matter spongiosis. Brain graft studies suggested that anchored PrPsen expression was required for gray matter spongiosis during prion infection. Furthermore, electron and light microscopic studies in infected transgenic mice demonstrated several pathogenic processes not seen in typical prion disease, including cerebral amyloid angiopathy and ultrastructural alterations in perivascular neuropil. These findings were similar to certain human familial prion diseases as well as to non-prion human neurodegenerative diseases, such as Alzheimer's disease. 13. Discovery and identification of Serum Amyloid A protein elevated in lung cancer serum Institute of Scientific and Technical Information of China (English) 2007-01-01 Two hundred and eighteen serum samples from 175 lung cancer patients and 43 healthy individuals were analyzed by using Surface Enhaced Laser Desorption/Ionization Time of Flight Mass Spectrome- try (SELDI-TOF-MS). The data analyzed by both Biomarker Wizard? and Biomarker Patterns? software showed that a protein peak with the molecular weight of 11.6 kDa significantly increased in lung cancer. Meanwhile,the level of this biomarker was progressively increased with the clinical stages of lung cancer. The candidate biomarker was then obtained from tricine one-dimensional sodium dodecyl sul- fate-polyacrylamide gel electrophoresis by matching the molecular weight with peaks on WCX2 chips and was identified as Serum Amyloid A protein (SAA) by MALDI/MS-MS and database searching. It was further validated in the same serum samples by immunoprecipitation with commercial SAA antibody. To confirm the SAA differential expression in lung cancer patients, the same set of serum samples was measured by ELISA assay. The result showed that at the cutoff point 0.446(OD value)on the Receiver Operating Characteristic (ROC) curve, SAA could better discriminate lung cancer from healthy indi- viduals with sensitivity of 84.1% and specificity of 80%. These findings demonstrated that SAA could be characterized as a biomarker related to pathological stages of lung cancer. 14. Developmental regulation of expression of C-reactive protein and serum amyloid A in Syrian hamsters. Science.gov (United States) Dowton, S B; Waggoner, D J; Mandl, K D 1991-11-01 The fetal and maternal concentration of various plasma proteins alters during pregnancy. Cells in the livers of fetal hamsters accumulate serum amyloid A (SAA) and C-reactive protein (CRP) mRNA, major acute phase reactants, when lipopolysaccharide is administered to the fetal circulation. No fetal SAA or CRP mRNA response is seen when the mother is stimulated at a remote site by endotoxin or a nonspecific inflammatory agent. In addition, cells of the fetal hamster liver do not respond by accumulating SAA mRNA when exposed to the specific cytokines, tumor necrosis factor, IL-1, and IL-6. CRP mRNA levels increased in fetal livers after administration of tumor necrosis factor and IL-1. These data suggest that cells contained in the fetal liver can respond during an acute phase reaction but that the capacity of some acute phase reactant genes to respond to cytokines may be developmentally regulated. Studies of immature hamsters after birth show that the responses of CRP and SAA genes to lipopolysaccharide, tumor necrosis factor, IL-1, and IL-6 are reduced when compared with induction of mRNA accumulation for these acute phase reactants in adult animals. 15. Transient expression of a mitochondrial precursor protein - A new approach to study mitochondrial protein import in cells of higher eukaryotes NARCIS (Netherlands) Huckriede, A; Heikema, A; Wilschut, J; Agsteribbe, E 1996-01-01 In order to study mitochondrial protein import in the context of whole cell metabolism, we have used the transfection technique based on Semliki Forest virus (SFV) to express a mitochondrial precursor protein within BHK21 cells and human fibroblasts. Recombinant SFV particles mediate a highly effici 16. Diversity, biogenesis and function of microbial amyloids OpenAIRE 2011-01-01 Amyloid is a distinct β-sheet-rich fold that many proteins can acquire. Frequently associated with neurodegenerative diseases in humans, including Alzheimer’s, Parkinson’s and Huntington’s, amyloids are traditionally considered the product of protein misfolding. However, the amyloid fold is now recognized as a ubiquitous part of normal cellular biology. ‘Functional’ amyloids have been identified in nearly all facets of cellular life, with microbial functional amyloids leading the way. Unlike ... 17. Chronic pre-treatment with memantine prevents amyloid-beta protein-mediated long-term potentiation disruption Institute of Scientific and Technical Information of China (English) Fushun Li; Xiaowei Chen; Feiming Wang; Shujun Xu; Lan Chang; Roger Anwyl; Qinwen Wang 2013-01-01 Previous studies indicate that memantine, a low-affinity N-methyl-D-aspartate receptor antagonist, exerted acute protective effects against amyloidprotein-induced neurotoxicity. In the present study, the chronic effects and mechanisms of memantine were investigated further using electrophysiological methods. The results showed that 7-day intraperitoneal application of memantine, at doses of 5 mg/kg or 20 mg/kg, did not alter hippocampal long-term potentiation induction in rats, while 40 mg/kg memantine presented potent long-term potentiation inhibition. Then further in vitro studys were carried out in 5 mg/kg and 20 mg/kg memantine treated rats. We found that 20 mg/kg memantine attenuated the potent long-term potentiation inhibition caused by exposure to amyloidprotein in the dentate gyrus in vitro. These findings are the first to demonstrate the antagonizing effect of long-term systematic treatment of memantine against amyloidprotein triggered long-term potentiation inhibition to improve synaptic plasticity. 18. The OPEP protein model: from single molecules, amyloid formation, crowding and hydrodynamics to DNA/RNA systems. Science.gov (United States) Sterpone, Fabio; Melchionna, Simone; Tuffery, Pierre; Pasquali, Samuela; Mousseau, Normand; Cragnolini, Tristan; Chebaro, Yassmine; St-Pierre, Jean-Francois; Kalimeri, Maria; Barducci, Alessandro; Laurin, Yoann; Tek, Alex; Baaden, Marc; Nguyen, Phuong Hoang; Derreumaux, Philippe 2014-07-07 The OPEP coarse-grained protein model has been applied to a wide range of applications since its first release 15 years ago. The model, which combines energetic and structural accuracy and chemical specificity, allows the study of single protein properties, DNA-RNA complexes, amyloid fibril formation and protein suspensions in a crowded environment. Here we first review the current state of the model and the most exciting applications using advanced conformational sampling methods. We then present the current limitations and a perspective on the ongoing developments. 19. Purification and Refolding to Amyloid Fibrils of (His)6-tagged Recombinant Shadoo Protein Expressed as Inclusion Bodies in E. coli. Science.gov (United States) Li, Qiaojing; Richard, Charles-Adrien; Moudjou, Mohammed; Vidic, Jasmina 2015-12-19 The Escherichia coli expression system is a powerful tool for the production of recombinant eukaryotic proteins. We use it to produce Shadoo, a protein belonging to the prion family. A chromatographic method for the purification of (His)6-tagged recombinant Shadoo expressed as inclusion bodies is described. The inclusion bodies are solubilized in 8 M urea and bound to a Ni(2+)-charged column to perform ion affinity chromatography. Bound proteins are eluted by a gradient of imidazole. Fractions containing Shadoo protein are subjected to size exclusion chromatography to obtain a highly purified protein. In the final step purified Shadoo is desalted to remove salts, urea and imidazole. Recombinant Shadoo protein is an important reagent for biophysical and biochemical studies of protein conformation disorders occurring in prion diseases. Many reports demonstrated that prion neurodegenerative diseases originate from the deposition of stable, ordered amyloid fibrils. Sample protocols describing how to fibrillate Shadoo into amyloid fibrils at acidic and neutral/basic pHs are presented. The methods on how to produce and fibrillate Shadoo can facilitate research in laboratories working on prion diseases, since it allows for production of large amounts of protein in a rapid and low cost manner. 20. Amyloid-β Activates Microglia and Regulates Protein Expression in a Manner Similar to Prions. Science.gov (United States) Tu, Jian; Chen, Baian; Yang, Lifeng; Qi, Kezong; Lu, Jing; Zhao, Deming 2015-06-01 Prions are the only convincingly demonstrated proteinaceous infectious particle, yet recent studies find that amyloid-β peptide (Aβ) aggregates are capable of self-propagation, which induces amyloidosis pathology in Alzheimer's disease (AD) model mice that is similar to the self-propagation phenomenon of prions in neurons. Gliosis is a common hallmark of AD and prion diseases, in which activated microglia accumulate around abnormal protein deposits. Analyses of the characteristics of activated microglia induced by Aβ in comparison with those induced by prions will provide new insight into the pathogenesis of AD. Therefore, we compared the characteristics of BV-2 cells (model microglia) activated by Aβ fibrillar peptides (Aβ1-42) and prions (PrP106-126). Aβ1-42 and PrP106-126, as well as the supernatants of the media collected from BV-2 cells cocultured with Aβ1-42 and PrP106-126, were potent activators of BV-2 microglial activity, but the chemotaxis index (CI) induced by Aβ1-42 was significantly higher than that induced by PrP106-126 at each concentration. Aβ1-42 and PrP106-126 increased the proliferation index (PI) and upregulated monocyte chemoattractant protein-1 (MCP-1) and transforming growth factor beta 1 (TGF-β1) expression after 12 h of exposure. Our results show that Aβ activates microglia and regulates microglial protein expression in a manner similar to prions and, thus, provide new insight into the pathogenesis of AD. 1. Truncated prion protein PrP226* - A structural view on its role in amyloid disease. Science.gov (United States) Kovač, Valerija; Zupančič, Blaž; Ilc, Gregor; Plavec, Janez; Čurin Šerbec, Vladka 2017-02-26 In the brain of patients with transmissible spongiform encephalopathies, besides PrP(Sc) aggregates, deposition of truncated PrP molecules was described. Jansen et al. reported two clinical cases with deposition of C-terminally truncated PrP, one of them ending with Tyr226. We have previously described the discovery of monoclonal antibody V5B2 that selectively recognizes this version of the prion protein, which we called PrP226. Using monoclonal antibody V5B2 we showed that accumulation of PrP226 is characteristic for most types of human and animal TSEs. Its distribution correlates to the distribution of PrP(Sc) aggregates. To gain insight into the structural basis of its presence and distribution in PrP aggregates, we have determined the NMR structure of recombinant PrP226. The structure of the protein consists of a disordered N-terminal part (residues 90-125) and a structured C-terminal part (residues 126-226). The C-terminal segment consists of four α-helices and a short antiparallel β-sheet. Our model predicts a break in the C-terminal helix and reorganized hydrophobic interactions between helix α3 and β2-α2 loop due to the shorter C-terminus. The structural model gives information on the possible role of the protein in the development of amyloid disease and can serve as a foundation to develop tools for prevention and treatment of prion diseases. 2. New Insights in the Amyloid-Beta Interaction with Mitochondria Directory of Open Access Journals (Sweden) Carlos Spuch 2012-01-01 Full Text Available Biochemical and morphological alterations of mitochondria may play an important role in the pathogenesis of Alzheimer’s disease (AD. Particularly, mitochondrial dysfunction is a hallmark of amyloid-beta-induced neuronal toxicity in Alzheimer’s disease. The recent emphasis on the intracellular biology of amyloid-beta and its precursor protein (APP has led researchers to consider the possibility that mitochondria-associated and mitochondrial amyloid-beta may directly cause neurotoxicity. Both proteins are known to localize to mitochondrial membranes, block the transport of nuclear-encoded mitochondrial proteins to mitochondria, interact with mitochondrial proteins, disrupt the electron transport chain, increase reactive oxygen species production, cause mitochondrial damage, and prevent neurons from functioning normally. In this paper, we will outline current knowledge of the intracellular localization of amyloid-beta. Moreover, we summarize evidence from AD postmortem brain as well as animal AD models showing that amyloid-beta triggers mitochondrial dysfunction through a number of pathways such as impairment of oxidative phosphorylation, elevation of reactive oxygen species production, alteration of mitochondrial dynamics, and interaction with mitochondrial proteins. Thus, this paper supports the Alzheimer cascade mitochondrial hypothesis such as the most important early events in this disease, and probably one of the future strategies on the therapy of this neurodegenerative disease. 3. Parallel in-register intermolecular β-sheet architectures for prion-seeded prion protein (PrP) amyloids. Science.gov (United States) Groveman, Bradley R; Dolan, Michael A; Taubner, Lara M; Kraus, Allison; Wickner, Reed B; Caughey, Byron 2014-08-29 Structures of the infectious form of prion protein (e.g. PrP(Sc) or PrP-Scrapie) remain poorly defined. The prevalent structural models of PrP(Sc) retain most of the native α-helices of the normal, noninfectious prion protein, cellular prion protein (PrP(C)), but evidence is accumulating that these helices are absent in PrP(Sc) amyloid. Moreover, recombinant PrP(C) can form amyloid fibrils in vitro that have parallel in-register intermolecular β-sheet architectures in the domains originally occupied by helices 2 and 3. Here, we provide solid-state NMR evidence that the latter is also true of initially prion-seeded recombinant PrP amyloids formed in the absence of denaturants. These results, in the context of a primarily β-sheet structure, led us to build detailed models of PrP amyloid based on parallel in-register architectures, fibrillar shapes and dimensions, and other available experimentally derived conformational constraints. Molecular dynamics simulations of PrP(90-231) octameric segments suggested that such linear fibrils, which are consistent with many features of PrP(Sc) fibrils, can have stable parallel in-register β-sheet cores. These simulations revealed that the C-terminal residues ∼124-227 more readily adopt stable tightly packed structures than the N-terminal residues ∼90-123 in the absence of cofactors. Variations in the placement of turns and loops that link the β-sheets could give rise to distinct prion strains capable of faithful template-driven propagation. Moreover, our modeling suggests that single PrP monomers can comprise the entire cross-section of fibrils that have previously been assumed to be pairs of laterally associated protofilaments. Together, these insights provide a new basis for deciphering mammalian prion structures. 4. Gene expression profile of amyloid beta protein-injected mouse model for Alzheimer disease Institute of Scientific and Technical Information of China (English) Ling-na KONG; Ping-ping ZUO; Liang MU; Yan-yong LIU; Nan YANG 2005-01-01 Aim: To investigate the gene expression profile changes in the cerebral cortex of mice injected icv with amyloid beta-protein (Aβ) fragment 25-35 using cDNA microarray. Methods: Balb/c mice were randomly divided into a control group and Aβ-treated group. The Morris water maze test was performed to detect the effect of Aβ-injection on the learning and memory of mice. Atlas Mouse 1.2 Expression Arrays containing 1176 genes were used to investigate the gene expression pattern of each group. Results: The gene expression profiles showed that 19 genes including TBX1, NF-κB, AP-1/c-Jun, cadherin, integrin, erb-B2, and FGFR1 were up-regulated after 2 weeks oficv administration of Aβ; while 12 genes were downregulated, including NGF, glucose phosphate isomerase 1, AT motif binding factor 1, Na+/K+-ATPase, and Akt. Conclusions: The results provide important leads for pursuing a more complete understanding of the molecular events of Aβ-injection into mice with Alzheimer disease. 5. Alzheimer's associated β-amyloid protein inhibits influenza A virus and modulates viral interactions with phagocytes. Directory of Open Access Journals (Sweden) Mitchell R White Full Text Available Accumulation of β-Amyloid (βA is a key pathogenetic factor in Alzheimer's disease; however, the normal function of βA is unknown. Recent studies have shown that βA can inhibit growth of bacteria and fungi. In this paper we show that βA also inhibits replication of seasonal and pandemic strains of H3N2 and H1N1 influenza A virus (IAV in vitro. The 42 amino acid fragment of βA (βA42 had greater activity than the 40 amino acid fragment. Direct incubation of the virus with βA42 was needed to achieve optimal inhibition. Using quantitative PCR assays βA42 was shown to reduce viral uptake by epithelial cells after 45 minutes and to reduce supernatant virus at 24 hours post infection. βA42 caused aggregation of IAV particles as detected by light transmission assays and electron and confocal microscopy. βA42 did not stimulate neutrophil H2O2 production or extracellular trap formation on its own, but it increased both responses stimulated by IAV. In addition, βA42 increased uptake of IAV by neutrophils. βA42 reduced viral protein synthesis in monocytes and reduced IAV-induced interleukin-6 production by these cells. Hence, we demonstrate for the first time that βA has antiviral activity and modulates viral interactions with phagocytes. 6. The Alzheimer's disease-associated amyloid beta-protein is an antimicrobial peptide. Directory of Open Access Journals (Sweden) Stephanie J Soscia Full Text Available BACKGROUND: The amyloid beta-protein (Abeta is believed to be the key mediator of Alzheimer's disease (AD pathology. Abeta is most often characterized as an incidental catabolic byproduct that lacks a normal physiological role. However, Abeta has been shown to be a specific ligand for a number of different receptors and other molecules, transported by complex trafficking pathways, modulated in response to a variety of environmental stressors, and able to induce pro-inflammatory activities. METHODOLOGY/PRINCIPAL FINDINGS: Here, we provide data supporting an in vivo function for Abeta as an antimicrobial peptide (AMP. Experiments used established in vitro assays to compare antimicrobial activities of Abeta and LL-37, an archetypical human AMP. Findings reveal that Abeta exerts antimicrobial activity against eight common and clinically relevant microorganisms with a potency equivalent to, and in some cases greater than, LL-37. Furthermore, we show that AD whole brain homogenates have significantly higher antimicrobial activity than aged matched non-AD samples and that AMP action correlates with tissue Abeta levels. Consistent with Abeta-mediated activity, the increased antimicrobial action was ablated by immunodepletion of AD brain homogenates with anti-Abeta antibodies. CONCLUSIONS/SIGNIFICANCE: Our findings suggest Abeta is a hitherto unrecognized AMP that may normally function in the innate immune system. This finding stands in stark contrast to current models of Abeta-mediated pathology and has important implications for ongoing and future AD treatment strategies. 7. The effect of zinc on amyloid β-protein assembly and toxicity: A mechanistic investigation Science.gov (United States) Solomonov, Inna; Sagi, Irit 2014-10-01 Neurotoxic assemblies of amyloid β-protein (Aβ) are widely believed to be the cause for Alzheimer's disease (AD). Therefore, understanding the factors and mechanisms that control, modulate, and inhibit formation of these assemblies is crucial for the development of therapeutic intervention of AD. This information also can contribute significantly to our understanding of the mechanisms of other amyloidosis diseases, such as Parkinson's disease, Huntington's disease, type 2 diabetes, amyotrophic lateral sclerosis (Lou Gehrig's disease) and prion diseases (e.g. Mad Cow disease). We have developed a multidisciplinary experimental strategy to study structural and dynamic mechanistic aspects that underlie the Aβ assembly process. Utilizing this strategy, we explored the molecular basis leading to the perturbation of the Aβ assembly process by divalent metal ions, mainly Zn2+ ions. Using Zn2+ as reaction physiological relevant probes, it was demonstrated that Zn2+ rapidly (milliseconds) induce self-assembly of Aβ aggregates and stabilize them in a manner that prevents formation of Aβ fibrils. Importantly, the early-formed intermediates are substantially more neurotoxic than fibrils. Our results suggest that relevant Aβ modulators should be targeted against the rapidly evolved intermediate states of Aβ assembly. The design of such modulators is challenging, as they have to compete with different natural mediators (such as Zn2+) of Aβ aggregation, which diverse Aβ assemblies in both specific and nonspecific manners. 8. Familial Alzheimer's disease mutations differentially alter amyloid β-protein oligomerization. Science.gov (United States) Gessel, Megan Murray; Bernstein, Summer; Kemper, Martin; Teplow, David B; Bowers, Michael T 2012-11-21 Although most cases of Alzheimer's disease (AD) are sporadic, ∼5% of cases are genetic in origin. These cases, known as familial Alzheimer's disease (FAD), are caused by mutations that alter the rate of production or the primary structure of the amyloid β-protein (Aβ). Changes in the primary structure of Aβ alter the peptide's assembly and toxic activity. Recently, a primary working hypothesis for AD has evolved where causation has been attributed to early, soluble peptide oligomer states. Here we posit that both experimental and pathological differences between FAD-related mutants and wild-type Aβ could be reflected in the early oligomer distributions of these peptides. We use ion mobility-based mass spectrometry to probe the structure and early aggregation states of three mutant forms of Aβ40 and Aβ42: Tottori (D7N), Flemish (A21G), and Arctic (E22G). Our results indicate that the FAD-related amino acid substitutions have no noticeable effect on Aβ monomer cross section, indicating there are no major structural changes in the monomers. However, we observe significant changes to the aggregation states populated by the various Aβ mutants, indicating that structural changes present in the monomers are reflected in the oligomers. Moreover, the early oligomer distributions differ for each mutant, suggesting a possible structural basis for the varied pathogenesis of different forms of FAD. 9. Human J-protein DnaJB6b Cures a Subset of Saccharomyces cerevisiae Prions and Selectively Blocks Assembly of Structurally Related Amyloids. Science.gov (United States) Reidy, Michael; Sharma, Ruchika; Roberts, Brittany-Lee; Masison, Daniel C 2016-02-19 Human chaperone DnaJB6, an Hsp70 co-chaperone whose defects cause myopathies, protects cells from polyglutamine toxicity and prevents purified polyglutamine and Aβ peptides from forming amyloid. Yeast prions [URE3] and [PSI(+)] propagate as amyloid forms of Ure2 and Sup35 proteins, respectively. Here we find DnaJB6-protected yeast cells from polyglutamine toxicity and cured yeast of both [URE3] prions and weak variants of [PSI(+)] prions but not strong [PSI(+)] prions. Weak and strong variants of [PSI(+)] differ only in the structural conformation of their amyloid cores. In line with its anti-prion effects, DnaJB6 prevented purified Sup35NM from forming amyloids at 37 °C, which produce predominantly weak [PSI(+)] variants when used to infect yeast, but not at 4 °C, which produces mostly strong [PSI(+)] variants. Thus, structurally distinct amyloids composed of the same protein were differentially sensitive to the anti-amyloid activity of DnaJB6 both in vitro and in vivo. These findings have important implications for strategies using DnaJB6 as a target for therapy in amyloid disorders. 10. A setup for simultaneous measurement of infrared spectra and light scattering signals: Watching amyloid fibrils grow from intact proteins Energy Technology Data Exchange (ETDEWEB) Li, Yang; Maurer, Jürgen; Roth, Andreas; Vogel, Vitali; Winter, Ernst; Mäntele, Werner, E-mail: maentele@biophysik.uni-frankfurt.de [Institut für Biophysik, Goethe-Universität Frankfurt am Main, Max-von Laue-Straße 1, D-60438 Frankfurt am Main (Germany) 2014-08-15 A setup for the simultaneous measurement of mid-infrared spectra and static light scattering is described that can be used for the analysis of the formation of nanoscale and microscopic aggregates from smaller molecules to biopolymers. It can be easily integrated into sample chambers of infrared spectrometers or combined with laser beams from tunable infrared lasers. Here, its use for the analysis of the formation of amyloid fibrils from intact proteins is demonstrated. The formation of amyloid fibrils or plaques from proteins is a widespread and pathogenetic relevant process, and a number of diseases are caused and correlated with the deposition of amyloid fibrils in cells and tissues. The molecular mechanisms of these transformations, however, are still unclear. We report here the simultaneous measurement of infrared spectra and static light scattering for the analysis of fibril formation from egg-white lysozyme. The transformation of the native form into non-native forms rich in β-sheet structure is measured by analysis of the amide I spectral region in the infrared spectra, which is sensitive for local structures. At the same time, light scattering signals at forward direction as well as the forward/backward ratio, which are sensitive for the number of scattering centers and their approximate sizes, respectively, are collected for the analysis of fibril growth. Thermodynamic and kinetic parameters as well as mechanistic information are deduced from the combination of the two complementary techniques. 11. The repeat domain of the melanosome fibril protein Pmel17 forms the amyloid core promoting melanin synthesis. Science.gov (United States) McGlinchey, Ryan P; Shewmaker, Frank; McPhie, Peter; Monterroso, Begoña; Thurber, Kent; Wickner, Reed B 2009-08-18 Pmel17 is a melanocyte protein necessary for eumelanin deposition 1 in mammals and found in melanosomes in a filamentous form. The luminal part of human Pmel17 includes a region (RPT) with 10 copies of a partial repeat sequence, pt.e.gttp.qv., known to be essential in vivo for filament formation. We show that this RPT region readily forms amyloid in vitro, but only under the mildly acidic conditions typical of the lysosome-like melanosome lumen, and the filaments quickly become soluble at neutral pH. Under the same mildly acidic conditions, the Pmel filaments promote eumelanin formation. Electron diffraction, circular dichroism, and solid-state NMR studies of Pmel17 filaments show that the structure is rich in beta sheet. We suggest that RPT is the amyloid core domain of the Pmel17 filaments so critical for melanin formation. 12. Serum amyloid P (female protein) of the Syrian hamster. Gene structure and expression. Science.gov (United States) Rudnick, C M; Dowton, S B 1993-10-15 The structure and expression of the gene encoding serum amyloid P (SAP) component of the Syrian hamster have been studied by isolation of cosmid clones, nucleotide sequence analyses, and quantitation of nuclear run-on transcripts, nuclear RNA, mRNA, and protein levels. Hamster SAP, originally identified as female protein (FP), is a unique pentraxin because pretranslational expression of this gene is modulated by mediators of inflammation and sex steroids. SAP(FP) levels are high in sera from female hamsters and low in males. The response to inflammation is divergent; SAP(FP) levels decrease in females and increase in males during an acute phase response. The SAP(FP) gene encodes a 211 amino acid residue mature polypeptide as well as a 22-residue signal peptide. The intron/exon organization is similar to that of other pentraxins, but additional transcripts are generated from alternate polyadenylation sites in the 3' region. Circulating levels of SAP(FP) and the corresponding hepatic transcript levels are augmented by estrogen, while testosterone, dexamethasone, and progesterone cause a decrease in these levels. In addition the cytokines interleukin-1, -6, and tumor necrosis factor mediate a decrease in hepatic SAP(FP) transcript levels in female hamsters but did not cause a significant elevation of SAP(FP) mRNA in livers of male hamsters. The differences in expression of the SAP(FP) gene between male and female hamsters and between unstimulated male hamsters and male hamsters stimulated with an injection of lipopolysaccharide are due, at least in part, to alterations in transcription. 13. α-Ketoacids as precursors for phenylalanine and tyrosine labelling in cell-based protein overexpression. Science.gov (United States) Lichtenecker, Roman J; Weinhäupl, Katharina; Schmid, Walther; Konrat, Robert 2013-12-01 (13)C-α-ketoacid metabolic precursors of phenylalanine and tyrosine effectively enter the metabolism of a protein overexpressing E. coli strain to label Phe- and Tyr-residues devoid of any cross-labelling. The methodology gives access to highly selective labelling patterns as valuable tools in protein NMR spectroscopy without the need of (15)N-chiral amino acid synthesis using organic chemistry. 14. Bapineuzumab alters aβ composition: implications for the amyloid cascade hypothesis and anti-amyloid immunotherapy. Directory of Open Access Journals (Sweden) Alex E Roher 15. Self-assembly of a nine-residue amyloid-forming peptide fragment of SARS corona virus E-protein: mechanism of self aggregation and amyloid-inhibition of hIAPP. Science.gov (United States) Ghosh, Anirban; Pithadia, Amit S; Bhat, Jyotsna; Bera, Supriyo; Midya, Anupam; Fierke, Carol A; Ramamoorthy, Ayyalusamy; Bhunia, Anirban 2015-04-01 Molecular self-assembly, a phenomenon widely observed in nature, has been exploited through organic molecules, proteins, DNA, and peptides to study complex biological systems. These self-assembly systems may also be used in understanding the molecular and structural biology which can inspire the design and synthesis of increasingly complex biomaterials. Specifically, use of these building blocks to investigate protein folding and misfolding has been of particular value since it can provide tremendous insights into peptide aggregation related to a variety of protein misfolding diseases, or amyloid diseases (e.g., Alzheimer's disease, Parkinson's disease, type-II diabetes). Herein, the self-assembly of TK9, a nine-residue peptide of the extra membrane C-terminal tail of the SARS corona virus envelope, and its variants were characterized through biophysical, spectroscopic, and simulated studies, and it was confirmed that the structure of these peptides influences their aggregation propensity, hence, mimicking amyloid proteins. TK9, which forms a beta-sheet rich fibril, contains a key sequence motif that may be critical for beta-sheet formation, thus making it an interesting system to study amyloid fibrillation. TK9 aggregates were further examined through simulations to evaluate the possible intra- and interpeptide interactions at the molecular level. These self-assembly peptides can also serve as amyloid inhibitors through hydrophobic and electrophilic recognition interactions. Our results show that TK9 inhibits the fibrillation of hIAPP, a 37 amino acid peptide implicated in the pathology of type-II diabetes. Thus, biophysical and NMR experimental results have revealed a molecular level understanding of peptide folding events, as well as the inhibition of amyloid-protein aggregation are reported. 16. Human Islet Amyloid Polypeptide DEFF Research Database (Denmark) Kosicka, Iga 2014-01-01 Diabetes mellitus type II is a metabolic disease affecting millions of people worldwide. The disease is associated with occurence of insoluble, fibrillar, protein aggregates in islets of Langerhans in the pancreas - islet amyloid. The main constituent of these protein fibers is the human islet...... of diabetes type II, while revealing the structure(s) of islet amyloid fibrils is necessary for potential design of therapeutic agents.... 17. The β-amyloid protein induces S100β expression in rat hippocampus through a mechanism that involves IL-1 Institute of Scientific and Technical Information of China (English) 2007-01-01 Objective To explore the effect of β-amyloid protein (Aβ) on S100β expression in rat hippocampus and its mechanisms. Methods At 7 days after bilateral stereotaxis injection of different dose of fibrillar Aβ 25-35 and interluekin-1 receptor antagonist (IL-1ra) into the rat CA1 region, the learning and memory abilities of rats were tested with passive avoidance task. Amyloid deposition was detected by using Congo red staining technique. Nissl staining and immunohistochemical techniques were used to analyze the number of neurons, and GFAP and the S100β expression in hippocampal CA1 region , respectively. Results After fibrillar Aβ injection, the step-through latency of rats was significantly shortened compared to that of the control group. The GFAP positive astrocytes were found surrounding amyloid deposition. Neuronal loss occurred in the pyramidal cell layer of CA1 region. The number of S100β positive cells in Aβ-treated group was significantly increased compared with that in the control group. After IL-1ra injection, the number of S100β positive cells was significantly decreased. Conclusion Intrahippocampal injection of Aβ 25-35 could cause similar pathologic changes of Alzheimer's disease. Aβ 25-35 was capable of up-regulating S100β expression in a dose-dependent manner. The injection of IL-1ra could attenuate the effect of Aβ on S100β expression. 18. The involvement of homocysteine in stress-induced Aβ precursor protein misprocessing and related cognitive decline in rats. Science.gov (United States) Xie, Fang; Zhao, Yun; Ma, Jing; Gong, Jing-Bo; Wang, Shi-Da; Zhang, Liang; Gao, Xiu-Jie; Qian, Ling-Jia 2016-09-01 Chronic stress is a risk factor in the development of cognitive decline and even Alzheimer's disease (AD), although its underlying mechanism is not fully understood. Our previous data demonstrated that the level of homocysteine (Hcy) was significantly elevated in the plasma of stressed animals, which suggests the possibility that Hcy is a link between stress and cognitive decline. To test this hypothesis, we compared the cognitive function, plasma concentrations of Hcy, and the brain beta-amyloid (Aβ) level between rats with or without chronic unexpected mild stress (CUMS). A lower performance by rats in behavioral tests indicated that a significant cognitive decline was induced by CUMS. Stress also disturbed the normal processing of Aβ precursor protein (APP) and resulted in the accumulation of Aβ in the brains of rats, which showed a positive correlation with the hyperhomocysteinemia (HHcy) that appeared in stressed rats. Hcy-targeting intervention experiments were used to verify further the involvement of Hcy in stress-induced APP misprocessing and related cognitive decline. The results showed that diet-induced HHcy could mimic the cognitive impairment and APP misprocessing in the same manner as CUMS, while Hcy reduction by means of vitamin B complex supplements and betaine could alleviate the cognitive deficits and dysregulation of Aβ metabolism in CUMS rats. Taken together, the novel evidence from our present study suggests that Hcy is likely to be involved in chronic stress-evoked APP misprocessing and related cognitive deficits. Our results also suggested the possibility of Hcy as a target for therapy and the potential value of vitamin B and betaine intake in the prevention of stress-induced cognitive decline. 19. Identification of UDP-linked murein precursors as contaminants in recombinant proteins of low molecular weight. Science.gov (United States) Ram, M K; Andrade, L J; Phillips, T B; van Schravendijk, M R 1999-11-01 The A(280)/A(260) ratio of a purified protein is frequently used as an indication of the purity of the preparation with respect to nucleic acids. We show here that for low-molecular-weight recombinant proteins purified from Escherichia coli, a low A(280)/A(260) ratio can also result from contamination with UDP-linked murein precursors derived from bacterial cell wall metabolism. Although these precursors are small molecules of molecular weight 1000-1200, they comigrate in gel filtration with recombinant human FKBP (MW 11,820). This gel filtration behavior, which is distinct from that of unmodified mononucleotides, does not reflect binding interactions with FKBP, but is an intrinsic property of these precursors. Therefore, these molecules would be expected to copurify with other low-molecular-weight proteins, especially in the abbreviated purification protocols made possible by freeze-thaw release of recombinant proteins from E. coli (Johnson, B. H., and Hecht, M. H. (1994) BioTechnology 12, 1357-1360). Several alternative strategies are discussed for integrating these findings into the design of improved purification procedures for low-molecular-weight recombinant proteins. 20. Microglial Amyloid-β1-40 Phagocytosis Dysfunction Is Caused by High-Mobility Group Box Protein-1: Implications for the Pathological Progression of Alzheimer’s Disease Directory of Open Access Journals (Sweden) Kazuyuki Takata 2012-01-01 Full Text Available In Alzheimer disease (AD patient brains, the accumulation of amyloid-β (Aβ peptides is associated with activated microglia. Aβ is derived from the amyloid precursor protein; two major forms of Aβ, that is, Aβ1-40 (Aβ40 and Aβ1-42 (Aβ42, exist. We previously reported that rat microglia phagocytose Aβ42, and high mobility group box protein 1 (HMGB1, a chromosomal protein, inhibits phagocytosis. In the present study, we investigated the effects of exogenous HMGB1 on rat microglial Aβ40 phagocytosis. In the presence of exogenous HMGB1, Aβ40 markedly increased in microglial cytoplasm, and the reduction of extracellular Aβ40 was inhibited. During this period, HMGB1 was colocalized with Aβ40 in the cytoplasm. Furthermore, exogenous HMGB1 inhibited the degradation of Aβ40 induced by the rat microglial cytosolic fraction. Thus, extracellular HMGB1 may internalize with Aβ40 in the microglial cytoplasm and inhibit Aβ40 degradation by microglia. This may subsequently delay Aβ40 clearance. We further confirmed that in AD brains, the parts of senile plaques surrounded by activated microglia are composed of Aβ40, and extracellular HMGB1 is deposited on these plaques. Taken together, microglial Aβ phagocytosis dysfunction may be caused by HMGB1 that accumulates extracellularly on Aβ plaques, and it may be critically involved in the pathological progression of AD. 1. Serum Amyloid A Protein Concentration in Blood is Influenced by Genetic Differences in the Cheetah (Acinonyx jubatus). Science.gov (United States) Franklin, Ashley D; Schmidt-Küntzel, Anne; Terio, Karen A; Marker, Laurie L; Crosier, Adrienne E 2016-03-01 Systemic amyloid A (AA) amyloidosis is a major cause of morbidity and mortality among captive cheetahs. The self-aggregating AA protein responsible for this disease is a byproduct of serum amyloid A (SAA) protein degradation. Transcriptional induction of the SAA1 gene is dependent on both C/EBPβ and NF-κB cis-acting elements within the promoter region. In cheetahs, 2 alleles exist for a single guanine nucleotide deletion in the putative NF-κB binding site. In this study, a novel genotyping assay was developed to screen for the alleles. The results show that the SAA1A (-97delG) allele is associated with decreased SAA protein concentrations in the serum of captive cheetahs (n = 58), suggesting genetic differences at this locus may be affecting AA amyloidosis prevalence. However, there was no significant difference in the frequency of the SAA1A (-97delG) allele between individuals confirmed AA amyloidosis positive versus AA amyloidosis negative at the time of necropsy (n = 48). Thus, even though there is evidence that having more copies of the SAA1A (-97delG) allele results in a potentially protective decrease in serum concentrations of SAA protein in captive cheetahs, genotype is not associated with this disease within the North American population. These results suggest that other factors are playing a more significant role in the pathogenesis of AA amyloidosis among captive cheetahs. 2. Comparison of serum amyloid A and C-reactive protein as diagnostic markers of systemic inflammation in dogs DEFF Research Database (Denmark) Christensen, Michelle Brønniche; Langhorn, Rebecca; Goddard, Amelia 2014-01-01 The diagnostic performance of canine serum amyloid A (SAA) was compared with that of C-reactive protein (CRP) in the detection of systemic inflammation in dogs. Sera from 500 dogs were retrospectively included in the study. C-reactive protein and SAA were measured using validated automated assays....... The overlap performance, clinical decision limits, overall diagnostic performance, correlations, and agreement in the clinical classification between these 2 diagnostic markers were compared. Significantly higher concentrations of both proteins were detected in dogs with systemic inflammation (SAA range: 48.......75 to > 2700 mg/L; CRP range: 0.4 to 907.4 mg/L) compared to dogs without systemic inflammation (SAA range: 1.06 to 56.4 mg/L; CRP range: 0.07 to 24.7 mg/L). Both proteins were shown to be sensitive and specific markers of systemic inflammation in dogs. Significant correlations and excellent diagnostic... 3. Proteomic profiling of the mitochondrial ribosome identifies Atp25 as a composite mitochondrial precursor protein. Science.gov (United States) Woellhaf, Michael W; Sommer, Frederik; Schroda, Michael; Herrmann, Johannes M 2016-10-15 Whereas the structure and function of cytosolic ribosomes are well characterized, we only have a limited understanding of the mitochondrial translation apparatus. Using SILAC-based proteomic profiling, we identified 13 proteins that cofractionated with the mitochondrial ribosome, most of which play a role in translation or ribosomal biogenesis. One of these proteins is a homologue of the bacterial ribosome-silencing factor (Rsf). This protein is generated from the composite precursor protein Atp25 upon internal cleavage by the matrix processing peptidase MPP, and in this respect, it differs from all other characterized mitochondrial proteins of baker's yeast. We observed that cytosolic expression of Rsf, but not of noncleaved Atp25 protein, is toxic. Our results suggest that eukaryotic cells face the challenge of avoiding negative interference from the biogenesis of their two distinct translation machineries. 4. Melatonin attenuates β-amyloid-induced inhibition of neurofilament expression Institute of Scientific and Technical Information of China (English) Ying-chun ZHANG; Ze-fen WANG; Qun WANG; Yi-peng WANG; Jian-zhi WANG 2004-01-01 AIM: To explore the effect of β-amyloid (Aβ) on metabolism of cytoskeletal protein neurofilament, and search for effective cure to the lesion. METHODS: Wild type murine neuroblastoma N2a (N2awt) and N2a stably transfected with wild type amyloid precursor protein (N2aAPP) were cultured. Sandwich ELISA, immunocytochemistry, and Western blot were used respectively to measure the level of Aβ, the expression and phosphorylation of neurofilament proteins. RESULTS: The immunoreactivity of neurofilament protein was almost abolished in N2aAPP, which beard a significantly higher level of Aβ. Melatonin effectively decreased the level of Aβ, and restored partially the level of phosphorylated and non-phosphorylated neurofilament in N2aAPP. CONCLUSION: Overproduction of Aβ inhibits neurofilament expression, and melatonin attenuates the Aβ-induced lesion in cytoskeletal protein. 5. Modeling amyloids in bacteria Directory of Open Access Journals (Sweden) Villar-Piqué Anna 2012-12-01 Full Text Available Abstract An increasing number of proteins are being shown to assemble into amyloid structures, self-seeding fibrillar aggregates that may lead to pathological states or play essential biological functions in organisms. Bacterial cell factories have raised as privileged model systems to understand the mechanisms behind amyloid assembly and the cellular fitness cost associated to the formation of these aggregates. In the near future, these bacterial systems will allow implementing high-throughput screening approaches to identify effective modulators of amyloid aggregation. 6. Comparable autoantibody serum levels against amyloid- and inflammation-associated proteins in Parkinson's disease patients and controls. Directory of Open Access Journals (Sweden) Walter Maetzler Full Text Available Naturally occurring autoantibodies (NAbs against a number of potentially disease-associated cellular proteins, including Amyloid-beta1-42 (Abeta1-42, Alpha-synuclein (Asyn, myelin basic protein (MBP, myelin oligodendrocyte glycoprotein (MOG, and S100 calcium binding protein B (S100B have been suggested to be associated with neurodegenerative disorders, in particular Alzheimer's (AD and Parkinson's disease (PD. Whereas the (reduced occurrence of specific NAbs in AD is widely accepted, previous literature examining the relation of these NAb titres between PD patients and controls, as well as comparing these levels with demographic and clinical parameters in PD patients have produced inconsistent findings. We therefore aimed, in a cross-sectional approach, to determine serum titres of the above NAbs in a cohort of 93 PD patients (31 of them demented and 194 controls. Levels were correlated with demographic and clinical variables, cerebrospinal fluid Abeta1-42, total tau and phospho-tau levels, as well as with single nucleotide polymorphisms (SNPs of genes which either have been reported to influence the immune system, the amyloid cascade or the occurrence of PD (ApoE, GSK3B, HLA-DRA, HSPA5, SNCA, and STK39. The investigated NAb titres were neither significantly associated with the occurrence of PD, nor with demographic and clinical parameters, neurodegenerative markers or genetic variables. These results argue against a major potential of blood-borne parameters of the adaptive immune system to serve as trait or state markers in PD. 7. Occupational exposure levels of bioaerosol components are associated with serum levels of the acute phase protein Serum Amyloid A in greenhouse workers DEFF Research Database (Denmark) Madsen, Anne Mette; Thilsing, Trine; Bælum, Jesper; 2016-01-01 to elevated levels of bioaerosols. The objective of this study is to assess whether greenhouse workers personal exposure to bioaerosol components was associated with serum levels of the acute phase proteins Serum Amyloid A (SAA) and C-reactive protein (CRP). METHODS: SAA and CRP levels were determined... 8. Sycamore amyloplasts can import and process precursors of nuclear encoded chloroplast proteins. Science.gov (United States) Strzalka, K; Ngernprasirtsiri, J; Watanabe, A; Akazawa, T 1987-12-16 Amyloplasts isolated from white-wild suspension-cultured cells of sycamore (Acer pseudoplatanus L.) are found to import and process the precursor of the small subunit (pS) of ribulose-1,5-bisphosphate carboxylase/oxygenase of spinach, but they lack the ability to form its holoenzyme due to the absence of both the large subunit and its binding-protein. They also import the precursor of the 33-kDa extrinsic protein (p33-kDa) of the O2-evolving complex of Photosystem II from spinach, but process is only to an intermediate form (i33-kDa). Chloroplasts from green-mutant cells of sycamore process p33-kDa to its mature form in this heterologous system. These results suggest that the thylakoid-associated protease responsible for the second processing step of p33-kDa is missing in amyloplasts, possibly due to the absence of thylakoid-membranes. In contrast, the apparent import of the precursor of the light-harvesting chlorophyll a/b-binding apoprotein (pLHCP) from spinach was not detected. Sycamore amyloplasts may lack the ability to import this particular thylakoid-protein, or rapidly degrade the imported molecules in the absence of thylakoid-membranes for their proper insertion. 9. The epsilon isoform of 14-3-3 protein is a component of the prion protein amyloid deposits of Gerstmann-Sträussler-Scheinker disease. Science.gov (United States) Di Fede, Giuseppe; Giaccone, Giorgio; Limido, Lucia; Mangieri, Michela; Suardi, Silvia; Puoti, Gianfranco; Morbin, Michela; Mazzoleni, Giulia; Ghetti, Bernardino; Tagliavini, Fabrizio 2007-02-01 The 14-3-3 proteins are highly conserved, ubiquitous molecules involved in a variety of biologic events, such as transduction pathway modulation, cell cycle control, and apoptosis. Seven isoforms have been identified that are abundant in the brain, preferentially localized in neurons. Remarkable increases in 14-3-3 are seen in the cerebrospinal fluid of patients with Creutzfeldt-Jakob disease (CJD), and it has been found in pathologic inclusions of several neurodegenerative diseases. Moreover, the zeta isoform has been detected in prion protein (PrP) amyloid deposits of CJD patients. To further investigate the cerebral distribution of 14-3-3 in prion-related encephalopathies, we carried out an immunohistochemical and biochemical analysis of brain tissue from patients with Gerstmann-Sträussler-Scheinker disease (GSS) and sporadic, familial and acquired forms of CJD, using specific antibodies against the seven 14-3-3 isoforms. The study showed a strong immunoreactivity of PrP amyloid plaques of GSS patients for the 14-3-3 epsilon isoform, but not for the other isoforms. The epsilon isoform of 14-3-3 was not found in PrP deposits of CJD. These results indicate that the epsilon isoform of 14-3-3 is a component of PrP amyloid deposits of GSS and suggest that this is the sole 14-3-3 isoform specifically involved in the neuropathologic changes associated with this disorder. 10. Pathogenesis of cerebral amyloid angiopathy. NARCIS (Netherlands) Rensink, A.A.M.; Waal, R.M.W. de; Kremer, H.P.H.; Verbeek, M.M. 2003-01-01 Cerebral amyloid angiopathy (CAA) is the result of the deposition of an amyloidogenic protein in cortical and leptomeningeal vessels. The most common type of CAA is caused by amyloid beta-protein (Abeta), which is particularly associated with Alzheimer's disease (AD). Excessive Abeta-CAA formation c 11. Investigation on apoptosis of neuronal cells induced by Amyloid beta-Protein Institute of Scientific and Technical Information of China (English) 罗本燕; 徐增斌; 陈智; 陈峰; 唐敏 2004-01-01 Objective: To construct a PC12 cell strain with neuronal differentiation, and observe the apoptosis and pro-liferation activity effects induced these cells by Amyloid beta-Protein (Aβ3-43). Methods: 1) PC12 cells in logarithmic growth phase were subcultured for 24 h. After the culture fluid was changed, the cells were treated with Rat-β-NGF and cultured for 9 days. 2) Neuronal differentiation of PC 12 cells in logarithmic growth phase were divided into four groups:control group (0), experimental group (1), experimental group (2) and experimental group (3). The concentrations of Aβ in the four groups were 0 μmol/L, 1.25 μmol/L, 2.5 μmol/L and 5 μmol/L, respectively. The cells were harvested at 24, 48 and 72 h later and stained with AnnexinV-FITC/PI after centrifugation and washing. Then flow cytometry was conducted to examine the apoptosis percentage. 3) NGF-induced PC12 cells were selected and Aβ with different concentrations was added. The final concentrations of Aβ were 0 μmol/L, 1.25 μmol/L, 2.5 μmol/L and 5 μmol/L, respectively. After the cells were incubated in an atmosphere of 5% CO2 at 37 ℃ in an incubator for 72 h, the OD values were examined. Results: 1)Neuronal differentiated PC12 cell lines were successfully established. 2) Flow cytometric examination indicated that Aβ(1.25, 2.5, and 5.0 μmol/L) could effectively induce apoptosis of neuronal-differented cells at the 24 h, 48 h and 72 h time points. 3) Aβ (0-5.00 μmol/L) had no obvious effect on proliferation or restraining of the neuronal differentiation of the PC 12 cells after a 72 h interacting process. Conclusion: This investigation revealed successful neuronal differentiation of the PC12 cell strain. The induction of apoptosis of the neurocytes by various concentrations of Aβ was observed and the in-fluence of Aβ on induced proliferation of PC 12 cells by Rat-β-NGF was revealed. This study may provide basis for future research on the molecular cure of AD and interdiction of AD 12. On the origin of Alzheimer's disease. Trials and tribulations of the amyloid hypothesis. Science.gov (United States) 2014-01-01 The amyloid cascade hypothesis, which implicates the amyloid Aβ peptide as the pathological initiator of both familial and sporadic, late onset Alzheimer's disease (AD), continues to guide the majority of research. We believe that current evidence does not support the amyloid cascade hypothesis for late onset AD. Instead, we propose that Aβ is a key regulator of brain homeostasis. During AD, while Aβ accumulation may occur in the long term in parallel with disease progression, it does not contribute to primary pathogenesis. This view predicts that amyloid-centric therapies will continue to fail, and that progress in developing successful alternative therapies for AD will be slow until closer attention is paid to understanding the physiological function of Aβ and its precursor protein. 13. Monte Carlo simulations of protein amyloid formation reveal origin of sigmoidal aggregation kinetics. Science.gov (United States) Linse, Björn; Linse, Sara 2011-07-01 Severe conditions and lack of cure for many amyloid diseases make it highly desired to understand the underlying principles of formation of fibrillar aggregates (amyloid). Here, amyloid formation from peptides was studied using Monte Carlo simulations. Systems of 20, 50, 100, 200 or 500 hexapeptides were simulated. Association kinetics were modeled equal for fibrillar and other (inter- and intra-peptide) contacts and assumed to be faster the lower the effective contact order, which represents the distance in space. Attempts to form contacts were thus accepted with higher probability the lower the effective contact order, whereby formation of new contacts next to preexisting ones is favored by shorter physical separation. Kinetic discrimination was invoked by using two different life-times for formed contacts. Contacts within amyloid fibrils were assumed to have on average longer life-time than other contacts. We find that the model produces fibrillation kinetics with a distinct lag phase, and that the fibrillar contacts need to dissociate on average 5-20 times slower than all other contacts for the fibrillar structure to dominate at equilibrium. Analysis of the species distribution along the aggregation process shows that no other intermediate is ever more populated than the dimer. Instead of a single nucleation event there is a concomitant increase in average aggregate size over the whole system, and the occurrence of multiple parallel processes makes the process more reproducible the larger the simulated system. The sigmoidal shape of the aggregation curves arises from cooperativity among multiple interactions within each pair of peptides in a fibril. A governing factor is the increasing probability as the aggregation process proceeds of neighboring reinforcing contacts. The results explain the very strong bias towards cross β-sheet fibrils in which the possibilities for cooperativity among interactions involving neighboring residues and the repetitive use of 14. Polymorphism of amyloid fibrils formed by a peptide from the yeast prion protein Sup35: AFM and Tip-Enhanced Raman Scattering studies Energy Technology Data Exchange (ETDEWEB) Krasnoslobodtsev, Alexey V., E-mail: akrasnos@unomaha.edu [Department of Pharmaceutical Sciences, University of Nebraska Medical Center, 986025 Nebraska Medical Center, Omaha, NE 68198 (United States); Department of Physics, University of Nebraska Omaha, Omaha, NE 68182 (United States); Deckert-Gaudig, Tanja [IPHT-Leibniz Institute of Photonic Technology, Albert-Einstein-Str. 9, D-07745 Jena (Germany); Zhang, Yuliang [Department of Pharmaceutical Sciences, University of Nebraska Medical Center, 986025 Nebraska Medical Center, Omaha, NE 68198 (United States); Deckert, Volker [IPHT-Leibniz Institute of Photonic Technology, Albert-Einstein-Str. 9, D-07745 Jena (Germany); Institute for Physical Chemistry and Abbe Center of Photonics, University of Jena, Helmholtzweg 4, D-07743 Jena (Germany); Lyubchenko, Yuri L., E-mail: ylyubchenko@unmc.edu [Department of Pharmaceutical Sciences, University of Nebraska Medical Center, 986025 Nebraska Medical Center, Omaha, NE 68198 (United States) 2016-06-15 Aggregation of prion proteins is the cause of various prion related diseases. The infectious form of prions, amyloid aggregates, exist as multiple strains. The strains are thought to represent structurally different prion protein molecules packed into amyloid aggregates, but the knowledge on the structure of different types of aggregates is limited. Here we report on the use of AFM (Atomic Force Microscopy) and TERS (Tip-Enhanced Raman Scattering) to study morphological heterogeneity and access underlying conformational features of individual amyloid aggregates. Using AFM we identified the morphology of amyloid fibrils formed by the peptide (CGNNQQNY) from the yeast prion protein Sup35 that is critically involved in the aggregation of the full protein. TERS results demonstrate that morphologically different amyloid fibrils are composed of a distinct set of conformations. Fibrils formed at pH 5.6 are composed of a mixture of peptide conformations (β-sheets, random coil and α-helix) while fibrils formed in pH~2 solution primarily have β-sheets. Additionally, peak positions in the amide III region of the TERS spectra suggested that peptides have parallel arrangement of β-sheets for pH~2 fibrils and antiparallel arrangement for fibrils formed at pH 5.6. We also developed a methodology for detailed analysis of the peptide secondary structure by correlating intensity changes of Raman bands in different regions of TERS spectra. Such correlation established that structural composition of peptides is highly localized with large contribution of unordered secondary structures on a fibrillar surface. - Highlights: • Amyloid polymorphs were characterized by AFM and TERS. • A mixture of peptide secondary structures in fibrils were identified using TERS. • TERS recognizes packing arrangement (parallel versus antiparallel) of peptides. • TERS is a powerful tool for high resolution structural analysis of fibrils. 15. Highly conserved residues in the helical domain of dengue virus type 1 precursor membrane protein are involved in assembly, precursor membrane (prM) protein cleavage, and entry. Science.gov (United States) Hsieh, Szu-Chia; Wu, Yi-Chieh; Zou, Gang; Nerurkar, Vivek R; Shi, Pei-Yong; Wang, Wei-Kung 2014-11-28 The envelope and precursor membrane (prM) proteins of dengue virus (DENV) are present on the surface of immature virions. During maturation, prM protein is cleaved by furin protease into pr peptide and membrane (M) protein. Although previous studies mainly focusing on the pr region have identified several residues important for DENV replication, the functional role of M protein, particularly the α-helical domain (MH), which is predicted to undergo a large conformational change during maturation, remains largely unknown. In this study, we investigated the role of nine highly conserved MH domain residues in the replication cycle of DENV by site-directed mutagenesis in a DENV1 prME expression construct and found that alanine substitutions introduced to four highly conserved residues at the C terminus and one at the N terminus of the MH domain greatly affect the production of both virus-like particles and replicon particles. Eight of the nine alanine mutants affected the entry of replicon particles, which correlated with the impairment in prM cleavage. Moreover, seven mutants were found to have reduced prM-E interaction at low pH, which may inhibit the formation of smooth immature particles and exposure of prM cleavage site during maturation, thus contributing to inefficient prM cleavage. Taken together, these results are the first report showing that highly conserved MH domain residues, located at 20-38 amino acids downstream from the prM cleavage site, can modulate the prM cleavage, maturation of particles, and virus entry. The highly conserved nature of these residues suggests potential targets of antiviral strategy. 16. Amyloid Beta and Tau Proteins as Therapeutic Targets for Alzheimer’s Disease Treatment: Rethinking the Current Strategy Directory of Open Access Journals (Sweden) Siddhartha Mondragón-Rodríguez 2012-01-01 Full Text Available Alzheimer’s disease (AD is defined by the concurrence of accumulation of abnormal aggregates composed of two proteins: Amyloid beta (Aβ and tau, and of cellular changes including neurite degeneration and loss of neurons and cognitive functions. Based on their strong association with disease, genetically and pathologically, it is not surprising that there has been a focus towards developing therapies against the aggregated structures. Unfortunately, current therapies have but mild benefit. With this in mind we will focus on the relationship of synaptic plasticity with Aβ and tau protein and their role as potential targets for the development of therapeutic drugs. Finally, we will provide perspectives in developing a multifactorial strategy for AD treatment. 17. Evaluation of Sialic Acid and Acute Phase Proteins (Haptoglobin and Serum Amyloid A in Clinical and Subclinical Bovine Mastitis Directory of Open Access Journals (Sweden) S. Nazifi, M. Haghkhah1, Z. Asadi, M. Ansari-Lari2, M. R. Tabandeh3, Z. Esmailnezhad and M. Aghamiri 2011-01-01 Full Text Available The present study was conducted to evaluate the concentrations of sialic acids (total, lipid bound and protein bound and their correlation with acute phase proteins (haptoglobin and serum amyloid A in clinical and subclinical mastitis of cattle. Thirty subclinical mastitic cows with positive California mastitis test (CMT test and no clinical signs of mastitis, 10 clinical mastitic cows and 10 healthy cows with negative CMT test and normal somatic cell count were selected. Milk and blood samples were collected after confirmation of clinical and subclinical mastitis by somatic cell count and bacterial identification. Serum haptoglobin (Hp, serum amyloid A (SAA, total sialic acid (TSA, lipid bound sialic acid (LBSA and protein bound sialic acid (PBSA were measured by validated standard methods. Haptoglobin and SAA increased significantly in both types of mastitis compared with control group (P<0.001. However, the ratio of HP/SAA was significantly different from the control group only in clinical mastitis. The results showed that TSA and LBSA were significantly different in control group compared with clinical and subclinical mastitis (P<0.001. Protein bound sialic acid did not change in subclinical mastitis in comparison with control group (P=0.86. There was positive correlation between LBSA and PBSA in clinical mastitis (r=0.72, P=0.02 whereas significant negative correlation was observed between LBSA and PBSA in subclinical mastitis (r=-0.62, P<0.001. Results also showed no correlation between Hp and SAA with each other or with any other parameters in study groups. 18. Antioxidant role of amyloid β protein in cell-free and biological systems: implication for the pathogenesis of Alzheimer disease. Science.gov (United States) Sinha, Maitrayee; Bhowmick, Pritha; Banerjee, Anindita; Chakrabarti, Sasanka 2013-03-01 In contrast to many studies showing the pro-oxidative nature of amyloid peptide, this work shows that aggregated Aβ42 peptide in varying concentrations (2-20 μM) in cell-free systems inhibits the formation of hydroxyl radicals and H(2)O(2) from a mixture of iron (20 μM FeSO(4)) and ascorbate (2mM) as measured by benzoate hydroxylation assay and coumarin carboxylic acid assay. Aggregated Aβ42 in similar concentrations further prevents protein and lipid oxidation in isolated rat brain mitochondria incubated alone or with FeSO(4) and ascorbate. Moreover, mitochondria exposed to FeSO(4) and ascorbate show enhanced formation of reactive oxygen species and this phenomenon is also abolished by aggregated Aβ42. It is suggested that the antioxidant property of Aβ42 in various systems is mediated by metal chelation and it is nearly as potent as a typical metal chelator, such as diethylenetriaminepentaacetic acid, in preventing oxidative damage. However, aggregated Aβ42 causes mitochondrial functional impairment in the form of membrane depolarization and a loss of phosphorylation capacity without involving reactive oxygen species in the process. Thus, the present results suggest that the amyloid peptide exhibits a protective antioxidant role in biological systems, but also has toxic actions independent of oxidative stress. 19. Telencephalin protects PAJU cells from amyloid beta protein-induced apoptosis by activating the ezrin/radixin/moesin protein family/phosphatidylinositol-3-kinase/protein kinase B pathway Institute of Scientific and Technical Information of China (English) Heping Yang; Dapeng Wu; Xiaojie Zhang; Xiang Wang; Yi Peng; Zhiping Hu 2012-01-01 Telencephalin is a neural glycoprotein that reduces apoptosis induced by amyloid beta protein in the human neural tumor cell line PAJU.In this study,we examined the role of the ezrin/radixin/moesin protein family/phosphatidylinositol-3-kinase/protein kinase B pathway in this process.Western blot analysis demonstrated that telencephalin,phosphorylated ezrin/radixin/moesin and phosphatidylinositol-3-kinase/protein kinase B were not expressed in PAJU cells transfected with empty plasmid,while they were expressed in PAJU cells transfected with a telencephalin expression plasmid.After treatment with 1.0 nM amyloid beta protein 42,expression of telencephalin and phosphorylated phosphatidylinositol-3-kinase/protein kinase B in the transfected cells gradually diminished,while levels of phosphorylated ezrin/radixin/moesin increased.In addition,the high levels of telencephalin,phosphorylated ezrin/radixin/moesin and phosphatidylinositol-3-kinase/protein kinase B expression in PAJU cells transfected with a telencephalin expression plasmid could be suppressed by the phosphatidylinositol-3-kinase inhibitor LY294002.These findings indicate that telencephalin activates the ezrin/radixin/moesin family/phosphatidylinositol-3-kinase/protein kinase B pathway and protects PAJU cells from amyloid beta protein-induced apoptosis. 20. THE OPEP COARSE-GRAINED PROTEIN MODEL: FROM SINGLE MOLECULES, AMYLOID FORMATION, ROLE OF MACROMOLECULAR CROWDING AND HYDRODYNAMICS TO RNA/DNA COMPLEXES OpenAIRE Sterpone, Fabio; Melchionna, Simone; Tuffery, Pierre; Pasquali, Samuela; Mousseau, Normand; Cragnolini, Tristan; Chebaro, Yassmine; Saint-Pierre, Jean-Francois; Kalimeri, Maria; Barducci, Alessandro; Laurin, Yohan; Tek, Alex; Baaden, Marc; Nguyen, Phuong Hoang; Derreumaux, Philippe 2014-01-01 The OPEP coarse-grained protein model has been applied to a wide range of applications since its first release 15 years ago. The model, which combines energetic and structural accuracy and chemical specificity, allows studying single protein properties, DNA/RNA complexes, amyloid fibril formation and protein suspensions in a crowded environment. Here we first review the current state of the model and the most exciting applications using advanced conformational sampling methods. We then presen... 1. Hacking the code of amyloid formation: the amyloid stretch hypothesis. Science.gov (United States) Pastor, M Teresa; Esteras-Chopo, Alexandra; Serrano, Luis 2007-01-01 Many research efforts in the last years have been directed towards understanding the factors determining protein misfolding and amyloid formation. Protein stability and amino acid composition have been identified as the two major factors in vitro. The research of our group has been focused on understanding the relationship between amino acid sequence and amyloid formation. Our approach has been the design of simple model systems that reproduce the biophysical properties of natural amyloids. An amyloid sequence pattern was extracted that can be used to detect amyloidogenic hexapeptide stretches in proteins. We have added evidence supporting that these amyloidogenic stretches can trigger amyloid formation by nonamyloidogenic proteins. Some experimental results in other amyloid proteins will be analyzed under the conclusions obtained in these studies. Our conclusions together with evidences from other groups suggest that amyloid formation is the result of the interplay between a decrease of protein stability, and the presence of highly amyloidogenic regions in proteins. As many of these results have been obtained in vitro, the challenge for the next years will be to demonstrate their validity in in vivo systems. 2. Aggregation properties of a short peptide that mediates amyloid fibril formation in model proteins unrelated to disease Nitin Chaudhary; Shashi Singh; Ramakrishnan Nagaraj 2011-09-01 Short peptides have been identified from amyloidogenic proteins that form amyloid fibrils in isolation. The hexapeptide stretch 21DIDLHL26 has been shown to be important in the self-assembly of the Src homology 3 (SH3) domain of p85 subunit of bovine phosphatidylinositol-3-kinase (PI3-SH3). The SH3 domain of chicken brain -spectrin, which is otherwise non-amyloidogenic, is rendered amyloidogenic if 22EVTMKK27 is replaced by DIDLHL. In this article, we describe the aggregation behaviour of DIDLHL-COOH and DIDLHL-CONH2. Our results indicate that DIDLHL-COOH and DIDLHL-CONH2 aggregate to form spherical structures at pH 5 and 6. At pH 5, in the presence of mica, DIDLHL-CONH2 forms short fibrous structures. The presence of NaCl along with mica results in fibrillar structures. At pH 6, DIDLHL-CONH2 forms largely spherical aggregates. Both the peptides are unstructured in solution but adopt -conformation on drying. The aggregates formed by DIDLHL-COOH and DIDLHL-CONH2 are formed during drying process and their structures are modulated by the presence of mica and salt. Our study suggests that a peptide need not have intrinsic amyloidogenic propensity to facilitate the selfassembly of the full-length protein. The propensity of peptides to form self-assembled structures that are non-amyloidogenic could be important in potentiating the self-assembly of full-length proteins into amyloid fibrils. 3. Effects of beta-amyloid protein on M1 and M2 subtypes of muscarinic acetylcholine receptors in the medial septum-diagonal band complex of the rat: relationship with cholinergic, GABAergic, and calcium-binding protein perikarya. Science.gov (United States) González, Iván; Arévalo-Serrano, Juan; Sanz-Anquela, José Miguel; Gonzalo-Ruiz, Alicia 2007-06-01 Cortical cholinergic dysfunction has been correlated with the expression and processing of beta-amyloid precursor protein. However, it remains unclear as to how cholinergic dysfunction and beta-amyloid (Abeta) formation and deposition might be related to one another. Since the M1- and M2 subtypes of muscarinic acetylcholine receptors (mAChRs) are considered key molecules that transduce the cholinergic message, the purpose of the present study was to assess the effects of the injected Abeta peptide on the number of M1mAchR- and M2mAChR-immunoreactive cells in the medial septum-diagonal band (MS-nDBB) complex of the rat. Injections of Abeta protein into the retrosplenial cortex resulted in a decrease in M1mAChR and M2mAChR immunoreactivity in the MS-nDBB complex. Quantitative analysis revealed a significant reduction in the number of M1mAChR- and M2mAChR-immunoreactive cells in the medial septum nucleus (MS) and in the horizontal nucleus of the diagonal band of Broca (HDB) as compared to the corresponding hemisphere in control animals and with that seen in the contralateral hemisphere, which corresponds to the PBS-injected side. Co-localization studies showed that the M1mAChR protein is localized in GABA-immunoreactive cells of the MS-nDBB complex, in particular those of the MS nucleus, while M2mAChR protein is localized in both the cholinergic and GABAergic cells. Moreover, GABAergic cells containing M2mAChR are mainly localized in the MS nucleus, while cholinergic cells containing M2mAChR are localized in the MS and the HDB nuclei. Our findings suggest that Abeta induces a reduction in M1mAChR- and M2mAChR-containing cells, which may contribute to impairments of cholinergic and GABAergic transmission in the MS-nDBB complex. 4. Traffic jam at the blood-brain barrier promotes greater accumulation of Alzheimer's disease amyloidproteins in the cerebral vasculature. Science.gov (United States) Agyare, Edward K; Leonard, Sarah R; Curran, Geoffry L; Yu, Caroline C; Lowe, Val J; Paravastu, Anant K; Poduslo, Joseph F; Kandimalla, Karunya K 2013-05-06 Amyloid-β (Aβ) deposition in the brain vasculature results in cerebral amyloid angiopathy (CAA), which occurs in about 80% of Alzheimer's disease (AD) patients. While Aβ42 predominates parenchymal amyloid plaques in AD brain, Aβ40 is prevalent in the cerebrovascular amyloid. Dutch mutation of Aβ40 (E22Q) promotes aggressive cerebrovascular accumulation and leads to severe CAA in the mutation carriers; knowledge of how DutchAβ40 drives this process more efficiently than Aβ40 could reveal various pathophysiological events that promote CAA. In this study we have demonstrated that DutchAβ40 shows preferential accumulation in the blood-brain-barrier (BBB) endothelial cells due to its inefficient blood-to-brain transcytosis. Consequently, DutchAβ40 establishes a permeation barrier in the BBB endothelium, prevents its own clearance from the brain, and promotes the formation of amyloid deposits in the cerebral microvessels. The BBB endothelial accumulation of native Aβ40 is not robust enough to exercise such a significant impact on its brain clearance. Hence, the cerebrovascular accumulation of Aβ40 is slow and may require other copathologies to precipitate into CAA. In conclusion, the magnitude of Aβ accumulation in the BBB endothelial cells is a critical factor that promotes CAA; hence, clearing vascular endothelium of Aβ proteins may halt or even reverse CAA. 5. A major protein precursor of zebra mussel (Dreissena polymorpha) byssus: deduced sequence and significance. Science.gov (United States) Anderson, K E; Waite, J H 1998-04-01 The zebra mussel is a nonindigenous invader of North American lakes and rivers and one of the few freshwater bivalve molluscs having a byssus--a sclerotized organ used by the mussel for opportunistic attachment to hard surfaces. We have sequenced a foot-specific cDNA whose composite protein sequence was deduced from a series of overlapping but occasionally nonidentical cDNA fragments. The overall deduced sequence matches tryptic peptides from a major byssal precursor protein--Dreissena polymorpha foot protein 1 (Dpfp1). The calculated mass of Dpfp1 is 49 kDa; but this is known to be extensively hydroxylated and O-glycosylated during maturation. Purified native Dpfp1 analyzed using matrix-assisted laser-desorption ionization mass spectrometry with time-of-flight indicates that the protein occurs as at least two size variants with masses of 48.6 and 54.5 kDa. In all probability, the sequence variants reported in this study are related to the larger mass variant. Dpfp1 has a block copolymer-like structure defined by two consensus motifs that are sharply segregated into domains. The N-terminal side of Dpfp1 has 22 tandem repeats of a heptapeptide consensus (P-[V/E]-Y-P-[T/S/delta]-[K/Q]-X); the C-terminal side has 16 repeats of a tridecapeptide motif (K-P-G-P-Y-D-Y-D-G-P-Y-D-K). Both consensus repeats are unique, with some limited homology to other proteins functioning in tension: marine mussel adhesives, plant extensins, titin, and trematode eggshell precursors. 6. Lipopolysaccharide binding protein and serum amyloid A secretion by human intestinal epithelial cells during the acute phase response. Science.gov (United States) Vreugdenhil, A C; Dentener, M A; Snoek, A M; Greve, J W; Buurman, W A 1999-09-01 The acute phase proteins LPS binding protein (LBP) and serum amyloid A (SAA) are produced by the liver and are present in the circulation. Both proteins have been shown to participate in the immune response to endotoxins. The intestinal mucosa forms a large surface that is continuously exposed to these microbial products. By secretion of antimicrobial and immunomodulating agents, the intestinal epithelium contributes to the defense against bacteria and their products. The aim of this study was to explore the influence of the inflammatory mediators TNF-alpha, IL-6, and IL-1beta on the release of LBP and SAA by intestinal epithelial cells (IEC). In addition, the induction of LBP and SAA release by cell lines of intestinal epithelial cells and hepatic cells was compared. The data obtained show that in addition to liver cells, IEC also expressed LBP mRNA and released bioactive LBP and SAA upon stimulation. Regulation of LBP and SAA release by IEC and hepatocytes was typical for class 1 acute phase proteins, although differences in regulation between the cell types were observed. Endotoxin did not induce LBP and SAA release. Glucocorticoids were demonstrated to strongly enhance the cytokine-induced release of LBP and SAA by IEC, corresponding to hepatocytes. The data from this study, which imply that human IEC can produce LBP and SAA, suggest a role for these proteins in the local defense mechanism of the gut to endotoxin. Furthermore, the results demonstrate that tissues other than the liver are involved in the acute phase response. 7. Alterations in amyloid beta-protein and apolipoprotein E in cerebrospinal fluid after subarachnoid hemorrhage Institute of Scientific and Technical Information of China (English) Xinzhong Wen; Yonghong Zhang; Leiming Huo 2007-01-01 BACKGROUND: The findings about the alterations in cerebrospinal fluid beta-amyloid protein (Aβ) and apolipoprotein E (ApoE) after subarachnoid hemorrhage indicate that they have significant correlation with prognosis of patients.OBJECTIVE: To observe the alterations in cerebrospinal fluid Aβ and ApoE after subarachnoid hemorrhage (SAH).DESIGN: Contrast observation.SETTING: Department of Neurosurgery, the First Hospital of Lanzhou University.PARTICIPANTS: A total of 25 SAH patients including 16 males and 9 females aged from 13 to 72 years were selected form Department of Neurosurgery, the First Affiliated Hospital of Lanzhou University from October 2003 to February 2004. The Hunt-Hess grade ranged from Ⅰ to Ⅳ, and patients admitted hospital in 24 hours after invasion, affirmed by the brain CT scan and lumbar vertebra puncture, no other severe complications and important organs' functional defect and severe infection, no hematological system disease.METHODS: All admitted patients were collected CSF by lumbar vertebra puncture in 24 hours. The cerebrospinal fluid (CSF) of control group came from the admitted 15 patients of our hospital that have no nervous system disease. Aβ content was detected by enzyme linked immunosorbent assay (ELISA), the kit was provided by the Central Laboratory of the First Hospital of Lanzhou University; ApoE concentration was detected by monoclone enzyme linked immunosorbent assay (ELISA), the kit was provided by the Immunotechnique Research Institute of the Fourth Military Medical University. S100B concentration was detected by enzyme linked immunosorbent assay double antibody sandwich method, the kit was provided by the Physiological Research Room of the Fourth Military Medical University. The data were indicated on Mean±SD and were analyzed by SPSS 10.0 statistical package. All data were handled through test of significance variance analysis, and groups were compared through independent sampler t test. The concentration was 8. Effects of grape seed-derived polyphenols on amyloid beta-protein self-assembly and cytotoxicity. Science.gov (United States) Ono, Kenjiro; Condron, Margaret M; Ho, Lap; Wang, Jun; Zhao, Wei; Pasinetti, Giulio M; Teplow, David B 2008-11-21 Epidemiological evidence suggests that moderate consumption of red wine reduces the incidence of Alzheimer disease (AD). To study the protective effects of red wine, experiments recently were executed in the Tg2576 mouse model of AD. These studies showed that a commercially available grape seed polyphenolic extract, MegaNatural-AZ (MN), significantly attenuated AD-type cognitive deterioration and reduced cerebral amyloid deposition (Wang, J., Ho, L., Zhao, W., Ono, K., Rosensweig, C., Chen, L., Humala, N., Teplow, D. B., and Pasinetti, G. M. (2008) J. Neurosci. 28, 6388-6392). To elucidate the mechanistic bases for these observations, here we used CD spectroscopy, photo-induced cross-linking of unmodified proteins, thioflavin T fluorescence, size exclusion chromatography, and electron microscopy to examine the effects of MN on the assembly of the two predominant disease-related amyloid beta-protein alloforms, Abeta40 and Abeta42. We also examined the effects of MN on Abeta-induced cytotoxicity by assaying 3-[4,5-dimethylthiazol-2-yl]-2,5-diphenyltetrazolium bromide metabolism and lactate dehydrogenase activity in Abeta-treated, differentiated pheochromocytoma (PC12) cells. Initial studies revealed that MN blocked Abeta fibril formation. Subsequent evaluation of the assembly stage specificity of the effect showed that MN was able to inhibit protofibril formation, pre-protofibrillar oligomerization, and initial coil --> alpha-helix/beta-sheet secondary structure transitions. Importantly, MN had protective effects in assays of cytotoxicity in which MN was mixed with Abeta prior to peptide assembly or following assembly and just prior to peptide addition to cells. These data suggest that MN is worthy of consideration as a therapeutic agent for AD. 9. The Flavivirus Precursor Membrane-Envelope Protein Complex: Structure and Maturation Energy Technology Data Exchange (ETDEWEB) Li, Long; Lok, Shee-Mei; Yu, I-Mei; Zhang, Ying; Kuhn, Richard J.; Chen, Jue; Rossmann, Michael G. (Purdue) 2008-09-17 Many viruses go through a maturation step in the final stages of assembly before being transmitted to another host. The maturation process of flaviviruses is directed by the proteolytic cleavage of the precursor membrane protein (prM), turning inert virus into infectious particles. We have determined the 2.2 angstrom resolution crystal structure of a recombinant protein in which the dengue virus prM is linked to the envelope glycoprotein E. The structure represents the prM-E heterodimer and fits well into the cryo-electron microscopy density of immature virus at neutral pH. The pr peptide {beta}-barrel structure covers the fusion loop in E, preventing fusion with host cell membranes. The structure provides a basis for identifying the stages of its pH-directed conformational metamorphosis during maturation, ending with release of pr when budding from the host. 10. Genome-wide association study of CSF levels of 59 alzheimer's disease candidate proteins: significant associations with proteins involved in amyloid processing and inflammation. Directory of Open Access Journals (Sweden) John S K Kauwe 2014-10-01 11. DSP-PP precursor protein cleavage by tolloid-related-1 protein and by bone morphogenetic protein-1. Science.gov (United States) Ritchie, Helena H; Yee, Colin T; Tang, Xu-Na; Dong, Zhihong; Fuller, Robert S 2012-01-01 Dentin sialoprotein (DSP) and phosphophoryn (PP), acidic proteins critical to dentin mineralization, are translated from a single transcript as a DSP-PP precursor that undergoes specific proteolytic processing to generate DSP and PP. The cleavage mechanism continues to be controversial, in part because of the difficulty of obtaining DSP-PP from mammalian cells and dentin matrix. We have infected Sf9 cells with a recombinant baculovirus to produce large amounts of secreted DSP-PP(240), a variant form of rat DSP-PP. Mass spectrometric analysis shows that DSP-PP(240) secreted by Sf9 cells undergoes specific cleavage at the site predicted from the N-terminal sequence of PP extracted from dentin matrix: SMQG(447)↓D(448)DPN. DSP-PP(240) is cleaved after secretion by a zinc-dependent activity secreted by Sf9 cells, generating DSP(430) and PP(240) products that are stable in the medium. DSP-PP processing activity is constitutively secreted by Sf9 cells, but secretion is diminished 3 days after infection. Using primers corresponding to the highly conserved catalytic domain of Drosophila melanogaster tolloid (a mammalian BMP1 homolog), we isolated a partial cDNA for a Spodopotera frugiperda tolloid-related-1 protein (TLR1) that is 78% identical to Drosophila TLR1 but only 65% identical to Drosophila tolloid. Tlr1 mRNA decreased rapidly in Sf9 cells after baculovirus infection and was undetectable 4d after infection, paralleling the observed decrease in secretion of the DSP-PP(240) processing activity after infection. Human BMP1 is more similar to Sf9 and Drosophila TLR1 than to tolloid, and Sf9 TLR1 is more similar to BMP1 than to other mammalian homologs. Recombinant human BMP1 correctly processed baculovirus-expressed DSP-PP(240) in a dose-dependent manner. Together, these data suggest that the physiologically accurate cleavage of mammalian DSP-PP(240) in the Sf9 cell system represents the action of a conserved processing enzyme and support the proposed role of BMP1 in 12. DSP-PP precursor protein cleavage by tolloid-related-1 protein and by bone morphogenetic protein-1. Directory of Open Access Journals (Sweden) Helena H Ritchie Full Text Available Dentin sialoprotein (DSP and phosphophoryn (PP, acidic proteins critical to dentin mineralization, are translated from a single transcript as a DSP-PP precursor that undergoes specific proteolytic processing to generate DSP and PP. The cleavage mechanism continues to be controversial, in part because of the difficulty of obtaining DSP-PP from mammalian cells and dentin matrix. We have infected Sf9 cells with a recombinant baculovirus to produce large amounts of secreted DSP-PP(240, a variant form of rat DSP-PP. Mass spectrometric analysis shows that DSP-PP(240 secreted by Sf9 cells undergoes specific cleavage at the site predicted from the N-terminal sequence of PP extracted from dentin matrix: SMQG(447↓D(448DPN. DSP-PP(240 is cleaved after secretion by a zinc-dependent activity secreted by Sf9 cells, generating DSP(430 and PP(240 products that are stable in the medium. DSP-PP processing activity is constitutively secreted by Sf9 cells, but secretion is diminished 3 days after infection. Using primers corresponding to the highly conserved catalytic domain of Drosophila melanogaster tolloid (a mammalian BMP1 homolog, we isolated a partial cDNA for a Spodopotera frugiperda tolloid-related-1 protein (TLR1 that is 78% identical to Drosophila TLR1 but only 65% identical to Drosophila tolloid. Tlr1 mRNA decreased rapidly in Sf9 cells after baculovirus infection and was undetectable 4d after infection, paralleling the observed decrease in secretion of the DSP-PP(240 processing activity after infection. Human BMP1 is more similar to Sf9 and Drosophila TLR1 than to tolloid, and Sf9 TLR1 is more similar to BMP1 than to other mammalian homologs. Recombinant human BMP1 correctly processed baculovirus-expressed DSP-PP(240 in a dose-dependent manner. Together, these data suggest that the physiologically accurate cleavage of mammalian DSP-PP(240 in the Sf9 cell system represents the action of a conserved processing enzyme and support the proposed role of BMP 13. Mannose-Binding Lectin Binds to Amyloid Protein and Modulates Inflammation Directory of Open Access Journals (Sweden) Mykol Larvie 2012-01-01 Full Text Available Mannose-binding lectin (MBL, a soluble factor of the innate immune system, is a pattern recognition molecule with a number of known ligands, including viruses, bacteria, and molecules from abnormal self tissues. In addition to its role in immunity, MBL also functions in the maintenance of tissue homeostasis. We present evidence here that MBL binds to amyloid β peptides. MBL binding to other known carbohydrate ligands is calcium-dependent and has been attributed to the carbohydrate-recognition domain, a common feature of other C-type lectins. In contrast, we find that the features of MBL binding to Aβ are more similar to the reported binding characteristics of the cysteine-rich domain of the unrelated mannose receptor and therefore may involve the MBL cysteine-rich domain. Differences in MBL ligand binding may contribute to modulation of inflammatory response and may correlate with the function of MBL in processes such as coagulation and tissue homeostasis. 14. Atomic Resolution Structure of Monomorphic Aβ42 Amyloid Fibrils. Science.gov (United States) Colvin, Michael T; Silvers, Robert; Ni, Qing Zhe; Can, Thach V; Sergeyev, Ivan; Rosay, Melanie; Donovan, Kevin J; Michael, Brian; Wall, Joseph; Linse, Sara; Griffin, Robert G 2016-08-03 Amyloid-β (Aβ) is a 39-42 residue protein produced by the cleavage of the amyloid precursor protein (APP), which subsequently aggregates to form cross-β amyloid fibrils that are a hallmark of Alzheimer's disease (AD). The most prominent forms of Aβ are Aβ1-40 and Aβ1-42, which differ by two amino acids (I and A) at the C-terminus. However, Aβ42 is more neurotoxic and essential to the etiology of AD. Here, we present an atomic resolution structure of a monomorphic form of AβM01-42 amyloid fibrils derived from over 500 (13)C-(13)C, (13)C-(15)N distance and backbone angle structural constraints obtained from high field magic angle spinning NMR spectra. The structure (PDB ID: 5KK3 ) shows that the fibril core consists of a dimer of Aβ42 molecules, each containing four β-strands in a S-shaped amyloid fold, and arranged in a manner that generates two hydrophobic cores that are capped at the end of the chain by a salt bridge. The outer surface of the monomers presents hydrophilic side chains to the solvent. The interface between the monomers of the dimer shows clear contacts between M35 of one molecule and L17 and Q15 of the second. Intermolecular (13)C-(15)N constraints demonstrate that the amyloid fibrils are parallel in register. The RMSD of the backbone structure (Q15-A42) is 0.71 ± 0.12 Å and of all heavy atoms is 1.07 ± 0.08 Å. The structure provides a point of departure for the design of drugs that bind to the fibril surface and therefore interfere with secondary nucleation and for other therapeutic approaches to mitigate Aβ42 aggregation. 15. Stabilization of native amyloid β-protein oligomers by Copper and Hydrogen peroxide Induced Cross-linking of Unmodified Proteins (CHICUP). Science.gov (United States) Williams, Thomas L; Serpell, Louise C; Urbanc, Brigita 2016-03-01 Oligomeric assemblies are postulated to be proximate neurotoxic species in human diseases associated with aberrant protein aggregation. Their heterogeneous and transient nature makes their structural characterization difficult. Size distributions of oligomers of several amyloidogenic proteins, including amyloid β-protein (Aβ) relevant to Alzheimer's disease (AD), have been previously characterized in vitro by photo-induced cross-linking of unmodified proteins (PICUP) followed by sodium dodecyl sulfate-polyacrylamide gel electrophoresis (SDS-PAGE). Due to non-physiological conditions associated with the PICUP chemistry, Aβ oligomers cross-linked by PICUP may not be representative of in vivo conditions. Here, we examine an alternative Copper and Hydrogen peroxide Induced Cross-linking of Unmodified Proteins (CHICUP), which utilizes naturally occurring divalent copper ions and hydrogen peroxide and does not require photo activation. Our results demonstrate that CHICUP and PICUP applied to the two predominant Aβ alloforms, Aβ40 and Aβ42, result in similar oligomer size distributions. Thioflavin T fluorescence data and atomic force microscopy images demonstrate that both CHICUP and PICUP stabilize Aβ oligomers and attenuate fibril formation. Relative to noncross-linked peptides, CHICUP-treated Aβ40 and Aβ42 cause prolonged disruption to biomimetic lipid vesicles. CHICUP-stabilized Aβ oligomers link the amyloid cascade, metal, and oxidative stress hypotheses of AD into a more comprehensive understanding of the molecular basis of AD pathology. Because copper and hydrogen peroxide are elevated in the AD brain, CHICUP-stabilized Aβ oligomers are biologically relevant and should be further explored as a new therapeutic target. 16. Amyloid-like fibrils from an 18-residue peptide analogue of a part of the central domain of the B-family of silkmoth chorion proteins. Science.gov (United States) Iconomidou, V A; Chryssikos, G D; Gionis, V; Vriend, G; Hoenger, A; Hamodrakas, S J 2001-06-22 Chorion is the major component of silkmoth eggshell. More than 95% of its dry mass consists of the A and B families of low molecular weight structural proteins, which have remarkable mechanical and chemical properties, and protect the oocyte and the developing embryo from the environment. We present data from negative staining, Congo red binding, X-ray diffraction, Fourier transform-Raman, attenuated total reflectance infrared spectroscopy and modelling studies of a synthetic peptide analogue of a part of the central domain of the B family of silkmoth chorion proteins, indicating that this peptide folds and self-assembles, forming amyloid-like fibrils. These results support further our proposal, based on experimental data from a synthetic peptide analogue of the central domain of the A family of chorion proteins, that silkmoth chorion is a natural, protective amyloid [Iconomidou et al., FEBS Lett. 479 (2000) 141-145]. 17. Monoacylated Cellular Prion Proteins Reduce Amyloid-β-Induced Activation of Cytoplasmic Phospholipase A2 and Synapse Damage Directory of Open Access Journals (Sweden) Ewan West 2015-06-01 Full Text Available Alzheimer’s disease (AD is a progressive neurodegenerative disease characterized by the accumulation of amyloid-β (Aβ and the loss of synapses. Aggregation of the cellular prion protein (PrPC by Aβ oligomers induced synapse damage in cultured neurons. PrPC is attached to membranes via a glycosylphosphatidylinositol (GPI anchor, the composition of which affects protein targeting and cell signaling. Monoacylated PrPC incorporated into neurons bound “natural Aβ”, sequestering Aβ outside lipid rafts and preventing its accumulation at synapses. The presence of monoacylated PrPC reduced the Aβ-induced activation of cytoplasmic phospholipase A2 (cPLA2 and Aβ-induced synapse damage. This protective effect was stimulus specific, as treated neurons remained sensitive to α-synuclein, a protein associated with synapse damage in Parkinson’s disease. In synaptosomes, the aggregation of PrPC by Aβ oligomers triggered the formation of a signaling complex containing the cPLA2.a process, disrupted by monoacylated PrPC. We propose that monoacylated PrPC acts as a molecular sponge, binding Aβ oligomers at the neuronal perikarya without activating cPLA2 or triggering synapse damage. 18. Probing folding free energy landscape of small proteins through minimalistic models: Folding of HP-36 and -amyloid Arnab Mukherjee; Biman Bagchi 2003-10-01 Folding dynamics and energy landscape picture of protein conformations of HP-36 and -amyloid (A) are investigated by extensive Brownian dynamics simulations, where the inter amino acid interactions are given by a minimalistic model (MM) we recently introduced [J. Chem. Phys. 118 4733 (2003)]. In this model, a protein is constructed by taking two atoms for each amino acid. One atom represents the backbone C atom, while the other mimics the whole side chain residue. Sizes and interactions of the side residues are all different and specific to a particular amino acid. The effect of water-mediated folding is mapped into the MM by suitable choice of interaction parameters of the side residues obtained from the amino acid hydropathy scale. A new non-local helix potential is incorporated to generate helices at the appropriate positions in a protein. Simulations have been done by equilibrating the protein at high temperature followed by a sudden quench. The subsequent folding is monitored to observe the dynamics of topological contacts (topo), relative contact order parameter (RCO), and the root mean square deviation (RMSD) from the realprotein native structure. The folded structures of different model proteins (HP-36 and ) resemble their respective real native state rather well. The dynamics of folding shows multistage decay, with an initial hydrophobic collapse followed by a long plateau. Analysis of topo and RCO correlates the late stage folding with rearrangement of the side chain residues, particularly those far apart in the sequence. The long plateau also signifies large entropic free energy barrier near the native state, as predicted from theories of protein folding. 19. Mitogen-activated protein kinase signaling pathways promote low-density lipoprotein receptor-related protein 1-mediated internalization of beta-amyloid protein in primary cortical neurons. Science.gov (United States) Yang, Wei-Na; Ma, Kai-Ge; Qian, Yi-Hua; Zhang, Jian-Shui; Feng, Gai-Feng; Shi, Li-Li; Zhang, Zhi-Chao; Liu, Zhao-Hui 2015-07-01 Mounting evidence suggests that the pathological hallmarks of Alzheimer's disease (AD) are caused by the intraneuronal accumulation of beta-amyloid protein (Aβ). Reuptake of extracellular Aβ is believed to contribute significantly to the intraneuronal Aβ pool in the early stages of AD. Published reports have claimed that the low-density lipoprotein receptor-related protein 1 (LRP1) mediates Aβ1-42 uptake and lysosomal trafficking in GT1-7 neuronal cells and mouse embryonic fibroblast non-neuronal cells. However, there is no direct evidence supporting the role of LRP1 in Aβ internalization in primary neurons. Our recent study indicated that p38 MAPK and ERK1/2 signaling pathways are involved in regulating α7 nicotinic acetylcholine receptor (α7nAChR)-mediated Aβ1-42 uptake in SH-SY5Y cells. This study was designed to explore the regulation of MAPK signaling pathways on LRP1-mediated Aβ internalization in neurons. We found that extracellular Aβ1-42 oligomers could be internalized into endosomes/lysosomes and mitochondria in cortical neurons. Aβ1-42 and LRP1 were also found co-localized in neurons during Aβ1-42 internalization, and they could form Aβ1-42-LRP1 complex. Knockdown of LRP1 expression significantly decreased neuronal Aβ1-42 internalization. Finally, we identified that p38 MAPK and ERK1/2 signaling pathways regulated the internalization of Aβ1-42 via LRP1. Therefore, these results demonstrated that LRP1, p38 MAPK and ERK1/2 mediated the internalization of Aβ1-42 in neurons and provided evidence that blockade of LRP1 or inhibitions of MAPK signaling pathways might be a potential approach to lowering brain Aβ levels and served a potential therapeutic target for AD. 20. Association of cardiovascular factors and Alzheimer's disease plasma amyloid-beta protein in subjective memory complainers. Science.gov (United States) Bates, Kristyn A; Sohrabi, Hamid R; Rodrigues, Mark; Beilby, John; Dhaliwal, Satvinder S; Taddei, Kevin; Criddle, Arthur; Wraith, Megan; Howard, Matthew; Martins, Georgia; Paton, Athena; Mehta, Pankaj; Foster, Jonathan K; Martins, Ian J; Lautenschlager, Nicola T; Mastaglia, Frank L; Laws, Simon M; Gandy, Samuel E; Martins, Ralph N 2009-01-01 A strong link is indicated between cardiovascular disease (CVD) and risk for developing Alzheimer's disease (AD), which may be exacerbated by the major AD genetic risk factor apolipoprotein Eepsilon4 (APOEepsilon4). Since subjective memory complaint (SMC) may potentially be an early indicator for cognitive decline, we examined CVD risk factors in a cohort of SMC. As amyloid-beta (Abeta) is considered to play a central role in AD, we hypothesized that the CVD risk profile (increased LDL, reduced HDL, and increased body fat) would be associated with plasma Abeta levels. We explored this in 198 individuals with and without SMC (average age = 63 years). Correlations between Abeta40 and HDL were observed, which were stronger in non-APOEepsilon4 carriers (rho = -0.315, p association between HDL and Abeta, which if demonstrated to be causal has implications for the development of lifestyle interventions and/or novel therapeutics. The relationship between HDL and Abeta and the potential significance of such an association needs to be validated in a larger longitudinal study. 1. ANTIAMNESIC POTENTIAL OF SOLASODINE AGAINST β-AMYLOID PROTEIN INDUCED AMNESIA IN MICE Directory of Open Access Journals (Sweden) Desai Alpesh B 2011-05-01 Full Text Available Alzheimer’s disease (AD, the most common form of dementia in the elderly population, is characterized by an insidious onset with memory impairment and an inexorable progression of cognitive decline. Nootropic agents are a heterogeneous groups of drugs developed for use in dementia and other cerebral disorders. Nootropics agents are being primarily used to improve memory, mood and behavior. However, the resulting adverse effects associated with these agents have limited their use. Therefore, it is worthwhile to explore the utility of traditional medicines for the treatment of various cognitive disorders. The present study was undertaken to assess the potential of solasodine on β-amyloid induced amnesia in mice. Elevated plus maze (EPM and Morris water maze (MWM was employed to evaluate learning and memory parameters. Piracetam was used as the standard drug. Solasodine (1, 2 and 4 mg/kg, p.o. was screened for claimed potential in mice. Solasodine improved both short term memory and long term memory when assessed on Elevated pluz maze and Morris Water maze respectively. Hence, solasodine might prove to be a useful memory restorative agent in the treatment of dementia seen in the Alzheimer’s disease. 2. Pro-Inflammatory S100A8 and S100A9 Proteins: Self-Assembly into Multifunctional Native and Amyloid Complexes Directory of Open Access Journals (Sweden) Ludmilla A. Morozova-Roche 2012-03-01 Full Text Available S100A8 and S100A9 are EF-hand Ca2+ binding proteins belonging to the S100 family. They are abundant in cytosol of phagocytes and play critical roles in numerous cellular processes such as motility and danger signaling by interacting and modulating the activity of target proteins. S100A8 and S100A9 expression levels increased in many types of cancer, neurodegenerative disorders, inflammatory and autoimmune diseases and they are implicated in the numerous disease pathologies. The Ca2+ and Zn2+-binding properties of S100A8/A9 have a pivotal influence on their conformation and oligomerization state, including self-assembly into homo- and heterodimers, tetramers and larger oligomers. Here we review how the unique chemical and conformational properties of individual proteins and their structural plasticity at the quaternary level account for S100A8/A9 functional diversity. Additional functional diversification occurs via non-covalent assembly into oligomeric and fibrillar amyloid complexes discovered in the aging prostate and reproduced in vitro. This process is also regulated by Ca2+and Zn2+-binding and effectively competes with the formation of the native complexes. High intrinsic amyloid-forming capacity of S100A8/A9 proteins may lead to their amyloid depositions in numerous ailments characterized by their elevated expression patterns and have additional pathological significance requiring further thorough investigation. 3. Hemodynamic effects of combined focal cerebral ischemia and amyloid protein toxicity in a rat model: a functional CT study. Directory of Open Access Journals (Sweden) Jun Yang Full Text Available BACKGROUND/OBJECTIVE: Clinical evidence indicates that cerebral ischemia (CI and a pathological factor of Alzheimer's disease, the β-amyloid (Aβ protein, can increase the rate of cognitive impairment in the ageing population. Using the CT Perfusion (CTP functional imaging, we sought to investigate the interaction between CI and the Aβ protein on cerebral hemodynamics. METHODS: A previously established rat model of CI and Aβ was used for the CTP study. Iodinated contrast was given intravenously, while serial CT images of sixteen axial slices were acquired. Cerebral blood flow (CBF and blood volume (CBV parametric maps were co-registered to a rat brain atlas and regions of interest were drawn on the maps. Microvascular alteration was investigated with histopathology. RESULTS: CTP results revealed that ipsilateral striatum of Aβ+CI and CI groups showed significantly lower CBF and CBV than control at the acute phase. Striatal CBF and CBV increased significantly at week 1 in the CI and Aβ+CI groups, but not in the Aβ alone or control group. Histopathology showed that average density of dilated microvessels in the ipsilateral striatum in CI and Aβ+CI groups was significantly higher than control at week 1, indicating this could be associated with hyperperfusion and hypervolemia observed from CTP results. CONCLUSION: These results demonstrate that CTP can quantitatively measure the hemodynamic disturbance on CBF and CBV functional maps in a rat model of CI interacting with Aβ. 4. Amyloid Beta as a Modulator of Synaptic Plasticity OpenAIRE Parihar, Mordhwaj S.; Gregory J. Brewer 2010-01-01 Alzheimer’s disease is associated with synapse loss, memory dysfunction and pathological accumulation of amyloid beta in plaques. However, an exclusively pathological role for amyloid beta is being challenged by new evidence for an essential function of amyloid beta at the synapse. Amyloid beta protein exists in different assembly states in the central nervous system and plays distinct roles ranging from synapse and memory formation to memory loss and neuronal cell death. Amyloid beta is pres... 5. The nicotinic alpha7 acetylcholine receptor agonist ssr180711 is unable to activate limbic neurons in mice overexpressing human amyloid-beta1-42 DEFF Research Database (Denmark) Soderman, A.; Spang-Thomsen, Mogens; Hansen, H. 2008-01-01 7 nAChR have not been examined. The aim of this study has been to evaluate the efficacy of alpha7 nAChR modulators in transgene mice that overexpress human amyloid precursor protein and accumulate Abeta1-40 and Abeta1-42. In accordance with observations in human Alzheimer tissues, we show here... 6. Bacoside-A, an anti-amyloid natural substance, inhibits membrane disruption by the amyloidogenic determinant of prion protein through accelerating fibril formation. Science.gov (United States) Malishev, Ravit; Nandi, Sukhendu; Kolusheva, Sofiya; Shaham-Niv, Shira; Gazit, Ehud; Jelinek, Raz 2016-09-01 Bacosides, class of compounds extracted from the Bacopa monniera plant, exhibit interesting therapeutic properties, particularly enhancing cognitive functions and putative anti-amyloid activity. We show that bacoside-A exerted significant effects upon fibrillation and membrane interactions of the amyloidogenic fragment of the prion protein [PrP(106-126)]. Specifically, when co-incubated with PrP(106-126), bacoside-A accelerated fibril formation in the presence of lipid bilayers and in parallel inhibited bilayer interactions of the peptide aggregates formed in solution. These interesting phenomena were studied by spectroscopic and microscopic techniques, which suggest that bacoside A-promoted fibrillation reduced the concentration of membrane-active pre-fibrillar species of the prion fragment. This study suggests that induction of fibril formation and corresponding inhibition of membrane interactions are likely the underlying factors for ameliorating amyloid protein toxicity by bacoside-A. 7. Automatic segmentation of amyloid plaques in MR images using unsupervised support vector machines. Science.gov (United States) Iordanescu, Gheorghe; Venkatasubramanian, Palamadai N; Wyrwicz, Alice M 2012-06-01 Deposition of the β-amyloid peptide (Aβ) is an important pathological hallmark of Alzheimer's disease (AD). However, reliable quantification of amyloid plaques in both human and animal brains remains a challenge. We present here a novel automatic plaque segmentation algorithm based on the intrinsic MR signal characteristics of plaques. This algorithm identifies plaque candidates in MR data by using watershed transform, which extracts regions with low intensities completely surrounded by higher intensity neighbors. These candidates are classified as plaque or nonplaque by an unsupervised learning method using features derived from the MR data intensity. The algorithm performance is validated by comparison with histology. We also demonstrate the algorithm's ability to detect age-related changes in plaque load ex vivo in amyloid precursor protein (APP) transgenic mice that coexpress five familial AD mutations (5xFAD mice). To our knowledge, this study represents the first quantitative method for characterizing amyloid plaques in MRI data. The proposed method can be used to describe the spatiotemporal progression of amyloid deposition, which is necessary for understanding the evolution of plaque pathology in mouse models of Alzheimer's disease and to evaluate the efficacy of emergent amyloid-targeting therapies in preclinical trials. 8. Formaldehyde at low concentration induces protein tau into globular amyloid-like aggregates in vitro and in vivo. Directory of Open Access Journals (Sweden) Chun Lai Nie Full Text Available Recent studies have shown that neurodegeneration is closely related to misfolding and aggregation of neuronal tau. Our previous results show that neuronal tau aggregates in formaldehyde solution and that aggregated tau induces apoptosis of SH-SY5Y and hippocampal cells. In the present study, based on atomic force microscopy (AFM observation, we have found that formaldehyde at low concentrations induces tau polymerization whilst acetaldehyde does not. Neuronal tau misfolds and aggregates into globular-like polymers in 0.01-0.1% formaldehyde solutions. Apart from globular-like aggregation, no fibril-like polymerization was observed when the protein was incubated with formaldehyde for 15 days. SDS-PAGE results also exhibit tau polymerizing in the presence of formaldehyde. Under the same experimental conditions, polymerization of bovine serum albumin (BSA or alpha-synuclein was not markedly detected. Kinetic study shows that tau significantly misfolds and polymerizes in 60 minutes in 0.1% formaldehyde solution. However, presence of 10% methanol prevents protein tau from polymerization. This suggests that formaldehyde polymerization is involved in tau aggregation. Such aggregation process is probably linked to the tau's special "worm-like" structure, which leaves the epsilon-amino groups of Lys and thiol groups of Cys exposed to the exterior. Such a structure can easily bond to formaldehyde molecules in vitro and in vivo. Polymerizing of formaldehyde itself results in aggregation of protein tau. Immunocytochemistry and thioflavin S staining of both endogenous and exogenous tau in the presence of formaldehyde at low concentrations in the cell culture have shown that formaldehyde can induce tau into amyloid-like aggregates in vivo during apoptosis. The significant protein tau aggregation induced by formaldehyde and the severe toxicity of the aggregated tau to neural cells may suggest that toxicity of methanol and formaldehyde ingestion is related to 9. Diagnostic utility and limitations of glutamine synthetase and serum amyloid-associated protein immunohistochemistry in the distinction of focal nodular hyperplasia and inflammatory hepatocellular adenoma. Science.gov (United States) Joseph, Nancy M; Ferrell, Linda D; Jain, Dhanpat; Torbenson, Michael S; Wu, Tsung-Teh; Yeh, Matthew M; Kakar, Sanjay 2014-01-01 Inflammatory hepatocellular adenoma can show overlapping histological features with focal nodular hyperplasia, including inflammation, fibrous stroma, and ductular reaction. Expression of serum amyloid-associated protein in inflammatory hepatocellular adenoma and map-like pattern of glutamine synthetase in focal nodular hyperplasia can be helpful in this distinction, but the pitfalls and limitations of these markers have not been established. Morphology and immunohistochemistry were analyzed in 54 inflammatory hepatocellular adenomas, 40 focal nodular hyperplasia, and 3 indeterminate lesions. Morphological analysis demonstrated that nodularity, fibrous stroma, dystrophic blood vessels, and ductular reaction were more common in focal nodular hyperplasia, while telangiectasia, hemorrhage, and steatosis were more common in inflammatory hepatocellular adenoma, but there was frequent overlap of morphological features. The majority of inflammatory hepatocellular adenomas demonstrated perivascular and/or patchy glutamine synthetase staining (73.6%), while the remaining cases had diffuse (7.5%), negative (3.8%), or patchy pattern of staining (15%) that showed subtle differences from the classic map-like staining pattern and was designated as pseudo map-like staining. Positive staining for serum amyloid-associated protein was seen in the majority of inflammatory hepatocellular adenomas (92.6%) and in the minority of focal nodular hyperplasia (17.5%). The glutamine synthetase staining pattern was map-like in 90% of focal nodular hyperplasia cases, with the remaining 10% of cases showing pseudo map-like staining. Three cases were labeled as indeterminate and showed focal nodular hyperplasia-like morphology but lacked map-like glutamine synthetase staining pattern; these cases demonstrated a patchy pseudo map-like glutamine synthetase pattern along with the expression of serum amyloid-associated protein. Our results highlight the diagnostic errors that can be caused by variant 10. Hypoxia alters cell cycle regulatory protein expression and induces premature maturation of oligodendrocyte precursor cells. Directory of Open Access Journals (Sweden) Ravi Shankar Akundi Full Text Available BACKGROUND: Periventricular white matter injury (PWMI is a common form of brain injury sustained by preterm infants. A major factor that predisposes to PWMI is hypoxia. Because oligodendrocytes (OLs are responsible for myelination of axons, abnormal OL development or function may affect brain myelination. At present our understanding of the influences of hypoxia on OL development is limited. To examine isolated effects of hypoxia on OLs, we examined the influences of hypoxia on OL development in vitro. METHODOLOGY/FINDINGS: Cultures of oligodendrocyte precursor cells (OPCs were prepared from mixed glial cultures and were 99% pure. OPCs were maintained at 21% O(2 or hypoxia (1% or 4% O(2 for up to 7 days. We observed that 1% O(2 lead to an increase in the proportion of myelin basic protein (MBP-positive OLs after 1 week in culture, and a decrease in the proportion of platelet-derived growth factor receptor alpha (PDGFRalpha-positive cells suggesting premature OL maturation. Increased expression of the cell cycle regulatory proteins p27(Kip1 and phospho-cdc2, which play a role in OL differentiation, was seen as well. CONCLUSIONS: These results show that hypoxia interferes with the normal process of OL differentiation by inducing premature OPC maturation. 11. α-Hemoglobin-stabilizing Protein: An Effective Marker for Erythroid Precursors in Bone Marrow Biopsy Specimens. Science.gov (United States) Yu, Hongbo; Pinkus, Jack L; Pinkus, Geraldine S 2016-01-01 Accurate analysis of the erythroid lineage is essential in evaluating bone marrow biopsies and can be particularly challenging in settings of dyserythropoiesis. α-Hemoglobin-stabilizing protein (AHSP) is an erythroid-specific chaperone protein and represents a potential specific marker for erythroid elements. This study defines the immunohistochemical profile of AHSP, as compared with an established erythroid marker CD71, in 101 bone marrow biopsies including normal marrows and cases of acute pure erythroid leukemia, acute erythroid/myeloid leukemia, other types of acute myeloid leukemia, myelodysplastic syndrome, chronic myelogenous leukemia, other types of myeloproliferative neoplasm, chronic myelomonocytic leukemia, acute lymphoblastic leukemia, plasma cell neoplasm, and metastatic carcinoma. In acute pure erythroid leukemia, blasts in 7 of 11 cases showed similar reactivity for CD71 and AHSP, whereas less extensive reactivity was observed for AHSP as compared with CD71 in the remaining 4 cases. In normal marrows and other various disorders, reactivity for AHSP was similar to CD71 and was restricted to the erythroid lineage. Mature erythrocytes were negative for AHSP as were myeloblasts, lymphoblasts, nonerythroid hematopoietic marrow elements, plasma cells, and carcinoma cells. AHSP is an effective marker for detection of normal or abnormal erythroid precursors in bone marrow biopsies and is a useful addition to an immunohistochemical panel for assessment of neoplastic cells of possible erythroid derivation. 12. Overexpression of estrogen receptor beta alleviates the toxic effects of beta-amyloid protein on PC12 cells via non-hormonal ligands Institute of Scientific and Technical Information of China (English) Hui Wang; Lihui Si; Xiaoxi Li; Weiguo Deng; Haimiao Yang; Yuyan Yang; Yan Fu 2012-01-01 After binding to the estrogen receptor, estrogen can alleviate the toxic effects of beta-amyloid protein, and thereby exert a therapeutic effect on Alzheimer's disease patients. Estrogen can increase the incidence of breast carcinoma and endometrial cancer in post-menopausal women, so it is not suitable for clinical treatment of Alzheimer's disease. There is recent evidence that the estrogen receptor can exert its neuroprotective effects without estrogen dependence. Real-time quantitative PCR and flow cytometry results showed that, compared with non-transfected PC12 cells, adenovirus-mediated estrogen receptor β gene-transfected PC12 cells exhibited lower expression of tumor necrosis factor α and interleukin 1β under stimulation with beta-amyloid protein and stronger protection from apoptosis. The Akt-specific inhibitor Abi-2 decreased the anti-inflammatory and anti-apoptotic effects of estrogen receptor β gene-transfection. These findings suggest that overexpression of estrogen receptor β can alleviate the toxic effect of beta-amyloid protein on PC12 cells, without estrogen dependence. The Akt pathway is one of the potential means for the anti-inflammatory and anti-apoptotic effects of the estrogen receptor. 13. THE OPEP COARSE-GRAINED PROTEIN MODEL: FROM SINGLE MOLECULES, AMYLOID FORMATION, ROLE OF MACROMOLECULAR CROWDING AND HYDRODYNAMICS TO RNA/DNA COMPLEXES Science.gov (United States) Sterpone, Fabio; Melchionna, Simone; Tuffery, Pierre; Pasquali, Samuela; Mousseau, Normand; Cragnolini, Tristan; Chebaro, Yassmine; Saint-Pierre, Jean-Francois; Kalimeri, Maria; Barducci, Alessandro; Laurin, Yohan; Tek, Alex; Baaden, Marc; Nguyen, Phuong Hoang; Derreumaux, Philippe 2015-01-01 The OPEP coarse-grained protein model has been applied to a wide range of applications since its first release 15 years ago. The model, which combines energetic and structural accuracy and chemical specificity, allows studying single protein properties, DNA/RNA complexes, amyloid fibril formation and protein suspensions in a crowded environment. Here we first review the current state of the model and the most exciting applications using advanced conformational sampling methods. We then present the current limitations and a perspective on the on-going developments. PMID:24759934 14. Binding of complement proteins C1q and C4bp to serum amyloid P component (SAP) in solid contra liquid phase DEFF Research Database (Denmark) Sørensen, Inge Juul; Nielsen, EH; Andersen, Ove; 1996-01-01 Serum amyloid P component (SAP), a member of the conserved pentraxin family of plasma proteins, binds calcium dependently to its ligands. The authors investigated SAPs interaction with the complement proteins C4b binding protein (C4bp) and C1q by ELISA, immunoelectrophoresis and electron microscopy...... affinity, did not interfere with the subsequent binding of C4bp or C1q to SAP. In contrast, collagen I and IV showed partial competition with the binding of C1q to SAP. Using fresh serum, immobilized native SAP bound C4bp whereas binding of C1q/C1 could not be demonstrated. Altogether the results indicate... 15. Data supporting beta-amyloid dimer structural transitions and protein–lipid interactions on asymmetric lipid bilayer surfaces using MD simulations on experimentally derived NMR protein structures Directory of Open Access Journals (Sweden) Sara Y. Cheng 2016-06-01 Full Text Available This data article supports the research article entitled “Maximally Asymmetric Transbilayer Distribution of Anionic Lipids Alters the Structure and interaction with Lipids of an Amyloidogenic Protein Dimer Bound to the Membrane Surface” [1]. We describe supporting data on the binding kinetics, time evolution of secondary structure, and residue-contact maps of a surface-absorbed beta-amyloid dimer protein on different membrane surfaces. We further demonstrate the sorting of annular and non-annular regions of the protein/lipid bilayer simulation systems, and the correlation of lipid-number mismatch and surface area per lipid mismatch of asymmetric lipid membranes. 16. Traditional Chinese Nootropic Medicine Radix Polygalae and Its Active Constituent Onjisaponin B Reduce β-Amyloid Production and Improve Cognitive Impairments. Science.gov (United States) Li, Xiaohang; Cui, Jin; Yu, Yang; Li, Wei; Hou, Yujun; Wang, Xin; Qin, Dapeng; Zhao, Cun; Yao, Xinsheng; Zhao, Jian; Pei, Gang 2016-01-01 Decline of cognitive function is the hallmark of Alzheimer's disease (AD), regardless of the pathological mechanism. Traditional Chinese medicine has been used to combat cognitive impairments and has been shown to improve learning and memory. Radix Polygalae (RAPO) is a typical and widely used herbal medicine. In this study, we aimed to follow the β-amyloid (Aβ) reduction activity to identify active constituent(s) of RAPO. We found that Onjisaponin B of RAPO functioned as RAPO to suppress Aβ production without direct inhibition of β-site amyloid precursor protein cleaving enzyme 1 (BACE1) and γ-secretase activities. Our mechanistic study showed that Onjisaponin B promoted the degradation of amyloid precursor protein (APP). Further, oral administration of Onjisaponin B ameliorated Aβ pathology and behavioral defects in APP/PS1 mice. Taken together, our results indicate that Onjisaponin B is effective against AD, providing a new therapeutic agent for further drug discovery. 17. Traditional Chinese Nootropic Medicine Radix Polygalae and Its Active Constituent Onjisaponin B Reduce β-Amyloid Production and Improve Cognitive Impairments. Directory of Open Access Journals (Sweden) Xiaohang Li Full Text Available Decline of cognitive function is the hallmark of Alzheimer's disease (AD, regardless of the pathological mechanism. Traditional Chinese medicine has been used to combat cognitive impairments and has been shown to improve learning and memory. Radix Polygalae (RAPO is a typical and widely used herbal medicine. In this study, we aimed to follow the β-amyloid (Aβ reduction activity to identify active constituent(s of RAPO. We found that Onjisaponin B of RAPO functioned as RAPO to suppress Aβ production without direct inhibition of β-site amyloid precursor protein cleaving enzyme 1 (BACE1 and γ-secretase activities. Our mechanistic study showed that Onjisaponin B promoted the degradation of amyloid precursor protein (APP. Further, oral administration of Onjisaponin B ameliorated Aβ pathology and behavioral defects in APP/PS1 mice. Taken together, our results indicate that Onjisaponin B is effective against AD, providing a new therapeutic agent for further drug discovery. 18. Human serum amyloid A3 (SAA3 protein, expressed as a fusion protein with SAA2, binds the oxidized low density lipoprotein receptor. Directory of Open Access Journals (Sweden) Takeshi Tomita Full Text Available Serum amyloid A3 (SAA3 possesses characteristics distinct from the other serum amyloid A isoforms, SAA1, SAA2, and SAA4. High density lipoprotein contains the latter three isoforms, but not SAA3. The expression of mouse SAA3 (mSAA3 is known to be up-regulated extrahepatically in inflammatory responses, and acts as an endogenous ligand for the toll-like receptor 4/MD-2 complex. We previously reported that mSAA3 plays an important role in facilitating tumor metastasis by attracting circulating tumor cells and enhancing hyperpermeability in the lungs. On the other hand, human SAA3 (hSAA3 has long been regarded as a pseudogene, which is in contrast to the abundant expression levels of the other isoforms. Although the nucleotide sequence of hSAA3 is very similar to that of the other SAAs, a single oligonucleotide insertion in exon 2 causes a frame-shift to generate a unique amino acid sequence. In the present study, we identified that hSAA3 was transcribed in the hSAA2-SAA3 fusion transcripts of several human cell lines. In the fusion transcript, hSAA2 exon 3 was connected to hSAA3 exon 1 or hSAA3 exon 2, located approximately 130kb downstream from hSAA2 exon 3 in the genome, which suggested that it is produced by alternative splicing. Furthermore, we succeeded in detecting and isolating hSAA3 protein for the first time by an immunoprecipitation-enzyme linked immune assay system using monoclonal and polyclonal antibodies that recognize the hSAA3 unique amino acid sequence. We also demonstrated that hSAA3 bound oxidized low density lipoprotein receptor (oxLDL receptor, LOX-1 and elevated the phosphorylation of ERK, the intracellular MAP-kinase signaling protein. 19. Ilex latifolia Prevents Amyloid β Protein (25-35)-Induced Memory Impairment by Inhibiting Apoptosis and Tau Phosphorylation in Mice. Science.gov (United States) Kim, Joo Youn; Lee, Hong Kyu; Jang, Ji Yeon; Yoo, Jae Kuk; Seong, Yeon Hee 2015-12-01 Ilex latifolia Thunb. (Aquifoliaceae), a Chinese bitter tea called "kudingcha," has been widely consumed as a health beverage and found to possess antioxidant, antidiabetic, antihypertensive, anti-inflammatory, and anti-ischemic activities. The aim of the present study was to investigate the neuroprotective effects of an ethanol extract of I. latifolia against amyloid β protein (Aβ)-induced memory impairment in mice and neurotoxicity in cultured rat cortical neurons. Memory impairment in mice was induced by intracerebroventricular injection of 15 nmol Aβ (25-35) and measured by the passive avoidance test and Morris water maze test. Chronic administration of I. latifolia (25-100 mg/kg, p.o.) significantly prevented Aβ (25-35)-induced memory loss. I. latifolia also prevented the decrease of glutathione concentrations, increased lipid peroxidation, expression of phosphorylated tau (p-tau), and changes in apoptosis-associated proteins in the memory-impaired mouse brain. Exposure of cultured cortical neurons to 10 μM Aβ (25-35) for 36 h induced neuronal apoptotic death. The neuronal cell death, elevation of intracellular Ca(2+) concentration, generation of reactive oxygen species, and expression of proapoptotic proteins caused by Aβ (25-35) in the cultured neurons were inhibited by treatment with I. latifolia (1-50 μg/mL). These results suggest that I. latifolia may have a possible therapeutic role in managing cognitive impairment associated with Alzheimer's disease. The underlying mechanism might involve the antiapoptotic effects mediated by antioxidant activity and inhibition of p-tau formation. 20. Expression of feline immunodeficiency virus gag and env precursor proteins in Spodoptera frugiperda cells and their use in immunodiagnosis NARCIS (Netherlands) Horzinek, M.C.; Verschoor, E.J.; Vliet, A.L.W. van; Egberink, H.F.; Hesselink, W.; Ronde, A. de 1993-01-01 The gag and env genes of the feline immunodeficiency virus strain UT113 were cloned into a baculovirus transfer vector. The recombinant plasmids were used to create recombinant baculoviruses that expressed either the gag or the env precursor protein in insect cells (Sf9 cells). Leader sequence cleav 1. Targeting amyloid-degrading enzymes as therapeutic strategies in neurodegeneration. Science.gov (United States) Turner, Anthony J; Fisk, Lilia; Nalivaeva, Natalia N 2004-12-01 The levels of amyloid beta-peptides (Abeta) in the brain represent a dynamic equilibrium state as a result of their biosynthesis from the amyloid precursor protein (APP) by beta- and gamma-secretases, their degradation by a team of amyloid-degrading enzymes, their subsequent oligomerization, and deposition into senile plaques. While most therapeutic attention has focused on developing inhibitors of secretases to prevent Abeta formation, enhancing the rate of Abeta degradation represents an alternative and viable strategy. Current evidence both in vivo and in vitro suggests that there are three major players in amyloid turnover: neprilysin, endothelin converting enzyme(s), and insulin-degrading enzyme, all of which are zinc metallopeptidases. Other proteases have also been implicated in amyloid metabolism, including angiotensin-converting enzyme, and plasmin but for these the evidence is less compelling. Neprilysin and endothelin converting enzyme(s) are homologous membrane proteins of the M13 peptidase family, which normally play roles in the biosynthesis and/or metabolism of regulatory peptides. Insulin-degrading enzyme is structurally and mechanistically distinct. The regional, cellular, and subcellular localizations of these enzymes differ, providing an efficient and diverse mechanism for protecting the brain against the normal accumulation of toxic Abeta peptides. Reduction in expression levels of some of these proteases following insults (e.g., hypoxia and ischemia) or aging might predispose to the development of Alzheimer's disease. Conversely, enhancement of their levels by gene delivery or pharmacological means could be neuroprotective. Even a relatively small enhancement of Abeta metabolism could slow the inexorable progression of the disease. The relative merits of targeting these enzymes for the treatment of Alzheimer's disease will be reviewed and possible side-effects of enhancing their activity evaluated. 2. Thrombus precursor protein for monitoring anticoagulation in patients with mechanical valve prosthesis Institute of Scientific and Technical Information of China (English) Qin Chuan; Xiao Yingbin 2009-01-01 Objective: To evaluate the plasma concentration of thrombus precursor protein (TPP) in patients after mechanical heart valve replacement, and to explore whether it can be used as a marker for monitoring anticoagulation. Methods: Totally 60 patients who took warfarin after mitral valve replacement and 20 control patients with non-valvular heart diseases were subjected in this study. Their plasma TPP concentration and international normalized ratio (INR) were determined, and compared not only between the anticoagulant patients and the control patients, but also between the patients with atrial fibrillaiton (AF, n=37) and the patients with sinus rhythm (SR, n=23) after mechanical valve replacement. The relationship between plasma TPP concentration and INR in the 60 anticoagulant patients was analyzed with linear regression. Results: It was found that the anticoagulant therapy effectively decreased plasma TPP concentration and elevated INR. In the anticoagulant group, the patients with AF had higher plasma TPP concentration than the others with sinus rhythm (P0.05). No significant correlation was found between plasma TPP concentration and INR in the anticoagulant patients (P>0.05). INR did not accord with plasma TPP concentration in several patients. Conclusion: INR can't reflect the coagulation status and guide the anticoagulation correctly sometimes; TPP may be a valuable assistant marker for monitoring anticoagulation in patients with mechanical heart valve prothesis; Patients with AF may require higher density of anticoagulation and TPP is strongly suggested to be monitored in these patients. 3. Protein: MPA4 [TP Atlas Lifescience Database Archive (English) Full Text Available MPA4 γ-secretase Bace1 Bace Beta-secretase 1 Aspartyl protease 2, Beta-site amyloid precursor prot...ein cleaving enzyme 1, Memapsin-2, Membrane-associated aspartic protease 2 10090 Mus musculus 23821 P56818 23821 P56818 21543615 ... 4. Protein: MPA4 [TP Atlas Lifescience Database Archive (English) Full Text Available MPA4 γ-secretase BACE1 BACE, KIAA1149 BACE1 Beta-secretase 1 Aspartyl protease 2, B...eta-site amyloid precursor protein cleaving enzyme 1, Memapsin-2, Membrane-associated aspartic protease 2 96 5. The mechanism of amyloid-fibril formation by stefin B: temperature and protein concentration dependence of the rates. Science.gov (United States) Skerget, Katja; Vilfan, Andrej; Pompe-Novak, Marusa; Turk, Vito; Waltho, Jonathan P; Turk, Dusan; Zerovnik, Eva 2009-02-01 Cystatins, a family of structurally related cysteine proteinase inhibitors, have proved to be useful model system to study amyloidogenesis. We have extended previous studies of the kinetics of amyloid-fibril formation by human stefin B (cystatin B) and some of its mutants, and proposed an improved model for the reaction. Overall, the observed kinetics follow the nucleation and growth behavior observed for many other amyloidogenic proteins. The minimal kinetic scheme that best fits measurements of changes in CD and thioflavin T fluorescence as a function of protein concentration and temperature includes nucleation (modeled as N(I) irreversible transitions with equivalent rates (k(I)), which fitted with N(I) = 64), fibril growth and nonproductive oligomerization, best explained by an off-pathway state with a rate-limiting escape rate. Three energies of activation were derived from global fitting to the minimal kinetic scheme, and independently through the fitting of the individual component rates. Nucleation was found to be a first-order process within an oligomeric species with an enthalpy of activation of 55 +/- 4 kcal mol(-1). Fibril growth was a second-order process with an enthalpy of activation (27 +/- 5 kcal mol(-1)), which is indistinguishable from that of tetramer formation by cystatins, which involves limited conformational changes including proline trans to cis isomerization. The highest enthalpy of activation (95 +/- 5 kcal mol(-1) at 35 degrees C), characteristic of a substantial degree of unfolding as observed prior to domain-swapping reactions, equated with the escape rate of the off-pathway oligomeric state. 6. Amyloid-related biomarkers and axonal damage proteins in parkinsonian syndromes DEFF Research Database (Denmark) Bech, Sara; Hjermind, Lena E; Salvesen, Lisette; 2012-01-01 Clinical differentiation between parkinsonian syndromes (PS) remains a challenge despite well-established clinical diagnostic criteria. Specific diagnostic biomarkers have yet to be identified, though in recent years, studies have been published on the aid of certain brain related proteins (BRP... 7. Deposition of kappa and lambda light chains in amyloid filaments of dialysis-related amyloidosis. Science.gov (United States) Brancaccio, D; Ghiggeri, G M; Braidotti, P; Garberi, A; Gallieni, M; Bellotti, V; Zoni, U; Gusmano, R; Coggi, G 1995-10-01 beta 2-Microglobulin (beta 2m) is considered to be the amyloidogenic precursor in dialysis-related amyloidosis, although the implication of other relevant cofactors in the pathogenesis of this disease has also been hypothesized. It is conceivable that substances found in amyloid deposits might represent something more than simple codeposition, possibly playing a pathogenic role in amyloidogenesis. Along these lines, a detailed analysis of the protein composition of amyloid fibrils purified from synovial material surgically obtained from nine patients on long-term dialysis was carried out. By the use of sodium dodecyl sulfate-polyacrylamide gel electrophoresis, several other protein components, in addition to beta 2m, were found. These were characterized by NH2 amino-terminal sequencing and immunoblotting. In fibrils obtained by water extraction, which fulfill the electron microscopy criteria of highly pure amyloid material, polyclonal kappa and lambda light chains were detected with a concentration of 15 micrograms/mL in the water extraction material; the beta 2m concentration was 200 micrograms/mL. Light microscopy immunohistochemistry was performed on samples from five patients. Amyloid deposits reacted with anti-beta 2m, and anti-light (kappa, lambda), chain antibodies. The immunoreaction of amyloid filaments to anti-beta 2m, anti-lambda, and anti-kappa light chain antibodies was also tested by electron microscopy by use of the immunogold staining procedure. Amyloid filaments were labeled by the three antibodies and showed a different intensity of immunostaining apparently related to their different aggregation pattern. These observations demonstrate that polyclonal immunoglobulin light chains (kappa and lambda) are not contaminants but, together with beta 2m, represent a major constituent of amyloid deposits in dialysis-related osteoarticular amyloidosis, thus indicating their possible role in amyloidogenesis. 8. Viral precursor protein P3 and its processed products perform discrete and essential functions in the poliovirus RNA replication complex. Science.gov (United States) Spear, Allyn; Ogram, Sushma A; Morasco, B Joan; Smerage, Lucia Eisner; Flanegan, James B 2015-11-01 The differential use of protein precursors and their products is a key strategy used during poliovirus replication. To characterize the role of protein precursors during replication, we examined the complementation profiles of mutants that inhibited 3D polymerase or 3C-RNA binding activity. We showed that 3D entered the replication complex in the form of its precursor, P3 (or 3CD), and was cleaved to release active 3D polymerase. Furthermore, our results showed that P3 is the preferred precursor that binds to the 5'CL. Using reciprocal complementation assays, we showed that one molecule of P3 binds the 5'CL and that a second molecule of P3 provides 3D. In addition, we showed that a second molecule of P3 served as the VPg provider. These results support a model in which P3 binds to the 5'CL and recruits additional molecules of P3, which are cleaved to release either 3D or VPg to initiate RNA replication. 9. The Formation of Fibrils by Intertwining of Filaments: Model and Application to AmyloidProtein Science.gov (United States) van Gestel, Jeroen; de Leeuw, Simon W. 2007-01-01 We outline a model that describes the interaction of rods that form intertwined bundles. In this simple model, we compare the elastic energy penalty that arises due to the deformation of the rods to the gain in binding energy upon intertwining. We find that, for proper values of the bending Young's modulus and the binding energy, a helical pitch may be found for which the energy of intertwining is most favorable. We apply our description to the problem of Alzheimer's Aβ protein fibrillization. If we forbid configurations that exhibit steric overlap between the protofilaments that make up a protein fibril, our model predicts that fibrils consisting of three protofilaments shall form. This agrees well with experimental results. Our model can also provide an estimate for the helical pitch of suitable fibrils. PMID:17114229 10. Ionic self-complementarity induces amyloid-like fibril formation in an isolated domain of a plant copper metallochaperone protein Directory of Open Access Journals (Sweden) Salom David 2004-06-01 Full Text Available Abstract Background Arabidopsis thaliana copper metallochaperone CCH is a functional homologue of yeast antioxidant ATX1, involved in cytosolic copper transport. In higher plants, CCH has to be transported to specialised cells through plasmodesmata, being the only metallochaperone reported to date that leaves the cell where it is synthesised. CCH has two different domains, the N-terminal domain conserved among other copper-metallochaperones and a C-terminal domain absent in all the identified non-plant metallochaperones. The aim of the present study was the biochemical and biophysical characterisation of the C-terminal domain of the copper metallochaperone CCH. Results The conformational behaviour of the isolated C-domain in solution is complex and implies the adoption of mixed conformations in different environments. The ionic self-complementary peptide KTEAETKTEAKVDAKADVE, derived from the C-domain of CCH, adopts and extended conformation in solution with a high content in β-sheet structure that induces a pH-dependent fibril formation. Freeze drying electron microscopy studies revealed the existence of well ordered amyloid-like fibrils in preparations from both the C-domain and its derivative peptide. Conclusion A number of proteins related with copper homeostasis have a high tendency to form fibrils. The determinants for fibril formation, as well as the possible physiological role are not fully understood. Here we show that the plant exclusive C-domain of the copper metallochaperone CCH has conformational plasticity and forms fibrils at defined experimental conditions. The putative influence of these properties with plant copper delivery will be addressed in the future. 11. Amyloid β-protein differentially affects NMDA receptor- and GABAA receptor-mediated currents in rat hippocampal CA1 neurons Institute of Scientific and Technical Information of China (English) Junfang Zhang; Lei Hou; Xiuping Gao; Fen Guo; Wei Jing; Jinshun Qi; Jiantian Qiao 2009-01-01 Although the aggregated amyloid β-protein (Aβ) in senile plaques is one of the key neuropathological features of Alzheimer's disease (AD), soluble forms of Aβ also interfere with synaptic plasticity at the early stage of AD. The suppressive action of acute application of Aβ on hippocampal long-term potentiation (LTP) has been reported widely, whereas the mechanism underlying the effects of Aβ is still mostly unknown. The present study, using the whole-cell patch clamp technique, investigated the effects of Aβ fragments (Aβ25-35 and Aβ31-35) on the LTP induction-related postsynaptic ligand-gated channel currents in isolated hippocampal CA1 neurons. The results showed a rapid but opposite action of both peptides on excitatory and inhibitory receptor currents. Glutamate application-induced currents were suppressed by A β25-35 in a dose-dependent manner, and further N-methyl-I>aspartate (NMDA) receptor-mediated currents were selec-tively inhibited. In contrast, pretreatment with Aβ fragments potentiated γ-aminobutyric acid (GABA)-induced whole-cell currents. As a control, Aβ35-31 the reversed sequence of Aβ35-31 showed no effect on the currents induced by glutamate, NMDA or GABA. These results may partly explain the impaired effects of Aβ on hippocampal LTP, and suggest that the functional down-regulation of N M DA receptors and up-regulation of GABAA receptors may play an important role in remodeling the hippocampal synaptic plasticity in early AD. 12. PB1-F2 influenza A virus protein adopts a beta-sheet conformation and forms amyloid fibers in membrane environments. Science.gov (United States) Chevalier, Christophe; Al Bazzal, Ali; Vidic, Jasmina; Février, Vincent; Bourdieu, Christiane; Bouguyon, Edwige; Le Goffic, Ronan; Vautherot, Jean-François; Bernard, Julie; Moudjou, Mohammed; Noinville, Sylvie; Chich, Jean-François; Da Costa, Bruno; Rezaei, Human; Delmas, Bernard 2010-04-23 The influenza A virus PB1-F2 protein, encoded by an alternative reading frame in the PB1 polymerase gene, displays a high sequence polymorphism and is reported to contribute to viral pathogenesis in a sequence-specific manner. To gain insights into the functions of PB1-F2, the molecular structure of several PB1-F2 variants produced in Escherichia coli was investigated in different environments. Circular dichroism spectroscopy shows that all variants have a random coil secondary structure in aqueous solution. When incubated in trifluoroethanol polar solvent, all PB1-F2 variants adopt an alpha-helix-rich structure, whereas incubated in acetonitrile, a solvent of medium polarity mimicking the membrane environment, they display beta-sheet secondary structures. Incubated with asolectin liposomes and SDS micelles, PB1-F2 variants also acquire a beta-sheet structure. Dynamic light scattering revealed that the presence of beta-sheets is correlated with an oligomerization/aggregation of PB1-F2. Electron microscopy showed that PB1-F2 forms amorphous aggregates in acetonitrile. In contrast, at low concentrations of SDS, PB1-F2 variants exhibited various abilities to form fibers that were evidenced as amyloid fibers in a thioflavin T assay. Using a recombinant virus and its PB1-F2 knock-out mutant, we show that PB1-F2 also forms amyloid structures in infected cells. Functional membrane permeabilization assays revealed that the PB1-F2 variants can perforate membranes at nanomolar concentrations but with activities found to be sequence-dependent and not obviously correlated with their differential ability to form amyloid fibers. All of these observations suggest that PB1-F2 could be involved in physiological processes through different pathways, permeabilization of cellular membranes, and amyloid fiber formation. 13. PB1-F2 Influenza A Virus Protein Adopts a β-Sheet Conformation and Forms Amyloid Fibers in Membrane Environments Science.gov (United States) Chevalier, Christophe; Al Bazzal, Ali; Vidic, Jasmina; Février, Vincent; Bourdieu, Christiane; Bouguyon, Edwige; Le Goffic, Ronan; Vautherot, Jean-François; Bernard, Julie; Moudjou, Mohammed; Noinville, Sylvie; Chich, Jean-François; Da Costa, Bruno; Rezaei, Human; Delmas, Bernard 2010-01-01 The influenza A virus PB1-F2 protein, encoded by an alternative reading frame in the PB1 polymerase gene, displays a high sequence polymorphism and is reported to contribute to viral pathogenesis in a sequence-specific manner. To gain insights into the functions of PB1-F2, the molecular structure of several PB1-F2 variants produced in Escherichia coli was investigated in different environments. Circular dichroism spectroscopy shows that all variants have a random coil secondary structure in aqueous solution. When incubated in trifluoroethanol polar solvent, all PB1-F2 variants adopt an α-helix-rich structure, whereas incubated in acetonitrile, a solvent of medium polarity mimicking the membrane environment, they display β-sheet secondary structures. Incubated with asolectin liposomes and SDS micelles, PB1-F2 variants also acquire a β-sheet structure. Dynamic light scattering revealed that the presence of β-sheets is correlated with an oligomerization/aggregation of PB1-F2. Electron microscopy showed that PB1-F2 forms amorphous aggregates in acetonitrile. In contrast, at low concentrations of SDS, PB1-F2 variants exhibited various abilities to form fibers that were evidenced as amyloid fibers in a thioflavin T assay. Using a recombinant virus and its PB1-F2 knock-out mutant, we show that PB1-F2 also forms amyloid structures in infected cells. Functional membrane permeabilization assays revealed that the PB1-F2 variants can perforate membranes at nanomolar concentrations but with activities found to be sequence-dependent and not obviously correlated with their differential ability to form amyloid fibers. All of these observations suggest that PB1-F2 could be involved in physiological processes through different pathways, permeabilization of cellular membranes, and amyloid fiber formation. PMID:20172856 14. Amyloid and tau cerebrospinal fluid biomarkers in HIV infection Directory of Open Access Journals (Sweden) Rosengren Lars 2009-12-01 Full Text Available Abstract Background Because of the emerging intersections of HIV infection and Alzheimer's disease, we examined cerebrospinal fluid (CSF biomarkers related of amyloid and tau metabolism in HIV-infected patients. Methods In this cross-sectional study we measured soluble amyloid precursor proteins alpha and beta (sAPPα and sAPPβ, amyloid beta fragment 1-42 (Aβ1-42, and total and hyperphosphorylated tau (t-tau and p-tau in CSF of 86 HIV-infected (HIV+ subjects, including 21 with AIDS dementia complex (ADC, 25 with central nervous system (CNS opportunistic infections and 40 without neurological symptoms and signs. We also measured these CSF biomarkers in 64 uninfected (HIV- subjects, including 21 with Alzheimer's disease, and both younger and older controls without neurological disease. Results CSF sAPPα and sAPPβ concentrations were highly correlated and reduced in patients with ADC and opportunistic infections compared to the other groups. The opportunistic infection group but not the ADC patients had lower CSF Aβ1-42 in comparison to the other HIV+ subjects. CSF t-tau levels were high in some ADC patients, but did not differ significantly from the HIV+ neuroasymptomatic group, while CSF p-tau was not increased in any of the HIV+ groups. Together, CSF amyloid and tau markers segregated the ADC patients from both HIV+ and HIV- neuroasymptomatics and from Alzheimer's disease patients, but not from those with opportunistic infections. Conclusions Parallel reductions of CSF sAPPα and sAPPβ in ADC and CNS opportunistic infections suggest an effect of CNS immune activation or inflammation on neuronal amyloid synthesis or processing. Elevation of CSF t-tau in some ADC and CNS infection patients without concomitant increase in p-tau indicates neural injury without preferential accumulation of hyperphosphorylated tau as found in Alzheimer's disease. These biomarker changes define pathogenetic pathways to brain injury in ADC that differ from those 15. Promotion of formation of amyloid fibrils by aluminium adenosine triphosphate (AlATP). Science.gov (United States) Exley, C; Korchazhkina, O V 2001-04-01 The formation of amyloid fibrils is considered to be an important step in the aetiology of Alzheimer's disease and other amyloidoses. Fibril formation in vitro has been shown to depend on many different factors including modifications to the amino acid profile of fibrillogenic peptides and interactions with both large and small molecules of physiological significance. How these factors might contribute to amyloid fibril formation in vivo is not clear as very little is known about the promotion of fibril formation in undersaturated solutions of amyloidogenic peptides. We have used thioflavin T fluorescence and reverse phase high performance liquid chromatography to show that ATP, and in particular AlATP, promoted the formation of thioflavin T-reactive fibrils of beta amyloid and, an unrelated amyloidogenic peptide, amylin. Evidence is presented that induction of fibril formation followed the complexation of AIATP by one or more monomers of the respective peptide. However, the complex formed could not be identified directly and it is suggested that AlATP might be acting as a chaperone in the assembly of amyloid fibrils. The effect of AlATP was not mimicked by either AlADP or AlAMP. However, it was blocked by suramin, a P2 ATP receptor antagonist, and this has prompted us to speculate that the precursor proteins to beta amyloid and amylin may be substrates or receptors for ATP in vivo. 16. Amyloid β Protein Aggravates Neuronal Senescence and Cognitive Deficits in 5XFAD Mouse Model of Alzheimer's Disease Institute of Scientific and Technical Information of China (English) Zhen Wei; Xiao-Chun Chen; Yue Song; Xiao-Dong Pan; Xiao-Man Dai; Jing Zhang; Xiao-Li Cui 2016-01-01 Background:Amyloid β (Aβ) has been established as a key factor for the pathological changes in the brains of patients with Alzheimer's disease (AD),and cellular senescence is closely associated with aging and cognitive impairment.However,it remains blurred whether,in the AD brains,Aβ accelerates the neuronal.senescence and whether this senescence,in turn,impairs the cognitive function.This study aimed to explore the expression of senescence-associated genes in the hippocampal tissue from young to aged 5XFAD mice and their age-matched wild type (WT) mice to determine whether senescent neurons are present in the transgenic AD mouse model.Methods:The 5XFAD mice and age-matched wild type mice,both raised from 1 to 18 months,were enrolled in the study.The senescence-associated genes in the hippocampus were analyzed and differentially expressed genes (DEGs) were screened by quantitative real-time polymerase chain reaction.Cognitive performance of the mice was evaluated by Y-maze and Morris water maze tests.Oligomeric Aβ (oAβ) (1-42) was applied to culture primary neurons to simulate the in vivo manifestation.Aging-related proteins were detected by Western blotting analysis and immunofluorescence.Results:In 5XFAD mice,of all the DEGs,the senescence-associated marker p 16 was most significantly increased,even at the early age.It was mainly localized in neurons,with a marginal expression in astrocytes (labeled as glutamine synthetase),nil expression in activated microglia (labeled as Iba1),and negatively correlated with the spatial cognitive impairments of 5XFAD mice.oAβ (1-42) induced the production of senescence-related protein p 16,but not p53 in vitro,which was in line with the in vivo manifestation.Conclusions:oAβ-accelerated neuronal senescence may be associated with the cognitive impairment in 5XFAD mice.Senescence-associated marker p 16 can serve as an indicator to estimate the cognitive prognosis for AD population. 17. Towards a Pharmacophore for Amyloid Energy Technology Data Exchange (ETDEWEB) Landau, Meytal; Sawaya, Michael R.; Faull, Kym F.; Laganowsky, Arthur; Jiang, Lin; Sievers, Stuart A.; Liu, Jie; Barrio, Jorge R.; Eisenberg, David (UCLA) 2011-09-16 Diagnosing and treating Alzheimer's and other diseases associated with amyloid fibers remains a great challenge despite intensive research. To aid in this effort, we present atomic structures of fiber-forming segments of proteins involved in Alzheimer's disease in complex with small molecule binders, determined by X-ray microcrystallography. The fiber-like complexes consist of pairs of {beta}-sheets, with small molecules binding between the sheets, roughly parallel to the fiber axis. The structures suggest that apolar molecules drift along the fiber, consistent with the observation of nonspecific binding to a variety of amyloid proteins. In contrast, negatively charged orange-G binds specifically to lysine side chains of adjacent sheets. These structures provide molecular frameworks for the design of diagnostics and drugs for protein aggregation diseases. The devastating and incurable dementia known as Alzheimer's disease affects the thinking, memory, and behavior of dozens of millions of people worldwide. Although amyloid fibers and oligomers of two proteins, tau and amyloid-{beta}, have been identified in association with this disease, the development of diagnostics and therapeutics has proceeded to date in a near vacuum of information about their structures. Here we report the first atomic structures of small molecules bound to amyloid. These are of the dye orange-G, the natural compound curcumin, and the Alzheimer's diagnostic compound DDNP bound to amyloid-like segments of tau and amyloid-{beta}. The structures reveal the molecular framework of small-molecule binding, within cylindrical cavities running along the {beta}-spines of the fibers. Negatively charged orange-G wedges into a specific binding site between two sheets of the fiber, combining apolar binding with electrostatic interactions, whereas uncharged compounds slide along the cavity. We observed that different amyloid polymorphs bind different small molecules, revealing that a 18. Rescue of Early bace-1 and Global DNA Demethylation by S-Adenosylmethionine Reduces Amyloid Pathology and Improves Cognition in an Alzheimer’s Model Science.gov (United States) Do Carmo, Sonia; Hanzel, Cecilia E.; Jacobs, Marie L.; Machnes, Ziv; Iulita, M. Florencia; Yang, Jingyun; Yu, Lei; Ducatenzeiler, Adriana; Danik, Marc; Breuillaud, Lionel S.; Bennett, David A.; Szyf, Moshe; Cuello, A. Claudio 2016-01-01 General DNA hypomethylation is associated with Alzheimer’s disease (AD), but it is unclear when DNA hypomethylation starts or plays a role in AD pathology or whether DNA re-methylation would rescue early amyloid-related cognitive impairments. In an APP transgenic mouse model of AD-like amyloid pathology we found that early intraneuronal amyloid beta build-up is sufficient to unleash a global and beta-site amyloid precursor protein cleaving enzyme 1 (bace-1) DNA demethylation in AD-vulnerable brain regions. S-adenosylmethionine administration at these early stages abolished this hypomethylation, diminished the amyloid pathology and restored cognitive capabilities. To assess a possible human significance of findings, we examined the methylation at 12 CpGs sites in the bace-1 promoter, using genome-wide DNA methylation data from 740 postmortem human brains. Thus, we found significant associations of bace-1 promoter methylation with β-amyloid load among persons with AD dementia, and PHFtau tangle density. Our results support a plausible causal role for the earliest amyloid beta accumulation to provoke DNA hypomethylation, influencing AD pathological outcomes. PMID:27681803 19. Prolyl oligopeptidase colocalizes with α-synuclein, β-amyloid, tau protein and astroglia in the post-mortem brain samples with Parkinson's and Alzheimer's diseases. Science.gov (United States) Hannula, M J; Myöhänen, T T; Tenorio-Laranga, J; Männistö, P T; Garcia-Horsman, J A 2013-07-09 Prolyl oligopeptidase (EC 3.4.21.26, PREP) is a serine protease that hydrolyzes proline-containing peptides shorter than 30-mer but it has also nonhydrolytic functions. PREP has been shown to accelerate aggregation of wild-type α-synuclein (α-syn) under cell-free conditions, and PREP inhibitors can block this aggregation both in vitro and in vivo. α-syn is the main component of Lewy bodies in Parkinson's disease (PD) and Lewy body dementia. To clarify the possible interaction of PREP with other markers of neurodegenerative diseases, we studied colocalizations of PREP and (1) α-syn, (2) β-amyloid, (3) tau protein and (4) astroglial and microglial cells in human post-mortem brain samples from PD, Alzheimer's disease (AD) patients and in healthy control brain samples. In the substantia nigra of PD brains, an intense colocalization with PREP and α-syn was evident. PREP colocalized also with β-amyloid plaques in AD brains and with tau protein in AD and in healthy brains. PREP was also found in astroglial cells in PD, AD and control brains, but not in the microglia. Our findings are the first ones to demonstrate colocalization of PREP and pathological proteins in the human brain and support the view that, at least in spatial terms, PREP could be associated with pathogenesis of neurodegenerative diseases. 20. Hacking the Code of Amyloid Formation Science.gov (United States) Pastor, M Teresa; Esteras-Chopo, Alexandra 2007-01-01 Many research efforts in the last years have been directed towards understanding the factors determining protein misfolding and amyloid formation. Protein stability and amino acid composition have been identified as the two major factors in vitro. The research of our group has been focused on understanding the relationship between amino acid sequence and amyloid formation. Our approach has been the design of simple model systems that reproduce the biophysical properties of natural amyloids. An amyloid sequence pattern was extracted that can be used to detect amyloidogenic hexapeptide stretches in proteins. We have added evidence supporting that these amyloidogenic stretches can trigger amyloid formation by nonamyloidogenic proteins. Some experimental results in other amyloid proteins will be analyzed under the conclusions obtained in these studies. Our conclusions together with evidences from other groups suggest that amyloid formation is the result of the interplay between a decrease of protein stability, and the presence of highly amyloidogenic regions in proteins. As many of these results have been obtained in vitro, the challenge for the next years will be to demonstrate their validity in in vivo systems. PMID:19164912 1. Charge neutralization of the central lysine cluster in prion protein (PrP) promotes PrP(Sc)-like folding of recombinant PrP amyloids. Science.gov (United States) Groveman, Bradley R; Kraus, Allison; Raymond, Lynne D; Dolan, Michael A; Anson, Kelsie J; Dorward, David W; Caughey, Byron 2015-01-09 The structure of the infectious form of prion protein, PrP(Sc), remains unclear. Most pure recombinant prion protein (PrP) amyloids generated in vitro are not infectious and lack the extent of the protease-resistant core and solvent exclusion of infectious PrP(Sc), especially within residues ∼90-160. Polyanionic cofactors can enhance infectivity and PrP(Sc)-like characteristics of such fibrils, but the mechanism of this enhancement is unknown. In considering structural models of PrP(Sc) multimers, we identified an obstacle to tight packing that might be overcome with polyanionic cofactors, namely, electrostatic repulsion between four closely spaced cationic lysines within a central lysine cluster of residues 101-110. For example, in our parallel in-register intermolecular β-sheet model of PrP(Sc), not only would these lysines be clustered within the 101-110 region of the primary sequence, but they would have intermolecular spacings of only ∼4.8 Å between stacked β-strands. We have now performed molecular dynamics simulations predicting that neutralization of the charges on these lysine residues would allow more stable parallel in-register packing in this region. We also show empirically that substitution of these clustered lysine residues with alanines or asparagines results in recombinant PrP amyloid fibrils with extended proteinase-K resistant β-sheet cores and infrared spectra that are more reminiscent of bona fide PrP(Sc). These findings indicate that charge neutralization at the central lysine cluster is critical for the folding and tight packing of N-proximal residues within PrP amyloid fibrils. This charge neutralization may be a key aspect of the mechanism by which anionic cofactors promote PrP(Sc) formation. 2. The prognostic value ofserum C-reactive protein-bound serum amyloid A inearly-stage lung cancer Institute of Scientific and Technical Information of China (English) XueYanZhang; GeZhang; YingJiang; DanLiu; ManZhiLi; QianZhong; ShanQiZeng; WanLiLiu; MuShengZeng 2015-01-01 Background:Elevated levels of serum C‑reactive protein (CRP) have been reported to have prognostic signiifcance in lung cancer patients. This study aimed to further identify CRP‑bound components as prognostic markers for lung cancer and validate their prognostic value. Methods:CRP‑bound components obtained from the serum samples from lung cancer patients or healthy controls were analyzed by differential proteomics analysis. CRP‑bound serum amyloid A (CRP‑SAA) was evaluated by co‑immunoprecipitation (IP). Serum samples from two independent cohorts with lung cancer (retrospective cohort, 242 patients; prospective cohort, 222 patients) and healthy controls (159 subjects) were used to evaluate the prognostic value of CRP‑SAA by enzyme‑linked immunosorbent assay. Results:CRP‑SAA was identiifed speciifcally in serum samples from lung cancer patients by proteomic analysis. CRP binding to SAA was conifrmed by co‑IP in serum samples from lung cancer patients and cell culture media. The level of CRP‑SAA was signiifcantly higher in patients than in healthy controls (0.37±0.58 vs. 0.03±0.04,P<0.001). Elevated CRP‑SAA levels were signiifcantly associated with severe clinical features of lung cancer. The elevation of CRP‑SAA was associated with lower survival rates for both the retrospective (hazard ration [HR]=2.181, 95% conifdence interval [CI]=1.641–2.897,P<0.001) and the prospective cohorts (HR=2.744, 95% CI=1.810–4.161,P<0.001). Multivariate Cox analysis showed that CRP‑SAA was an independent prognostic marker for lung cancer. Remarkably, in stages I–II patients, only CRP‑SAA, not total SAA or CRP, showed signiifcant association with overall survival in two cohorts. Moreover, univariate and multivariate Cox analyses also showed that only CRP‑SAA could be used as an inde‑pendent prognostic marker for early‑stage lung cancer patients. Conclusion:CRP‑SAA could be a better prognostic marker for lung cancer than total SAA or CRP 3. Natural polyphenols binding to amyloid: a broad class of compounds to treat different human amyloid diseases. Science.gov (United States) Ngoungoure, Viviane L Ndam; Schluesener, Jan; Moundipa, Paul F; Schluesener, Hermann 2015-01-01 Polyphenols are a large group of phytonutrients found in herbal beverages and foods. They have manifold biological activities, including antioxidative, antimicrobial, and anti-inflammatory properties. Interestingly, some polyphenols bind to amyloid and substantially ameliorate amyloid diseases. Misfolding, aggregation, and accumulation of amyloid fibrils in tissues or organs leads to a group of disorders, called amyloidoses. Prominent diseases are Alzheimer's, Parkinson's, and Huntington's disease, but there are other, less well-known diseases wherein accumulation of misfolded protein is a prominent feature. Amyloidoses are a major burden to public health. In particular, Alzheimer's disease shows a strong increase in patient numbers. Accelerated development of effective therapies for amyloidoses is a necessity. A viable strategy can be the prevention or reduction of protein misfolding, thus reducing amyloid build-up by restoring the cellular aggretome. Amyloid-binding polyphenols affect amyloid formation on various levels, e.g. by inhibiting fibril formation or steering oligomer formation into unstructured, nontoxic pathways. Consequently, preclinical studies demonstrate reduction of amyloid-formation by polyphenols. Amyloid-binding polyphenols might be suitable lead structures for development of imaging agents for early detection of disease and monitoring amyloid deposition. Intake of dietary polyphenols might be relevant to the prevention of amyloidoses. Nutraceutical strategies might be a way to reduce amyloid diseases. 4. Concentrations of C-reactive protein, serum amyloid A, and haptoglobin in uterine arterial and peripheral blood in bitches with pyometra. Science.gov (United States) Dąbrowski, Roman; Kostro, Krzysztof; Szczubiał, Marek 2013-09-15 Pyometra is a life-threatening reproductive disorder that affects the uterus of female dogs. This study was designed to identify the possible indicators of uterine inflammation by comparing C-reactive protein (CRP), serum amyloid A (SAA), and haptoglobin (Hp) concentrations in uterine arterial and peripheral venous blood in bitches with open- and closed-cervix pyometra. CRP, SAA, and Hp concentrations were higher in bitches with closed-cervix pyometra irrespective of the site of blood collection. Higher acute-phase protein concentrations were observed in peripheral compared with uterine arterial blood in bitches with closed-cervix pyometra, whereas the levels were comparable in dogs with open-cervix pyometra. Our results indicate that mean acute-phase protein concentrations differ according to pyometra type/severity and blood source and suggest the possible use of peripheral blood levels of CRP, SAA, and Hp to monitor inflammation during the course of pyometra. 5. Minocycline corrects early, pre-plaque neuroinflammation and inhibits BACE-1 in a transgenic model of Alzheimer's disease-like amyloid pathology Directory of Open Access Journals (Sweden) Ferretti Maria 2012-04-01 Full Text Available Abstract Background A growing body of evidence indicates that inflammation is one of the earliest neuropathological events in Alzheimer's disease. Accordingly, we have recently shown the occurrence of an early, pro-inflammatory reaction in the hippocampus of young, three-month-old transgenic McGill-Thy1-APP mice in the absence of amyloid plaques but associated with intracellular accumulation of amyloid beta petide oligomers. The role of such a pro-inflammatory process in the progression of the pathology remained to be elucidated. Methods and results To clarify this we administered minocycline, a tetracyclic derivative with anti-inflammatory and neuroprotective properties, to young, pre-plaque McGill-Thy1-APP mice for one month. The treatment ended at the age of three months, when the mice were still devoid of plaques. Minocycline treatment corrected the up-regulation of inducible nitric oxide synthase and cyclooxygenase-2 observed in young transgenic placebo mice. Furthermore, the down-regulation of inflammatory markers correlated with a reduction in amyloid precursor protein levels and amyloid precursor protein-related products. Beta-site amyloid precursor protein cleaving enzyme 1 activity and levels were found to be up-regulated in transgenic placebo mice, while minocycline treatment restored these levels to normality. The anti-inflammatory and beta-secretase 1 effects could be partly explained by the inhibition of the nuclear factor kappa B pathway. Conclusions Our study suggests that the pharmacological modulation of neuroinflammation might represent a promising approach for preventing or delaying the development of Alzheimer's disease neuropathology at its initial, pre-clinical stages. The results open new vistas to the interplay between inflammation and amyloid pathology. 6. Serum amyloid A, protein Z, and C4b-binding protein β chain as new potential biomarkers for pulmonary tuberculosis Science.gov (United States) Jiang, Ting-Ting; Shi, Li-Ying; Wei, Li-Liang; Li, Xiang; Yang, Su; Wang, Chong; Liu, Chang-Ming; Chen, Zhong-Liang; Tu, Hui-Hui; Li, Zhong-Jie; Li, Ji-Cheng 2017-01-01 The aim of this study was to discover novel biomarkers for pulmonary tuberculosis (TB). Differentially expressed proteins in the serum of patients with TB were screened and identified by iTRAQ-two dimensional liquid chromatography tandem mass spectrometry analysis. A total of 79 abnormal proteins were discovered in patients with TB compared with healthy controls. Of these, significant differences were observed in 47 abnormally expressed proteins between patients with TB or pneumonia and chronic obstructive pulmonary disease (COPD). Patients with TB (n = 136) exhibited significantly higher levels of serum amyloid A (SAA), vitamin K-dependent protein Z (PROZ), and C4b-binding protein β chain (C4BPB) than those in healthy controls (n = 66) (P<0.0001 for each) albeit significantly lower levels compared with those in patients with pneumonia (n = 72) (P<0.0001 for each) or COPD (n = 72) (P<0.0001, P<0.0001, P = 0.0016, respectively). After 6 months of treatment, the levels of SAA and PROZ were significantly increased (P = 0.022, P<0.0001, respectively), whereas the level of C4BPB was significantly decreased (P = 0.0038) in treated TB cases (n = 72). Clinical analysis showed that there were significant differences in blood clotting and lipid indices in patients with TB compared with healthy controls, patients with pneumonia or COPD, and treated TB cases (P<0.05). Correlation analysis revealed significant correlations between PROZ and INR (rs = 0.414, P = 0.044), and between C4BPB and FIB (rs = 0.617, P = 0.0002) in patients with TB. Receiver operating characteristic curve analysis revealed that the area under the curve value of the diagnostic model combining SAA, PROZ, and C4BPB to discriminate the TB group from the healthy control, pneumonia, COPD, and cured TB groups was 0.972, 0.928, 0.957, and 0.969, respectively. Together, these results suggested that SAA, PROZ, and C4BPB may serve as new potential biomarkers for TB. Our study may thus provide experimental data for 7. Neuroprotective approaches in experimental models of beta-amyloid neurotoxicity : Relevance to Alzheimer's disease NARCIS (Netherlands) Harkany, T.; Hortobágyi, Tibor; Sasvari, M.; Konya, C.; Penke, B; Luiten, P.G.M.; Nyakas, C. 1999-01-01 1. beta-Amyloid peptides (A beta s) accumulate abundantly in the Alzheimer's disease (AD) brain in areas subserving information acquisition arid processing, and memory formation. A beta fragments are producedin a process of abnormal proteolytic cleavage of their precursor, the amyloid precursor prot 8. Familial amyloid polyneuropathy. Science.gov (United States) Planté-Bordeneuve, Violaine; Said, Gerard 2011-12-01 Familial amyloid polyneuropathies (FAPs) are a group of life-threatening multisystem disorders transmitted as an autosomal dominant trait. Nerve lesions are induced by deposits of amyloid fibrils, most commonly due to mutated transthyretin (TTR). Less often the precursor of amyloidosis is mutant apolipoprotein A-1 or gelsolin. The first identified cause of FAP-the TTR Val30Met mutation-is still the most common of more than 100 amyloidogenic point mutations identified worldwide. The penetrance and age at onset of FAP among people carrying the same mutation vary between countries. The symptomatology and clinical course of FAP can be highly variable. TTR FAP typically causes a nerve length-dependent polyneuropathy that starts in the feet with loss of temperature and pain sensations, along with life-threatening autonomic dysfunction leading to cachexia and death within 10 years on average. TTR is synthesised mainly in the liver, and liver transplantation seems to have a favourable effect on the course of neuropathy, but not on cardiac or eye lesions. Oral administration of tafamidis meglumine, which prevents misfolding and deposition of mutated TTR, is under evaluation in patients with TTR FAP. In future, patients with FAP might benefit from gene therapy; however, genetic counselling is recommended for the prevention of all types of FAP. 9. Lasso Peptide Biosynthetic Protein LarB1 Binds Both Leader and Core Peptide Regions of the Precursor Protein LarA. Science.gov (United States) Cheung, Wai Ling; Chen, Maria Y; Maksimov, Mikhail O; Link, A James 2016-10-26 Lasso peptides are a member of the superclass of ribosomally synthesized and posttranslationally modified peptides (RiPPs). Like all RiPPs, lasso peptides are derived from a gene-encoded precursor protein. The biosynthesis of lasso peptides requires two enzymatic activities: proteolytic cleavage between the leader peptide and the core peptide in the precursor protein, accomplished by the B enzymes, and ATP-dependent isopeptide bond formation, accomplished by the C enzymes. In a subset of lasso peptide biosynthetic gene clusters from Gram-positive organisms, the B enzyme is split between two proteins. One such gene cluster is found in the organism Rhodococcus jostii, which produces the antimicrobial lasso peptide lariatin. The B enzyme in R. jostii is split between two open reading frames, larB1 and larB2, both of which are required for lariatin biosynthesis. While the cysteine catalytic triad is found within the LarB2 protein, LarB1 is a PqqD homologue expected to bind to the lariatin precursor LarA based on its structural homology to other RiPP leader peptide binding domains. We show that LarB1 binds to the leader peptide of the lariatin precursor protein LarA with a sub-micromolar affinity. We used photocrosslinking with the noncanonical amino acid p-azidophenylalanine and mass spectrometry to map the interaction of LarA and LarB1. This analysis shows that the LarA leader peptide interacts with a conserved motif within LarB1 and, unexpectedly, the core peptide of LarA also binds to LarB1 in several positions. A Rosetta model built from distance restraints from the photocrosslinking experiments shows that the scissile bond between the leader peptide and core peptide in LarA is in a solvent-exposed loop. 10. Cerebrospinal Fluid Amyloid Beta and Tau Concentrations Are Not Modulated by 16 Weeks of Moderate- to High-Intensity Physical Exercise in Patients with Alzheimer Disease DEFF Research Database (Denmark) Jensen, Camilla Steen; Portelius, Erik; Siersma, Volkert 2016-01-01 Background: Physical exercise may have some effect on cognition in patients with Alzheimer disease (AD). However, the underlying biochemical effects are unclear. Animal studies have shown that amyloid beta (Aβ), one of the pathological hallmarks of AD, can be altered with high levels of physical...... of Life, Physical Health and Functional Ability in Alzheimer's Disease: The Effect of Physical Exercise (ADEX) study we analyzed cerebrospinal fluid samples for Aβ species, total tau (t-tau), phosphorylated tau (p-tau) and soluble amyloid precursor protein (sAPP) species. We also assessed the patients... 11. Pre-amyloid oligomers of the proteotoxic RepA-WH1 prionoid assemble at the bacterial nucleoid Science.gov (United States) Moreno-del Álamo, María; de la Espina, Susana Moreno-Díaz; Fernández-Tresguerres, M. Elena; Giraldo, Rafael 2015-01-01 Upon binding to short specific dsDNA sequences in vitro, the N-terminal WH1 domain of the plasmid DNA replication initiator RepA assembles as amyloid fibres. These are bundles of single or double twisted tubular filaments in which distorted RepA-WH1 monomers are the building blocks. When expressed in Escherichia coli, RepA-WH1 triggers the first synthetic amyloid proteinopathy in bacteria, recapitulating some of the features of mammalian prion diseases: it is vertically transmissible, albeit non-infectious, showing up in at least two phenotypically distinct and interconvertible strains. Here we report B3h7, a monoclonal antibody specific for oligomers of RepA-WH1, but which does not recognize the mature amyloid fibres. Unlike a control polyclonal antibody generated against the soluble protein, B3h7 interferes in vitro with DNA-promoted or amyloid-seeded assembly of RepA-WH1 fibres, thus the targeted oligomers are on-pathway amyloidogenic intermediates. Immuno-electron microscopy with B3h7 on thin sections of E. coli cells expressing RepA-WH1 consistently labels the bacterial nucleoid, but not the large cytoplasmic aggregates of the protein. This observation points to the nucleoid as the place where oligomeric amyloid precursors of RepA-WH1 are generated, and suggests that, once nucleated by DNA, further growth must continue in the cytoplasm due to entropic exclusion. PMID:26423724 12. Transmembrane Protein 147 (TMEM147) Is a Novel Component of the Nicalin-NOMO Protein Complex* OpenAIRE Dettmer, Ulf; Kuhn, Peer-Hendrik; Abou-Ajram, Claudia; Lichtenthaler, Stefan F.; Krüger, Marcus; Kremmer, Elisabeth; Haass, Christian; Haffner, Christof 2010-01-01 Nicastrin and its relative Nicalin (Nicastrin-like protein) are both members of larger protein complexes, namely γ-secretase and the Nicalin-NOMO (Nodal modulator) complex. The γ-secretase complex, which contains Presenilin, APH-1, and PEN-2 in addition to Nicastrin, catalyzes the proteolytic cleavage of the transmembrane domain of various proteins including the β-amyloid precursor protein and Notch. Nicalin and its binding partner NOMO form a complex that was shown to modulate Nodal signalin... 13. Characterization of Amyloid Cores in Prion Domains Science.gov (United States) Sant’Anna, Ricardo; Fernández, Maria Rosario; Batlle, Cristina; Navarro, Susanna; de Groot, Natalia S.; Serpell, Louise; Ventura, Salvador 2016-01-01 Amyloids consist of repetitions of a specific polypeptide chain in a regular cross-β-sheet conformation. Amyloid propensity is largely determined by the protein sequence, the aggregation process being nucleated by specific and short segments. Prions are special amyloids that become self-perpetuating after aggregation. Prions are responsible for neuropathology in mammals, but they can also be functional, as in yeast prions. The conversion of these last proteins to the prion state is driven by prion forming domains (PFDs), which are generally large, intrinsically disordered, enriched in glutamines/asparagines and depleted in hydrophobic residues. The self-assembly of PFDs has been thought to rely mostly on their particular amino acid composition, rather than on their sequence. Instead, we have recently proposed that specific amyloid-prone sequences within PFDs might be key to their prion behaviour. Here, we demonstrate experimentally the existence of these amyloid stretches inside the PFDs of the canonical Sup35, Swi1, Mot3 and Ure2 prions. These sequences self-assemble efficiently into highly ordered amyloid fibrils, that are functionally competent, being able to promote the PFD amyloid conversion in vitro and in vivo. Computational analyses indicate that these kind of amyloid stretches may act as typical nucleating signals in a number of different prion domains. PMID:27686217 14. Characterization of the ectodomain of the envelope protein of dengue virus type 4: expression, membrane association, secretion and particle formation in the absence of precursor membrane protein. Directory of Open Access Journals (Sweden) Szu-Chia Hsieh Full Text Available The envelope (E of dengue virus (DENV is the major target of neutralizing antibodies and vaccine development. After biosynthesis E protein forms a heterodimer with precursor membrane (prM protein. Recent reports of infection enhancement by anti-prM monoclonal antibodies (mAbs suggest anti-prM responses could be potentially harmful. Previously, we studied a series of C-terminal truncation constructs expressing DENV type 4 prM/E or E proteins and found the ectodomain of E protein alone could be recognized by all 12 mAbs tested, suggesting E protein ectodomain as a potential subunit immunogen without inducing anti-prM response. The characteristics of DENV E protein ectodomain in the absence of prM protein remains largely unknown.In this study, we investigated the expression, membrane association, glycosylation pattern, secretion and particle formation of E protein ectodomain of DENV4 in the presence or absence of prM protein. E protein ectodomain associated with membrane in or beyond trans-Golgi and contained primarily complex glycans, whereas full-length E protein associated with ER membrane and contained high mannose glycans. In the absence of prM protein, E protein ectodomain can secrete as well as form particles of approximately 49 nm in diameter, as revealed by sucrose gradient ultracentrifugation with or without detergent and electron microscopy. Mutational analysis revealed that the secretion of E protein ectodomain was affected by N-linked glycosylation and could be restored by treatment with ammonia chloride.Considering the enhancement of DENV infectivity by anti-prM antibodies, our findings provide new insights into the expression and secretion of E protein ectodomain in the absence of prM protein and contribute to future subunit vaccine design. 15. Effect of chronic intermittent hypoxia on the expression of Nip3, cell apoptosis, β-amyloid protein deposit in mice brain cortex Institute of Scientific and Technical Information of China (English) ZENG Yi-ming; CAI Kai-jin; CHEN Xiao-yong; WU Minx-ia; LIN Xi 2009-01-01 Background Chronic intermittent hypoxia (CIH) is the most important pathophysiologic feature of sleep apnea syndrome (SAS). To explore the relationship between SAS and dementia, the effects of CIH on the expression of Nip3, neuron apoptosis andβ-amyloid protein deposit in the brain cortex of the frontal lobe of mice were evaluated in this study. Methods Thirty male ICR mice were divided into four groups: control group (A, n=-10, sham hypoxia/reoxygenation), 2 weeks CIH group (B, n=-5), 4 weeks CIH group (C, n=-5), and 8 weeks CIH group (D, n=10). The ICR mice were placed in a chamber and exposed to intermittent hypoxia (oxygen concentration changed periodically from (21.72±0.55)% to (6.84±0.47)% every two minutes, eight hours per day). Neuron apoptosis of the cortex of the frontal lobe was detected by means of terminal deoxy-nucleotidyl transferase-mediated in situ end labeling (TUNEL). Immunohistochemical staining was performed for measuring expression of Nip3 and β-amyloid protein. The ultrastructure of neurons was observed under a transmission electron microscope. Results TUNEL positive neurons in each square millimeter in the cortex of the frontal lobe were categorized by median or Ri into group A (1,5.5), group B (133, 13), group C (252, 21), and group D (318, 24). There were significant differences among the above four groups (P=0.000). The significance test was performed between the control group and each CIH group respectively: group A and B (P>0.05); group A and C (P 0.05); groups A and C (P<0.005); and groups A and D (P<0.005). There was no significant difference between groups B and C, groups B and D, and groups C and D. The expression of Nip3 was closely correlated with neuron apoptosis in the brain (P <0.05). The expression ofβ-amyloid protein in the brain of mice was negative in all CIH groups and the control group. Ultrastructure observation showed karyopyknosis of nucleus, swelling of chondriosomes, deposit of lipofuscins and degeneration of 16. Amyloid fibrils compared to peptide nanotubes. Science.gov (United States) Zganec, Matjaž; Zerovnik, Eva 2014-09-01 Prefibrillar oligomeric states and amyloid fibrils of amyloid-forming proteins qualify as nanoparticles. We aim to predict what biophysical and biochemical properties they could share in common with better researched peptide nanotubes. We first describe what is known of amyloid fibrils and prefibrillar aggregates (oligomers and protofibrils): their structure, mechanisms of formation and putative mechanism of cytotoxicity. In distinction from other neuronal fibrillar constituents, amyloid fibrils are believed to cause pathology, however, some can also be functional. Second, we give a review of known biophysical properties of peptide nanotubes. Finally, we compare properties of these two macromolecular states side by side and discuss which measurements that have already been done with peptide nanotubes could be done with amyloid fibrils as well. 17. Transport of the GlcNAc-1-phosphotransferase α/β-subunit precursor protein to the Golgi apparatus requires a combinatorial sorting motif. Science.gov (United States) Franke, Mine; Braulke, Thomas; Storch, Stephan 2013-01-11 The Golgi-resident N-acetylglucosamine-1-phosphotransferase (PT) complex is composed of two α-, β-, and γ-subunits and represents the key enzyme for the biosynthesis of mannose 6-phosphate recognition marker on soluble lysosomal proteins. Mutations in the PT complex cause the lysosomal storage diseases mucolipidosis II and III. A prerequisite for the enzymatic activity is the site-1 protease-mediated cleavage of the PT α/β-subunit precursor protein in the Golgi apparatus. Here, we have investigated structural requirements of the PT α/β-subunit precursor protein for its efficient export from the endoplasmic reticulum (ER). Both wild-type and a cleavage-resistant type III membrane PT α/β-subunit precursor protein are exported whereas coexpressed separate α- and β-subunits failed to reach the cis-Golgi compartment. Mutational analyses revealed combinatorial, non-exchangeable dileucine and dibasic motifs located in a defined sequence context in the cytosolic N- and C-terminal domains that are required for efficient ER exit and subsequent proteolytic activation of the α/β-subunit precursor protein in the Golgi. In the presence of a dominant negative Sar1 mutant the ER exit of the PT α/β-subunit precursor protein is inhibited indicating its transport in coat protein complex II-coated vesicles. Expression studies of missense mutations identified in mucolipidosis III patients that alter amino acids in the N- and C-terminal domains demonstrated that the substitution of a lysine residue in close proximity to the dileucine sorting motif impaired ER-Golgi transport and subsequent activation of the PT α/β-subunit precursor protein. The data suggest that the oligomeric type III membrane protein PT complex requires a combinatorial sorting motif that forms a tertiary epitope to be recognized by distinct sites within the coat protein complex II machinery. 18. Designed amyloid fibers as materials for selective carbon dioxide capture. Science.gov (United States) Li, Dan; Furukawa, Hiroyasu; Deng, Hexiang; Liu, Cong; Yaghi, Omar M; Eisenberg, David S 2014-01-07 New materials capable of binding carbon dioxide are essential for addressing climate change. Here, we demonstrate that amyloids, self-assembling protein fibers, are effective for selective carbon dioxide capture. Solid-state NMR proves that amyloid fibers containing alkylamine groups reversibly bind carbon dioxide via carbamate formation. Thermodynamic and kinetic capture-and-release tests show the carbamate formation rate is fast enough to capture carbon dioxide by dynamic separation, undiminished by the presence of water, in both a natural amyloid and designed amyloids having increased carbon dioxide capacity. Heating to 100 °C regenerates the material. These results demonstrate the potential of amyloid fibers for environmental carbon dioxide capture. 19. Early-onset and robust amyloid pathology in a new homozygous mouse model of Alzheimer's disease. Directory of Open Access Journals (Sweden) Antje Willuweit Full Text Available BACKGROUND: Transgenic mice expressing mutated amyloid precursor protein (APP and presenilin (PS-1 or -2 have been successfully used to model cerebral beta-amyloidosis, one of the characteristic hallmarks of Alzheimer's disease (AD pathology. However, the use of many transgenic lines is limited by premature death, low breeding efficiencies and late onset and high inter-animal variability of the pathology, creating a need for improved animal models. Here we describe the detailed characterization of a new homozygous double-transgenic mouse line that addresses most of these issues. METHODOLOGY/PRINCIPAL FINDINGS: The transgenic mouse line (ARTE10 was generated by co-integration of two transgenes carrying the K670N/M671L mutated amyloid precursor protein (APP(swe and the M146V mutated presenilin 1 (PS1 both under control of a neuron-specific promoter. Mice, hemi- as well as homozygous for both transgenes, are viable and fertile with good breeding capabilities and a low rate of premature death. They develop robust AD-like cerebral beta-amyloid plaque pathology with glial inflammation, signs of neuritic dystrophy and cerebral amyloid angiopathy. Using our novel image analysis algorithm for semi-automatic quantification of plaque burden, we demonstrate an early onset and progressive plaque deposition starting at 3 months of age in homozygous mice with low inter-animal variability and 100%-penetrance of the phenotype. The plaques are readily detected in vivo by PiB, the standard human PET tracer for AD. In addition, ARTE10 mice display early loss of synaptic markers and age-related cognitive deficits. By applying a gamma-secretase inhibitor we show a dose dependent reduction of soluble amyloid beta levels in the brain. CONCLUSIONS: ARTE10 mice develop a cerebral beta-amyloidosis closely resembling the beta-amyloid-related aspects of human AD neuropathology. Unifying several advantages of previous transgenic models, this line particularly qualifies for Science.gov (United States) Drüeke, T B 1999-12-01 The major clinical manifestations of dialysis-associated A beta 2M amyloidosis are chronic arthralgias, destructive arthropathy and the carpal tunnel syndrome. For dialysis patients who have been maintained on renal replacement therapy for more than 10-15 years, this complication may become a major physical handicap. It may even be life-threatening in some instances due to cervical cord compression. Amyloid deposits in joint areas precede clinical symptoms and signs by several years. Systemic deposits may also occur but their clinical manifestations are infrequent. The diagnosis of dialysis arthropathy associated with beta 2-microglobulin-associated (A beta 2M) amyloidosis mostly relies on indirect clinical and radiological evidence. Histologic proof is rarely obtained in vivo. The pathogenesis of the disease is complex. It includes reduced elimination of beta 2M and potentially also as impaired degradation of A beta 2M as well as enhanced production of A beta 2M amyloid fibrils. Non enzymatic modifications of beta 2M probably play a role, including beta 2M protein modification with advanced glycation end-products (AGE) and advanced oxidation protein products. Modified beta 2M, collagen and proteoglycans appear actively involved in the induction of a local inflammatory response and beta 2M amyloid formation. There is also evidence in favor of treatment-related factors such as the type of hemodialysis membrane and the purity of dialysis water. Hopefully, the translation of our improving knowledge of all the factors involved will lead to a better treatment and eventually to the prevention of this dramatic complication of dialysis. 1. PARP-1 modulates amyloid beta peptide-induced neuronal damage. Directory of Open Access Journals (Sweden) Sara Martire Full Text Available Amyloid beta peptide (Aβ causes neurodegeneration by several mechanisms including oxidative stress, which is known to induce DNA damage with the consequent activation of poly (ADP-ribose polymerase (PARP-1. To elucidate the role of PARP-1 in the neurodegenerative process, SH-SY5Y neuroblastoma cells were treated with Aβ25-35 fragment in the presence or absence of MC2050, a new PARP-1 inhibitor. Aβ25-35 induces an enhancement of PARP activity which is prevented by cell pre-treatment with MC2050. These data were confirmed by measuring PARP-1 activity in CHO cells transfected with amylod precursor protein and in vivo in brains specimens of TgCRND8 transgenic mice overproducing the amyloid peptide. Following Aβ25-35 exposure a significant increase in intracellular ROS was observed. These data were supported by the finding that Aβ25-35 induces DNA damage which in turn activates PARP-1. Challenge with Aβ25-35 is also able to activate NF-kB via PARP-1, as demonstrated by NF-kB impairment upon MC2050 treatment. Moreover, Aβ25-35 via PARP-1 induces a significant increase in the p53 protein level and a parallel decrease in the anti-apoptotic Bcl-2 protein. These overall data support the hypothesis of PARP-1 involvment in cellular responses induced by Aβ and hence a possible rationale for the implication of PARP-1 in neurodegeneration is discussed. 2. Atomic View of a Toxic Amyloid Small Oligomer Energy Technology Data Exchange (ETDEWEB) Laganowsky, Arthur; Liu, Cong; Sawaya, Michael R.; Whitelegge, Julian P.; Park, Jiyong; Zhao, Minglei; Pensalfini, Anna; Soriaga, Angela B.; Landau, Meytal; Teng, Poh K.; Cascio, Duilio; Glabe, Charles; Eisenberg, David (UCI); (UCLA) 2012-04-30 Amyloid diseases, including Alzheimer's, Parkinson's, and the prion conditions, are each associated with a particular protein in fibrillar form. These amyloid fibrils were long suspected to be the disease agents, but evidence suggests that smaller, often transient and polymorphic oligomers are the toxic entities. Here, we identify a segment of the amyloid-forming protein {alpha}{beta} crystallin, which forms an oligomeric complex exhibiting properties of other amyloid oligomers: {beta}-sheet-rich structure, cytotoxicity, and recognition by an oligomer-specific antibody. The x-ray-derived atomic structure of the oligomer reveals a cylindrical barrel, formed from six antiparallel protein strands, that we term a cylindrin. The cylindrin structure is compatible with a sequence segment from the {beta}-amyloid protein of Alzheimer's disease. Cylindrins offer models for the hitherto elusive structures of amyloid oligomers. 3. Binding of complement proteins C1q and C4bp to serum amyloid P component (SAP) in solid contra liquid phase DEFF Research Database (Denmark) Sørensen, Inge Juul; Nielsen, EH; Andersen, Ove; 1996-01-01 Serum amyloid P component (SAP), a member of the conserved pentraxin family of plasma proteins, binds calcium dependently to its ligands. The authors investigated SAPs interaction with the complement proteins C4b binding protein (C4bp) and C1q by ELISA, immunoelectrophoresis and electron microscopy....... Binding of these proteins to SAP was demonstrated when SAP was immobilized using F(ab')2 anti-SAP, but not when SAP reacted with these proteins in liquid phase; thus the binding to human SAP was markedly phase state dependent. Presaturation of solid phase SAP with heparin, which binds SAP with high...... affinity, did not interfere with the subsequent binding of C4bp or C1q to SAP. In contrast, collagen I and IV showed partial competition with the binding of C1q to SAP. Using fresh serum, immobilized native SAP bound C4bp whereas binding of C1q/C1 could not be demonstrated. Altogether the results indicate... 4. The Alzheimer's Amyloid-Degrading Peptidase, Neprilysin: Can We Control It? Directory of Open Access Journals (Sweden) N. N. Nalivaeva 2012-01-01 Full Text Available The amyloid cascade hypothesis of Alzheimer's disease (AD postulates that accumulation in the brain of amyloid β-peptide (Aβ is the primary trigger for neuronal loss specific to this pathology. In healthy brain, Aβ levels are regulated by a dynamic equilibrium between Aβ release from the amyloid precursor protein (APP and its removal by perivascular drainage or by amyloid-degrading enzymes (ADEs. During the last decade, the ADE family was fast growing, and currently it embraces more than 20 members. There are solid data supporting involvement of each of them in Aβ clearance but a zinc metallopeptidase neprilysin (NEP is considered as a major ADE. NEP plays an important role in brain function due to its role in terminating neuropeptide signalling and its decrease during ageing or after such pathologies as hypoxia or ischemia contribute significantly to the development of AD pathology. The recently discovered mechanism of epigenetic regulation of NEP by the APP intracellular domain (AICD opens new avenues for its therapeutic manipulation and raises hope for developing preventive strategies in AD. However, consideration needs to be given to the diverse physiological roles of NEP. This paper critically evaluates general biochemical and physiological functions of NEP and their therapeutic relevance. 5. Amyloid Imaging in Aging and Dementia: Testing the Amyloid Hypothesis In Vivo Directory of Open Access Journals (Sweden) G. D. Rabinovici 2009-01-01 Full Text Available Amyloid imaging represents a major advance in neuroscience, enabling the detection and quantification of pathologic protein aggregations in the brain. In this review we survey current amyloid imaging techniques, focusing on positron emission tomography (PET with ^{11}carbon-labelled Pittsburgh Compound-B (11C-PIB, the most extensively studied and best validated tracer. PIB binds specifically to fibrillar beta-amyloid (Aβ deposits, and is a sensitive marker for Aβ pathology in cognitively normal older individuals and patients with mild cognitive impairment (MCI and Alzheimer’s disease (AD. PIB-PET provides us with a powerful tool to examine in vivo the relationship between amyloid deposition, clinical symptoms, and structural and functional brain changes in the continuum between normal aging and AD. Amyloid imaging studies support a model in which amyloid deposition is an early event on the path to dementia, beginning insidiously in cognitively normal individuals, and accompanied by subtle cognitive decline and functional and structural brain changes suggestive of incipient AD. As patients progress to dementia, clinical decline and neurodegeneration accelerate and proceed independently of amyloid accumulation. In the future, amyloid imaging is likely to supplement clinical evaluation in selecting patients for anti-amyloid therapies, while MRI and FDG-PET may be more appropriate markers of clinical progression. 6. Atypical presentation of atypical amyloid. Science.gov (United States) Holanda, Danniele G; Acharya, Veena K; Dogan, Ahmet; Racusen, Lorraine C; Atta, Mohamed G 2011-01-01 Amyloidosis is a group of diseases categorized by precipitation of a group of protein aggregates (amyloid) in tissues, including the kidney, and proteinuria is usually the commonest, though not exclusive, hallmark of clinical presentation. AL and AA are the most commonly recognized forms of amyloidosis involving the kidney, but other forms have been described. We present a case of renal amyloidosis due to a novel amyloidogenic protein, leucocyte cell-derived chemotaxin 2, without proteinuria at presentation or on subsequent follow-up. 7. Regulation of serum amyloid A gene expression in Syrian hamsters by cytokines. Science.gov (United States) Dowton, S B; Peters, C N; Jestus, J J 1991-10-01 Amyloid A (AA) protein is derived from serum amyloid A (SAA) and deposited as beta-pleated sheet fibrils in reactive amyloidosis, a disease that occurs spontaneously in golden Syrian hamsters. The precursor SAA is an acute-phase reactant in many species including hamsters, and in this report we have defined the in vivo kinetic and dosage responses for SAA mRNA accumulation in hamsters following administration of various cytokines. Elevations in levels of hepatic SAA mRNA were documented when the doses of interleukin-1, interleukin-6, and tumor necrosis factor were increased. The increase in dosages applied ranged from 2 1/2-fold for interleukin-6 to 10-fold for interleukin-1. SAA transcript levels were highest 8 h following administration of interleukin-6 or tumor necrosis factor, whereas maximal amounts of SAA-specific mRNA were found 24 h after administration of interleukin-1. 8. A complex between contactin-1 and the protein tyrosine phosphatase PTPRZ controls the development of oligodendrocyte precursor cells Energy Technology Data Exchange (ETDEWEB) Lamprianou, Smaragda; Chatzopoulou, Elli; Thomas, Jean-Léon; Bouyain, Samuel; Harroch, Sheila (IP-Korea); (UPMC); (UMKC) 2013-09-23 The six members of the contactin (CNTN) family of neural cell adhesion molecules are involved in the formation and maintenance of the central nervous system (CNS) and have been linked to mental retardation and neuropsychiatric disorders such as autism. Five of the six CNTNs bind to the homologous receptor protein tyrosine phosphatases gamma (PTPRG) and zeta (PTPRZ), but the biological roles of these interactions remain unclear. We report here the cocrystal s	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5362354516983032, "perplexity": 19857.677680976514}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-43/segments/1508187822822.66/warc/CC-MAIN-20171018070528-20171018090528-00446.warc.gz"}
http://mathoverflow.net/questions/71360/on-the-boundedness-of-linear-representations-of-formal-power-series-of-languages	# On the boundedness of linear representations of formal power series of languages. Let $\Sigma$ be a finite non-empty set of symbols (i.e. an alphabet). Fix $\pi, \eta\in\mathbb{R}^{1\times m}$ and for every $\sigma\in\Sigma$ fix $A(\sigma)\in\mathbb{R}^{m\times m}$. We also require that for every $1 \leq i,j\leq m$ $\pi_i, \eta_i, (A(\sigma))_{i,j} \geq 0$ but $\pi,\eta,A(\sigma)\neq 0$. If $w:=w_1\cdots w_n\in\Sigma^$ let $A(w) := \prod_{i=1}^{n} A(w_i)$. Suppose that there exists a real $K$ such that for every $w\in\Sigma^$ one has $\|\pi A(w)\eta^{t} \|\leq K$. Is it true that this imply the existence of $K'$ such that for every $w\in\Sigma^*$ $\|\|\pi A(w)\|\|\leq K'$ for some $K'$? If not, any counterexample? Here $\|\|\cdot\|\|$ denotes the usual $\ell_2$ norm of a real vector. - Is $\eta$ fixed? If $\eta$ is 0 you can't say anything. If $\eta\| is strictly positive things look better. – Benjamin Steinberg Jul 26 '11 at 21:40 Thank you for replying. We fix$\eta, \pi$and$A(\sigma)$but we rule out the case$\eta=0$. I've edited the question. Thank you. – Carlo Jul 26 '11 at 21:59 I also guess there should be a counter-example with some η not strictly-positive and that the theorem might be true adding η>0 to hypothesis. Any hint or ref on this will be of great help. Thank you. – Carlo Jul 26 '11 at 22:12 As stated nothing works. Just choose matrices whose rows are orthogonal to$\eta$. Maybe you might want strictly positive matrices and vectors? – Benjamin Steinberg Jul 27 '11 at 0:27 add comment ## 1 Answer Here is a counterexample. Suppose that$A(\sigma)$is upper triangular with a$1$in upper left position, and that$\eta=[1\ 0\ 0\ \cdots\ 0]$and$\pi=[1\ 1\ 1\cdots\ 1]$. Note that$A(w)$is also upper triangular with a$1$at upper left, and that$A(w)\eta^t=[1\ 0\ 0\ \cdots\ 0]^t$and so$\pi A(w)\eta^t=1$for all$w$. But meanwhile, it is easy to arrange that$\pi A(w)$can become unboundedly large by taking$w$large. For a concrete example, use$A(\sigma)=[1\ 1;\ 0\ 1]$and$\eta=[1\ 0]$and$\pi=[1\ 1]\$. - This is an answer to the original question; it doesn't answer the strictly-positive version of the question. (So it would be fine, Recursive, to de-accept it, in the hope of getting an answer to the edited question.) – Joel David Hamkins Jul 27 '11 at 15:31 Ok I've re-edited, now the statement should be ok with my intended interpretation of the problem. Your counterexample answer my question. Thank you! – Carlo Jul 27 '11 at 16:57	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9870564937591553, "perplexity": 298.8438675807481}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2013-48/segments/1386164929439/warc/CC-MAIN-20131204134849-00094-ip-10-33-133-15.ec2.internal.warc.gz"}
https://socratic.org/questions/what-is-the-isotope-symbol-for-an-atom-that-contain-2-protons-and-1-neutron	Chemistry Topics # What is the isotope symbol for an atom that contain 2 protons and 1 neutron? Aug 5, 2018 ""_2^3He #### Explanation: The subscript of 2 represents the two protons the superscript of 3 represents the total mass of 3 2 protons + 1 neutron = 3 amu mass. Aug 5, 2018 The isotope symbol for helium-3 is $\text{_2^3"He}$. #### Explanation: Helium-3 contains 2 protons and 1 neutron. Here's the general formula to write isotope symbols $\text{_B^A"C}$ A Represents the mass number B represents the atomic number C Represents the element symbol ##### Impact of this question 20517 views around the world	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 3, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5854322910308838, "perplexity": 3546.9973792472424}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-21/segments/1652662515501.4/warc/CC-MAIN-20220517031843-20220517061843-00035.warc.gz"}
http://mathhelpforum.com/algebra/189390-simplify-question-help.html	1. ## Simplify Question Help $y4 x3/yx6$ Okay, i have not a clue what to do here. 2. ## Re: Simplify Question Help Originally Posted by HellBunny $y4 x3/yx6$ [TEX]\frac{y^4x^3}{yx^6}[/TEX] gives $\frac{y^4x^3}{yx^6}$ $\frac{y^4x^3}{yx^6}=\frac{y^{4-1}}{x^{6-3}}$	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 4, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9902355074882507, "perplexity": 8400.232234623725}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2016-50/segments/1480698544678.42/warc/CC-MAIN-20161202170904-00412-ip-10-31-129-80.ec2.internal.warc.gz"}
https://asone.ai/polymath/index.php?title=Correlation.tex&oldid=1770	# Correlation.tex \section{Line-free sets correlate with insensitive set intersections} In this section we make rigorous the argument described in Section~\ref{sec:outline-corr}; we show that a dense subset $A$ either contains a combinatorial line, or it has slight correlation with a union of $ab$-insensitive sets. \noteryan{I think it would be good to go through the paper and soften explicit constants to $O(\cdot)$'s, for readability. } First we reduce to the case where the set is dense under both $\eqs{k}$ and $\eqs{k-1}$. \begin{lemma} \label{lem:32} Let $k \geq 3$, suppose $A \subseteq [k]^n$ satisfies $\eqs{k}(A) \geq \delta$, and let $\theta$ satisfy $10 k \frac{\ln n}{\sqrt{n}} \leq \theta \leq \delta.$ Then there exists a restriction $(J, x_\barJ)$ with $\abs{J} \geq (\theta/5k) \sqrt{n}$ such that one of the following two conditions holds: \begin{enumerate} \item \label{eqn:lem32_1} $\eqs{k}^J(A_{x_\barJ}) \geq \delta + \theta$; or, \item \label{eqn:lem32_2} both $\eqs{k}^J(A_{x_\barJ}) \geq \delta - 3\theta^{1/4}\delta^{1/2}$ and $\eqs{k-1}^J(A_{x_\barJ}) \geq \delta - 3\theta^{1/2}$. \end{enumerate} \end{lemma} \begin{proof} Let $r = \lceil (\theta/5k) \sqrt{n} \rceil$. As in Lemma~\ref{lem:distributions}, let $J$ be an $[r,4r]$-random subset of $[n]$ and let $x$ be drawn from $\eqs{k}^{\barJ}$. If $\Ex_{J, x}[\eqs{k}(A_{x})^2] \geq (\delta + \theta)^2$, then there must exist some restriction $(J,x)$ with $\abs{J} \geq r$ and $\eqs{k}^J(A_{x}) \geq \delta + \theta$. In this case, conclusion~\ref{eqn:lem32_1} above holds. We henceforth assume $$\label{eqn:moment} \Ex_{J, x}[\eqs{k}(A_{x})^2] < (\delta + \theta)^2$$ and show that conclusion~\ref{eqn:lem32_2} holds. \ignore{Let $y$ be drawn from $\eqs{k}^{J}$, and let $z$ be drawn from $\eqs{k-1}^{J}$.} Since $\eqs{k}(A) \geq \delta$, two applications of Lemma~\ref{lem:distributions}.\ref{eqn:distrs-eqs-eqs} yield \begin{align} \Ex_{J, x}[\eqs{k}(A_{x})] & \geq \delta - 4kr/\sqrt{n} \geq \delta - \theta \label{eqn:mean3} \\ \Ex_{J, x}[\eqs{k-1}(A_{x})] & \geq \delta - 4kr/\sqrt{n} \geq \delta - \theta, \label{eqn:mean2} \end{align} where we've used our definition of $r$ (and the hypothesis $\theta \geq (10 k \ln n)/\sqrt{n}$ ensures that $r \geq 2 \ln n$ as required for the lemma.) Combining~\eqref{eqn:moment}, \eqref{eqn:mean3} gives $\Varx_{J,x}[\eqs{k}(A_{x})] < (\delta + \theta)^2 - (\delta - \theta)^2 = 4 \theta \delta.$ Thus Chebyshev's inequality implies that except with probability at most $\theta^{1/2}$ over the choice of $(J,x)$, we have that $\eqs{k}(A_x)$ is within $\theta^{-1/4} \cdot (4 \theta \delta)^{1/2} = 2 \theta^{1/4} \delta^{1/2}$ of its expectation. When this happens, $$\label{eqn:conc2a} \eqs{k}(A_x) \geq \delta - \theta - 2 \theta^{1/4} \delta^{1/2} \geq \delta - 3 \theta^{1/4} \delta^{1/2}$$ (using $\theta \leq \delta$). On the other hand, from~\eqref{eqn:mean2} we immediately deduce that with probability at least $2\theta^{1/2}$ over the choice of $(J,x)$ we have $$\label{eqn:conc2b} \eqs{k-1}(A_{x}) \geq \delta - \theta - 2 \theta^{1/2} \geq \delta - 3\theta^{1/2}.$$ Thus with probability at least $2\theta^{1/2} - \theta^{1/2} > 0$ over the choice of $(J,x)$, we have both~\eqref{eqn:conc2a}, \eqref{eqn:conc2b}, establishing conclusion~\ref{eqn:lem32_2} of the lemma. \end{proof} We now come to the main theorem in this section, deducing a key step in the proof of DHJ($k$) from the probabilistic DHJ($k-1$) theorem. \begin{theorem} \label{thm:correlate} Let $k \geq 3$ and suppose we have established the probabilistic DHJ($k-1$) theorem. Further suppose $A \subseteq [k]^n$ has $\ens{k}(A) \geq \delta_k$ and $\ens{k-1}(A) \geq \delta_{k-1}$. Finally, assume $n \geq \Pdhj{k-1}{\delta_{k-1}}$. Then either $A$ contains a combinatorial line (of length $k$), or there exists $B \subseteq [k]^n$ with $\ens{k}(B) \geq \delta_k$ and $\frac{\ens{k}(A \cap B)}{\ens{k}(B)} \geq \delta_k + \delta_k \cdot \pdhj{k-1}{\delta_{k-1}}$ such that $B = B_{1} \cup B_2 \cup \cdots \cup B_{k-1},$ where for each $a \in [k-1]$, $B_a$ is $ak$-insensitive. \end{theorem} \begin{proof} For $a \in [k-1]$, let $L_a = \{x \in [k]^n : \chg{x}{k}{a} \in A\}$, an $ak$-insensitive set. Let $L = L_1 \cap L_2 \cap \cdots \cap L_{k-1}$. In other words, $L$ is the set line templates over $[k-1]^n$ (possibly degenerate) whose corresponding lines are entirely in $A$. Let $L' \subseteq L$ be the nondegenerate such line templates; i.e., $L' = \{x \in L : \exists j \in [n] \text{ s.t.\ } x_j = k\}$. Note that $\ens{k}(L \setminus L') = 0$. The key observation is that if $A \cap L' \neq \emptyset$, we have a (nondegenerate) combinatorial line of length~$k$ entirely in $A$. So assume otherwise; hence $A \subseteq \overline{L'} = [k]^n \setminus L'$. Since $\ens{k-1}(A) \geq \delta_{k-1}$ and $n \geq \Pdhj{k-1}{\delta_{k-1}}$, the probabilistic DHJ($k-1$) theorem implies that $\ens{k}(L') = \ens{k}(L) \geq \pdhj{k-1}{\delta_{k-1}}$. It follows that $\frac{\ens{k}(A \cap \overline{L})}{\ens{k}(\overline{L})} = \frac{\ens{k}(A \cap \overline{L'})}{\ens{k}(\overline{L'})} = \frac{\eqs{k}(A)}{\eqs{k}(\overline{L'})} \geq \frac{\delta_k}{1 - \pdhj{k-1}{\delta_{k-1}}} \geq \delta_k + \delta_k \cdot \pdhj{k-1}{\delta_{k-1}}.$ The proof is completed by taking $B = \overline{L}$; this has $\ens{k}(B) = \ens{k}(\overline{L'}) \geq \delta_k$ because $\overline{L'} \supseteq A$. \end{proof} We will prefer to obtain this relative density increment under the uniform distribution, rather than under equal-nondegenerate-slices: \begin{lemma} \label{lem:back-to-uniform} Suppose $A \subseteq B \subseteq [k]^n$ satisfy $\ens{k}(B) = \beta$ and $\ens{k}(A) \geq \delta \cdot \ens{k}(B)$. Let $0 < \eta < 3\delta$ be a parameter, define $r = (\beta \eta /15k) \sqrt{n}$, and assume $2\ln n \leq r \leq n/2$. Then there exists a restriction $(J,x_{\barJ})$ with $\abs{J} \geq r$ under which $\unif_k(B_{x_\barJ}) \geq (\eta/3) \beta$ and $\unif_k(A_{x_\barJ}) \geq (\delta - \eta) \unif_k(B_{x_\barJ})$.\noteryan{And if $B$ was a union of $ij$-insensitive sets before\dots} \end{lemma} \begin{proof} Let $J$ be an $[r,4r]$-random subset of $[n]$, let $x \sim \eqs{k}^{\barJ}$, and let $y \sim \unif_k^J$. From Lemma~\ref{lem:distributions}, the distribution on $(x,y)$ is $(4kr/\sqrt{n})$-close to $\eqs{k}^n$. Further, from~\eqref{prop:degen} the total variation distance between $\eqs{k}^n$ and $\ens{k}^n$ is at most $k(k-1)/n \leq kr/\sqrt{n}$\noteryan{uses $k \leq \sqrt{n}$ or so}. By choice of $r$, the combined distance bound $5kr/\sqrt{n}$ is at most $(\eta/3)\beta$. We therefore have $$\label{eqn:AxBx} \Ex_{J,x}[\unif_k(A_x)] \geq \delta \beta - (\eta/3)\beta, \qquad \Ex_{J,x}[\unif_k(B_x)] \leq \beta + (\eta/3)\beta.$$ Let $H$ be the event that $\unif_k(B_x) \geq (\eta/3)\beta$. On one hand, since $A_x \subseteq B_x$ always we have $\Ex_{J,x}[\unif_k(A_x)] \leq \Ex_{J,x}[\unif_k(A_x) \mid H] \Pr[H] + (\eta/3)\beta.$ On the other hand, we have $\Ex_{J,x}[\unif_k(B_x)] \geq \Ex_{J,x}[\unif_k(B_x) \mid H] \Pr[H].$ Combining these two deductions with~\eqref{eqn:AxBx} yields $\Ex_{J,x}[\unif_k(B_x) \mid H] \Pr[H] \leq \beta(1+\eta/3), \qquad (\delta - 2\eta/3)\beta \leq \Ex_{J,x}[\unif_k(A_x) \mid H] \Pr[H].$ Thus $\frac{\delta - 2\eta/3}{1+\eta/3} \cdot \Ex_{J,x}[\unif_k(B_x) \mid H] \Pr[H] \leq \Ex_{J,x}[\unif_k(A_x) \mid H] \Pr[H],$ whence $0 \leq \Ex_{J,x}[\unif_k(A_x) - (\delta - \eta)\unif_k(B_x) \mid H],$ where we used $(\delta - 2\eta/3)/(1+\eta/3) \geq \delta - \eta$. Thus there exist some $(J,x)$ where $H$ occurs and also $\unif_k(A_x) \geq (\delta - \eta) \unif_k(B_x)$, completing the proof. \end{proof} Finally, the set $B$ we get from Theorem~\ref{thm:correlate} is a union of insensitive sets; we would prefer an intersection: \begin{lemma} \label{lem:switch} Suppose $B = B_1 \cup B_2 \cup \cdots B_{k-1} \subseteq [k]^n$, where $B_a$ is $ak$-insensitive. Then $B$ is a disjoint union of $k-1$ sets $C_1, \dots, C_{k-1}$, where $C_b$ is an intersection of $ak$-insensitive sets, $a = 1 \dots b$. \end{lemma} \begin{proof} Take $C_b = B_b \setminus (B_1 \cup \cdots \cup B_{b-1})$. \end{proof}	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 2, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 1, "equation": 4, "x-ck12": 0, "texerror": 0, "math_score": 0.9998530149459839, "perplexity": 205.44358099217698}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-24/segments/1590347415315.43/warc/CC-MAIN-20200601071242-20200601101242-00483.warc.gz"}
https://aviation.stackexchange.com/questions/2058/how-do-i-tell-a-garmin-430-not-to-exit-a-hold/2063#2063	# How do I tell a Garmin 430 not to exit a hold? Let's say that we're directly west of CATLI and have been cleared direct CATLI for the RNAV approach. We load the approach into the GNS430 and proceed direct the fix. After crossing CATLI outbound for the hold-in-lieu-of-procedure-turn, we realize that we want to stay in the hold for a few more turns. How do I tell the 430 that I don't want it to sequence to ZAMGI upon arrival at CATLI?	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5368647575378418, "perplexity": 2272.8497776845375}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-05/segments/1642320305242.48/warc/CC-MAIN-20220127072916-20220127102916-00520.warc.gz"}
http://mathhelpforum.com/calculus/82096-transformation.html	# Math Help - Transformation 1. ## Transformation (2x)d2t/dx2 - 6(dx/dt)^2 = x^2 - 3x^4 show that the substitution y=1/x^2 transforms this differential eqn into d2y/dt2 + y = 3 So i've work out -2/x^3(d2x/dt2) + 6/x^4(dx/dt) i think the latter part of this eqn is wrong as the mark scheme says it's 6/x^4(dx/dt)^2 Can anyone explain this? 2. Originally Posted by Erghhh (2x)d2t/dx2 - 6(dx/dt)^2 = x^2 - 3x^4 show that the substitution y=1/x^2 transforms this differential eqn into d2y/dt2 + y = 3 So i've work out -2/x^3(d2x/dt2) + 6/x^4(dx/dt) i think the latter part of this eqn is wrong as the mark scheme says it's 6/x^4(dx/dt)^2 Can anyone explain this? Sure $y = x^{-2}$ so $\frac{dy}{dt} = -2x^{-3} \frac{dx}{dt}$. Thus, $\frac{d^2y}{dt^2} = \frac{d}{dt} \left(-2x^{-3} \frac{dx}{dt}\right) = 6x^{-4} \underbrace{\frac{dx}{dt} \cdot \frac{dx}{dt}}_{ \dot{x}^2 } -2x^{-3} \frac{d^2x}{dt^2}$	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 3, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9687358736991882, "perplexity": 3906.7509289600093}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-15/segments/1397609535775.35/warc/CC-MAIN-20140416005215-00462-ip-10-147-4-33.ec2.internal.warc.gz"}
http://mathhelpforum.com/advanced-applied-math/53818-strain-gauge-mechanics.html	Math Help - Strain Gauge Mechanics 1. Strain Gauge Mechanics I have some strain gauge calculations to complete to produce a mohr-coloumn circle for rock mechanics, but I seem to be missing a trick with completing the initial calculations. To be honest, the application probably doesn't matter as the bit I'm stuck on is more a rearrangement of equations. Q is the radius of the circle which is what I am trying to find, along with E1 and E2 to produce the circle. The example I have runs through as follows: Q.Cos 2θ = -363 Q.Sin 2θ = -90.64 Q2 = Q2.Sin2 2θ+ Q2Cos2 2θ = 131769+8215.61 Q = 374.15 The 2's in green are to represent squared symbols as I can't produce an elevated 2 in the message composition box. I have calculated Q.Cos 2θ and Q.Sin 2θ for my problem, but can't figure out how to get Q2.Sin2 2θ+ Q2Cos2 2θ as eveything is squared apart from 2θ. Am I missing something obvious?! All help would be greatly appreciated. 2. I found a way of solving the above using the following, but I still don't get how the example sorts things through. tan2θ = 0.249 2θ = tan-1 0.249 = 13.98 θ = 7 Q.cos13.98 = -363 Q.0.970 = -363 Q= -374.2	{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8935105204582214, "perplexity": 2099.5475440509585}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2016-26/segments/1466783397797.77/warc/CC-MAIN-20160624154957-00001-ip-10-164-35-72.ec2.internal.warc.gz"}
http://ec.citizendium.org/wiki/index.php?title=Closure_(topology)&diff=34001&oldid=294165	# Difference between revisions of "Closure (topology)" Main Article Discussion Related Articles [?] Bibliography [?] Citable Version [?] This editable Main Article is under development and subject to a disclaimer. In mathematics, the closure of a subset A of a topological space X is the set union of A and all its limit points in X. It is usually denoted by ${\displaystyle {\overline {A}}}$. Other equivalent definitions of the closure of A are as the smallest closed set in X containing A, or the intersection of all closed sets in X containing A. ## Properties • A set is contained in its closure, ${\displaystyle A\subseteq {\overline {A}}}$. • The closure of a closed set F is just F itself, ${\displaystyle F={\overline {F}}}$. • Closure is idempotent: ${\displaystyle {\overline {\overline {A}}}={\overline {A}}}$. • Closure distributes over finite union: ${\displaystyle {\overline {A\cup B}}={\overline {A}}\cup {\overline {B}}}$. • The complement of the closure of a set in X is the interior of the complement of that set; the complement of the interior of a set in X is the closure of the complement of that set. ${\displaystyle (X-A)^{\circ }=X-{\overline {A}};~~{\overline {X-A}}=X-A^{\circ }.}$	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 6, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9332706928253174, "perplexity": 296.81558981210173}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 5, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-40/segments/1664030337529.69/warc/CC-MAIN-20221004215917-20221005005917-00688.warc.gz"}
https://scicomp.stackexchange.com/questions/10107/petsc-input-format-for-linear-solvers	# PETSc input format for linear solvers I’m going through some considerable effort to translate one of my codes from MATLAB. It’s a type of finite element code and I haven’t implemented the solver yet but comparing CPU times for simply assembling the global system between MATLAB and C, the latter is more than two orders of magnitude faster... Anyways, I have no idea how to use PETSc but will attempt to learn it in the next few weeks. Just reading over some code and documentation, it seems like it might be pretty hard to translate my code for PETSc. I noticed that there’s an option to read a matrix from a “file” (see here). I’m just wondering if I go through with translating my code as I’m doing now, can I just save matrix/rhs to a .dat file or something then read from there? I don’t have all that much experience with C so I don’t know if this would be difficult to do or not, especially for larger systems like I’ll have. In my code, I’ll have to solve a linear system at every Newton iteration (it’s a nonlinear system), and combine this with the fact that the problem is time-dependent. The only time in my entire code that I’ll need PETSc is for the linear solve (admittedly, it’s a lot of linear solves...). If I’m going to have to learn the syntax for PETSc now, I’d just like to know so I’m not frustrated later. On another note, I’m really surprised how much faster the code is in C so far. Maybe my MATLAB coding isn’t that efficient, but I’ve been keeping the for loops at a minimum where possible. I would recommend looking at a time-dependent example because PETSc can provide a lot more diagnostics if you formulate at that level. For example, you could use a Rosenbrock method, an additive Runge-Kutta IMEX method, or others. Some involve Newton iteration, but that is not required and is not always the best approach. To use those methods, you can start by just providing your residual function, $f(t,u)$, as in $\dot u = f(t,u)$, or alternatively, $g$ in $g(t,u,\dot u) = 0$. PETSc can automatically compute a Jacobian via coloring, and if you later decide to assemble the Jacobian for efficiency, PETSc can check whether what you assembled was correct and show you the errors. If you roll your own time integration and your own Newton, these algorithmic variants and debugging features will not be available unless you write them yourself. Your proposal to use the file system will be a huge bottleneck even in serial. It complicates the workflow greatly and will limit the methods that you can use. But if you just want to test a matrix once, you can use PetscBinaryWrite() from MATLAB and load the system and solve using src/ksp/ksp/examples/tutorials/ex10.c. • My understanding from your other question is that you have a sparse matrix. Storing that in a dense format turns an $O(n)$ algorithm into $O(n^2)$ storage, which is crippling if you want to solve larger problems. For testing, I recommend using PetscBinaryWrite() to write the sparse MATLAB matrix, plus a vector, to the file. You can use -ksp_view_solution binary:solution.petsc with the example (ex10.c), and read that with PetscBinaryRead() from MATLAB. Nov 20 '13 at 16:49 • ah, I see. I’m looking through some of the examples now. If I’m set on writing the assembly and such on my own for now, it seems that I could go through my code and translate the types for compatibility? i.e. int to PetscInt, double to PetscScalar, etc.? And same for implicit functions like malloc. I guess there’s nothing to it but to start coding a very small example. Also, I apologize for all these questions that must seem very silly; for someone just learning this gist of PETSc, the documentation is pretty dense. Nov 20 '13 at 18:25	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.45745787024497986, "perplexity": 545.2329006083587}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-43/segments/1634323585201.94/warc/CC-MAIN-20211018093606-20211018123606-00002.warc.gz"}
https://time.ekitan.com/train/TimeStation/449-48_D2.shtml	# iw SÉ{iS򕌕ʁj x̎\łB ## SÉ{iw[܂Ȃ] [HIɖ߂] x [] 48 [] 09 [] 34 [] 52 [] 20 [] 37 [] 57 [] 09 [] 24 [] 39 [] 55 [] 09 [] 24 [] 39 [] 55 [] 10 [] 24 [] 40 [] 54 [] 10 [] 24 [] 40 [] 54 [] 10 [] 24 [] 40 [] 54 [] 10 [] 24 [] 40 [] 54 [] 10 [] 24 [] 40 [] 54 [] 10 [] 24 [] 40 [] 54 [] 10 [] 24 [] 39 [] 54 [] 09 [] 25 [] 39 [] 55 [] 09 [] 25 [] 39 [] 55 [] 09 [] 25 [] 39 [] 55 [] 09 [] 25 [] 39 [] 55 [] 25 [] 55 [] 25 [] 54 [] 26 [] 53 [] 24 • EEES{ • EEES	{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9999220371246338, "perplexity": 12344.06977632163}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-05/segments/1516084890795.64/warc/CC-MAIN-20180121155718-20180121175718-00009.warc.gz"}
https://chemistry.stackexchange.com/questions/105171/will-gamma-radiation-cause-thermal-decomposition-of-sodium-bicarbonate	# Will gamma radiation cause “thermal” decomposition of sodium bicarbonate? I am conducting research for a new drug that contains powdered sodium bicarbonate, and the drug will need to be sterilized after placement into it's container/closure system. Typically, this is performed with steam, at 122.5 °C for 15 minutes, but in the case of sodium bicarbonate, this would cause decomposition: $$\ce{2 NaHCO3 → Na2CO3 + H2O + CO2}$$ The alternative is to sterilize with ionizing (gamma) radiation. Will this also cause decomposition? Any help or referral to another authority is much appreciated. • You may already be aware, but the term you're looking for is "radiolysis". A cursory Google search shows some results for bicarbonate radiolysis, but I haven't parsed anything. My instinct is that while it could theoretically cause some decomposition, almost all of the bicarbonate will remain intact in any reasonable sterilising gamma flux. Living matter is far more fragile than an inorganic salt. – Nicolau Saker Neto Dec 4 '18 at 9:14 • Long story short, don't worry: the drug will decompose way sooner than bicarbonate. – Ivan Neretin Jan 29 '20 at 13:13 There is an equilibrium between decomposition and recombination, i.e. as $$\ce{CO2}$$ is given off, it joins back to the $$\ce{Na2CO3}$$ to form $$\ce{NaHCO3}$$. $$\ce{2NaHCO3 <-->Na2CO3 + CO2}$$ So for moderate doses, given at moderate rates, it's unlikely great pressure would develop, but you'd need to test to see if the drug is degraded by decomposition products. The likely issue is the presence of any water (which can also be sourced as you noted by the heating of NaHCO3). Here is a source to quote: The radiolysis of water due to ionizing radiation results in the production of electrons, H● atoms, ●OH radicals, H3O+ ions and molecules (dihydrogen H2 and hydrogen peroxide H2O2).	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 5, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6619266867637634, "perplexity": 2645.01979735221}, "config": {"markdown_headings": true, "markdown_code": false, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-17/segments/1618038084601.32/warc/CC-MAIN-20210415065312-20210415095312-00066.warc.gz"}
http://www.zora.uzh.ch/58829/	Quick Search: Browse by: Zurich Open Repository and Archive # CMS Collaboration,; Amsler, C; Chiochia, V; Favaro, C; Verzetti, M; Snoek, H; De Visscher, S; Schmitt, A; Otyugova, P; Storey, J; Millan, B; Ivova, M; Aguiló, E (2011). Measurement of the Tau pairs production cross section in proton-proton collisions at √s =7 TeV. Physics Letters B, 700(3-4):187-206. Full text not available from this repository. View at publisher ## Abstract A measurement of the double-differential inclusive dijet production cross section in proton–proton collisions at √s = 7 TeV is presented as a function of the dijet invariant mass and jet rapidity. The data correspond to an integrated luminosity of 36 pb−1, recorded with the CMS detector at the LHC. The measurement covers the dijet mass range 0.2 TeV to 3.5 TeV and jet rapidities up to \|y\| = 2.5. It is found to be in good agreement with next-to-leading-order QCD predictions. ## Citations 27 citations in Web of Science® 37 citations in Scopus®	{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9954625964164734, "perplexity": 14601.051716071443}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2015-06/segments/1422115856087.17/warc/CC-MAIN-20150124161056-00000-ip-10-180-212-252.ec2.internal.warc.gz"}
http://hal.in2p3.fr/in2p3-00287563	# Measurement of b-jet Shapes in Inclusive Jet Production in p pbar Collisions at sqrt{s} = 1.96 TeV Abstract : We present a measurement of the shapes of b-jets using 300 pb-1 of data obtained with the upgraded Collider Detector at Fermilab (CDF II) in p pbar collisions at center of mass energy sqrt{s}=1.96 TeV. This measurement covers a wide transverse momentum range, from 52 to 300 GeV/c. Samples of heavy-flavor enhanced jets together with inclusive jets are used to extract the average shapes of b-jets. The b-jets are expected to be broader than inclusive jets. Moreover, b-jets containing a single b-quark are expected to be narrower than those containing a b bbar pair from gluon splitting. The measured b-jet shapes are found to be significantly broader than expected from the PYTHIA and HERWIG Monte Carlo simulations. This effect may arise from an underestimation of the fraction of b-jets originating from gluon splitting in these simulations. Document type : Preprints, Working Papers, ... Complete list of metadatas http://hal.in2p3.fr/in2p3-00287563 Contributor : Swarna Bassava <> Submitted on : Thursday, June 12, 2008 - 2:04:14 PM Last modification on : Wednesday, May 27, 2020 - 7:20:03 PM ### Identifiers • HAL Id : in2p3-00287563, version 1 • ARXIV : 0806.1699 ### Citation T. Aaltonen, J. Adelman, T. Akimoto, M.G. Albrow, B. Alvarez Gonzalez, et al.. Measurement of b-jet Shapes in Inclusive Jet Production in p pbar Collisions at sqrt{s} = 1.96 TeV. 2008. ⟨in2p3-00287563⟩ Record views	{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9345302581787109, "perplexity": 10677.860134157814}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 5, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-40/segments/1600400193391.9/warc/CC-MAIN-20200920031425-20200920061425-00631.warc.gz"}
http://www.zazzle.com/map+of+anguilla+postcards	Showing All Results 41 results Related Searches: panoramic, flag, language Got it! We won't show you this product again! Undo Got it! We won't show you this product again! Undo Got it! We won't show you this product again! Undo Got it! We won't show you this product again! Undo Got it! We won't show you this product again! Undo Got it! We won't show you this product again! Undo Got it! We won't show you this product again! Undo Got it! We won't show you this product again! Undo Got it! We won't show you this product again! Undo Got it! We won't show you this product again! Undo Got it! We won't show you this product again! Undo Got it! We won't show you this product again! Undo Got it! We won't show you this product again! Undo Got it! We won't show you this product again! Undo Got it! We won't show you this product again! Undo Got it! We won't show you this product again! Undo Got it! We won't show you this product again! Undo Got it! We won't show you this product again! Undo Got it! We won't show you this product again! Undo Got it! We won't show you this product again! Undo Got it! We won't show you this product again! Undo Got it! We won't show you this product again! Undo Got it! We won't show you this product again! Undo Got it! We won't show you this product again! Undo Got it! We won't show you this product again! Undo Got it! We won't show you this product again! Undo Got it! We won't show you this product again! Undo Got it! We won't show you this product again! Undo Got it! We won't show you this product again! Undo Got it! We won't show you this product again! Undo Got it! We won't show you this product again! Undo Got it! We won't show you this product again! Undo Got it! We won't show you this product again! Undo Got it! We won't show you this product again! Undo Got it! We won't show you this product again! Undo Got it! We won't show you this product again! Undo Got it! We won't show you this product again! Undo Got it! We won't show you this product again! Undo Got it! We won't show you this product again! Undo Got it! We won't show you this product again! Undo Got it! We won't show you this product again! Undo No matches for Showing All Results 41 results	{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8135697841644287, "perplexity": 4678.314440965962}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-10/segments/1394678694885/warc/CC-MAIN-20140313024454-00088-ip-10-183-142-35.ec2.internal.warc.gz"}
https://www.physicsforums.com/threads/thermodynamic-basis-of-the-exclusion-principle.336196/	# Thermodynamic Basis of the Exclusion Principle 1. Sep 10, 2009 ### Modey3 Hello, I was wondering if there has been any theoretical work regarding the thermodynamic justification of the Exclusion Principle. It is my view that all open systems proceed to the lowest free-energy state and all closed systems go to the highest entropy state. Of course, these states must be available. modey3 2. Sep 10, 2009 ### sokrates You have asked a very interesting question, but as far as I know there's no thermodynamic principle that predicts the exclusion principle. One problem of such a principle would be to be able to distinguish bosons in contrast to fermions because they don't have such an exclusion principle. So as far as thermodynamics is concerned, you cannot justify exclusion principle bringing semi-classical arguments such as "marbles" and "spheres" to model particles as commonly done in thermo., say in deriving the Boltzmann distribution function. So, others could correct me on this, but my take would be, no there isn't such easy justification, that would be wonderful if there WAS a reason though... 3. Sep 11, 2009 ### alxm It sounds too 'soft' if you ask me. AFAIK, the Pauli exclusion principle is absolute. There are no known violations of it. I'm pretty sure a violation of it would be fundamentally, mathematically at odds with QM. It's not prohibited for being too energetic, it's just not possible. 4. Sep 11, 2009 ### sokrates He asked whether there was any thermodynamical basis for the exclusion principle, because at first sight it looks fundamentally in tension with "occupation of lowest energy state" arguments from thermodynamics. Nobody was challenging the exclusion principle itself. 5. Sep 11, 2009 ### alxm Then what's the problem? The states aren't available. 6. Sep 11, 2009 ### D H Staff Emeritus The supposition arises from a misunderstanding of thermodynamics. Neither of those statements is true. There is no telling what an open system will do in general; it's open. Energy can come in or go out. A sufficiently small closed system can and has been observed to undergo violations of the second law of thermodynamics. The laws of thermodynamics are statistical rather than absolute laws. A collection of a few hundred molecules or less can easily violate the second law of thermodynamics. Up that collection by a couple of orders of magnitude in number and violations becomes highly unlikely. For a collection of 1023 molecules, the odds against a violation are effectively infinite. The exclusion principle is an absolute law. It is much deeper than the laws of thermodynamics. 7. Sep 11, 2009 ### Modey3 Open systems can exchange energy/mass with its surroundings. If left unperturbed an open system will proceed towards the lowest energy state by exchange of energy with it surroundings. Closed systems cannot exchange energy with their surroundings, but are not precluded from internally generating entropy and hence proceed to a state where entropy is at a maximum. The entropy in this case cannot decrease as energy would need to be provided, but energy can't be provided since the system is closed. I don't know what a sufficiently closed system is. In my experience there is no such thing as a truly closed system. It's more of a hypothetical assumption. 8. Sep 11, 2009 ### xepma That's a misconception again I'm afraid. Open systems are, by definition, in contact with some surrounding - for instance a small system in contact with a heat bath which has a temperature T. In that case the smaller system also tends to a (thermodynamic) state described by the temperature T. And that state is not the lowest energy state. Open systems rather tend to an equilibrium with their surrounding (temperature, chemical potential, etc). 9. Sep 12, 2009 ### Modey3 Yes of course an open system tends to equilibrium with it's surrounding. Suppose you define a temperature and chemical composition multi-dimensional energy surface which describes the particular closed system. THAT energy surface depends on the surroundings in which the open system is in contact with.	{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8721631765365601, "perplexity": 652.864969630859}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-13/segments/1521257648226.72/warc/CC-MAIN-20180323122312-20180323142312-00772.warc.gz"}
http://isiarticles.com/article/27684	دانلود مقاله ISI انگلیسی شماره 27684 عنوان فارسی مقاله # طراحی کنترل یادگیری تکراری مقاوم محدوده فرکانس محدود و تأیید تجربی کد مقاله سال انتشار مقاله انگلیسی ترجمه فارسی تعداد کلمات 27684 2013 11 صفحه PDF سفارش دهید محاسبه نشده خرید مقاله پس از پرداخت، فوراً می توانید مقاله را دانلود فرمایید. عنوان انگلیسی Robust finite frequency range iterative learning control design and experimental verification منبع Publisher : Elsevier - Science Direct (الزویر - ساینس دایرکت) Journal : Control Engineering Practice, Volume 21, Issue 10, October 2013, Pages 1310–1320 کلمات کلیدی کنترل یادگیری تکرار ی - طراحی کنترل کننده - نابرابری ماتریس خطی - کنترل مقاوم پیش نمایش مقاله #### چکیده انگلیسی Iterative learning control is an application for two-dimensional control systems analysis where it is possible to simultaneously address error convergence and transient response specifications but there is a requirement to enforce frequency attenuation of the error between the output and reference over the complete spectrum. In common with other control algorithm design methods, this can be a very difficult specification to meet but often the control of physical/industrial systems is only required over a finite frequency range. This paper uses the generalized Kalman–Yakubovich–Popov lemma to develop a two-dimensional systems based iterative learning control law design algorithm where frequency attenuation is only imposed over a finite frequency range to be determined from knowledge of the application and its operation. An extension to robust control law design in the presence of norm-bounded uncertainty is also given and its applicability relative to alternative settings for design discussed. The resulting designs are experimentally tested on a gantry robot used for the same purpose with other iterative learning control algorithms. #### مقدمه انگلیسی Many industrial systems execute a task over a finite duration, reset to the starting location and then completes this task over and over again. Each execution is known as a trial or pass and the duration the trial length. Once a trial has been completed all data generated is available to update the control signal for the next trial and thereby improve performance from trial-to-trial. This area is known as Iterative Learning Control (ILC) and since the initial work, widely credited to Arimoto, Kawamura, and Miyazaki (1984), has been an established area of control systems research and application, where one starting point for the literature is the survey papers (Ahn et al., 2007 and Bristow et al., 2006). Major application areas include robotics, with recent work in, for example (Barton & Alleyene, 2011), flexible valve actuation for non-throttled engine load control (Heinzen, Gillella, & Sun, 2011) and also a transfer from engineering to next generation healthcare for robotic-assisted upper limb stroke rehabilitation with supporting clinical trials (Freeman et al., 2009 and Freeman et al., 2012). A significant part of the currently published ILC research starts from a linear time-invariant discrete model of the system dynamics in either state-space or shift operator/transfer-function form. In this case, one way to do control law design is, since the trial duration is finite, to define super-vectors for the variables. For example, let y k(p ) be the scalar, for ease of presentation with a natural extension to the vector case, output on trial k , which is of length α<∞α<∞. Then the super-vector, for linear dynamics and systems with a nonzero first Markov parameter, is View the MathML sourceYk=[yk(0)yk(1)⋯yk(α-1)]⊤, Turn MathJax on and the ILC problem can hence be written as a system of linear difference equations with updating in k. The current trial error is the difference between the supplied reference signal and the trial output and, since the trial length is finite, trial-to-trial error convergence is independent of the state matrix. This, in turn, could lead to unacceptable along the trial dynamics. In the lifting approach, this problem can be addressed by applying a feedback control law to stabilize the system and/or improve transient performance and then design the ILC law for the controlled system. An alternative is to use a two-dimensional (2D) systems setting where ILC can be represented in this form with one direction of information propagation from trial-to-trial and the other along the trial. Given that the trial length is finite, ILC fits naturally into the repetitive process setting for analysis, where these processes (Rogers, Gałkowski, & Owens, 2007) have their origins in the mining and metal rolling industries and a substantial body of systems theory and control law design algorithms exists for them. Using the repetitive process setting, it is possible to simultaneously design a control law for trial-to-trial error convergence and along the trial performance. The method is to use a form of stability for repetitive processes that demands a bounded-input bounded-output property independent of the trial length. Control laws designed in this setting have been experimentally tested on a gantry robot replicating a robotic pick and place operation that often arises in industrial applications to which ILC is applicable (Hładowski et al., 2010 and Hładowski et al., 2012). This previous ILC design in a repetitive process setting includes a stability condition that requires frequency gain attenuation over the complete frequency range and hence, by analogy with the standard linear systems case, is a very strict condition, especially as the reference signal many only have significant frequency content over a finite range. This paper develops a new control law design method where frequency attenuation is enforced over a finite range to be decided by frequency decomposition of the reference signal. The design makes use of the generalized Kalman–Yakubovich–Popov (KYP) lemma to establish the equivalence between frequency domain inequalities over finite and/or semi-finite frequency ranges for a transfer-function and a linear matrix inequality (LMI) defined in terms of its state-space realization (Iwasaki & Hara, 2005). The resulting design algorithm is experimentally applied to the gantry robot used in Hładowski et al., 2010 and Hładowski et al., 2012, including the extension to robust design using a norm bounded uncertainty representation that offers advances not possible for the same problem in the lifted setting. The following notation is used throughout this paper. For a matrix X , X⊤X⊤ and X ⁎ denote its transpose and complex conjugate transpose respectively. The null and identity matrices with appropriate dimensions are denoted by 0 and I respectively. Moreover, the notation X≽YX≽Y (respectively X≻YX≻Y) means that the matrix X−YX−Y is positive semi-definite (respectively, positive definite). Also sym{X}sym{X} is used to denote the symmetric matrix X+X⊤X+X⊤ and X⊥X⊥ denotes the orthogonal complement of the matrix X , that is, a matrix whose columns form a basis of the nullspace of X . The symbol (⋆)(⋆) denotes block entries in symmetric matrices and ρ(·)ρ(·) denotes the spectral radius of its matrix argument, that is, if hihi, 1≤i≤h1≤i≤h, is an eigenvalue of the h×hh×h matrix H then ρ(H)=max1≤i≤h\|λi\|ρ(H)=max1≤i≤h\|λi\|. #### نتیجه گیری انگلیسی This paper has developed new results on the design and experimental verification of ILC laws for discrete linear systems in the repetitive process setting. The new design algorithm enforces a required frequency attenuation over a finite frequency range in comparison to previous results that demanded this attenuation over the entire frequency range. The results have been established by using the generalized KYP lemma to transform frequency domain inequalities over finite and/or semi-finite frequency ranges for a transfer-function to LMIs. The resulting control law has a well defined physical basis and the analysis extends to allow norm-bounded uncertainty. Experimental verification of the control law design algorithm on a gantry robot has also been undertaken with very good agreement between predicted and measured data. In comparison to design using stability along the pass (Hładowski et al., 2010) no optimization is required, i.e., maximizing the value of K2 in the control law to increase the speed of pass-to-pass error convergence. Also in this previous design a low-pass filter is added to attenuate high frequencies but is not required in this new design. It is, however, possible to include a low-pass filter with pass-band edge above 5 Hz with the aim of increasing the pass-to-pass error convergence. The previous design was completed over the entire frequency range and then the pass-band limited by adding a low-pass filer, whereas the new design limits the frequency range within the design procedure. In the new design there exists possibility that the upper frequency can be maximized, that is, extend the bandwidth and hence the resulting control law will ensure better performance by trading-off between robustness and fast convergence (performance). Also in experimental verification of the design in Hładowski et al. (2010) it was necessary to zero-phase filter the error on each trial. The robust control design in this paper avoids an issue that arises in lifted model approaches by avoiding the product of matrices that define the uncertainty. These results require much further development and comparison with alternative, such as van de Wijdeven, Donkers, and Bosgra (2011) robust control design algorithms. Further work is also required to develop the option of directly maximizing the range of frequencies over which the learning is performed. This can be done by formulating the problem as the minimization of a linear objective function under LMI constraints. خرید مقاله پس از پرداخت، فوراً می توانید مقاله را دانلود فرمایید.	{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8327975273132324, "perplexity": 1305.1188584675178}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2016-50/segments/1480698540909.75/warc/CC-MAIN-20161202170900-00483-ip-10-31-129-80.ec2.internal.warc.gz"}
https://gmatclub.com/forum/if-x-y-z-which-of-the-following-can-be-true-251261.html	GMAT Question of the Day - Daily to your Mailbox; hard ones only It is currently 16 Nov 2018, 08:07 GMAT Club Daily Prep Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email. Customized for You we will pick new questions that match your level based on your Timer History Track every week, we’ll send you an estimated GMAT score based on your performance Practice Pays we will pick new questions that match your level based on your Timer History Events & Promotions Events & Promotions in November PrevNext SuMoTuWeThFrSa 28293031123 45678910 11121314151617 18192021222324 2526272829301 Open Detailed Calendar • Free GMAT Strategy Webinar November 17, 2018 November 17, 2018 07:00 AM PST 09:00 AM PST Nov. 17, 7 AM PST. Aiming to score 760+? Attend this FREE session to learn how to Define your GMAT Strategy, Create your Study Plan and Master the Core Skills to excel on the GMAT. • GMATbuster's Weekly GMAT Quant Quiz # 9 November 17, 2018 November 17, 2018 09:00 AM PST 11:00 AM PST Join the Quiz Saturday November 17th, 9 AM PST. The Quiz will last approximately 2 hours. Make sure you are on time or you will be at a disadvantage. If x > y > z, which of the following can be true? new topic post reply Question banks Downloads My Bookmarks Reviews Important topics Author Message TAGS: Hide Tags Manager Joined: 07 Jun 2017 Posts: 174 Location: India Concentration: Technology, General Management GMAT 1: 660 Q46 V38 GPA: 3.6 WE: Information Technology (Computer Software) If x > y > z, which of the following can be true? [#permalink] Show Tags 11 Oct 2017, 21:04 1 00:00 Difficulty: 85% (hard) Question Stats: 54% (02:37) correct 46% (01:54) wrong based on 65 sessions HideShow timer Statistics If $$x > y > z$$, which of the following can be true? I. $$\frac{x}{y} >\frac{y}{z}$$ II. $$\frac{z}{x}>\frac{y}{x}$$ III. $$\frac{z}{y}>\frac{x}{y}$$ A. I only B. II only C. I and II only D. I and III only E. I, II, and III _________________ Regards, Naveen email: nkmungila@gmail.com Please press kudos if you like this post Manager Joined: 03 May 2014 Posts: 161 Location: India WE: Sales (Mutual Funds and Brokerage) If x > y > z, which of the following can be true? [#permalink] Show Tags 11 Oct 2017, 21:42 Initially, i got (I) as wrong but additional plugin helped. The process given is lengthy but could not think of any other way Plug in values Since we are given that x>y>z then x,y and can be positive, negative or fraction. This is could be question so we need one value which satisfies the given inequality. Let X=3, Y=2, & Z=1 X=-1,Y=-2, & Z=-3 X=0.8, Y=0.5, & Z=0.2 X=1, Y=1/3, & Z=1/4. I. $$\frac{x}{y}$$>$$\frac{y}{z}$$=(1)/(1/3)>(1/3)/(1/4) or 3>(4/3)-possible II. $$\frac{z}{x}$$>$$\frac{y}{x}$$=(-3)/(-1)>(-2)/(-1) or 3>2-possible III. $$\frac{z}{y}$$>$$\frac{x}{y}$$=(-3)/(-2)>(-1)/(-2) or 3/2>1/2 or 1.5>0.5-possible. E is the answer If x > y > z, which of the following can be true? &nbs [#permalink] 11 Oct 2017, 21:42 Display posts from previous: Sort by If x > y > z, which of the following can be true? new topic post reply Question banks Downloads My Bookmarks Reviews Important topics Powered by phpBB © phpBB Group \| Emoji artwork provided by EmojiOne Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.33296453952789307, "perplexity": 9925.195881534672}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-47/segments/1542039743105.25/warc/CC-MAIN-20181116152954-20181116174954-00283.warc.gz"}
https://hal.in2p3.fr/in2p3-00799961	# Search for supersymmetry in hadronic final states with missing transverse energy using the variables AlphaT and b-quark multiplicity in pp collisions at 8 TeV Abstract : An inclusive search for supersymmetric processes that produce final states with jets and missing transverse energy is performed in pp collisions at a centre-of-mass energy of 8 TeV. The data sample corresponds to an integrated luminosity of 11.7 inverse femtobarns collected by the CMS experiment at the LHC. In this search, a dimensionless kinematic variable, AlphaT, is used to discriminate between events with genuine and misreconstructed missing transverse energy. The search is based on an examination of the number of reconstructed jets per event, the scalar sum of transverse energies of these jets, and the number of these jets identified as originating from bottom quarks. No significant excess of events over the standard model expectation is found. Exclusion limits are set in the parameter space of simplified models, with a special emphasis on both compressed-spectrum scenarios and direct or gluino-induced production of third-generation squarks. Document type : Journal articles http://hal.in2p3.fr/in2p3-00799961 Contributor : Sylvie Flores Connect in order to contact the contributor Submitted on : Wednesday, March 13, 2013 - 7:24:51 AM Last modification on : Monday, March 28, 2022 - 9:39:18 AM ### Citation S. Chatrchyan, M. Besançon, S. Choudhury, F. Couderc, M. Dejardin, et al.. Search for supersymmetry in hadronic final states with missing transverse energy using the variables AlphaT and b-quark multiplicity in pp collisions at 8 TeV. European Physical Journal C: Particles and Fields, Springer Verlag (Germany), 2013, 73, pp.2568. ⟨10.1140/epjc/s10052-013-2568-6⟩. ⟨in2p3-00799961⟩ Record views	{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9715092182159424, "perplexity": 2775.6343823798816}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-33/segments/1659882572304.13/warc/CC-MAIN-20220816120802-20220816150802-00628.warc.gz"}
https://jerrington.me/posts/2016-05-02-neovim-terminal-quicknav.html	# Quick navigation with Neovim terminals Posted on May 2, 2016 I’ve recently started using Neovim as a substitute for tmux on OSX. (On Linux I just use Xmonad to lay out terminals, but I’ve got to say that the integrated experience that comes from using terminals within vim is really nice.) The new terminal buffers are pretty impressive, but one thing they lack out of the box is decent navigation. ## Neovim terminal theory The terminal emulator support in Neovim works in the following way. First, a new kind of buffer is introduced, called a terminal buffer. We can programmatically determine whether the current buffer is a terminal buffer by comparing the value of the buftype setting with the string 'terminal'. if &buftype ==# 'terminal' echo 'The buffer is a terminal.' endif Terminal buffers are not modifiable, so commands that delete text won’t work. Second, a new kind of input mode is introduced, called terminal mode. Terminal mode is essentially insert mode, but there are some differences. 1. Instead of --INSERT--, the input mode indicator reads --TERMINAL--. This difference doesn’t really matter, but it’s a difference nonetheless. 2. A whole new family of mapping commands is added; they start with the letter t, e.g. tnoremap. 3. By default, the way to exit terminal mode is only with the sequence <C-\><C-n>. (This sequence can in fact be used to go to normal mode from any mode.) First, since in order to change windows in vim I have <C-j> mapped to <C-w><C-j>, it would be nice if pressing <C-j> did the same in terminal windows. tnoremap <C-h> <C-\><C-n><C-h> tnoremap <C-j> <C-\><C-n><C-j> tnoremap <C-k> <C-\><C-n><C-k> tnoremap <C-l> <C-\><C-n><C-l> Already this is pretty good, but an invariant I had grown accustomed to is now broken: <C-h> followed by <C-l> is no longer a no-op! Enter terminal mode in a terminal buffer, and press <C-h> followed by <C-l>; we’ve returned to the terminal buffer we were in (assuming there are no horizontal splits), but we’re now in normal mode. A simple fix is to make vim automatically enter terminal mode when entering a window that’s viewing a terminal buffer. We can use an autocommand for this. autocmd WinEnter * \ if &buftype ==# 'terminal' \| \ startinsert \| \ endif This solution is somewhat dissatisfying when moving between tabs though. Suppose you move to the next tab, and the window that has focus in that tab is viewing a terminal buffer. Then this autocommand will cause vim to enter terminal mode in that window. This means that you need to exit terminal mode before being able to change tabs again. If you know a solution to this, please let me know.	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.3371417224407196, "perplexity": 3499.8690833622595}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-47/segments/1542039744381.73/warc/CC-MAIN-20181118135147-20181118161147-00193.warc.gz"}
https://xianblog.wordpress.com/2011/10/06/that-the-likelihood-principle-does-not-hold/comment-page-1/	## That the likelihood principle does not hold… Coming to Section III in Chapter Seven of Error and Inference, written by Deborah Mayo, I discovered that she considers that the likelihood principle does not hold (at least as a logical consequence of the combination of the sufficiency and of the conditionality principles), thus that Allan Birnbaum was wrong…. As well as the dozens of people working on the likelihood principle after him! Including Jim Berger and Robert Wolpert [whose book sells for \$214 on amazon!, I hope the authors get a hefty chunk of that ripper!!! Esp. when it is available for free on project Euclid…] I had not heard of (nor seen) this argument previously, even though it has apparently created enough of a bit of a stir around the likelihood principle page on Wikipedia. It does not seem the result is published anywhere but in the book, and I doubt it would get past a review process in a statistics journal. [Judging from a serious conversation in Zürich this morning, I may however be wrong!] The core of Birnbaum’s proof is relatively simple: given two experiments and about the same parameter θ with different sampling distributions and , such that there exists a pair of outcomes (y¹,y²) from those experiments with proportional likelihoods, i.e. as a function of θ $f^1(y^1\|\theta) = c f^2(y^2\|\theta),$ one considers the mixture experiment E⁰ where and are each chosen with probability ½. Then it is possible to build a sufficient statistic T that is equal to the data (j,x), except when j=2 and x=y², in which case T(j,x)=(1,y¹). This statistic is sufficient since the distribution of (j,x) given T(j,x) is either a Dirac mass or a distribution on {(1,y¹),(2,y²)} that only depends on c. Thus it does not depend on the parameter θ. According to the weak conditionality principle, statistical evidence, meaning the whole range of inferences possible on θ and being denoted by Ev(E,z), should satisfy $Ev(E^0, (j,x)) = Ev(E^j,x)$ Because the sufficiency principle states that $Ev(E^0, (j,x)) = Ev(E^0,T(j,x))$ this leads to the likelihood principle $Ev(E^1,y^1)=Ev(E^0, (j,y^j)) = Ev(E^2,y^2)$ (See, e.g., The Bayesian Choice, pp. 18-29.) Now, Mayo argues this is wrong because “The inference from the outcome (Ej,yj) computed using the sampling distribution of [the mixed experiment] E⁰ is appropriately identified with an inference from outcome yj based on the sampling distribution of Ej, which is clearly false.” (p.310) This sounds to me like a direct rejection of the conditionality principle, so I do not understand the point. (A formal rendering in Section 5 using the logic formalism of A’s and Not-A’s reinforces my feeling that the conditionality principle is the one criticised and misunderstood.) If Mayo’s frequentist stance leads her to take the sampling distribution into account at all times, this is fine within her framework. But I do not see how this argument contributes to invalidate Birnbaum’s proof. The following and last sentence of the argument may bring some light on the reason why Mayo considers it does: “The sampling distribution to arrive at Ev(E⁰,(j,yj)) would be the convex combination averaged over the two ways that yj could have occurred. This differs from the sampling distributions of both Ev(E1,y1) and Ev(E2,y2).” (p.310) Indeed, and rather obviously, the sampling distribution of the evidence Ev(E,z) will differ depending on the experiment. But this is not what is stated by the likelihood principle, which is that the inference itself should be the same for and . Not the distribution of this inference. This confusion between inference and its assessment is reproduced in the “Explicit Counterexample” section, where p-values are computed and found to differ for various conditional versions of a mixed experiment. Again, not a reason for invalidating the likelihood principle. So, in the end, I remain fully unconvinced by this demonstration that Birnbaum was wrong. (If in a bystander’s agreement with the fact that frequentist inference can be built conditional on ancillary statistics.) ### 29 Responses to “That the likelihood principle does not hold…” 1. […] has started a series of informal seminars at the LSE on the philosophy of errors in statistics and the likelihood principle. and has also posted a long comment on my argument about only using wrong models. (The title is […] 2. I am finally getting time to check up on blog discussions that I was unable to even read, let alone comment on, in the past. I need to correct a serious misimpression, unless it is just a very different use of language. Roberts wrote: xi’an Says: October 16, 2011 at 5:38 pm Just an addendum on “the distribution of the inference”: as read today in Error and Inference (page 310), Deborah Mayo uses the sentence “This differs from the sampling distributions of both InfrE’ (y‘) and InfrE” (y”). Which seems to indicate she also considers inference has a distribution. The sampling distribution is the distribution of the (test) statistic. A frequentist has no inference without consideration of the sampling distribution of a (relevant) statistic. That is because without it there are no error probabilities. The sampling distributions I am referring to are the ones associated with the inferences that would be the outputs of these two observed outcomes from the two distinct experiments, E’ and E”, respectively. 3. I am finally getting time to check up on blog discussions that I was unable to even read, let alone comment on, in the past. I need to correct a serious misimpression, unless it is just a very different use of language. Roberts wrote: xi’an Says: October 16, 2011 at 5:38 pm Just an addendum on “the distribution of the inference”: as read today in Error and Inference (page 310), Deborah Mayo uses the sentence “This differs from the sampling distributions of both InfrE’ (y‘) and InfrE” (y”). Which seems to indicate she also considers inference has a distribution. The sampling distribution is the distribution of the (test) statistic. A frequentist has no inference without consideration of the sampling distribution of a (relevant) statistic. That is because without it there are no error probabilities. The sampling distributions I am referring to are the ones associated with the inferences that would be the outputs of these two observed outcomes from the two distinct experiments, E’ and E”, respectively. 4. […] reminds me of earlier results, with the related drawback that this optimality is incompatible with the sufficiency principle.) […] 5. Christian Hennig Says: Could it help to define properly what kind of thing Ev is? The equation proving the LP in Xi’An’s initial posting seems to me to assume that Ev is a well-defined mathematical entity, but I’m not sure whether it is. As far as I can see, Birnbaum doesn’t define it in his original 1962 paper, but rather states that its precise meaning has to be clarified (if I haven’t missed anything, later he gives examples but doesn’t define it generally and formally). Mayo’s point seems to be that due to the imprecise nature of Ev, it apparently happened that it doesn’t have precisely the same meaning in all involved equations, in which case Birnbaum’s arguments and the equations given here don’t make a valid mathematical proof. The problem is nicely illustrated by the discussion between Spanos and Xi’An, which to me indicates that they don’t agree about what precisely Ev is. This is not surprising because it hasn’t been properly defined. So if you want agreement, what about defining it unambiguously? Deciding the issue in Birnbaum’s favour from my point of view would imply that all the steps of the proof could be spelled out replacing Ev by its precise definition as a mathematical object. Of course Ev can be defined in such a way that the equations hold (ignoring interpretational issues it could for example be a constant), but I wonder whether it can be done in such a way that the argument grants the interpretational meaning that defenders of the LP usually assume (which Mayo denies). • Thanks Christian: this is a very good point and an issue that has always bothered me. Ev appears like a black box, hence can be defined in diverse ways and even perverted to have the LP hold no matter what or not hold no matter what. For instance, if one includes all estimators AND their frequentist distribution, no hope for the LP to hold. Of course, from a Bayesian perspective, representing the evidence Ev by the equivalent posterior distribution is unambiguous but outside the Bayesian realm it seems harder to agree on an unambiguous modus vivendi. • Aris Spanos Says: That is exactly why in my first comment I wrote: “Hence, the SLP assertion that the mixed experiment provides the same evidence about the unknown parameter as the model that actually gave rise to the data, is clearly false when evidence about the unknown parameter is evaluated in terms of the relevant error probabilities.” • @Christian Hennig: I got hung up on this point too. I tried two approaches to attack the issue. First I imagined writing R functions to serve as tentative Ev functions. Right away I got hung up on R’s weak typing. When I considered a strongly typed language, or equivalently, vigorous type-checking in the R function, or yet still equivalently, the domain of Ev, I noticed that the equation for the weak conditionality principle uses (j, x) as the second argument on one side and x on the other. My Haskell-fu is not up to figuring out whether the info about the type of the second argument can legitimately be packed into the first argument of Ev. My second approach was to think about what a generic p-value function would require. In addition to a description of the experiment (including the sampling distribution under the null hypothesis) and the observed outcome, it needs a statistic mapping outcomes to a set with a total ordering corresponding to some notion of “more extreme” relative to the null. So it takes three arguments, not two. Since Ev as given in Birmbaum’s proof doesn’t consider evidence functions that have a third argument that could take different values depending on whether (j, x) is observed or T(j, x) is observed, it doesn’t seem to rule out such functions. @Spanos: In your second comment, it was you who mentioned mean squared error first, not Xian. You also don’t appear to be using the term in the same sense as statisticians use it. Given that you and Xian don’t seem to be construing the jargon the same way, perhaps some discussion of explicit definitions is in order before you begin leveling accusations of intellectually dishonest argumentation. • Birnbaum is clear that Ev can be ANY inference or decision from data. A p-value is an example he gives. That is why his “proof” flounders. Fixed and optional stopping, just for one example, yield different p-values, and no one denies this. More generally, no one denies frequentist conflicts of the (strong) LP. The Birnbaum argument is based on starting from a LP violation. That is all one needs. The invalidity or unsoundness then follows along the lines I argue. I will soon be returning to “blogging the LP” on my errorstatistics blog. 6. The point is that the “proof” first requires you imagine being in a Birnbaum experiment that ” erases” which experiment the data came from and then the second step stipulates, at the same time, that you are NOT to evaluate evidence this way. So the premises are contradictory. Not to mention one can imagine lots of different Birnbaum mixtures that could have given rise to the data, shall we average over all of them? Why would we want to obliterate evaluating data from the experiment known to produce it in order to average with a variety of experiments not performed? That is what step 1 of the argument requires. But I allow this. Only then the second step contradicts it and says condition on the experiment performed! Erase and do not erase! The reasoning is fallacious, by burying what is going on, it has been missed. It could go through ONLY if you ignore the sampling distribution in the Birnbaum mixture. But that is to ASSUME the strong LP! 7. Aris Spanos Says: I just saw the above exchange and some of xi’an’s comments mystified me. In particular, the claim: “But this is not what is stated by the likelihood principle, which is that the inference itself should be the same for y¹ and y². Not the distribution of this inference.” To begin with there is no such thing as “the distribution of the inference”, but I assume he meant to say the relevant sampling distribution underlying the inference. As is well-known, there is no frequentist inference without sampling distributions, and the two are inextricably bound up; there is no inference without a sampling distribution. In particular, confidence intervals and frequentist tests cannot even be defined without error probabilities that stem from the relevant sampling distributions. Moreover, different error probabilities give rise to different inferences. In particular, different type I and II error probabilities, as well as different p-values are likely to give rise to totally different inferences! Hence, the SLP assertion that the mixed experiment provides the same evidence about the unknown parameter in question as the model that actually gave rise to the data, is clearly false when evidence about the unknown parameter is evaluated in terms of the relevant error probabilities. That is, the warranted inferences based on y¹ and y² cannot be the same when the relevant error probabilities are different. • Thanks for the comment. Unless we put different meanings to “inference”, I maintain there is a frequentist distribution of the inference: when your estimator of the mean is $(1-(p-2)/\|\|x\|\|^2)x$ say [to take the example of the James-Stein estimator], it is a random variable with a distribution. (Which is why we distinguish estimates from estimators in our courses and textbooks.) Now, this distribution is a projection of the sampling distribution and therefore depends on this distribution. That it does not agree with the SLP is [definitely] not a proof that the “SLP assertion (…) is clearly false”, just a signal of disagreement between the SLP and frequentist constructs: Nothing wrong with that, just two different approaches to statistical inference… • Aris Spanos Says: Invoking the James-Stein estimator and the Mean Square Error (MSE) criterion seems like a desperate attempt to cling to your undefedable position by confusing the issue! In my comment I mentioned inference-related sampling distributions and the relevant error probabilities, and neither element appears in your reply. Indeed, you ignored the traditional example used in these discussions by Berger and Wolpert (1988), Mayo (2010), etc, and instead used the James-Stein estimator, knowing that it is a bad example to illustrate the SLP anyway. Leaving that aside, I hope you are not suggesting that the inference in frequentist estimation is that the unknown parameter is equal to the estimate. Are you? This is not an inference a frequentist would make, without qualifying the uncertainty pertaining to such an inference using a proper error probability. Moreover, the MSE, as used in the James-Stein estimator case, is a decision-theoretic/Bayesian criterion and does not evaluate anything interesting from the frequentist perspective; it’s neither a proper error probability nor an error a frequentist would care about. In estimation a frequentist does not care what happens to the MSE for all possible values of the unknown parameter [the decision-theoretic quantifier]. What is relevant from the frequentist perspective pertains to any errors relative to the true value of the unknown parameter, whatever that happens to be. • Please keep the debate at a rational and scientific level. Otherwise, there is no point in debating. First and last warning. To follow from my previous reply, I used the James-Stein estimator as an arbitrary example of an estimator. The MLE and the p-value would have been other examples. They all have (frequentist) distributions as transforms of the data. Now, the James-Stein estimator or the p-value have long-term error performances. This is what I call frequentist statistics. To state that the mean square error is a Bayesian criterion contradicts the definition of the MSE, namely the average of the error over the observation space. This is the average error for a infinite repetition of observing the data based on the same parameter. This is exactly the same with the type I error, namely the average frequency of false rejection. If you refuse decision-theory and the use of a loss function to compare statistical procedures, as it sounds from the above comment, how do you pick your estimation and testing procedures from the infinity of such procedures? • Aris Spanos Says: Indeed, confusing the difference between an error probability of a test statistics evaluated under the null [a prespecified value of the unknown parameter], vs. the mean of a square loss function associated with an estimator and evaluated over all possible values of the unknown parameter, I think calls for an and to the discussion. Thanks for the exchange! • I do not think we had even started a discussion… Anyway, your final barb simply shows you are missing my argument that p-values should be evaluated for all possible values of the unknown parameter rather than under the null. In Hwang et al. (Annals of Statistics, 1992), we ran this frequentist evaluation under squared error loss and showed that p-values are inadmissible for two-sided hypotheses. • Just an addendum on “the distribution of the inference”: as read today in Error and Inference (page 310), Deborah Mayo uses the sentence “This differs from the sampling distributions of both InfrE’ (y‘) and InfrE” (y”). Which seems to indicate she also considers inference has a distribution. 8. Please do not automatically accept what the “higher authorities” say; we all know this has been touted as a “breakthrough” for 50 years, no surprise to find endorsements. Frequentist theory, we know violates the (strong) LP. Right? You have observed an outcome x from experiment E’ that could be used in an LP violation (i.e the antecedent of the strong LP is assumed: x has a proportional likelihood to y from another experiment, E”, not performed; but because of the difference in sampling distributions, the evidential appraisal of x differs from that of y—for a frequentist. For example, the p-value associated with x from E’ might be p’, and the p-value associated with outcome y from E” might be p”. p’ is unequal to p”. That is the given, for an LP violation, no one disagrees on that. Call y an “LP pair” for x (it is really an “LP violation” pair). Then Birnbaum suggests you consider x could have come from flipping a fair coin to decide whether to do the experiment you actually performed E’ or another one, E”, that could have produced the “LP pair” y. (You don’t know what this could be of course until after you observe x, but let us grant all this.) Further, you are to agree that if you had conducted this imaginary mixture (I call it a Birnbaum experiment E-BB) that you will report x whether or not x occurred or y occurred. Outcome x from E-BB is evidentially equivalent to outcome y from E-BB. That is part of the given definition of E-BB, and I grant all that—weird as it is. We’re playing the E-BB game. How is the evidence from x to be reported? It would be to average p’ and p”. The evidential assessment of x is (p’ + p”)/2. All of that is “step 1” of Birnbaum’s argument. But if you are to evaluate outcome x which came from experiment E’ as if it actually came from the funny mixture defined in E-BB, then you cannot AT THE SAME TIME say that you should not evaluate the evidential import of x as if it came from E-BB. And yet, that is precisely what is demanded in “step 2” of the argument. So the argument , reconstructed as deductively valid, is unsound (it’s premises contradict eachother). Alternatively, one can formulate it so that its premises are true, but it is no longer valid. For the details, see E & I, I realize I’m writing this very quickly (that is because I promised myself I would not respond, and here I am responding). By the way, Birnbaum rejected the strong LP. So maybe he was just showing that for those who accept the LP, the LP follows. • Thank you very much for rewriting your arguments for the Og readers. I hope it generates more discussion. At this stage, I fear we could be camping on our own positions for quite a while. So I will try to find time and energy to write a small note explaining more carefully why I [respectfully] disagree. As to “automatically accept what the “higher authorities” say”, pardon my French for being imprecise in the previous reply. I simply meant that I cross-checked with others that my understanding was correct and that I was not missing an issue in my post. Sorry for the use of “higher authorities” whose lost irony turned into a poor argument of authority… 9. I don’t know why I find it so blinding to read this blog—I mean it’s beautiful, but I think it is the black. Or maybe it’s that you go too fast over what I’ve argued in detail, and dismiss too quickly some of my points. Please note, as discussed in the Cox and Mayo article in E & I, that there’s a big difference between a mathematical identity, and a claim that a given result OUGHT to be construed as evidentially equal to such and such. I don’t reject WCP, as you suppose. I only reject saying BOTH that you ought to condition AND you ought not to, for purposes of interpreting a given result. The premises are contradictory. Anyway, there’s a little dialogue (an imaginary one between me and Birnbaum I guess) coming out in the RMM volume any day now that rehearses the flawed argument. If it is still unclear after that, I will say more. • Because of the small characters on my screen, I first read “binding” instead of “blinding”! Not the same at all, of course, and a wee on the harsh side… Well, the hit-and-run deeper nature of blog posts means that ‘going too fast’ is inherent to them. In the case of the current post, I actually checked with higher authorities [on the LP] that I was not missing the point. (And I did think carefully about it.) From both of your comments, it seems to me the dissension is at the linguistic level rather than mathematical or even logical levels, in that evidence is such a vague word that the different actors in the LP=SP+WCP debate put different meanings to it. The discussion I had in Zürich on Tuesday was illuminating in this respect. 10. If you think more carefully about the argument, you will see I am correct! It is the focus of a much more detailed presentation, but even the short one in E & I should suffice. An even shorter one is in the upcoming RMM volume as an appendix to my conversation with D.R. Cox.. It should be up any day. Bayesians forget that sufficiency, for a frequentist, still requires computing the evidential appraisal relative to the sampling distribution! The series of equivalences fails. (It doesn’t matter which version of the argument you use, either.) And even without alluding to the details here—why spoil the fun for your readers?–the key that the “proof” is actually circular should have been obvious from the fact that the biconditional is shown to hold (between the SLP and (WCP and S)). This site uses Akismet to reduce spam. Learn how your comment data is processed.	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 5, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.874523937702179, "perplexity": 863.6788194761747}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-34/segments/1596439738816.7/warc/CC-MAIN-20200811150134-20200811180134-00263.warc.gz"}
https://cstheory.stackexchange.com/questions/50719/hardness-of-computing-the-dimension-of-an-integral-polytope/50724	# Hardness of computing the dimension of an integral polytope? Given a set of linear inequalities $$Ax \leq b$$ let $$P = \text{conv}\{x \in \{0,1\}^n \mid A x \leq b \}$$ be the convex hull of all binary vectors that satisfy the given inequalities. I am interested in the hardness of computing the dimension of the polytope $$P$$. Equivalently we can formulate this as the decision problem by asking whether the dimension of $$P$$ is $$m$$ for some $$0 \leq m \leq n$$. To prove that the dimension is indeed $$m$$, we need to show that 1. There are $$m+1$$ affinely independent vectors in $$P$$ which yields that the dimension is at least $$m$$. 2. There are $$n-m$$ independent equalities that are satisfied by $$P$$ which yields that the dimension is at most $$m$$. I could not find any literature that considers this problem. Also I cannot think of a reduction to or from another problem. Answer thanks to Neil Young: • Condition 1 can be checked in polynomial time while this is not obvious for Condition 2. Therefore the problem "is the dimension of $$P$$ at least $$m$$?" is in NP and similarly the problem "is the dimension at most $$m$$?" is in co-NP. • The decision problem "is $$P$$ empty?" is well known to be NP-hard. This problem can be reduced to the decision of dimension as follows: Add $$m$$ additional free variables to $$P$$ to obtain $$P'$$. Then $$P$$ is not empty iff the dimension of $$P'$$ is at least $$m$$. Therefore "is $$P$$ empty?" can be reduced to "is the dimension of $$P'$$ at least $$m$$?". Together we obtain that "is the dimension of $$P$$ at least $$m$$?" is NP-complete and as a result that "is the dimension of $$P$$ equal $$m$$?" is NP-hard. However, if we additionally assume that $$P$$ is non-empty then this reduction does not work. It is unclear to me whether the problem remains NP-complete. (Edit thanks to Neal Young: Given a feasible solution, finding a second, different, feasible solution is NP-hard. And since two different vectors are affinely independent deciding "is the dimension of $$P$$ at least $$1$$?" is NP-hard for non-empty $$P$$. Again, by adding free variables, it follows that deciding "is dimension of $$P$$ at least $$m$$?" is NP-hard even for non-empty $$P$$) Originally, my interest in this problem arose from studying the convex hull of the feasible set of an ILP corresponding to a combinatorial optimization problem. Such polytopes have some additional structure and the general "proof" from above does not hold. So my follow-up question is: Are there examples of combinatorial optimization problems where it is hard to compute the dimension of the convex hull of all feasible solutions and where the set of feasible solutions is non-empty? And related: are there examples where it is hard to decide whether a valid inequality defines a facet (maybe even where the polytope is full dimensional and the facet has dimension $$n-1$$)? • Surely it's NP-hard, because determining whether an ILP is even feasible is NP-hard. Do you know whether the decision problem "is the dimension at least $m$"? is in NP? (At first glance, you could just guess a set of vectors for Condition 1 and check them... but you'd need to know that it suffices to consider vectors with encoding size polynomial in the encoding size of $(A, b)$...) If that problem is in NP, then your problem should be in DP (expressible as the intersection of languages in NP and coNP). Nov 11, 2021 at 14:16 • In my case I was thinking about bounded polytopes, even more specifically about 01-polytopes $P \subseteq \{0,1\}^n$. In that case a certificate for Conditions 1 and 2 can clearly be encoded in polynomial size and the problem is in NP. I am not sure about unbounded polyhedra. Nov 11, 2021 at 15:38 • Also in my case the polytopes are nonempty. Maybe the hardness of the decision problem "given $k$ affinely independent vectors in $P$, does there exist an additional vector that is affinely independent of the given $k$?" can be established by a reduction from feasibility of an ILP. Thanks for the pointer. Nov 11, 2021 at 15:44 • (i) How do you verify (in NP) Condition 2 for a given set of equalities even in the 0/1 case (given that you need to check whether all integer points in P satisfy those inequalities)? The problem "Does a given ILP polytope have dimension at most $k$" seems co-NP hard, e.g. by reduction from UNSAT. (ii) By "an additional vector that..." do you mean "an additional vector in P that..."? (iii) Assuming so, the case k=0 is testing whether P is empty (NP-hard), and it seems likely that the cases k >= 1 can be reduced to from any given polytope just by adding some artificial variables... Nov 11, 2021 at 19:17 • Please edit your question to include all relevant information, such as that you are working over $\{0,1\}^n$. People shouldn't have to read the comments to understand what you are asking. – D.W. Nov 12, 2021 at 2:53 Yes, MORE-SAT, defined below, is one example of a combinatorial optimization problem for which the natural 0/1 integer linear program (ILP) is guaranteed to be feasible, and determining the dimension of the convex hull of the feasible solutions is NP-hard. Here is the definition of MORE-SAT: Given a satisfiable CNF formula, does it have more than one satisfying assignment? Lemma 1. MORE-SAT is NP-complete. We postpone the proof, which is a standard exercise. Given a MORE-SAT instance $$\phi$$, let ILP$$(\phi)$$ represent its ILP formulation via the standard ILP for CNF-SAT. Then the number of satisfying assignments to $$\phi$$ equals the number of feasible points in ILP$$(\phi)$$, so ILP$$(\phi)$$ is guaranteed to be feasible, and it has more than one feasible solution iff $$\phi$$ has more than one satisfying assignment. So it is NP-hard to determine whether the dimension of the convex hull of the feasible points of ILP$$(\phi)$$ is at least 1. Note that it follows that the following problem is NP-hard: Given a feasible 0/1 integer linear program, does it have more than one feasible solution? Proof sketch for Lemma 1. Here is a reduction from CNF-SAT. Given a CNF-SAT instance $$\phi$$, let $$x_i$$ denote its $$i$$th variable and $$C_i$$ denote its $$i$$th clause. Introduce a new variable $$y$$, and define MORE-SAT instance $$\phi' = C'_1 \wedge C'_2 \wedge \cdots \wedge C'_m \wedge D_1 \wedge D_2 \wedge \cdots \wedge D_n$$ where $$C'_i = C_i \vee y$$ (for each clause $$C_i$$ of $$\phi)$$ and $$D_i = x_i \vee \overline y$$ (for each variable $$x_i$$ of $$\phi$$). Then setting $$x_1 = x_2 = \cdots = x_n = y =$$ true gives one satisfying assignment to $$\phi'$$, and the satisfying assignments with $$y=$$ false are exactly those where the assignment to $$x$$ satisfies $$\phi$$. So the number of satisfying assignments for $$\phi'$$ is exactly one more than the number for $$\phi$$. In particular, $$\phi'$$ is satisfiable, and it has more than one satisfying assignment iff $$\phi$$ is satisfiable. $$~~~\Box$$ Remark 1. Given that there are apparently parsimonious polynomial-time reductions from CNF-SAT to most other "natural" NP-complete problems, it follows that, for those other NP-complete problems, the problem of determining whether there is more than one solution (even when there is guaranteed to be at least one) is NP-hard, and likewise for the natural ILP formulations of many of those problems, determining whether the dimension is at least 1 (even when the ILP is guaranteed to be feasible) is NP-hard. Remark 2. It seems an easy exercise to generalize this to show that the following problem is NP-hard for any given $$k\ge 0$$: Given a 0/1 ILP such that the convex hull $$P$$ of its feasible solutions has dimension at least $$k$$, does $$P$$ have dimension at least $$k+1$$? (Reduce from CNF-SAT. Given $$\phi$$, apply the reduction in Lemma 1 to obtain MORE-SAT instance $$\phi'$$, and let $$\pi$$ be the standard ILP for $$\phi'$$. Then obtain ILP $$\pi'$$ from $$\pi$$ by adding $$k$$ new unconstrained 0/1 variables $$Z_1, Z_2, \ldots, Z_{k}$$. Then $$\pi'$$ will have $$2^{k}$$ solutions with $$X_1 = \cdots = X_n = Y=$$ 1 and the $$Z$$'s set arbitrarily, and these solutions have dimension $$k$$. And $$\phi$$ is satisfiable iff $$\pi'$$ has additional solutions with $$Y=0$$, which happens iff the dimension strictly exceeds $$k$$...)	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 90, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9364189505577087, "perplexity": 183.34622807674603}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-40/segments/1664030335504.22/warc/CC-MAIN-20220930181143-20220930211143-00500.warc.gz"}
http://www.brics.dk/RS/01/44/index.html	Predicate Abstraction for Dense Real-Time Systems M. Oliver Möller Harald Rueß Maria Sorea November 2001 ### Abstract: We propose predicate abstraction as a means for verifying a rich class of safety and liveness properties for dense real-time systems. First, we define a restricted semantics of timed systems which is observationally equivalent to the standard semantics in that it validates the same set of -calculus formulas without a next-step operator. Then, we recast the model checking problem for a timed automaton and a -calculus formula in terms of predicate abstraction. Whenever a set of abstraction predicates forms a so-called basis, the resulting abstraction is strongly preserving in the sense that validates iff the corresponding finite abstraction validates this formula . Now, the abstracted system can be checked using familiar -calculus model checking. Like the region graph construction for timed automata, the predicate abstraction algorithm for timed automata usually is prohibitively expensive. In many cases it suffices to compute an approximation of a finite bisimulation by using only a subset of the basis of abstraction predicates. Starting with some coarse abstraction, we define a finite sequence of refined abstractions that converges to a strongly preserving abstraction. In each step, new abstraction predicates are selected nondeterministically from a finite basis. Counterexamples from failed -calculus model checking attempts can be used to heuristically choose a small set of new abstraction predicates for refining the abstraction Available as PostScript, PDF.	{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9680516123771667, "perplexity": 1571.9180197666426}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-05/segments/1516084887600.12/warc/CC-MAIN-20180118190921-20180118210921-00763.warc.gz"}
http://mathhelpforum.com/calculus/82499-wierd-product-contour-integral.html	## Wierd product contour integral I was wondering if anyone could tell me something about this contour integral i ran into it and i have no idea what it is any info on it would be nice. ${\oint\oint\oint}_{lim_{k\rightarrow0}e^{-ki}}^{\infty}\prod_{k=1}^{\infty}tanh^{-1}\theta d\theta$ That is supposed to be a volume contour integral (not sure how to do that) thanks!	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 1, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9610649943351746, "perplexity": 179.7082244320076}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-35/segments/1408500823598.56/warc/CC-MAIN-20140820021343-00201-ip-10-180-136-8.ec2.internal.warc.gz"}
https://www.mathdoubts.com/cos-angle-sum-identity/	Cosine angle sum identity Formula $(1).\,\,$ $\cos{(a+b)}$ $\,=\,$ $\cos{a}\cos{b}$ $-$ $\sin{a}\sin{b}$ $(2).\,\,$ $\cos{(x+y)}$ $\,=\,$ $\cos{x}\cos{y}$ $-$ $\sin{x}\sin{y}$ Introduction Let us consider that $a$ and $b$ are two variables, which denote two angles. The sum of two angles is written as $a+b$, which is actually a compound angle. The cosine of a compound angle $a$ plus $b$ is expressed as $\cos{(a+b)}$ in trigonometry. The cosine of sum of angles $a$ and $b$ is equal to the subtraction of the product of sines of both angles $a$ and $b$ from the product of cosines of angles $a$ and $b$. $\cos{(a+b)}$ $\,=\,$ $\cos{a} \times \cos{b}$ $-$ $\sin{a} \times \sin{b}$ This mathematical equation is called the cosine angle sum trigonometric identity in mathematics. Usage The cosine angle sum identity is used in two different cases in trigonometric mathematics. Expansion The cosine of sum of two angles is expanded as the subtraction of the product of sines of angles from the product of cosines of angles. $\implies$ $\cos{(a+b)}$ $\,=\,$ $\cos{(a)}\cos{(b)}$ $-$ $\sin{(a)}\sin{(b)}$ Simplification The subtraction of the product of sines of angles from the product of cosines of angles is simplified as the cosine of sum of two angles. $\implies$ $\cos{(a)}\cos{(b)}$ $-$ $\sin{(a)}\sin{(b)}$ $\,=\,$ $\cos{(a+b)}$ Forms The angle sum identity in cosine function can be expressed in several forms but the following are some popularly used forms in the world. $(1).\,\,$ $\cos{(A+B)}$ $\,=\,$ $\cos{A}\cos{B}$ $-$ $\sin{A}\sin{B}$ $(2).\,\,$ $\cos{(x+y)}$ $\,=\,$ $\cos{x}\cos{y}$ $-$ $\sin{x}\sin{y}$ $(3).\,\,$ $\cos{(\alpha+\beta)}$ $\,=\,$ $\cos{\alpha}\cos{\beta}$ $-$ $\sin{\alpha}\sin{\beta}$ Proof Learn how to derive the cosine of angle sum trigonometric identity by a geometric method in trigonometry. Email subscription Math Doubts is a best place to learn mathematics and from basics to advanced scientific level for students, teachers and researchers. Know more	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9713530540466309, "perplexity": 234.5383396124563}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-04/segments/1610703518240.40/warc/CC-MAIN-20210119103923-20210119133923-00761.warc.gz"}
https://electronics.stackexchange.com/questions/452903/sound-to-voltage	# sound to voltage I'm searching for a method that can convert sound to voltage. I have a .wav format file. The .wav file format is 16bit and 44kHz sampling rate. I want to play the .wav file on my PC and convert PC wav data to voltage and see the electric signal on an oscilloscope. Is there another method to convert sound to voltage? Does the aux connector have + and - pin? If aux connector has Vcc,Gnd pins, must it have a voltage amplifier? • That's about the easiest way there is. Sound card out, and into the oscilloscope. I do this all the time for various things. No amplifier at all. The aux out has more than enough signal to see on the scope. – JRE Aug 14 '19 at 6:20 • JRE ) HI, Thanks to reply. But I don't have Sound Card. Is there a way to measure voltage only Aux? – sgb Aug 14 '19 at 6:28 • I don't have Sound Card ... what do you have? – jsotola Aug 14 '19 at 6:47 • But I don't have Sound Card. In your case it might not be a separate card, but integrated into the PC's motherboard. Does your PC have an AUX or headphone output? Then it does have a sound card, it might be part of the motherboard but that does not matter. – Bimpelrekkie Aug 14 '19 at 6:47 • Oh! Aux cable has gnd and right left signal! I catch the audio signal! Thanks you every one! – sgb Aug 14 '19 at 7:34 Your sound file on your computer is a set of data that represents different voltages over time induced by vibrations in a medium. Image Credit: GCSE Physics When you connect a microphone to your computer, oscillations in the voltage output of the microphone are recorded digitally (after some filtering/amplification) by using an Analog-to-Digital Converter. If you would like to learn more about how microphones generically convert sound into an electrical potential, here is a good link: GCSE Physics You are right in pointing out that you need a Digital-to-Analog converter to convert these digital points back into a variable potential on your output lines. Keep in mind that microphones which record two channels of audio will have two different outputs on the audio jack channels, where as either channel can be used for mono tracks. You can plug an audio cable into your computer, cut the cable, remove some of the insulation and expose the individual wires inside the cable. Probe these with an oscilloscope to see your resultant voltage waveform as you play the audio. You can connect a speaker as well so that you can hear what you are seeing on your scope :) The amplifier is in case you want to drive a more powerful speaker, which needs a higher electric potential across it. This is what an amp does. Luckily, your computer converts the digital signals to analog for you, so no additional ICs are required. I would recommend, as Peter pointed out, that you play your audio from a program like audacity, you can even change the speed and frequency, visualizing the results as you go. When it comes to audio jacks, you have some options. There is no + or -. You have left and right channels, and a ground for reference with traditional, three-wire audio jacks: Image Credit: Public Domain Make sure you know which wire is which. You can test them with a DMM. You now have a voltage oscillation over time on the ends of your wires which you can read with the oscilloscope. Don't try using it to power your toaster oven or high-power speaker though! You will need an amp with appropriate accommodations for such applications. You will find on most sound cards that the output voltage is less than one volt at peak. • yeah! thanks, I catch the aux connector has ground and audio R & L. now, I can see the signal in oscilloscope – sgb Aug 14 '19 at 7:53 I'm searching a methods that can convert sound to voltage Use a microphone - they convert sound to voltage. Is other method to convert sound to voltage? Most moving coil speakers will convert sound to voltage. Use a free program called "Audacity" - it will play your .wav file through your PC sound system, and will display the sound data in the .wav file like an oscilliscope would • Thanks to comment. I already implemented a .wav to graph by using C#. I just want to know 'Aux' connector voltage.(to measure oscilloscope) – sgb Aug 14 '19 at 6:31 Table from that article: Line levels and their approximate nominal voltage levels Use Nominal level Nominal level VRMS Peak ampl. VPK Peak2peak ampl. VPP Professional audio +4 dBu 1.228 1.736 3.472 Consumer audio −10 dBV 0.316 0.447 0.894	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.18732279539108276, "perplexity": 2225.77604490884}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-40/segments/1600401617641.86/warc/CC-MAIN-20200928234043-20200929024043-00564.warc.gz"}
https://brainly.com/question/206046	2014-12-01T21:30:56-05:00 If Terrance trains 6 miles in half an hour, that means he trains 12 miles in a whole hour. You can think of it as a fraction, and multiply the top and bottom of the fraction to get the unit rate or . Jesse runs 2 miles every 15 minutes. 15 minutes is a quarter of an hour, so 2 miles every quarter hour -> . Multiply the top and bottom by 4 to get the unit rate or . For the next question, use a proportion. We know that in an hour, Terrance will run 12 miles, but we want to know how long it takes for him to run 50 miles. Cross multiply: So it takes Terrance 4 1/6 hours to run 50 miles. A sixth of an hour is ten minutes, so that becomes 4 hours and 10 minutes. In an hour, Jesse runs 8 miles. How long will it take for him to run 50? Cross multiply: It takes Jesse 6 1/4 hours to run 50 miles. A quarter of an hour is 15 minutes, so that becomes 6 hours and 15 minutes. Sandra runs 8 miles in 45 minutes. If Lee runs 8 miles in an hour, that means Lee takes longer to run the same distance. Therefore, Sandra is faster than Lee. Terrance runs 12 miles in an hour. To compare his speed to Sandra's, we have to do some mathemagics: This might not have been the way your teacher showed you, but it's the way that makes sense to me. The new rate we have is really the same rate as before, we just made it look different so that the denominator would be the same as Sandra's rate. Now we can clearly see who is faster -- Sandra runs 8 miles in 45 minutes, Terrance runs 9 miles in 45 minutes, so Sandra is slower than Terrance.	{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8499327301979065, "perplexity": 464.6704698348178}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-04/segments/1484560280266.9/warc/CC-MAIN-20170116095120-00242-ip-10-171-10-70.ec2.internal.warc.gz"}
http://math.stackexchange.com/questions/209833/system-of-equations-solution-method	# System of Equations Solution Method Supposing I had two equations: $\alpha/\beta=\mu$ and $\alpha/\beta^{2}=\sigma^{2}$, where $\alpha$, $\beta$, $\sigma$ and $\mu \in \mathbb R$. How can I solve for $\alpha$ and $\beta$? Furthermore, is there a general method for this kind of system? - Divide. We get $\beta=\frac{\sigma^2}{\mu}$. Square the first expression and divide. We get $\alpha=\frac{\sigma^2}{\mu^2}$. – André Nicolas Oct 9 '12 at 14:24 Solving one equation for $\alpha$ gives p. e. $\alpha = \beta\mu$. Plug this into the other equation, giving $\beta\mu/\beta^2 = \sigma^2 \iff \beta = \mu/\sigma^2$. So $\alpha = \mu^2/\sigma^2$.	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9843259453773499, "perplexity": 172.77134746449022}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-23/segments/1406510276584.58/warc/CC-MAIN-20140728011756-00125-ip-10-146-231-18.ec2.internal.warc.gz"}
https://www.vedantu.com/question-answer/a-person-was-asked-to-state-his-age-in-years-his-class-8-maths-cbse-5f5e78e96e663a29cc564286	Question # A person was asked to state his age in years. His reply was “Take my age three years hence multiply it by 3 and then subtract three times my age 3 years ago and you will know how old I am.” What was the age of the person?A). 18 yearsB). 20 yearsC). 24 yearsD). 32 years Hint: Start by assuming the present age as some variable and try to form relations as per the statement given in the question. Solve the relationships formed and find out the value of the variable assumed, ignore negative value if found as age can never be negative. Complete step by step solution: Let us take the present age of the person to be ‘x’ years. Now, let us form the required relation of ages. The age of the person 3 years from now will be=$x + 3$years The age of the person 3 years ago was =$x - 3$years Now, according to the statement given in the question, we have $3(x + 3) - 3(x - 3) = x$ Solving this, we get $3x + 9 - 3x + 9 = x \\ \Rightarrow x = 18$ Therefore, the present age of the person is 18 years. So, option A is the correct answer. Note: Such similar problems can be solved by following the approach of part by part work, read a statement, and then form its equation or relation and repeat the same for the next statement. Attention is required while solving such questions as they can have quadratic equations, needed to be solved by either splitting middle term or discriminant rule and any negative values are to be neglected as age can never be negative.	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6595489978790283, "perplexity": 486.03107885872726}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-10/segments/1614178358203.43/warc/CC-MAIN-20210227054852-20210227084852-00425.warc.gz"}
https://openreview.net/forum?id=ryg7jhEtPB	## On importance-weighted autoencoders Sep 25, 2019 Blind Submission readers: everyone Show Bibtex • Abstract: The importance weighted autoencoder (IWAE) (Burda et al., 2016) is a popular variational-inference method which achieves a tighter evidence bound (and hence a lower bias) than standard variational autoencoders by optimising a multi-sample objective, i.e. an objective that is expressible as an integral over $K > 1$ Monte Carlo samples. Unfortunately, IWAE crucially relies on the availability of reparametrisations and even if these exist, the multi-sample objective leads to inference-network gradients which break down as $K$ is increased (Rainforth et al., 2018). This breakdown can only be circumvented by removing high-variance score-function terms, either by heuristically ignoring them (which yields the 'sticking-the-landing' IWAE (IWAE-STL) gradient from Roeder et al. (2017)) or through an identity from Tucker et al. (2019) (which yields the 'doubly-reparametrised' IWAE (IWAE-DREG) gradient). In this work, we argue that directly optimising the proposal distribution in importance sampling as in the reweighted wake-sleep (RWS) algorithm from Bornschein & Bengio (2015) is preferable to optimising IWAE-type multi-sample objectives. To formalise this argument, we introduce an adaptive-importance sampling framework termed adaptive importance sampling for learning (AISLE) which slightly generalises the RWS algorithm. We then show that AISLE admits IWAE-STL and IWAE-DREG (i.e. the IWAE-gradients which avoid breakdown) as special cases. • Keywords: variational inference, autoencoders, importance sampling • TL;DR: We show that most variants of importance-weighted autoencoders can be derived in a more principled manner as special cases of adaptive importance-sampling approaches like the reweighted-wake sleep algorithm. • Original Pdf: pdf 0 Replies	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9773111939430237, "perplexity": 5327.640504927408}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-05/segments/1579250594705.17/warc/CC-MAIN-20200119180644-20200119204644-00172.warc.gz"}
http://crypto.stackexchange.com/questions/15142/difference-between-lightweight-online-and-low-memory-authenticated-encryption-s	# Difference between lightweight, online and low memory Authenticated Encryption schemes What is the basic difference between the following types of Authenticated Encryption (AE) schemes? 1. Lightweight Authenticated encryption 2. Online Authenticated Encryption 3. Authenticated Encryption for low memory devices Are they all the same or is there a specific difference between them? - @downvoters: How so? I think this is a reasonable question, particularly given one or more of them are given as key features of CAESER submissions. – figlesquidge Mar 21 at 12:48 @figlesquidge I guess it's due to lack of research. The question doesn't have the seemingly obligatory "what have you tried" clause. OP if you can please add some details, like demonstrate how they are similar and why that is confusing, I guess it would re-open the question. I hope this helps. – rath Mar 21 at 18:10 That's a fair point, but two down-votes and 4 close-votes without anyone leaving a comment seems rather poor form. It is very clear what this question is asking. It might not have been asked well, but "unclear what you're asking" doesn't seem an acceptable reason to close it. [/rant] – figlesquidge Mar 21 at 18:12 @figlesquidge - I guess the question being closed because it's "unclear what you're asking" suffices in lieu of comments. I second Rath's comment. In my opinion, the question seems extremely vague, and too broadly open to interpretation. Adding some links, references, and/or previous research to the question might help provide context, and make the question answerable. However, if this question seems clear to you - go ahead and answer it. – hunter Mar 21 at 19:10 Related to the “unclear what you're asking” votes… here's my humble point of view. After all, we've accepted alike questions with similar research efforts. – e-sushi Mar 23 at 13:15 Thought I'd begin with some references for you that might be of interest. These terms are used as key 'selling points' for a number of schemes, including many of the CAESAR submissions. Some examples using the terms specifically are given below - most of which are from CAESER because I have the zoo in-front of me: • "Online": OCB, Ascon, CBA, APE, NORX • "memory-constrained devices": Ketje / Keyak / Spongewrap, • "lightweight": PRESENT, JAMBO, APE, BLINKER (presented CT-RSA14) Also, there was an eCrypt report on Lightweight crypto. I can't provide a decent distinction between the 1 & 3, since low memory footprint is a more specific sub-aim of lightweight. Both of these are types of schemes designed to be run in highly restricted environments, such as on embedded devices. These often have constraints that actually affect what operations you can/cannot run on them, such that more efficient algorithms than an AES-based mode may be preferred. Online AE deals with something completely different. Let A be some associated data, $M=(M_1,\dots,M_n)$ a message, encrypting to $C=(C_0,\dots,C_n)$ and tag $T$. The scheme is online if $C_i$ can be calculated without knowledge of $M_j$ for any $j>i$. Often lightweight or small footprint ciphers are 'online'. This is because it allows them to process plaintext blocks as they come through. In contrast, an offline cipher would have to collect the complete plaintext before calculating the ciphertext, which means it must have enough memory to store $n$ blocks of data, which not all devices will do - especially for example a small industrial sensor reporting on large amounts of data. Recently there has been some controversy about the validity of an online decryption function, since they release unverified plaintext (for example, see the CAESER mailing list or this paper). For categorization of some schemes under development, see here. - One may also note that there are "semi-online" schemes where the size of the input (but not the contents) must be known from start (e.g. CCM). – Thomas Pornin Mar 27 at 13:27	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6053789258003235, "perplexity": 1900.0383771094512}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-35/segments/1408500835844.19/warc/CC-MAIN-20140820021355-00119-ip-10-180-136-8.ec2.internal.warc.gz"}
https://deepai.org/publication/rediscovering-deep-neural-networks-in-finite-state-distributions	Rediscovering Deep Neural Networks in Finite-State Distributions We propose a new way of thinking about deep neural networks, in which the linear and non-linear components of the network are naturally derived and justified in terms of principles in probability theory. In particular, the models constructed in our framework assign probabilities to uncertain realizations, leading to Kullback-Leibler Divergence (KLD) as the linear layer. In our model construction, we also arrive at a structure similar to ReLU activation supported with Bayes' theorem. The non-linearities in our framework are normalization layers with ReLU and Sigmoid as element-wise approximations. Additionally, the pooling function is derived as a marginalization of spatial random variables according to the mechanics of the framework. As such, Max Pooling is an approximation to the aforementioned marginalization process. Since our models are comprised of finite state distributions (FSD) as variables and parameters, exact computation of information-theoretic quantities such as entropy and KLD is possible, thereby providing more objective measures to analyze networks. Unlike existing designs that rely on heuristics, the proposed framework restricts subjective interpretations of CNNs and sheds light on the functionality of neural networks from a completely new perspective. 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Baggenstoss, et al. ∙ 0 This week in AI Get the week's most popular data science and artificial intelligence research sent straight to your inbox every Saturday. 1 Introduction The ever-increasing complexity of Convolutional Neural Networks (CNN) and their associated set of layers demand deeper insight into the internal mechanics of CNNs. The functionality of CNNs is often understood as a series of projections and a variety of non-linearities to increase the capacity of the model [Hinton2009, Nair and Hinton2010, Ramachandran, Zoph, and Le2017, Zheng et al.2015] . Despite the fact that the prediction layer of CNNs (e.g., the Softmax layer) and the loss functions (e.g., Cross Entropy) are borrowed from the Bayesian framework, a clear connection of the functionality of the intermediate layers with probability theory remains elusive. The current understanding of CNNs leaves much to subjective designs with extensive experimental justifications. We informally argue that subjectivity is inherent to problems defined over real numbers. Accordingly, the confusion existing in the functionality of CNNs reflects the aforementioned theoretical subjectivity. Since real vector spaces are unbounded and uncountable, they require strong assumptions in the form of prior information about the underlying data distribution in a Bayesian inference framework. For example, fitting a Gaussian distribution to a set of samples requires that the prior distribution on the location parameter be non-vanishing near the samples. In this scenario, an uninformative prior needs to be close to the uniform distribution over real numbers; a paradoxical distribution. Since the real line is unbounded and uncountable, the choice of the model and its prior distribution is always highly informative [Jaynes1968]. Although the choice of the prior in univariate distributions is not a practical issue, the adverse effects of subjective priors are more evident in high dimensions. When the sample space is large and the data is comparatively sparse, either careful design of a prior or an uninformative prior is needed. Note that in the context of CNNs, the architecture, initialization, regularization, and other processes can be interpreted as imposing some form of prior on the distribution of real data. [Jaynes1957] shows that the correct extension of entropy to real distributions does not have a finite value. By switching to finite state distributions (FSDs), the entropy value is calculable and finite, providing potential for an information-theoretic treatment. In contrast to distributions defined over real numbers, working with FSDs makes the problem of objective inference theoretically more tractable. In problems where the data are represented by real numbers, the values can be treated as parameters of a finite-state distribution, therefore each sample represents a distribution over some finite space. Discrete modeling of the sample space reduces the complexity of the input domain, and treating the inputs as distributions reduces the chance of overfitting since every sample represents a set of realizations. In the case of natural images, the aforementioned modeling of input data is justified by the following observation. In conventional image acquisition devices, the intensity of pixels can be interpreted as the probability of presence of photons in a spatial position and some wavelength. Therefore, a single image is considered as the distribution of photons on the spatial plane with finite states when the number of pixels is finite. In this paper, we present a framework for classification with the key feature that unlike existing models inference is made on finite-state spaces. Classification of FSDs are attractive in the sense that it sets up the requirement for composition of classifiers, since the output of Bayesian classifiers are FSDs. To construct a Bayesian FSD classifier we borrow concepts from the Theory of Large Deviations and Information Geometry, introducing the KullBack-Leibler divergence (KLD) as the log-likelihood function. The composition of Bayesian classifiers are used to serve as a multilayer classification model. The resulting structure deeply resembles CNNs, namely modules similar to the core CNN layers are naturally derived and fit together. Specifically, we show that the popular non-linearities used in deep neural networks, e.g., ReLU and Sigmoid [Nair and Hinton2010], are in fact element-wise approximations of some normalization mapping. Moreover, we show that the linearities amount to calculating the KLD, while max pooling is an approximation to the marginalization of the indices. In our framework, there exists a natural correspondence between types of the nonlinearity and pooling. In particular, Sigmoid and ReLU correspond to Average Pooling and Max Pooling, respectively, while each pair is dictated by the type of KLD used. The models in our framework are statistically analyzable in all the layers; there is a clear statistical interpretation for every parameter, variable and layer. The interpretability of the parameters and variables provides insights into the initialization, encoding of parameters and the optimization process. Since the distributions are over finite states, the entropy is easily calculable for both the model and data, providing a crucial tool for both theoretical and empirical analysis. The organization of the paper is as follows. In Section 2, we review related work on FSDs and the analysis of CNNs. In Section 3, we describe the construction of the proposed framework and a single layer model for classification and explain the connections to CNNs. In Section 3, we describe the extension of the framework to multiple layers. Also, we introduce the extension to the convolutional model and provide a natural pooling layer by assuming stationarity of the data distribution. Furthermore, we explain the relation between vanilla CNNs and our model. In Section 4, we evaluate few baseline architectures in the proposed framework as a proof of concept, and provide an analysis on entropy measurements available in our framework. 2 Related Work A line of work on statistical inference in finite-state domains focuses on the problem of Binary Independent Component Analysis (BICA) and the extension over finite fields, influenced by [Barlow, Kaushal, and Mitchison1989, Barlow1989]. The general methodology in the context of BICA is to find an invertible transformation of input random variables which minimizes the sum of marginal entropies [Yeredor2011, Yeredor2007, e Silva et al.2011, Painsky, Rosset, and Feder2014, Painsky, Rosset, and Feder2016]. Although the input space is finite, the search space for the correct transformation is computationally intractable for high-dimensional distributions given the combinatorial nature of the problem. Additionally, the number of equivalent solutions is large and the probability of generalization is low. In the context of CNNs, a body of research concerns discretization of variables and parameters of neural networks [Courbariaux and Bengio, Soudry, Hubara, and Meir2014, Courbariaux, Bengio, and David2015]. [Rastegari et al.2016] introduced XNOR-Networks, in which the weights and the input variables take binary values. While discretization of values is motivated by efficiency, the optimization and learning the representation of the data are in the context of real numbers and follow similar dynamics as in CNNs. To formalize the functionality of CNNs, a wavelet theory perspective of CNNs was considered by [Mallat2016] and a mathematical baseline for the analysis of CNNs was established. [Tishby, Pereira, and Bialek2000] introduced the Information Bottleneck method (IBP) to remove irrelevant information and maintain the mutual information between two variables. [Tishby and Zaslavsky2015] proposed to use IBP, where the objective is to minimize the mutual information between consequent layers, while maximizing the mutual information of prediction variables and hidden representations. [Su, Carin, and others2017] introduce a framework for stochastic non-linearities where various non-linearities including ReLU and Sigmoid are produced by truncated Normal distributions. In the context of probabilistic networks, Sum Product Networks (SPNs) [Poon and Domingos2011, Gens and Domingos2012, Gens and Pedro2013] are of particular interest, where under some conditions, they represent the joint distribution of input random variables quite efficiently. A particularly important property of SPNs is their ability to calculate marginal probabilities and normalizing constants in linear time. The efficiency in the representation, however, is achieved at the cost of restrictions on the distributions that could be estimated using SPNs. [Patel, Nguyen, and Baraniuk2016] constructed Deep Rendering Mixture Models (DRMM) generating images given some nuisance variables. They showed that given that the image is generated by DRMM, the MAP inference of the class variable coincides with the operations in CNNs. 3 Proposed Framework We set up our framework by modeling the input data as a set of “uncertain realizations” over symbols. To be precise, we define an uncertain realization as a probability mass function (pmf) over states with non-zero entropy, and similarly a certain realization is a degenerate pmf over states. To demonstrate an example of interpreting real-valued data as uncertain realizations, consider a set of -pixel RGB image data. We can view each pixel as being generated from the set and further interpret the value of each channel as the unnormalized log-probability of being in the corresponding state. If we normalize the pmf of each pixel, we can interpret the image as a factored pmf over states and each pixel a pmf over states. Formally, we define a transfer function , where is the -dimensional simplex and is the dimension of the input vector space. In the previous example, each pixel is mapped from (i.e., ) to (i.e., ). Therefore, the entire image is mapped from to . In general, the choice of depends on the nature of the data and it can either be designed or estimated during the training process. Although probability assignment to a certain realization given a model is trivial, the extension to uncertain realizations requires further considerations. We consider Moment Projection (M-Projection) and Information Projection (I-Projection) and observe that both projections are used to obtain probabilities on distributions in two established scenarios, namely Sanov’s Theorem and the Dirichlet Distribution. Sanov’s theorem [Sanov1958] and the Probability of Type classes (Method of Types) [Cover and Thomas2012, Csiszár1998] use the KLD associated with I-Projection of the input distribution onto the underlying pmf (1) to calculate the probability of observing empirical distributions. On the other hand, the Dirichlet distribution uses the KLD associated with M-Projection (2) to asymptotically assign probabilities to the underlying distribution. We use the following approximations for probability assignments to distribution given the distribution PI(x\|q) =exp(−αD(x\|\|q)) (1) PM(x\|q) =exp(−αD(q\|\|x)), (2) where is the KLD. Inspired by the aforementioned probability assignments, we regard both types of KLD as the main tool for probability assignment on distributions in our model. We denote the KLD associated with I-Projection and M-Projection as I-KLD and M-KLD, respectively. Later, we will show that approximations to ReLU-type networks and Sigmoid-type networks are derived when employing M-KLD and I-KLD probability assignments, respectively. We define a single layer model for supervised classification as an example of using M-KLD. Constructing the I-KLD models follows a similar construction and is briefly described in Section 3. Let model be a mixture of a set of probability distributions over symbols, each representing the distribution of a class, M(x)=V∑v=1pvMv(x),p∈ΔV. (3) To calculate the membership probability of an input in class following the Bayesian framework, we have log(P(x∼Mv \|x=x(k)))= log(P(x=x(k)\|x∼Mv)P(x∼Mv))P(x=x(k)\|x∼M)) (4) where is the probability that is generated by . Substituting the log-likelihood term with M-KLD, we get log(P(x∼ Mv\|x=x(k))=−αD(Mv\|\|x(k))+log(pv) −log(V∑j=1exp(−αD(Mj\|\|x(k))+log(pj))) (5) Note that the KLD term is linear in . We can break the operation in (5) into composition of a linear mapping and a non-linear mapping , where the -th components of the outputs are defined as and for some input . To formally define Divg and LNorm, let us define the logarithmic simplex of dimension denoted by as ΔVℓ={x∈RV\|V∑v=1exv=1}. (6) Setting up the domain of Divg and the parameters as Divg:ΔDℓ→RV,B∈ΔVℓ,α∈R+, W∈{w∈RV×D\|(wi,:)T∈ΔD} (7) where is the -th row of the matrix , we define the function Divg as Divg (x;W,B,α)=α(Wx+H(W))+B (8) where each row of contains a distribution and calculates the entropy of each row. The weights and biases being the parameters of the model, are randomly initialized and trained according to some loss function. Unlike current CNNs, the familiar terms in (8 ) such as the linear transformation and the bias term are not arbitrary. Specifically, is the cross entropy of the sample and the distributions, while is the logarithm of the mixing coefficient in (3). The entropy can be thought as the regularizer matching the Maximum Entropy Principle [Jaynes1957]. The term biases the probability on distributions with the highest degree of uncertainty. The non-linear function is the Log Normalization function whose -th component is defined as LNormv(x)=xv−log(V∑j=1exj). (9) Note that the function is a multivariate operation. The behavior of LNorm in one dimension of the output and input is similar to that of ReLU. Furthermore, in (8) demonstrates the certainty in the choice of the model. For example, when , equal probability is assigned to all input distributions, whereas when is large, a slight deviation of the input from the distributions results in a significant decrease in the membership probability. We refer to as the concentration parameter, however in all the models presented we fix . Multilayer Model, Convolutional Model, and Pooling The model described in the previous section demonstrates a potential for a further recursive generalization, i.e., the input and output of the model are both distributions on finite states. We extend the model simply by stacking single layer models. The input of each layer are in , therefore the log-normalization performed by LNorm is crucial to maintain the recursion. The multilayer model (Finite Neural Network) is defined as the composition of Divg and LNorm layers, FNN(x)=LNormL∘DivgL∘…LNorml∘Divgl… ∘LNorm1∘Divg1(x) (10) where the superscript denotes the layer index and is the total number of layers. To elaborate, after each couple of layers, the input to the next layer are the log probabilities of membership to classes. Therefore, one can interpret the intermediate variables as distributions on a finite set of symbols (classes). In the case where I-KLD is used as the probability assignment mechanism, the input to the layers must be in the probability domain, therefore the nonlinearity reduces to Softmax, which in one dimension behaves similar to the Sigmoid function. Note that the entropy term in I-KLD is not linear with respect to the input. We focus on the M-KLD (ReLU-activated) version, however, the concepts developed herein are readily extendable to the I-KLD (Sigmoid-activated) networks. Convolutional Model: One of the key properties of the distribution of image data is strict sense stationarity, meaning that the joint distribution of pixels does not change with translation. Therefore, it is desirable that the model be shift-invariant. Inspired by CNNs, we impose shift invariance by convolutional KLD (KL-Conv) layers. In our convolutional model, a filter of size represents a factorized distribution with factors, each factor representing a pmf over states. The distribution associated with the filter is where is a single factor over states defined by the values in , is a neighborhood of pixels and is the -th state. In other words, the values across the channels of the filter represent a pmf and sum up to . In the RGB image example provided previously, the factors of the filters compatible with the input layer are over states. The input of the layer is log-normalized across the channels. We model the input with channels as a factorized distribution where each pixel represents a factor. The distribution is shifted along the spatial positions and the KLD of the filter distribution and each neighborhoods of pixels are calculated. As an example, we define the KL-Conv operation associated with M-KLD as xl+1 (13) where represents the set of filters in the layer (each filter representing a distribution), is the vector of distribution entropies, is the convolution operator used in conventional CNNs and is the concentration parameter. The non-linearity is applied to the input across the channels in the same manner as in the multilayer model, i.e., xl+1^r,^s,:=LNorm(xl^r,^s,:) (14) The overall operation of KL-Conv and LNorm layers is illustrated in Fig.1. Pooling: We define the pooling function as a marginalization of indices in a random vector. In the case of tensors extracted in FNNs, the indices correspond to the relative spatial positions. In other words, the distributions in the spatial positions are mixed together through the pooling function. Assume is the input to the pooling layer, where . The input is in the logarithm domain, therefore to calculate the marginalized distribution the input needs to be transferred to the probability domain. After marginalization over the spatial index, the output is transferred back to the logarithm domain. We define the logarithmic pooling function as xl+1^r,^s,k=log⎛⎜⎝∑i,j∈supp(pr,s)exp(xl^r+i,^s+j,k)pr,s(i,j)⎞⎟⎠, (15) where is the probability distribution over the relative spatial positions and denotes the support. In the usual setting of pooling functions and our model, is assumed to be a uniform distribution and the support of the distribution represents the pooling window. Note that the term in (15) is approximately equivalent to the Max function as the variables in the exponent deviate. Therefore, we hypothesize that Max Pooling in conventional CNNs is approximating (15). Evidently, the output of the pooling function is already normalized and is passed to the next layer. In the case that I-KLD is used, the input is in the probability domain and the pooling function will be identical to average pooling. Input Layer: The model presented so far considers finite state probability distributions as input to the layers. In the case of natural images, we chose to normalize all the pixel values to the interval . Each pixel value was interpreted as the expectation of a binary random variable with range . As a result, each filter with total number of variables is a probability distribution over a space of states. Note that our model is not restricted by the choice of the type of input distribution. Depending on the nature of the input, the user can modify the distribution represented by filters, e.g., distributions on real spaces. Parameterization As explained, the parameters of the model represent parameters of distributions which are constrained to some simplex. To eliminate the constraints of the parameters, we use a “Link Function”, , mapping the “Seed” parameters to the acceptable domain of parameters, i.e., logarithmic/probability simplex. The link function impacts the optimization process and partially reflects the prior distribution over the parameters. While the parameters are updated in uniformly, the mapped parameters change according to the link function. The filters in our model are factorized distributions and each component is a categorical distribution. Additionally, the biases are categorical distributions, therefore we use similar parameterization for biases and filter components. In general, the filters of the model are obtained by Fr,s,: =ψ(θr,s,:) (16) B =ψ(β) (17) where are the seed parameters of the filter in the spatial position and across all the channels, represents the channels of the filter in the position, is the seed parameter of bias and is the bias vector. Since the filters and biases comprise categorical distributions, we avoid complicating the notation by limiting the discussion to the parameterization of categorical distributions. We suggest two forms of parameterization of a categorical distribution , namely log-simplex and spherical parameterizations. Log-Simplex Parametrization We define the link function with respect to the natural parametrization of a categorical distribution, where the seed parameters are interpreted as the logarithm of unnormalized probabilities. Therefore, the link function is defined as the Softmax function πi=eθi∑Dj=1eθj (18) where is the seed parameter vector and the subscript denotes the index of the vector components. Writing down the Jacobian of (18) ∂πi∂θi=πi(1−πi),∂πi∂θj=−πjπii≠j (19) we can observe that the Jacobian only depends on and does not depend on the denominator in (18) and the link function is invariant to translation of along the vector . Log-Simplex parameterization completely removes the effect of the additional degree of freedom. Initialization: We initialize each factor of the filters by sampling from a Dirichlet distribution with parameters equal to . Therefore, the distribution’s components are generated uniformly on some simplex. We speculate that the initialization of the model should follow maximizing the mixing entropy or Shannon-Jensen Divergence (JSD) of the filters in a given layer , defined as ΔH=H(V∑v=1pvπ(v))−V∑v=1pvH(π(v)), (20) where is the total number of filters, is the -th filter and is the corresponding mixture proportion. There is a parallel between orthogonal initialization of filters in conventional CNNs and maximizing in M-KLD networks. In the extreme case where filters are degenerate distributions on unique states and the filters cover all possible states, is at the global maximum and the M-KLD operation is invertible. Similarly, orthogonal initialization of conventional CNNs is motivated by having invertible transformations to help with the information flow through the layers. Since it is hard to obtain a global maximizer for JSD, we minimize the entropy of individual filters (second term in (20) by scaling the log-probabilities with a factor . We set as a rule of thumb. Finally, the Bias seed components are initialized with zeros, indicating equal proportion of mixture components. Spherical Parameterization Here, we present an alternative parameterization method attempting to eliminate the learning rate hyper-parameter. Assume that we parameterize the categorical distribution by the link function πi=θ2i∑dj=1θ2j. (21) The expression in (21) maps to the unit sphere , where the square of the components are the probabilities. The mapping defined in (21) ensures that the value of the loss function and predictions are invariant to scaling . The Jacobian of (21) is ∂πi∂θi =2√πi∥θ∥2(1−πi)%sign(θi), ∂πi∂θj =2√πj∥θ∥2(−πi)% sign(θi),i≠j. (22) It is evident from (22) that the norm of the gradient has an inverse relation with . Scaling is equivalent to changing the step size, since the direction of gradients does not depend on . Additionally, the objective function is not dependent on , therefore the gradient vector obtained from the loss function is orthogonal to the vector . Considering the orthogonality property, updating along the gradients always increases the norm of the parameter vector. As a consequence, the learning rate decreases at each step of the iteration; independent of the network structure. Initialization: The seed parameters are initialized uniformly on . The standard way of generating samples uniformly on is to sample each component from a Normal distribution followed by normalization. 4 Experimental Evaluations We experimented with our model on the CIFAR-10 and CIFAR-100 datasets [Krizhevsky and Hinton2009] on the problem of classification. We employed three types of base-CNN architectures, namely Quick-CIFAR, Network in Network (NIN) [Lin, Chen, and Yan2013] and VGG [Simonyan and Zisserman2014, Liu and Deng2015] to experiment with different network sizes. The CNN architectures were transformed to their Finite CNN (FCNN ) versions by replacing Conv/ReLU/Pool with KL-Conv/LNorm/LPool. The inputs for the original architectures were whitened, while the whitening procedure was not applied for testing FCNNs. We first compared the performance of the original networks with their corresponding transformed architectures in finite states. We excluded certain layers from our transformation, e.g., the Dropout and the batch normalization (BatchNorm) [Ioffe and Szegedy2015], since we do not yet have a clear justification for their roles in our model. We did not use weight decay [Krizhevsky, Sutskever, and Hinton2012], regularization, and the learning rate was fixed to in the FCNNs. FCNNs were parameterized with log-simplex and spherical schemes for comparison. Experiments with I-KLD was excluded, since they achieved lower accuracy compared to M-KLD. We justify this observation by considering two facts about I-KLD: 1) Since the input is in the probability domain, the nonlinearity behaves similar to Sigmoid, therefore the gradient vanishing problem exists in I-KLD. 2) As opposed to LNorm, is not convex and interferes with the optimization process. Table 1 demonstrates the performance achieved by the baselines and their FCNN analogues. For all the conventional CNN networks, the data was centered at the origin and ZCA whitening was employed. Additionally, the original optimized learning rates were used to train the CNNs. The weights in all the models were regularized with norm, where in the case of NIN and VGG the regularization coefficient is defined per layer. VGG was unable to learn without being equipped with BatchNorm and Dropout layers. In the case of NIN, we could not train NIN without Dropout and BatchNorm, therefore we rely on the results reported in [Lin, Chen, and Yan2013] on vanilla NIN (without Dropout and BatchNorm) trained on CIFAR10 for 200 epochs. Figure 3 in [Lin, Chen, and Yan2013] reports the test error of vanilla NIN on CIFAR10 as roughly 19%, which is similar to the results obtained by the Finite counterpart. The final test error reduces to 14.51% over the number of epochs, which is unknown to us. The vanilla NIN results on CIFAR100 are not available in the original paper. FCNNs achieved lower performance in VGG and NIN architectures which are equipped with Dropout and BatchNorm. Note that FCNN performs without regularization, data preprocessing, hyper-parameter optimization, and change of learning rate. The results show that the finite state models’ performance is at the same scale as CNNs, considering the simplicity of FCNNs. Spherical parameterization performs better than Log Simplex in NIN-Finite and Quick-CIFAR-Finite networks, whereas in VGG-Finite Log Simplex is superior. We do not have a definite explanation for the difference in performance of parameterizations in different architecture settings. However, the results show that none are objectively superior as they stand. Entropy of Filters and Biases To analyze the behavior of the networks, we performed a qualitative analysis on the trend of the bias entropies and the filter entropies. In our experiments, M-KLD was used as the linearity. Since the input is represented by log-probability in the cross entropy term of M-KLD, the filter distribution naturally tends to low entropy distributions. However, in Figure 2, we observe that the average entropy of some layers starts to increase after some iterations. This trend is visible in the early layers of the networks. Since high entropy filters are more prone to result in high divergences when the input distribution is low-entropy (property of M-KLD), the network learns to approach the local optimum from low entropy distributions. The entropy of the input tensors of late layers are larger compared to that of the early layers, and start decreasing during the learning process. Therefore, the entropy of the filters decreases as the entropy of their input decreases. The entropy of bias distributions contain information about the architecture of networks. Note that the bias component is the logarithm of the mixing coefficients. Degeneracy in the bias distribution results in removing the effect of the corresponding filters from the prediction. The increase in the entropy of the biases could also demonstrate the complexity of the input, in the sense that the input distribution cannot be estimated with a mixture of factorized distributions given the current number of mixture components. 5 Conclusion Our work was motivated by the theoretical complications of objective inference in infinite state spaces. We argued that in finite states objective inference is theoretically feasible, while finite spaces are complex enough to express the data in high dimensions. The stepping stones for inference in high dimensional finite spaces were provided in the context of bayesian classification. The recursive application of Bayesian classifiers resulted in FNNs; a structure remarkably similar to Neural Networks in the sense of activations (ReLU/Sigmoid) and the linearity. Consequently, by introducing the shift invariance property (Strict Sense Stationarity assumption) using the convolution tool, FCNNs as finite state analogue of CNNs were produced. The pooling function in FCNNs was derived as marginalizing the spatial position variables. The Max Pool function was explained as an approximation to the marginalization of spatial variables in the log domain. In our work, it is evident that there exist a correspondence between M-KLD, ReLU and Max Pool and similarly between I-KLD, Sigmoid and Average Pool. In the context of classic CNNs, diverse interpretations for layers and values of the feature maps exist whereas in FNNs the roles of layers and the nature of every variable is clear. Additionally, the variables and parameters represent distributions, making the model ready for a variety of statistical tools, stochastic forward passes and stochastic optimization. The initialization and parameterization of the model points clearly and directly to the objective inference literature [Jeffreys1946, Jaynes1968], which would potentially reveal further directions on how to encode the functionality objectively. Open Questions: The pillar of our framework is assigning probabilities to uncertain events. We directed the reader to the literature that justifies usage of both KLD forms in asymptotic cases. I-KLD is used to assign probabilities to empirical distributions, while M-KLD is assigning probability to the true distribution, given some empirical distribution. The concentration parameter roughly represents the number of empirical data in both probability assignments. The following questions are subject of future investigations. 1. The experiments show that using M-KLD as opposed to I-KLD results in higher performance. How could one theoretically justify the performance gap? 2. Could both schemes of probability assignment be incorporated in the learning process? 3. The normalizing factors in the nonlinearities represent the probability of the observation given the mixture distribution of filters. Can they be included in the objective to train without supervision? References • [Barlow, Kaushal, and Mitchison1989] Barlow, H. B.; Kaushal, T. P.; and Mitchison, G. J. 1989. Finding minimum entropy codes. Neural Computation 1(3):412–423. • [Barlow1989] Barlow, H. B. 1989. Neural computation 1(3):295–311. • [Courbariaux and Bengio] Courbariaux, M., and Bengio, Y. Binarynet: Training deep neural networks with weights and activations constrained to+ 1 or-1. corr abs/1602.02830 (2016). • [Courbariaux, Bengio, and David2015] Courbariaux, M.; Bengio, Y.; and David, J.-P. 2015. Binaryconnect: Training deep neural networks with binary weights during propagations. In Advances in neural information processing systems, 3123–3131. • [Cover and Thomas2012] Cover, T. M., and Thomas, J. A. 2012. Elements of information theory. John Wiley & Sons. • [Csiszár1998] Csiszár, I. 1998. The method of types [information theory]. IEEE Transactions on Information Theory 44(6):2505–2523. • [e Silva et al.2011] e Silva, D. G.; Attux, R.; Nadalin, E. Z.; Duarte, L. T.; and Suyama, R. 2011. An immune-inspired information-theoretic approach to the problem of ica over a galois field. In IEEE Information Theory Workshop (ITW), 618–622. • [Gens and Domingos2012] Gens, R., and Domingos, P. 2012. Discriminative learning of sum-product networks. In Advances in Neural Information Processing Systems, 3239–3247. • [Gens and Pedro2013] Gens, R., and Pedro, D. 2013. Learning the structure of sum-product networks. In International conference on machine learning , 873–880. • [Hinton2009] Hinton, G. E. 2009. Scholarpedia 4(5):5947. • [Ioffe and Szegedy2015] Ioffe, S., and Szegedy, C. 2015. 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In Advances in neural information processing systems, 1097–1105. • [Lin, Chen, and Yan2013] Lin, M.; Chen, Q.; and Yan, S. 2013. Network in network. arXiv preprint arXiv:1312.4400. • [Liu and Deng2015] Liu, S., and Deng, W. 2015. Very deep convolutional neural network based image classification using small training sample size. In 3rd IAPR Asian Conference on Pattern Recognition (ACPR) , 730–734. IEEE. • [Mallat2016] Mallat, S. 2016. Understanding deep convolutional networks. Phil. Trans. R. Soc. A 374(2065):20150203. • [Nair and Hinton2010] Nair, V., and Hinton, G. E. 2010. In Proceedings of the 27th international conference on machine learning (ICML-10), 807–814. • [Painsky, Rosset, and Feder2014] Painsky, A.; Rosset, S.; and Feder, M. 2014. Generalized binary independent component analysis. In IEEE International Symposium on Information Theory (ISIT), 1326–1330. • [Painsky, Rosset, and Feder2016] Painsky, A.; Rosset, S.; and Feder, M. 2016. Large alphabet source coding using independent component analysis. arXiv preprint arXiv:1607.07003. • [Patel, Nguyen, and Baraniuk2016] Patel, A. B.; Nguyen, M. T.; and Baraniuk, R. 2016. A probabilistic framework for deep learning. In Advances in neural information processing systems, 2558–2566. • [Poon and Domingos2011] Poon, H., and Domingos, P. 2011. Sum-product networks: A new deep architecture. In IEEE International Conference on Computer Vision Workshops (ICCV Workshops) , 689–690. • [Ramachandran, Zoph, and Le2017] Ramachandran, P.; Zoph, B.; and Le, Q. V. 2017. Swish: a self-gated activation function. arXiv preprint arXiv:1710.05941. • [Rastegari et al.2016] Rastegari, M.; Ordonez, V.; Redmon, J.; and Farhadi, A. 2016. Xnor-net: Imagenet classification using binary convolutional neural networks. In European Conference on Computer Vision, 525–542. Springer. • [Sanov1958] Sanov, I. N. 1958. On the probability of large deviations of random variables. Technical report, North Carolina State University. Dept. of Statistics. • [Simonyan and Zisserman2014] Simonyan, K., and Zisserman, A. 2014. Very deep convolutional networks for large-scale image recognition. arXiv preprint arXiv:1409.1556. • [Soudry, Hubara, and Meir2014] Soudry, D.; Hubara, I.; and Meir, R. 2014. Expectation backpropagation: Parameter-free training of multilayer neural networks with continuous or discrete weights. In Advances in Neural Information Processing Systems, 963–971. • [Su, Carin, and others2017] Su, Q.; Carin, L.; et al. 2017. A probabilistic framework for nonlinearities in stochastic neural networks. In Advances in Neural Information Processing Systems, 4489–4498. • [Tishby and Zaslavsky2015] Tishby, N., and Zaslavsky, N. 2015. Deep learning and the information bottleneck principle. In IEEE Information Theory Workshop (ITW), 1–5. • [Tishby, Pereira, and Bialek2000] Tishby, N.; Pereira, F. C.; and Bialek, W. 2000. The information bottleneck method. arXiv preprint physics/0004057. • [Yeredor2007] Yeredor, A. 2007. ICA in boolean XOR mixtures. Independent Component Analysis and Signal Separation 827–835. • [Yeredor2011] Yeredor, A. 2011. Independent component analysis over galois fields of prime order. IEEE Transactions on Information Theory 57(8):5342–5359. • [Zheng et al.2015] Zheng, H.; Yang, Z.; Liu, W.; Liang, J.; and Li, Y. 2015. Improving deep neural networks using softplus units. In IEEE International Joint Conference on Neural Networks (IJCNN), 1–4.	{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8811216950416565, "perplexity": 1172.706488373493}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-40/segments/1600400198213.25/warc/CC-MAIN-20200920125718-20200920155718-00481.warc.gz"}
https://physics.stackexchange.com/questions/427393/is-there-a-relation-between-the-factorisation-of-the-joint-conditional-probabili	# Is there a relation between the factorisation of the joint conditional probability distribution and Bell inequality? I'm approaching the study of Bell's inequalities and I understood the reasoning under the Bell theorem (pdf : https://cds.cern.ch/record/111654/files/vol1p195-200_001.pdf) and how the postulate of locality was assumed at the start of demonstration. However, I find problematic to arrive at the equivalence $$E(\vec{a},\vec{b}) = \int_{\Lambda}d\lambda \rho(\lambda)A(\vec{a},\lambda)B(\vec{b},\lambda),$$ starting from the point of view expressed by the Clauser and Horne definition of locality. CH claimed that a system is local if there is a parameter $$\lambda$$ and a joint conditional probabilities that can be written as follows: $$p(a,b\|x,y,\lambda) = p(a\|x,\lambda)p(b\|y,\lambda),$$ and $$p(a,b\|x,y) = \int_\Lambda d\lambda \rho(\lambda) p(a\|x,\lambda)p(b\|y,\lambda)$$ which make sense since it affirms that the probability of obtaining the value $$a$$ depends only on the measument $$x = \vec{\sigma}\cdot\vec{x}$$ and the value of $$\lambda$$. However, if I use this expression to write down the expectation value of the products of the two components $$\vec{\sigma}\cdot\vec{a}$$ and $$\vec{\sigma}\cdot\vec{b}$$, I obtain as follows: $$E (\vec{a},\vec{b}) = \sum_{i,j}a_ib_jp(a,b\|x,y) = \\ = \sum_{ij}a_ib_j \int_\Lambda d\lambda \rho(\lambda) p(a\|x,\lambda)p(b\|y,\lambda) \\ = \int_\Lambda d\lambda \rho(\lambda) (\sum_{i}a_ip(a\|x,\lambda))(\sum_{i}b_ip(b\|y,\lambda))$$ where in the last equivalence I've used the fact that if the measument are independent their covariance must be equal to $$0$$. At this point, the terms in the RHS in the brackets are equal to: $$(\sum_{i}a_ip(a\|x,\lambda)) = E(a,\lambda) =? = A(\vec{a},\lambda)\quad \quad (\sum_{i}b_ip(b\|y,\lambda)) = E(b,\lambda) =?= B(\vec{b},\lambda)$$. That is not the equivalence that I want to find. In fact in the RHS of the first equation $$A(\vec{a},\lambda)$$ is, according to Bell original article, the result of measure $$\vec{\sigma}\cdot\vec{a}$$, and fixing both $$\vec{a}$$ and $$\lambda$$ it can assume only the values of $$\pm1$$. (The same is applied for $$B(\vec{b},\lambda)$$.) Some of you knows, where I fail? How can I obtain the original equivalence (that then is proved to be violate in the case of an entangled system) starting from the CH definition of reality? Edit #1: I've noted that I obtain the wanted equivalence only if I assume that $$p(ab\|xy\lambda) = E(\vec{a}\vec{b})$$, but is it possible? How can a conditional probabilities be linked to the mean value of the product of two components? Edit #2: Surfing the internet I found an article (https://arxiv.org/pdf/1709.04260.pdf, page 2, right on the top) which reports the same CH's local condition (to be accurate, the article presents the discrete version) and then affirm that: Blockquote "The central realization of Bell’s theorem is the fact that there are quantum correlations obtained by local measurements ($$M_a^x$$ and $$M_b^y$$) on distant parts of a joint entangled state $$\varrho$$, that according to quantum theory are described as: $$p_{Q}(a,b,\|x,y) = \text{Tr}(\varrho(M_a^x\otimes M_b^y)$$ and cannot be decomposed in the LHV form (i.e. The CH condition for locality)" So why $$p_Q(a,b\|x,y)$$ is seen as a measure of quantum correlation (that for definition is the mean of the product of the possible output)? It isn't a joint probability distribution (as stating while obtaining the LHV form)? Is there a link between the classical correlation ($$E(\vec{a},\vec{b})$$) and the joint probability distribution $$p(a,b\|x,y,\lambda)$$? NOTE: This question has also been asked on quantumcomputing.SE. Copied from the same answer on quantumcomputing.SE. First of all, you inverted $$a,b$$ with $$x,y$$ when trying to draw the analogy. In Bell's original paper, $$\vec a,\vec b$$ are used to denote the measurement directions, so the underlying probability distribution should be written as $$p(x,y\|\vec a,\vec b,\lambda)=p(x\|\vec a,\lambda)p(y\|\vec b,\lambda).$$ The expectation values $$A(\vec a,\lambda)$$ and $$B(\vec b,\lambda)$$ used in Bell's paper would then be given by $$A(\vec a,\lambda)=\sum_x x p(x\|\vec a,\lambda)$$ and similarly for $$B$$. The sum is here extended over the possible values that can correspond to the measurement choice $$\vec a$$. In the case of Bell's paper, this amounts to $$x=\pm 1$$. To get the expectation value $$E(\vec a,\vec b)$$ you now simply need to take the average over the possible values of the hidden variable $$\lambda$$.	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 38, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9700821042060852, "perplexity": 230.41097492211202}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 5, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-30/segments/1563195528687.63/warc/CC-MAIN-20190723022935-20190723044935-00032.warc.gz"}
https://www.albert.io/ie/geometry/find-the-points-of-intersection-of-two-circles	Free Version Difficult # Find the Points of Intersection of Two Circles GEOM-RBV5YK Two circles are pictured below. Their equations are as follows: ${ (x-3 })^{ 2 }+{ (y-2) }^{ 2 }=16$ (red circle) ${ (x+1 })^{ 2 }+{ (y-1) }^{ 2 }=9$ (blue circle) Where do these circles intersect? A $(0.791, -1.425)$ and $(-0.587, 3.965)$ B $(0.8619, -1.355)$ and $(-0.498, 4.012)$ C $(0.842, -1.368)$ and $(-0.489, 3.956)$ D $(0.855, -1.377)$ and $(-0.499, 3.929)$ E $(0.842, -1.377)$ and $(-0.489, 3.929)$ F $(0.855, -1.368)$ and $(-0.499, 3.956)$ G $(0.842, -1.355)$ and $(-0.587, 3.956)$	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5631740093231201, "perplexity": 4244.413289432147}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-09/segments/1487501171630.65/warc/CC-MAIN-20170219104611-00460-ip-10-171-10-108.ec2.internal.warc.gz"}
http://quant.stackexchange.com/users/106/richard-herron?tab=activity&sort=all&page=2	Richard Herron Reputation 3,433 Top tag Next privilege 3,500 Rep. Protect questions Jan 31 awarded Yearling Jan 4 awarded Nice Answer Dec 16 awarded Nice Answer Nov 30 comment zero-sum active management riddle (As well, I would guess that the Roll critique of these pricing models is particularly strong in these less-sophisticated markets.) Nov 30 comment zero-sum active management riddle @QuantGuy -- Other than the case of value-weighted portfolios and value-weighted market factor (i.e., CAPM), I don't know of a requirement for $\sum_i w_i \alpha_i = 0$ and $\sum_i w_i \beta_i = 1$, where $w_i$ is the value weighting for each portfolio $i$. Nov 29 comment How to generate a random price series with a specified range and correlation with an actual price? How? Try AAPL and MSFT. There are about 5000 more. Nov 28 answered How to generate a random price series with a specified range and correlation with an actual price? Nov 28 answered zero-sum active management riddle Nov 27 reviewed Approve How to use Itô's formula to deduce that a stochastic process is a martingale? Nov 18 comment Convexity of BS Equation for Call and Put My first stop is checking $Call(\cdot, \lambda \sigma^2_1 + (1 - \lambda) \sigma^2_2) \leq \lambda Call(\cdot, \sigma^2_1) + (1 - \lambda)Call(\cdot, \sigma^2_2)$. Nov 14 comment How to check if a timeseries is stationary? @Dail -- There are a variety of tests, but Wald tests that all coefficients are jointly zero is probably the easiest. I searched for how to do this in R, but wasn't too successful. You will likely have to grab a text book and code the tests yourself. (I switched to Stata for most analyses because hypothesis testing is so much easier). Nov 14 comment How to check if a timeseries is stationary? @SKRX -- Yes, thanks. I should have included more commentary. He asked how to fit a GARCH model in R, so I gave some code. Once he determines the best-fitting GARCH model with ll, ic, and ssr, he can perform joint tests on the GARCH model coefficients. Nov 14 comment How GARCH/ARCH models are useful to check the volatility? The plots are helpful, but to determine if the GARCH model fits, you should use statistics. Look at the log-likelihood, sum-of-squared-residuals, and information criteria across various specifications to see which fits best. Then perform joint test of the GARCH coefficients. If you fail to reject that all coefficients are jointly zero, then you don't need a GARCH model. Nov 14 comment How GARCH/ARCH models are useful to check the volatility? fitted.values has +/- sigt (why isn't clear to me). You want to plot the positive sigt versus some time index. Something like this: y <- arch_model\$fitted.values[, 1] then x <- seq(1, length(y)) then plot(x, y). Nov 14 answered How to check if a timeseries is stationary? Nov 14 comment How to check if a timeseries is stationary? @Dam -- I will post some code in an answer. Nov 13 comment Any recommendations for textbooks for an undergraduate course in mathematical finance? Are MFE/MSCF students not well-prepared? I would guess that you'll find the right level in Shreve's two book series. If these kids are really that tough, then use Duffie's. Although if these kids don't have exposure to the concepts in finance, then you may be best of with Hull's book and beefing up the math where necessary. Nov 13 comment How to check if a timeseries is stationary? @Dam -- You can reject the unit root and still have time-varying volatility. Maybe you want to fit an ARCH model? Nov 13 comment How to check if a timeseries is stationary? I agree with the Phillips-Perron test. The Augmented Dickey-Fuller test is not robust to the selection of the number of lags. The KPSS test differs from these two tests in its null hypothesis, which is trend stationarity. Sep 22 awarded Enlightened	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6404587626457214, "perplexity": 1687.9140120593775}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2015-48/segments/1448398449258.99/warc/CC-MAIN-20151124205409-00239-ip-10-71-132-137.ec2.internal.warc.gz"}
https://www.math.uconn.edu/research/seminars/show-poster/?TalkID=15312	# A Functional Analytic Approach to Self-improvement Properties ## Simon Bortz (University of Minnesota) ### Friday, March 9, 2018 1:30 pmMONT 414 In 1963, Norman Meyers showed that $W^{1,2}_{loc}$ solutions to divergence form elliptic operators have a gradient in $L^p$ for some $p > 2$. Modern proofs of this fact utilize the Gehring Lemma (1973). This property can be observed in fractional integro-differential equations. In fact, one can show that solutions to these fractional equations improve in differentiability as well; this was recently investigated by Kuusi, Mingione and Sire. Led by this, my co-authors and I sought to exploit hidden' non-local structure in parabolic equations to prove that solutions are locally HÃ¶lder in time with values in $L^p$ for some $p > 2$. While the Gehring' approach was effective, we found an alternative functional analytic proof that is quite simple. I will show how to apply this functional analysis approach to parabolic equations in detail, then I will indicate how this method applies to other equations. This is joint work with P. Auscher, M. Egert and O. Saari.	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9469664692878723, "perplexity": 825.7004963632746}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-39/segments/1537267160233.82/warc/CC-MAIN-20180924070508-20180924090908-00073.warc.gz"}
https://anengineersutopia.wordpress.com/2015/11/07/mplabx-build-projects-from-command-line/	HOW TO BUILD MPLAB X PROJECTS FROM THE COMMAND LINE? A Quick Introduction MPLAB X IDE is a software program that is used to develop applications for Microchip microcontrollers and digital signal controllers. This development tool is called an Integrated Development Environment, or IDE, because it provides a single integrated “environment” to develop code for embedded microcontrollers. Why build from Command line, when I can do with one click We can build the project in MPLAB X IDE with one click on any of the following icons In this way the IDE works great and makes it easy to develop and build projects. however, building releases locally on developer machines is not the ideal way to be releasing software. Usually we want to automate the build and test software continuously using a platform like Jenkins. Jenkins is cross-platform, continuous integration and continuous delivery application that increases your productivity. Using Jenkins to build and test your software projects continuously makes it easier for developers to integrate changes to the project and makes it easier for users to obtain a fresh build. It also allows you to continuously deliver your software by providing powerful ways to define your build pipelines and integrating with a large number of testing and deployment technologies. Continuous Integration (CI) and automated build servers solve this problem and are in widespread use by the software industry. To automate build, we need to set up Embedded toolchains which can be complicated and time-consuming. IDEs do a good job of making this easy, but build servers usually require building the projects through scripts and the command line. I’ve seen a lot of people asking questions about how to build their MPLABX projects through the command line, presumably so that they can set up automated build servers for their projects. The process is really quite simple once you understand how MPLABX builds a release., • Firstly it generates a Makefile based on the build configuration and settings of your project. • Secondly it runs the build using the generated Makefile. Following steps show how to set up and build from command line: Environment Setup 1. Make sure you have the latest version of MPLABX. Look inside your MPLABX installation folder and browse to batch file which creates makefile C:\Program Files(x86)\Microchip\MPLABX\v3.05\mplab_ide\bin\ . If you see a file called prjMakefilesGenerator.bat then move on to the next step. Otherwise, update your copy of MPLABX. 2. Add the folder containing prjMakefilesGenerator.bat to PATH. This will allow you to run the Makefile generator simply by typing its name on the command line. On Windows, the directory you will need to add to PATH will most likely be C:\Program Files(x86)\Microchip\MPLABX\v3.05\mplab_ide\bin\. 3. Add the MPLABX utilities required to run a Makefile to PATH. The utilities are located inside the MPLABX installation folder inside of \gnuBins\GnuWin32\bin\ . This will allow you to run the Makefile simply by using the command make . On Windows the directory you will need to add to PATH will most likely be C:\Program Files (x86)\Microchip\MPLABX\v3.05\gnuBins\GnuWin32\bin\ . Make sure that you don’t have any other make commands on your path else this might cause some issues. What Next Building the Project 1. Open up a command line and browse to the project’s root folder. 2. Run the prjMakefilesGenerator.bat to generate the Makefile. The Makefile should now appear in the project’s root directory. If you are going to be building on a build server, you won’t always know what the full path is. On a Windows build machine, you could use the following command instead: This will automatically insert the path of the current directory when you run the command. 3. Find out what the build command is by running the GUI version of MPLABX. Open the project you are trying to build and run the “Clean and Build” command. Then look in the Output window (If you don’t see it, try Windows > Output > Output) to see the command that was run. Look for the first command starting with make . The command should look something like this: 1. You can replace buildconfigname from the line above with whatever build configuration you want to build.	{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8940939903259277, "perplexity": 1596.8859246779084}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-34/segments/1502886120194.50/warc/CC-MAIN-20170823113414-20170823133414-00255.warc.gz"}
http://demonstrations.wolfram.com/EmpiricalCharacteristicFunction/	# Empirical Characteristic Function Requires a Wolfram Notebook System Interact on desktop, mobile and cloud with the free Wolfram CDF Player or other Wolfram Language products. Requires a Wolfram Notebook System Edit on desktop, mobile and cloud with any Wolfram Language product. The empirical characteristic function (ecf) of a random sample {, , ...} from a statistical distribution is defined by [more] In this representation, each random variable can be envisioned as a particle orbiting the unit circle in the complex plane. The ecf is the expected orbit or mean of the random variable orbits. For large , the ecf converges to the distribution characteristic function. The graphic shows the orbit of a standardized stable distribution with parameters and in blue. The orbit of the ecf of 500 random variables with the same parameters is shown in red and the position, at , of each random variable on the unit circle is shown as a blue dot. The red dot is the mean of these positions. Each time you change the or slider a new random sample is generated. When or , the distribution will be symmetric about zero and the characteristic function will be confined to the real line, the axis in this Demonstration. [less] Contributed by: Bob Rimmer (March 2011) Open content licensed under CC BY-NC-SA ## Details The characteristic function of a statistical distribution is the Fourier transform of the derivative of its distribution function. A stable distribution is used in the example. Stable distributions lack for most cases a distribution function with an explicit formula. The standardized stable characteristic function, however, is straightforward: . At , , as must the empirical characteristic function. The ecf converges with the characteristic function most quickly where is close to zero. As the sample size grows, the convergence becomes closer further from . Empirical characteristic functions can be used for parameter estimation in cases where the characteristic function of the statistical distribution is known. They can be used alone in the same way one would use a known characteristic function. For instance, the characteristic function of a sum of random variables is equal to the product of the characteristic functions of each independent random variable. Or a symmetrized characteristic function can be created from the product of the characteristic function and its conjugate. Examples and Mathematica code for use of empirical CharacterCode functions can be found at mathestate. ## Permanent Citation Bob Rimmer Feedback (field required) Email (field required) Name Occupation Organization Note: Your message & contact information may be shared with the author of any specific Demonstration for which you give feedback. Send	{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8160111308097839, "perplexity": 493.5837334780451}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-43/segments/1539583515041.68/warc/CC-MAIN-20181022113301-20181022134801-00383.warc.gz"}
https://www.physicsforums.com/threads/crames-rule-and-equation-of-a-plane.199957/	# Crames Rule and equation of a plane 1. Nov 22, 2007 ### succubus I am doing a presentation on the 3-point problem in Geology. We have to use Cramers Rule to solve for the equation of a plane. I can do it no problem, but since I have to present it, I want to be prepared to answer all questions my teacher may ask. For example: Why is the equation of a plane written like this \| x y z 1\| \|x1 y1 z1 1\| \|x2 y2 z2 1\| \|x3 y3 z3 1\| The top is just the vector we multiply by to come up with the equation of a line? (when we expand by cofactors) I'm not sure exactly. Unfortunately I did not take the required pre-req to get into this class, they let me in, so I took on a project that was a little beyond me at this point. Also, what is the definition of a determinant? I can show how they work, ubt I don't have a description of what they really represent. Everything I look up and every book I have just show you how to analyze them, not what they really represent. Any help on the explanation of this would be great. -Pati 2. Nov 22, 2007 ### Chris Hillman Attempting to answer a technically tricky question in an intuitive way Geometry? As in: find the equation of the plane through three given points in ordinary three-dimensional euclidean space? Well, can you answer this? Why is the equation of the line through two points in the plane $R^2$ given by $$\left\| \begin{array}{ccc} x & y & 1 \\ x_1 & y_1 & 1 \\ x_2 & y_2 & 1 \end{array} \right\| = 0$$ Well, proving the key property of determinants for nxn matrices, the multiplication law $$\det (A \, B) = \left( \det A \right) \, \left( \det B \right)$$ is a bit tricky. The preferred modern proof is nowadays done in a course on exterior algebra (Grassmann algebra). But there is a lovely and elementary proof from graph theory! (Can't find the citation right now, but I can't be the only one who is thinking of the paper I am thinking of, so speak up, please, if you think you might recall the citation I intend.) When I taught linear algebra, I explained this in terms of a "hierarchical counting problem", but this interpretation is more abstract than geometrical. As for intuition: geometrically speaking, the determinant is kind of like a signed volume; see section 10.3 of Birkhoff and Mac Lane, A Survey of Modern Algebra, 4th ed., MacMillan, 1977 for a proof of the following: Theorem (Gram's Formula). The squared volume of the parallipiped in $R^n$ with edges given by the rows of the nxn matrix A is $\det A A^t$ (This is a generalization of the cosine law from elementary trigonmetry.) Theorem. The linear operator P multiplies the volumes of all parallipipeds by $\pm \det P$ (depending on whether or not P reverses orientation). If you know about elementary matrices, as an exercise you can try to prove these yourself by considering more and more elaborate matrices. Last edited: Nov 22, 2007 3. Nov 22, 2007 ### succubus Geometry? As in: find the equation of the plane through three given points in ordinary three-dimensional euclidean space? The answer is yes. I guess I should have been more precise. You see, were doing the three point problem in Geology. You have 3 elevations and 3 coordinates (x,y) and you need to find strike, dip, and dip direction for the plane. Basically, we have to find the equation of the plane in order to determine those other elements. Which comes upon another question I have, which is regarding the strike. (Don't see clearly why you take the arctan of the partial derivative of x with respect to y instead of the opposite) In any case, I just need to be able to explain (at least I think) why the equation of a plane is written like that. And the equation of 2 points for that matter. So the answer is no, I don't see why it's written that way :) 4. Nov 22, 2007 ### Chris Hillman Ow, ow, ow (revenge of the dead trees!) ... Mrmph... eh? Oh, sorry, I've been trying to find that citation and so far can't, arghghgh! Probably one of those nifty papers by Philip Straffin... Anyway, from similar triangles, the equation of the line through the points $$(x_1, \, y_1), \; (x_2, \, y_2)$$ is (draw a sketch!): $$\frac{x-x_1}{x-x_2} = \frac{y-y_1}{y-y_2}$$ On the other hand $$\left\| \begin{array}{ccc} x & y & 1 \\ x_1 & y_1 & 1 \\ x_2 & y_2 & 1 \end{array} \right\| = \left\| \begin{array}{ccc} x & y & 1 \\ x-x_1 & y-y_1 & 0 \\ x-x_2 & y-y_2 & 0 \end{array} \right\| = \left\| \begin{array}{cc} x-x_1 & y-y_1 \\ x-x_2 & y-y_2 \end{array} \right\|$$ which vanishes iff the equation of the line holds true. (This is Exercise 10.1.10 in Birkhoff and Mac Lane, incidentally.) Here's a hint for the higher dimensional case: consider difference vectors wrt the undetermined point (x,y,z); what property do they have iff (x,y,z) lies in the plane spanning the three given points? I should have asked whether you have a preference for row vectors or column vectors (in the latter case, transpose the matrices in the argument I wrote out above). I am afraid I am not familiar with the terms from geology (surveying, perchance?) "dip", "strike". For the hyperplane through n points in $R^n$ we put n difference vectors in an n by n determinant and rewrite the latter as an n+1 by n+1 determinant as above, then apply the remark about the difference vectors having a certain familiar algebraic property iff the undetermined point lies in the hyperplane. Statement and proof are really about convex combinations of vectors so this is a fact about n-dimensional affine geometry. No notion of angle or distance is needed! For an algebraic interpretation of basically the same argument, see M. G. Kendall, A Course in the Geometry of n Dimensions, Dover reprint. Last edited: Nov 23, 2007 Similar Discussions: Crames Rule and equation of a plane	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8390898704528809, "perplexity": 472.8450280546167}, "config": {"markdown_headings": true, "markdown_code": false, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-26/segments/1498128323604.1/warc/CC-MAIN-20170628101910-20170628121910-00431.warc.gz"}
https://artofproblemsolving.com/wiki/index.php/1969_AHSME_Problems/Problem_28	# 1969 AHSME Problems/Problem 28 ## Problem Let be the number of points interior to the region bounded by a circle with radius , such that the sum of squares of the distances from to the endpoints of a given diameter is . Then is: ## Solution Let and be points on diameter. Extend , and mark intersection with circle as point . Because is a diameter, . Also, by Exterior Angle Theorem, , so , making an obtuse angle. By the Law of Cosines, . Since , substitute and simplify to get . This equation has infinite solutions because for every and , where and and are both less than , there can be an obtuse angle that satisfies the equation, so the answer is .	{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.989006519317627, "perplexity": 383.45531429844283}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-43/segments/1634323585507.26/warc/CC-MAIN-20211022114748-20211022144748-00015.warc.gz"}
http://mathoverflow.net/questions/71023/symplectic-matrices-with-integer-entries?sort=votes	# Symplectic Matrices with Integer Entries I have a couple questions regarding symplectic matrices, specifically those with integer entries. 1) Suppose we are trying to find symplectic matrices of dimension $4$ with integer entries. We know that eigenvalues come in reciprocal pairs; we are assuming that the symplectic matrix $A$ has irreducible characteristic polynomial so the eigenvalues are distinct. Also we want the eigenvalues real. Thus, it is necessary for the characteristic polynomial of $A$ to be of the form $$f = x^4 - nx^3 + (2+m)x^2 -nx+1$$ where $n,m \in \mathbb{Z}$. The question is, if we have an irreducible $f$ of this form, with roots $\lambda, \lambda ^{-1}, \mu, \mu^{-1}$, is it possible to construct an integer matrix which is symplectic with this characteristic polynomial? 2) Suppose the construction in 1) is possible, and we have matrix A. Are there any properties on matrices in the conjugacy class of A over $\mathbb{Q}$ which ensure that those matrices are symplectic? That is, is there a way to find matrices conjugate to a symplectic matrix A which are also symplectic? Thanks for any help or any suggestions on literature to read. - The answer to the first question is "yes", see p 21 of http://arxiv.org/pdf/math/0703532v1 On that same page, if you look at conditions (6-8), that should answer your second question with a little work... - Thank you for the reference; that is very helpful. – CCALNS Jul 23 '11 at 18:38 Thanks for the help - I still had a few questions, see below. – CCALNS Jul 24 '11 at 21:18 For some value of "below". – Gerry Myerson Jul 25 '11 at 5:49 I'm having some trouble constructing a 4 by 4 symplectic matrix with characteristic polynomial $f = x^4 - nx^3 + (2+m)x^2 -nx+1$ and I haven't been able to find where I'm going wrong. We have a matrix $$\left(\begin{array}{cccc} 0 & 0 & 1 & \mathrm{b2}\newline 0 & 0 & \mathrm{b2} & \mathrm{b3}\newline -\frac{\mathrm{b3}}{\mathrm{b3} - {\mathrm{b2}}^2} & \frac{\mathrm{b2}}{\mathrm{b3} - {\mathrm{b2}}^2} & -1 & \mathrm{f1} + 1\newline \frac{\mathrm{b2}}{\mathrm{b3} - {\mathrm{b2}}^2} & -\frac{1}{\mathrm{b3} - {\mathrm{b2}}^2} & 1 & \mathrm{f2} \end{array}\right)$$ as constructed in the paper. We can compute the characteristic polynomial and obtain the conditions on $f1, f2$ that $f1 = -n-m-2$, $f2 = n+1$. Then by requiring that $M^TJM = J$, where $J = \left(\begin{array}{cccc} 0 & 0 & 1 & 0\newline 0 & 0 & 0 & 1\newline -1 & 0 & 0 & 0\newline 0 & -1 & 0 & 0 \end{array}\right)$, we have that $-1 - m - n + b2\cdot (n+2) = b3$. Then plugging in for $b3$ in $M$ and using the fact that $\det B = 1$ we find $b2^2 - b2\cdot (2 + n) + m + n =0$. We want $b2$ to be an integer but I can't figure out how to get this to always be an integer for any arbitrary $n,m$. Also, I was wondering for the second part of the question, the above comment suggested that we look at the block form of the matrices. However, when we conjugate, we would need to get the inverse of a matrix in block form, so that looking at the matrix in block form does not seem to give an additional advantage. Are there any other conditions for matrices conjugate to a given symplectic matrix to be symplectic? For example, given a symplectic matrix $A$ where $B$ and $C$ are symplectic matrices conjugate to $A$ over $\mathbb{Z}$ (or $\mathbb{Q}$) thus $B = S^{-1} C S$, must $S^{-1} A S$ be symplectic? That is, if $S$ conjugates one symplectic matrix to another symplectic matrix in the conjugacy class of $A$ (over $\mathbb{Z}$ or $\mathbb{Q}$), will $S$ also conjugate $A$ to a symplectic matrix? -	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9721978306770325, "perplexity": 148.4794522741971}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2015-22/segments/1432207928102.74/warc/CC-MAIN-20150521113208-00017-ip-10-180-206-219.ec2.internal.warc.gz"}
http://mathhelpforum.com/differential-geometry/189768-can-open-balls-pairwise-intersections-balls-generate-topology-print.html	# Can open balls and pairwise intersections of balls generate a topology? • Oct 7th 2011, 03:06 PM algorytmus 1 Attachment(s) Can open balls and pairwise intersections of balls generate a topology? Hi, I have a question. Can the following topology base generate a topology(a family of sets)?: X - finite set of points, d - metric B - open ball in X r - ray, const value Additionally, how could be the cover of a family of sets in topology realized ? algorytmus • Oct 7th 2011, 03:41 PM hatsoff Re: Can open balls and pairwise intersections of balls generate a topology? A family $\mathcal{F}$ of sets generates a topology on $X$ just in case: (1) $\mathcal{F}\subseteq 2^X$; (2) $x\in X$ $\implies$ $\exists B\in\mathcal{F}$ such that $x\in B$; (3) $x\in B_1\cap B_2$ for $B_1,B_2\in\mathcal{F}$ $\implies$ $\exists B_3\in\mathcal{F}$ such that $x\in B_3\subseteq B_1\cap B_2$. Your collection satisfies these requirements. In fact, notice that the second term of the union is superfluous, and that $\mathcal{B}=\{B_d(x,r):x\in X,r>0\}$. Given that $X$ is finite, this means $\mathcal{B}=2^X\setminus\emptyset$, i.e. it generates the discrete topology. I'm not sure what you mean by realizing a cover of a family of sets though. • Oct 7th 2011, 04:21 PM algorytmus Re: Can open balls and pairwise intersections of balls generate a topology? Thank you for help! Could you correct me if I am wrong in the following: Let me illustrate examples geometrically. Given X={a, b, c} the topological base is $\mathcal{B}$={{B_a},{B_b},{B_c},{B_a,B_b},{B_b,B_c}} , for $\mathcal{B}$={{B_a},{B_b},{B_c}} Well if you mean that $\mathcal{B}=\{\{x\}:x\in X\}$, then it still generates the discrete topology.	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 18, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8228888511657715, "perplexity": 876.2409520137687}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-05/segments/1516084890893.58/warc/CC-MAIN-20180121214857-20180121234857-00484.warc.gz"}
http://rcd.ics.org.ru/archive/volume-2-number-1/	0 2013 Impact Factor # Volume 2, Number 1, 1997 Kozlov V. V. Closed Orbits and Chaotic Dynamics of a Charged Particle in a Periodic Electromagnetic Field Abstract We study motion of a charged particle on the two dimensional torus in a constant direction magnetic field. This analysis can be applied to the description of electron dynamics in metals, which admit a $2$-dimensional translation group (Bravais crystal lattice). We found the threshold magnetic value, starting from which there exist three closed Larmor orbits of a given energy. We demonstrate that if there are n lattice atoms in a primitive Bravais cell then there are $4+n$ different Larmor orbits in the nondegenerate case. If the magnetic field is absent the electron dynamics turns out to be chaotic, dynamical systems on the corresponding energy shells possess positive entropy in the case that the total energy is positive. Citation: Kozlov V. V., Closed Orbits and Chaotic Dynamics of a Charged Particle in a Periodic Electromagnetic Field, Regular and Chaotic Dynamics, 1997, vol. 2, no. 1, pp. 3-12 DOI:10.1070/RD1997v002n01ABEH000021 Bolsinov A. V., Dullin H. R. On Euler Case in Rigid Body Dynamics and Jacobi Problem Abstract Using two classical integrable problems, we demonstrate some methods of a new theory of orbital classification for integrable Hamiltonian systems with two degrees of freedom. We show that the Liouville foliations (i.e., decompositions of the phase space into Liouville tori) of the two systems under consideration are diffeomorphic. Moreover, these systems are orbitally topologically equivalent, but this equivalence cannot be made smooth. Citation: Bolsinov A. V., Dullin H. R., On Euler Case in Rigid Body Dynamics and Jacobi Problem, Regular and Chaotic Dynamics, 1997, vol. 2, no. 1, pp. 13-25 DOI:10.1070/RD1997v002n01ABEH000022 Rothos V. M., Bountis A. The Second Order Mel'nikov Vector Abstract Mel'nikov's perturbation method for showing the existence of transversal intersections between invariant manifolds of saddle fixed points of dynamical systems is extended here to second order in a small parameter $\epsilon$. More specifically, we follow an approach due to Wiggins and derive a formula for the second order Mel'nikov vector of a class of periodically perturbed $n$-degree of freedom Hamiltonian systems. Based on the simple zero of this vector, we prove an $O(\epsilon^2)$ sufficient condition for the existence of isolated homoclinic (or heteroclinic) orbits, in the case that the first order Mel'nikov vector vanishes identically. Our result is applied to a damped, periodically driven $1$-degree-of-freedom Hamiltonian and good agreement is obtained between theory and experiment, concerning the threshold of heteroclinic tangency. Citation: Rothos V. M., Bountis A., The Second Order Mel'nikov Vector, Regular and Chaotic Dynamics, 1997, vol. 2, no. 1, pp. 26-35 DOI:10.1070/RD1997v002n01ABEH000023 Bagrets A. A., Bagrets D. A. Nonintegrability of Hamiltonian systems in vortex dynamics. I. The interactions of three vortex rings Abstract The problem of the interaction of three coaxial vortex rings in an ideal fluid is studied. By introducing an artifical small parameter and using the separatrix split method the nonintegrability of the restricted problem is proved analytically. Citation: Bagrets A. A., Bagrets D. A., Nonintegrability of Hamiltonian systems in vortex dynamics. I. The interactions of three vortex rings, Regular and Chaotic Dynamics, 1997, vol. 2, no. 1, pp. 36-42 DOI:10.1070/RD1997v002n01ABEH000024 Morozov A. D., Dragunov T. N. On Research of Henon-Heiles-type Systems Abstract Three-parametrical family of systems with two degrees of freedom of a kind $$\begin{array}{rcl} \dfrac{d^2x_1}{dt^2}+x_1&=&-2\varepsilon x_1x_2\\ \dfrac{d^2x_2}{dt^2}+x_2-x_2^2&=&\varepsilon (-x_1^2+\delta\dot{x}_2+\gamma x_2\dot{x}_2), \end{array}\qquad\qquad()$$ where $\varepsilon>0$ is considered. Analytical research of trajectories behaviour of the system $()$ is carried out when $\varepsilon$ is small. The given research is connected, first of all, to the analysis of resonant zones. Alongside with the initial system, another system $$\ddot{x}_2+x_2-x_2^2=\varepsilon(-A^2\sin^2t+\delta\dot{x}_2+\gamma x_2\dot{x}_2)\qquad\qquad()$$ that is "close" to the original, is considered. A good concurrence of results for Poincare mapping, induced by an equation $()$ when $\delta=\gamma=0$, and for the mapping that was constructed by Henon and Heiles, is established. In addition, for system $(*)$ a transition to nonregular dynamics is numerically analyzed at increase of parameter $\varepsilon$ and $\delta=\gamma=0$. It is established, that the transition to nonregular dynamics is connected, in particular, with the period doubling bifurcation (known as Feigenbaum's script), and $\varepsilon_\infty\approx0.95$. Citation: Morozov A. D., Dragunov T. N., On Research of Henon-Heiles-type Systems, Regular and Chaotic Dynamics, 1997, vol. 2, no. 1, pp. 43-54 DOI:10.1070/RD1997v002n01ABEH000025 Eleonski V. M., Korolev V. G., Kulagin N. E. On Hamiltonian Dynamical Systems with Kinetic Energy Depending on Momenta Modules Abstract We consider a new class of Hamiltonian dynamical systems with two degrees of freedom whose kinetic energy is a function of momenta's modules. Equations of motion for such systems are easily integrated in each of succesive time intervals; thus, in principle, all the trajectories can be found explicitly. A Poincare mapping for such systems can be reduced to a mapping of the least positive root for a system of transcendental (in the general case) equations. On the other hand, dynamical systems of this type exhibit a number of properties typical to non-intergable systems (e.g., an existence of stable and unstable periodic orbits, their bifurcations, creation of stochastic layers in vicinity of destroyed separatrices, regions of global chaotic motion, etc.). As an example, a system with a simple potential that is quadratic in both coordinates is studied. Citation: Eleonski V. M., Korolev V. G., Kulagin N. E., On Hamiltonian Dynamical Systems with Kinetic Energy Depending on Momenta Modules, Regular and Chaotic Dynamics, 1997, vol. 2, no. 1, pp. 55-63 DOI:10.1070/RD1997v002n01ABEH000026 Borisov A. V., Simakov N. N. Period Doubling Bifurcation in Rigid Body Dynamics Abstract Taking a classical problem of motion of a rigid body in a gravitational field as an example, we consider Feigenbaum's script for transition to stochasticity. Numerical results are obtained using Andoyer-Deprit's canonical variables. We calculate universal constants describing "doubling tree" self-duplication scaling. These constants are equal for all dynamical systems, which can be reduced to the study of area-preserving mappings of a plan onto itself. We show that stochasticity in Euler-Poisson equations can progress according to Feigenbaum's script under some restrictions on the parameters of our system. Citation: Borisov A. V., Simakov N. N., Period Doubling Bifurcation in Rigid Body Dynamics, Regular and Chaotic Dynamics, 1997, vol. 2, no. 1, pp. 64-74 DOI:10.1070/RD1997v002n01ABEH000027 Karapetyan A. V. First Integrals, Invariant Sets and Bifurcations in Dissipative Systems Abstract The paper deals with dissipative mechanical systems. Problems of the existance of linear constants of motion and invariant sets, their stability and bifurcation are discussed. Citation: Karapetyan A. V., First Integrals, Invariant Sets and Bifurcations in Dissipative Systems, Regular and Chaotic Dynamics, 1997, vol. 2, no. 1, pp. 75-80 DOI:10.1070/RD1997v002n01ABEH000028 Moshchevitin N. G. Multidimensional Diophantine Approximations and Dynamical Systems Abstract The paper represents a brief review of some general laws of multidimensional Diophantine approximations and their applications to the theory of uniform distributions and certain dynamical systems. Citation: Moshchevitin N. G., Multidimensional Diophantine Approximations and Dynamical Systems, Regular and Chaotic Dynamics, 1997, vol. 2, no. 1, pp. 81-95 DOI:10.1070/RD1997v002n01ABEH000029 Matveev V. S. Quadratically Integrable Geodesic Flows on the Torus and on the Klein Bottle Abstract We classify integrable geodesic flows on the torus and on the Klein bottle, which in addition admit a quadratic in momenta first integral. We also study cases if there exists an additional linear integral. Citation: Matveev V. S., Quadratically Integrable Geodesic Flows on the Torus and on the Klein Bottle, Regular and Chaotic Dynamics, 1997, vol. 2, no. 1, pp. 96-102 DOI:10.1070/RD1997v002n01ABEH000030 Matveev V. S., Topalov P. I. Jacobi Vector Fields of Integrable Geodesic Flows Abstract We show that an invariant surface allows to construct the Jacobi vector field along a geodesic line and construct the formula for the normal part of the Jacobi field. If a geodesic line is the transversal intersection of two invariant surfaces (such situation we have, for example, if the geodesic line is hyperbolic) than we can construct the fundamental solution of Jacobi equation $\ddot{u}=-K(t)u$. That was done for quadratically integrable geodesic flows. Citation: Matveev V. S., Topalov P. I., Jacobi Vector Fields of Integrable Geodesic Flows, Regular and Chaotic Dynamics, 1997, vol. 2, no. 1, pp. 103-116 DOI:10.1070/RD1997v002n01ABEH000031 Back to the list	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8257362246513367, "perplexity": 459.52141227788456}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-39/segments/1568514571360.41/warc/CC-MAIN-20190915114318-20190915140318-00018.warc.gz"}
https://blogs.ams.org/visualinsight/2014/09/	# {3,3,7} Honeycomb Meets Plane at Infinity The {3,3,7} honeycomb is a honeycomb in 3d hyperbolic space. It is the dual of the {7,3,3} honeycomb shown last time. This image, drawn by Roice Nelson, shows the ‘boundary’ of the {3,3,7} honeycomb: that is, the set of points on the ‘plane at infinity’ that are limits of points in the {3,3,7} honeycomb.	{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9517344832420349, "perplexity": 2975.418960826811}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-24/segments/1590347391309.4/warc/CC-MAIN-20200526191453-20200526221453-00390.warc.gz"}
https://coolconversion.com/math/sigma-calculator/	Please get in touch with us if you: 1. Have any suggestions 2. Have any questions 3. Have found an error/bug 4. Anything else ... # Sigma Notation Calculator This sigma sum calculator computes the sum of a series over a given interval. Fill in the variables 'from', 'to', type an expression then click on the button calculate. This summation notation calculator can sum up many types of sequencies including the well known arithmetic and geometric sequencies, so it can help you to find the terms including the nth term as well as the sum of the first n terms of virtualy any series. Σ is the symbol used to denote sum. It is the uppercase Greek letter sigma. Σ n = toexpression from ## This video introduces sigma notation and explains how to determine a sum expressed using sigma notation. Below is a list of operators, functions and contants supported by our sum of series calculator. ### Suported Operators • - Subtraction operator • * Multiplication operator • / Division operator • ^ Power/Exponent operator • () Parentheses ### Constants • pi The constant π (3.1415926535897932384626433...). It is defined as the ratio of a circle's circumference C to its diameter d. • e Euler's Number (2.7182818284590452353602874...), the base for the natural logarithm ### Suported Functions • sin() sine function • cos() cosine function • tan() tangent function • asin() inverse sine (arcsine) function • acos() inverse cosine (arccos) function • atan() inverse tangent (arctangent) function • sqrt() square root function • log() The natural logarithm function • log10() The base-10 logarithm function • exp() e (the Euler Constant) raised to the power function • abs() Absolute value function ### Disclaimer While every effort is made to ensure the accuracy of the information provided on this website, we offer no warranties in relation to these informations.	{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8899856805801392, "perplexity": 4223.136568891266}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-51/segments/1544376823322.49/warc/CC-MAIN-20181210101954-20181210123454-00171.warc.gz"}
http://codeforces.com/problemset/problem/1076/D	Please subscribe to the official Codeforces channel in Telegram via the link: https://t.me/codeforces_official. × D. Edge Deletion time limit per test 2.5 seconds memory limit per test 256 megabytes input standard input output standard output You are given an undirected connected weighted graph consisting of $n$ vertices and $m$ edges. Let's denote the length of the shortest path from vertex $1$ to vertex $i$ as $d_i$. You have to erase some edges of the graph so that at most $k$ edges remain. Let's call a vertex $i$ good if there still exists a path from $1$ to $i$ with length $d_i$ after erasing the edges. Your goal is to erase the edges in such a way that the number of good vertices is maximized. Input The first line contains three integers $n$, $m$ and $k$ ($2 \le n \le 3 \cdot 10^5$, $1 \le m \le 3 \cdot 10^5$, $n - 1 \le m$, $0 \le k \le m$) — the number of vertices and edges in the graph, and the maximum number of edges that can be retained in the graph, respectively. Then $m$ lines follow, each containing three integers $x$, $y$, $w$ ($1 \le x, y \le n$, $x \ne y$, $1 \le w \le 10^9$), denoting an edge connecting vertices $x$ and $y$ and having weight $w$. The given graph is connected (any vertex can be reached from any other vertex) and simple (there are no self-loops, and for each unordered pair of vertices there exists at most one edge connecting these vertices). Output In the first line print $e$ — the number of edges that should remain in the graph ($0 \le e \le k$). In the second line print $e$ distinct integers from $1$ to $m$ — the indices of edges that should remain in the graph. Edges are numbered in the same order they are given in the input. The number of good vertices should be as large as possible. Examples Input 3 3 2 1 2 1 3 2 1 1 3 3 Output 2 1 2 Input 4 5 2 4 1 8 2 4 1 2 1 3 3 4 9 3 1 5 Output 2 3 2	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.4151967465877533, "perplexity": 189.94558892559658}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-51/segments/1544376823339.35/warc/CC-MAIN-20181210123246-20181210144746-00537.warc.gz"}
https://ltwork.net/2-tim-had-355-dollars-to-spend-on-9-books-after-buying-them--2310443	# 2. Tim had 355 dollars to spend on 9 books. After buying them he had 13 dollars. How muchdid each book cost?Equation: ###### Question: 2. Tim had 355 dollars to spend on 9 books. After buying them he had 13 dollars. How much did each book cost? Equation: ### In a certain city, 30% of the families have a MasterCard, 20% have an American Express card, and 25% have a Visa card.Eight percent In a certain city, 30% of the families have a MasterCard, 20% have an American Express card, and 25% have a Visa card. Eight percent of the families have both a MasterCard and an American Express card. Twelve percent have both a Visa card and a MasterCard. Six percent have both an American Express... ### Which of the following elasticities are compatible with a Marhallian demand gx(px, py, I) that is homogeneous Which of the following elasticities are compatible with a Marhallian demand gx(px, py, I) that is homogeneous of degree zero in prices and income if the good x is normal and the good x and the other good y are gross complements? (a) ex, px = 0.09, /ex, py = −0.91/ex, I = 0.82 (b) ex, px = −2.74... ### Enter your gross pay, taxes, and deductions below. Press calculate when you’re ready.Gross Pay1,837.00Tax362.81Deduction? Enter your gross pay, taxes, and deductions below. Press calculate when you’re ready. Gross Pay 1,837.00 Tax 362.81 Deduction ?... ### PLEASE HELP Below is a list of causes of the First World War. Rank These in order of significance (where PLEASE HELP Below is a list of causes of the First World War. Rank These in order of significance (where 1 is the most significant and 6 is the least) and give brief reasons for the positioning of each reason in your list: • the alliance system in Europe • the naval and arms race • the invasio... ### Read the sentence below and answer the question that follows. for my birthday, i received bongos six Read the sentence below and answer the question that follows. for my birthday, i received bongos six months’ worth of lessons. which word coordinates the ideas and completes the sentence? but however and furthermore... ### All the following are characteristics true of athens except what? a. they valued beauty and art. b. All the following are characteristics true of athens except what? a. they valued beauty and art. b. they believed in the study of war. c. they valued education and wisdom. d. they had a strong democracy.... ### Will mark brainiest: What is the area of a circle with a radius of 7 cm? (Use 3.14 for Pi and round to the nearest tenth.) 38.5 Will mark brainiest: What is the area of a circle with a radius of 7 cm? (Use 3.14 for Pi and round to the nearest tenth.) 38.5 centimeters squared 44.0 centimeters squared 150.0 centimeters squared 153.9 centimeters squared... ### John brown, harriet beecher stowe, and william lloyd garrison are all associated a.)abolition b.)woman’s John brown, harriet beecher stowe, and william lloyd garrison are all associated a.)abolition b.)woman’s suffrage c.) temperance d.)calvinism... ### What do 8 counters in 2 equal groups look like ? What do 8 counters in 2 equal groups look like ?... ### Write an INEQUALITY that represents the phrase: A player must have an ERA that is higher than 4.27 to try out for the MLB. Use e as your Write an INEQUALITY that represents the phrase: A player must have an ERA that is higher than 4.27 to try out for the MLB. Use e as your variable.... ### Solve 9=1 + 8x - 8 a. x=2 b. x=all real numbers c. x=8 d. x=10 Solve 9=1 + 8x - 8 a. x=2 b. x=all real numbers c. x=8 d. x=10... ### I need help, I am confused. I need help, I am confused. $I need help, I am confused.$... ### How do non-governmental oThe primary reason the United States advocated the Open Door Policy was to organizations differ from How do non-governmental oThe primary reason the United States advocated the Open Door Policy was to organizations differ from national governments?... ### Asoccer ball is kicked into the air from a height of 3 feet with an initial velocity of 72 feet per Asoccer ball is kicked into the air from a height of 3 feet with an initial velocity of 72 feet per second. how many seconds is the ball 84 feet above the ground?... ### B. The letter e is pronounced 'ay,' as in the English word 'pay.' Write three Spanishnumbers under ten that contain the letter B. The letter e is pronounced "ay," as in the English word "pay." Write three Spanish numbers under ten that contain the letter e. Say each word as you write it, paying special attention to the e.... ### Most asteroids are located between the orbits of mars and jupiter in the asteroids belt true or false Most asteroids are located between the orbits of mars and jupiter in the asteroids belt true or false... ### The most frequently abused drug among north american teenagers is: The most frequently abused drug among north american teenagers is:... Please give me the correct answer. $Please give me the correct answer.$...	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.34303736686706543, "perplexity": 3407.6884707664653}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-06/segments/1674764494974.98/warc/CC-MAIN-20230127065356-20230127095356-00788.warc.gz"}
https://brilliant.org/problems/intresting-modulus/	# Interesting modulus Algebra Level 3 Find the sum of all the integral roots of the equation $\|x −1\|+\|x\|+\|x +1\|=x +2.$ ×	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9998641014099121, "perplexity": 2812.40180363301}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-30/segments/1500549425352.73/warc/CC-MAIN-20170725182354-20170725202354-00013.warc.gz"}
http://math.stackexchange.com/questions/16066/designing-an-irrational-numbers-wall-clock/16099	# Designing an Irrational Numbers Wall Clock A friend sent me a link to this item today, which is billed as an "Irrational Numbers Wall Clock." There is at least one possible mistake in it, as it is not known whether $\gamma$ is irrational. Anyway, this started me wondering about how to improve the design of this clock from a mathematical standpoint. Here's my formulation of the problem: 1. Find 12 numbers that have been proved to be irrational to place around the outside of a clock. 2. Each of eleven of the numbers must approximate as closely as possible one of the integers from 1 through 11. The 12th can either be just smaller than 12 or just larger than 0. 3. The numbers must have expressions that are as simple as possible (in the spirit of - or even more simple than - those in the clock given in the picture here). Thus, for example, no infinite sums, no infinite products, and no continued fractions. Famous constants and transcendental functions evaluated at small integers encouraged. 4. Expressions should be as varied as possible. Better answers would include at least one use of trig functions, logarithms, roots, and famous constants. Obviously, goals 2, 3, and 4 act against each other. And, as Jonas Meyer points out, "as closely as possible" and "as simple as possible" are not well-defined. That is intentional. I am afraid that if I tried to define those precisely I would preclude some answers that I might otherwise consider good. Thus, in addition to the mathematics, there's a sizable artistic component that goes into what would be considered a good answer. Hence the "soft-question" tag. I'm really curious as to what the math.SE community comes up with and then what it judges (via upvoting) to be the best answers, subject to these not-entirely-well-defined constraints. Note that the designer of the clock given here was not trying to approximate the integers on a clock as closely as possible. Finally, it's currently New Year's Day in my time zone. Perhaps a time-related question is appropriate. :) Note: There is now a community wiki answer that people can edit if they just want to add a few suggestions rather than all twelve. - "As closely as possible" and "as simple as possible" are not defined. What's to stop you from taking rational powers of $2$ for each? – Jonas Meyer Jan 1 '11 at 23:20 As Jonas points out, variety might be nice. I'd suggest a #4: Expressions should ideally be as varied as possible (e.g., at most one root, at most one use of a trig function, etc.). – Matthew Conroy Jan 1 '11 at 23:29 Here's another (ahem) "timely" use of irrationals: piclock.com :) (Note: That's my product. I'll delete this comment if anyone objects to my mentioning it here.) – Blue Jan 2 '11 at 0:22 For $7$, how about $22/\pi$? By the way, I think this would work well as a community wiki question. – Jonas Meyer Jan 2 '11 at 1:56 I might add a bias towards over-estimates. That way, should anyone care to memorize the expressions, they can impress their friends by saying things like "e-to-the-phi is 5-point-something, I just forgot the 'something' at the moment". :) – Blue Jan 2 '11 at 5:03 Here's a list of irrational numbers which almost fulfill your criteria. Each were chosen to be accurate to within ±0.1, so that no two of them implicitly express the same mathematical approximation, and so that none of them "cheats" in order to fudge an exact result involving integers to obtain a slightly inexact, irrational result. Only the last number fails to meet your criteria, as it is slightly larger than 12. 1. $\ln(3)$ 2. $7\pi/11$ 3. $\sqrt 2 + \frac\pi2$ 4. $7/{\sqrt[3]5}$ 5. $\mathrm e^\phi$ 6. $\sec^2(20)$ 7. $4\sqrt3$ 8. $5\phi$ 9. $2\pi+\mathrm e$ 10. $\sinh(3)$ 11. $\pi^3-20$ 12. $\csc^2(16)$ I would prefer not to use cosecant, integers greater than 12, or more than two additions/subtractions — it is too easy to get results if you rely on these — but I think I've spent enough time on this diversion for now. :-) [EDIT: revised the formula for 4 two times now: this first to change the formula for 4 from √3 + √5 — which is too close to √4 + √4 — and the second time to correct the formula as I somehow copied a result which was not approximately 4.] Added: Since it seems that I can't sleep tonight, here is a list of approximate values: \begin{align} \ln(3) & \approx 1.0986 \\ 7\pi/11 & \approx 1.9992 \\ \sqrt 2 + \tfrac\pi2 & \approx 2.9850 \\ 7 / \sqrt[3]5 & \approx 4.0936 \\ \mathrm e^\phi & \approx 5.0432 \\ \sec^2(20) & \approx 6.0049 \\ 4\sqrt3 & \approx 6.9282 \\ 5\phi & \approx 8.0902 \\ 2\pi+\mathrm e & \approx 9.0015 \\ \sinh(3) & \approx 10.018 \\ \pi^3-20 & \approx 11.006 \\ \csc^2(16) & \approx 12.064 \end{align} - Nice! Could you add the approximate values? – Mike Spivey Jan 2 '11 at 3:48 Sure! The value of each expression is now displayed with its decimal value (rounded to the nearest multiple of 1/5). ;-) – Niel de Beaudrap Jan 2 '11 at 4:02 Good one, Niel. :) :) I meant so that I could see just how close each number is to the integer it's supposed to be approximating (more precisely than the 0.1 you've already mentioned). – Mike Spivey Jan 2 '11 at 4:09 I've made a correction, and added the approximate values. – Niel de Beaudrap Jan 2 '11 at 4:50 Is $2\pi+e$ known to be irrational? – simplequestions Jan 2 '11 at 13:34 Here are my meager suggestions: • For a new "zero", the symobl $\epsilon$, which although not representing a specific number, is nearly universally used to represent a very small positive quantity. • Alternatively, for zero one could use $\frac{1}{\omega}$, which is one of the most canonical infinitesimals in the surreal numbers. • For 2, one could use $\|1+i\|^2$. (I realize this is exact and hence rational, but the expression involves non-rational numbers.) As a mathematician who is also an antique clock collector, I love this question, and I would be interested if after some good answers are submitted, they are collected and made into a suitably attractive pdf image that could be printed and actually used for a clock face. My suggestion would be to adopt an old-style clock typography, if this is possible, since it might also help the clock face look more like a clock face. - Thanks. I particularly like the use of $\epsilon$ for an approximation of 0. – Mike Spivey Jan 2 '11 at 3:54 Your "2" wastes a square that might be used elsewhere. Instead, you might opt for $5 = \|3+4i\|$. This, too, has the rationality problem; on the other hand, tweaking to something like $8 \approx \|5+6i\|$ seems like a "cheat" in @Niel's sense. (BTW, I also like $\epsilon$ for $0$.) – Blue Jan 2 '11 at 4:52 Day Late, I agree. My preference would be to find completely natural instances, using only very low integers and perhaps avoiding + completely (except perhaps for complex numbers?). I don't see it as a problem if the expressions are rational or even integer-valued, provided that they are mathematically interesting. – JDH Jan 2 '11 at 5:32 This is intended to be a community wiki answer that people can edit if they just want to give a few numbers rather than all twelve. I'll start with suggestions currently in the comments. Feel free to add more! For 1: $-\sin 11$ For 3: $e + \sqrt{\frac{5}{63}}$ For 7: $22/\pi$ For 12: $\log_{1922}(1782^{12}+1841^{12})$ (Approximately 11.99999999996, featured on The Simpsons.) - I wonder if it is cheating to use both $-\sin(11)$ and $22/\pi$, considering that $\sin(11)$ is close to $-1$ because $11$ is close to $\frac{7\pi}{2}$. – Jonas Meyer Jan 2 '11 at 4:31 I really like the one for 12. – Raskolnikov Jan 2 '11 at 12:27 @Jonas: Feel free to remove one of them. After all, they were both suggestions of yours! – Mike Spivey Jan 3 '11 at 5:50 Good point :) I don't want to be too hard on myself. I was just wondering out loud after reading Niel's point about answers that implicitly express the same mathematical approximation. It's probably in the spirit of this thread to include redundant answers for the time being, and to take the best ones in the end. – Jonas Meyer Jan 3 '11 at 7:09 Suggestions 11: $e^{\pi i}$ 4: ${\sqrt 5}^{\sqrt 3}$ (aprox. 4.03019240+ ) While, it's no match for the previous entry, I can't resist giving one more for 11: $\frac{\sqrt[4]{104 + e^{\pi \sqrt{58}}}}{6^2}$ - $11 = -1 \mod 12$. Nice. :) – Mike Spivey Feb 26 '11 at 0:26 Despite the large constant, I like tanh(2011) for 1. It is very close and shows the year. - That could also be an idea, only using the number 2011 and elementary operations and transcendenatal functions try to construct 12 approximations to the the numbers from 1 to 12. – Raskolnikov Jan 2 '11 at 12:37 Some that I like: • I'm rather fond of $3 \approx \log 20$. Every so often I find myself taking large powers of $e$ in my head; knowing this is helpful. • $7 \approx 12 \log_2 (3/2)$. This expresses the fact that, in music, a fifth is seven-twelfths of an octave. • $6 \approx \log (\pi^4 + \pi^5)$; I've actually seen T-shirts claiming that $\pi^4 + \pi^5 = e^6$. • $\pi + \pi^2 \approx 13$, although unless we're in an Orwell book your clocks have no thirteen. The wikipedia article on mathematical coincidences may have more ideas. - +1 for the 6 – ypercube Feb 25 '11 at 23:46 You could write the 3 as $\log 10 + \log 1010$ – ypercube Feb 25 '11 at 23:49 Nice answers (especially the 6). Thought you might want to know that AcidFlask mentioned the "mathematical coincidences" site as well. – Mike Spivey Feb 26 '11 at 0:25 @Mike: I just did. Had to wait 40 minutes as I overused my votes yesterday :) – ypercube Feb 26 '11 at 0:34 @ypercube: Fair enough. My apologies for bugging you about it! I will delete my comment. :) – Mike Spivey Feb 26 '11 at 0:38 After seeing the ThinkGeek :: Pop Quiz Math Clock a few years ago I asked my friend David a question related to the one here: to use more interesting mathematical approaches to generate each of the integers 1-12. He provided a great answer at http://www.astronexus.com/comment/reply/153 - Have a look at Wikipedia for some interesting ideas: I like $\pi^2 \approx 9.87$. Fooling around with variations of what's there also yielded $$7( \pi - e) \approx 2.96$$ $$19 (\pi - e) \approx 8.05$$ Furthermore the numbers don't have to be limited to (0, 12], since you could always work in $\mod 12$. For example $(\pi + 20)^i \approx -1$ could be used for 11 o'clock. -	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8664929866790771, "perplexity": 848.3890979134508}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2015-18/segments/1429246634333.17/warc/CC-MAIN-20150417045714-00311-ip-10-235-10-82.ec2.internal.warc.gz"}
http://mathhelpforum.com/calculus/24198-proof-required.html	# Math Help - Proof required. 1. ## Proof required. Let f(x) be a function with n distinct zeros on [a, b]. Prove that, f'(x) has at least n − 1 distinct zeros on [a, b]. Don't really know where to start here, any help is appreciated. 2. But does it say if the function is differentiable in $(a,b)$? If so, remember Rolle's Theorem, given real numbers $c if $f(x)$ is continuous in $[c,d]$,differentiable in $(c,d)$, and $f(c)=f(d)$ then there is a certain $c$ in $(c,d)$ such that $f'(c)=0$ 3. yes the function is differentiable on {a b} and continuous. We need to prove that there is n-1 zeros and not that there is a zero(rolle's) --> f'(c)= 0. For example the function itself may have 5 zeros on [a b] so its derivative will have 4 on [a b], that what is required to prove 4. These are our zeros Let $x_1,x_2,x_3,...,x_n\in[a,b]$ such that $x_1, and $f(x_i)=0$ $\forall{i\in{N}}$ $1\leq{i}\leq{n}$ Consider $[x_1,x_2]$, $[x_2,x_3]$ ... $[x_{n-1},x_n]$ And apply Rolle's Theorem to them For example Since f(x) is continuos in $[x_1,x_2]$, differentiable in $(x_1,x_2)$ and $f(x_1)=f(x_2)=0$ we can assure there's a certain $c_1\in{(x_1,x_2)}$ such that $f'(c_1)=0$ 5. Hello, somestudent2! I must assume that the function is continuous on $[a,b].$ Let $f(x)$ be a function with $n$ distinct zeros on $[a, b].$ Prove that $f'(x)$ has at least $n - 1$ distinct zeros on $[a, b].$ Maybe a sketch will help you visualize the problem . . . Suppose $f(x)$ has four distinct zeros on $[a,b].$ Code: \| \| ---- \| * ---- \| * * * - - + - + - o - - - - - o - - - - o - - - -o- - - + - - \| a * * * b \| * --*-- \| Then there are at least three horizontal tangents on $[a,b].$ 6. thank you very much guys	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 32, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8771450519561768, "perplexity": 410.4715515187116}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-41/segments/1412037663612.31/warc/CC-MAIN-20140930004103-00114-ip-10-234-18-248.ec2.internal.warc.gz"}
https://planetmath.org/25TheHigherGroupoidStructureOfTypeFormers	# 2.5 The higher groupoid structure of type formers In http://planetmath.org/node/87533Chapter 1, we introduced many ways to form new types: cartesian products, disjoint unions, dependent products, dependent sums, etc. In §2.1 (http://planetmath.org/21typesarehighergroupoids),§2.2 (http://planetmath.org/22functionsarefunctors),§2.3 (http://planetmath.org/23typefamiliesarefibrations), we saw that all types in homotopy type theory behave like spaces or higher groupoids. Our goal in the rest of the chapter is to make explicit how this higher structure behaves in the case of the particular types defined in http://planetmath.org/node/87533Chapter 1. It turns out that for many types $A$, the equality types $x=_{A}y$ can be characterized, up to equivalence, in terms of whatever data was used to construct $A$. For example, if $A$ is a cartesian product $B\times C$, and $x\equiv(b,c)$ and $y\equiv(b^{\prime},c^{\prime})$, then we have an equivalence $\big{(}(b,c)=(b^{\prime},c^{\prime})\big{)}\simeq\big{(}(b=b^{\prime})\times(c% =c^{\prime})\big{)}.$ (2.5.1) In more traditional language, two ordered pairs are equal just when their components are equal (but the equivalence (2.5.1) says rather more than this). The higher structure of the identity types can also be expressed in terms of these equivalences; for instance, concatenating two equalities between pairs corresponds to pairwise concatenation. Similarly, when a type family $P:A\to\mathcal{U}$ is built up fiberwise using the type forming rules from http://planetmath.org/node/87533Chapter 1, the operation $\mathsf{transport}^{P}(p,\mathord{\hskip 1.0pt\text{--}\hskip 1.0pt})$ can be characterized, up to homotopy, in terms of the corresponding operations on the data that went into $P$. For instance, if $P(x)\equiv B(x)\times C(x)$, then we have $\mathsf{transport}^{P}(p,(b,c))=\big{(}\mathsf{transport}^{B}(p,b),\mathsf{% transport}^{C}(p,c)\big{)}.$ Finally, the type forming rules are also functorial, and if a function $f$ is built from this functoriality, then the operations $\mathsf{ap}_{f}$ and $\mathsf{apd}_{f}$ can be computed based on the corresponding ones on the data going into $f$. For instance, if $g:B\to B^{\prime}$ and $h:C\to C^{\prime}$ and we define $f:B\times C\to B^{\prime}\times C^{\prime}$ by $f(b,c):\!\!\equiv(g(b),h(c))$, then modulo the equivalence (2.5.1), we can identify $\mathsf{ap}_{f}$ with “$(\mathsf{ap}_{g},\mathsf{ap}_{h})$”. The next few sections (§2.6 (http://planetmath.org/26cartesianproducttypes) to §2.13 (http://planetmath.org/213naturalnumbers)) will be devoted to stating and proving theorems of this sort for all the basic type forming rules, with one section for each basic type former. Here we encounter a certain apparent deficiency in currently available type theories; as will become clear in later chapters, it would seem to be more convenient and intuitive if these characterizations of identity types, transport, and so on were judgmental equalities. However, in the theory presented in http://planetmath.org/node/87533Chapter 1, the identity types are defined uniformly for all types by their induction principle, so we cannot “redefine” them to be different things at different types. Thus, the characterizations for particular types to be discussed in this chapter are, for the most part, theorems which we have to discover and prove, if possible. Actually, the type theory of http://planetmath.org/node/87533Chapter 1 is insufficient to prove the desired theorems for two of the type formers: $\Pi$-types and universes. For this reason, we are forced to introduce axioms into our type theory, in order to make those “theorems” true. Type-theoretically, an axiom (c.f. §1.1 (http://planetmath.org/11typetheoryversussettheory)) is an “atomic” element that is declared to inhabit some specified type, without there being any rules governing its behavior other than those pertaining to the type it inhabits. The axiom for $\Pi$-types (§2.9 (http://planetmath.org/29pitypesandthefunctionextensionalityaxiom)) is familiar to type theorists: it is called function extensionality, and states (roughly) that if two functions are homotopic in the sense of §2.4 (http://planetmath.org/24homotopiesandequivalences), then they are equal. The axiom for universes (§2.10 (http://planetmath.org/210universesandtheunivalenceaxiom)), however, is a new contribution of homotopy type theory due to Voevodsky: it is called the univalence axiom, and states (roughly) that if two types are equivalent in the sense of §2.4 (http://planetmath.org/24homotopiesandequivalences), then they are equal. We have already remarked on this axiom in the introduction; it will play a very important role in this book.11We have chosen to introduce these principles as axioms, but there are potentially other ways to formulate a type theory in which they hold. See the Notes to this chapter. It is important to note that not all identity types can be “determined” by induction over the construction of types. Counterexamples include most nontrivial higher inductive types (see http://planetmath.org/node/87579Chapter 6,http://planetmath.org/node/87582Chapter 8). For instance, calculating the identity types of the types $\mathbb{S}^{n}$ (see §6.4 (http://planetmath.org/64circlesandspheres)) is equivalent to calculating the higher homotopy groups of spheres, a deep and important field of research in algebraic topology. Title 2.5 The higher groupoid structure of type formers \metatable	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 26, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9108815789222717, "perplexity": 462.47998579595793}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-17/segments/1618038461619.53/warc/CC-MAIN-20210417162353-20210417192353-00221.warc.gz"}
http://www.ellipsix.net/blog/2012/07/particles-gone-wild-the-higgs-mechanism-uncensored.html	## Particles gone wild: the Higgs mechanism, uncensored If you’ve been following the news about the discovery of the Higgs boson, you’ve probably noticed that it gets reported in two ways. There are the actual presentations with the full details of the experiments, which can only be understood by particle physicists their authors well, I’m assuming somebody knows what all of it means. Anyway, then there’s the other way. Sensationalized science journalism. “Hey, look, it’s a God Particle!!!11!” And Other Misrepresentations. I think some of us want a middle ground, though. Certainly I would have, not too long ago. So if you’re not actually a physicist, but you’re also not afraid to look at a little math, this post is for you. (This is adapted from a post on Physics Stack Exchange.) # Spontaneous symmetry breaking In order to understand the Higgs mechanism in detail, you need to know about two concepts that are involved in quantum field theory. The first is spontaneous symmetry breaking. This is actually a pretty simple idea: suppose that the physical laws that govern a system are symmetric in some way, meaning that you can make some kind of transformation on the system without changing the laws. That doesn’t necessarily mean the actual behavior of the system will be symmetric in the same way. The system might exist in a state that is affected by the transformation, even if the laws are not. A common example is balancing a pencil on its tip. If you could get the pencil perfectly balanced, the system would be rotationally symmetric about its axis. Same goes for the physical laws that govern its behavior (gravity, Newton’s laws, etc.): if you rotate the whole setup around the pencil, nothing changes. However, realistically, the pencil is going to fall in some direction, and at that point the system is no longer rotationally symmetric. Once the pencil is rolling around on the table, if you rotate the whole setup around the tip of the pencil, something does change, namely the direction in which the pencil is pointing. Technically, the physical laws are still symmetric, but you don’t see the effects of that rotational symmetry anymore: now your pencil will roll off the table if you orient it in the wrong direction. In its application to particle physics, spontaneous symmetry breaking occurs when there is some potential which has a local maximum that lies on the symmetry axis. This is the famous “Mexican hat potential.” Mathematically, it’s represented by an expression of the form $$V(\phi,\herm\phi) = -\frac{1}{2}\mu^2\abs{\phi}^2 + \frac{\lambda^2}{4}\abs{\phi}^4$$ In this expression, $$\mu$$ and $$\lambda$$ are constants and $$\phi$$ is a quantum field. You can think of it as a complex-valued variable which is related to the quantum state at a point in spacetime. Now, for our purposes, the universe will “try” to “seek out” whatever state minimizes its potential, just like the balanced pencil will “seek out” the state that minimizes its potential. The only difference is that whereas the pencil changes its state by adjusting its position, the universe changes its state by adjusting the value of the field $$\phi$$. Just as the pencil has to fall in some direction, the universe will have to experience a transition from its initial state on the peak in the center to some other state for which $$\phi$$ lies at or near the bottom of the valley, having $$\abs{\phi} = \frac{\mu}{\lambda}$$. # Local gauge invariance The other concept involved is local gauge invariance. This one is a little harder to explain, because there’s no simple physical analogy, and it takes a fair amount of math. Let me start with plain old invariance. This in itself is basically the same thing as symmetry: the idea that a physical theory doesn’t change under some sort of transformation. In the pencil example from above, the transformation was a physical rotation, which rearranges points in space. But you can also have a transformation that doesn’t affect points in space: in field theory, we have these fields which have associated values at every point in space, and a transformation could affect the values instead of the points. This is called a gauge transformation. Gauge invariance means that you should be able to make gauge transformations to the fields involved in your theory without the physical laws changing as a result. An example of a gauge transformation is the phase rotation $$\phi(x)\to e^{i\alpha}\phi(x)$$. It affects the value of a field at every point in space by multiplying it by a complex phase. If the parameter $$\alpha$$ depends on spacetime position, $$\alpha(x)$$, then we call it “local.” Now to the technical part: explaining the significance of gauge invariance. Bear with me for a moment. In quantum field theory, there are basically two ways the fields themselves can show up: either directly, or as a derivative. They always show up in pairs or larger groupings, usually of a conjugate and a normal field, like $$\herm{\phi}\phi$$. ($$\herm{\phi}$$ is the Hermitian conjugate, which is the complex conjugate and transpose of a matrix-valued field.) Terms like that which involve only the fields themselves are automatically gauge invariant under phase rotation, because when you make the transformation, you get $$\herm{\phi}e^{-i\alpha(x)}e^{i\alpha(x)}\phi = \herm{\phi}\phi$$; the phase factor just cancels out. But when you have a term that involves derivatives, like $$\partial\herm{\phi}\partial\phi$$ (where $$\partial = \frac{\partial}{\partial x}$$), called a kinetic term, you run into problems: $$\partial[e^{i\alpha(x)}\phi(x)] = i\alpha'(x) e^{i\alpha(x)}\phi(x) + e^{i\alpha(x)}\partial\phi(x)$$ If you plug this into the gauge transformed kinetic term, $$\partial[e^{-i\alpha(x)}\herm{\phi}(x)]\partial[e^{i\alpha(x)}\phi(x)]$$ (try expanding this for yourself), you’ll see that it will not simplify back to the original $$\partial\herm{\phi}(x)\partial\phi(x)$$, because of those extra terms introduced by taking the derivative of $$e^{i\alpha(x)}$$. In order to keep local phase rotations from changing the physical laws, we need to modify the derivative. Instead of the plain old partial derivative $$\partial$$, we’ll invent a new operator $$D$$ so that the combination $$D\herm{\phi}(x)D\phi(x)$$ is going to be gauge invariant. To do so, we add a connection $$A(x)$$ to the derivative, turning it into the gauge covariant derivative $$D\phi(x) = \partial\phi(x) - iqA(x)\phi(x)$$ What makes this work is a stipulation that, as part of making a gauge transformation, the connection has to change too. For the example I’ve been using of a local phase rotation, the connection will need to change like this: $$A(x) \to A(x) + \frac{1}{q}\partial\alpha(x)$$ Essentially, making a gauge transformation not only alters the field, but also alters the operation of differentiation so that the combination of $$D\phi(x)$$ doesn’t have any extra terms. Here’s how that works out: we start with $$D\phi(x) = \partial\phi(x) - iqA(x)\phi(x)$$ and make the gauge transformation, changing both $$A(x)$$ and $$\phi(x)$$, $$\partial\bigl[e^{i\alpha(x)}\phi(x)\bigr] - iq\biggl[A(x) + \frac{1}{q}\alpha'(x)\biggr]e^{i\alpha(x)}\phi(x)$$ A product rule and a bit of algebra gets you from there to $$i\alpha'(x)e^{i\alpha(x)}\phi(x) + e^{i\alpha(x)}\partial\phi(x) - iqA(x)e^{i\alpha(x)}\phi(x) - i\alpha'(x)e^{i\alpha(x)}\phi(x)$$ The first and last terms cancel out, and you’re left with $$e^{i\alpha(x)}\bigl[\partial - iqA(x)\bigr]\phi(x) = e^{i\alpha(x)}D\phi(x)$$ That means that the phase factor cancels out of $$D\herm{\phi} D\phi$$, just as it did with the normal field terms. Cool! # Putting it all together Where spontaneous symmetry breaking and local gauge invariance come together is in the Lagrangian. If you’re not familiar with what a Lagrangian is, you can kind of think of it as something like an energy density, but it’s not really that important. Just know that there are particular terms in it with particular meanings that I’ll identify as they come. In real-world mechanical systems, the Lagrangian is formed by subtracting the potential energy from the kinetic energy. We can do the same thing in quantum field theory: form a Lagrangian by subtracting the potential $$V(\phi)$$ from the kinetic term $$\frac{1}{2}D\phi^\dagger D\phi$$. Hopefully this is starting to look familiar: I talked about a potential in the section on spontaneous symmetry breaking, and I talked about a kinetic term in the section on local gauge invariance. As the heading suggests, this is where it all comes together. $$\mathcal{L} = \frac{1}{2}\bigl(\partial + iqA\bigr)\herm{\phi}\bigl(\partial - iqA\bigr)\phi +\frac{1}{2}\mu^2\herm{\phi}\phi - \frac{\lambda^2}{4}(\herm{\phi}\phi)^2$$ Most of quantum field theory is done perturbatively. This means we need the magnitude of the field (in this case $$\abs{\phi}$$) to be very small so that we can calculate interesting things as perturbation series, e.g. $$F(\phi) = F_0 + \phi F_1 + \cdots$$. That would be all well and good if $$\phi$$ were close to zero. But as I said in the section on spontaneous symmetry breaking, that’s typically not going to be the case. The universe will “seek out” the lowest potential, which means $$\abs{\phi}$$ is going have a value closer to $$\frac{\mu}{\lambda}$$, the minimum. The solution? Just redefine the field. Instead of using $$\phi$$, we’ll use $$\eta = \phi - \frac{\mu}{\lambda}$$, which will be close to zero. $$\frac{\mu}{\lambda}$$ is the vacuum expectation value of the field $$\phi$$. So spontaneous symmetry breaking causes us to rewrite the Lagrangian as $$\mathcal{L} = \frac{1}{2}\bigl(\partial + iqA\bigr)\herm{\eta}\bigl(\partial - iqA\bigr)\eta + \frac{2q^2\mu}{\lambda}A^2\eta + \frac{q^2\mu^2}{\lambda^2}A^2 - \frac{\lambda^2}{4}\eta^4 + \lambda\mu\eta^3 - \mu^2\eta^2 + \frac{\mu^4}{4\lambda^2}$$ It may seem like a pain, but seriously, you should work this out yourself. Plug the definition of $$\eta = \phi + \frac{\mu}{\lambda}$$ into the original Lagrangian two equations up, expand out the terms, and see that it really does work out to this last expression. It’s just algebra, nothing too complicated, but there are a couple of neat cancellations that take place. Now, as I said, I’m going to explain the meanings of some of the terms. In a QFT Lagrangian, there are three basic types: • Kinetic terms involve derivatives of the fields. They are of the form $$D\herm{\eta}D\eta$$, where $$\eta$$ is a field. Loosely speaking, they represent the energy of motion of the field. • Mass terms involve a product of the field and its conjugate, with some numerical coefficient. They are of the form $$M\herm{\eta}\eta$$. The constant $$M$$ is the mass of the particle that we associate with the field (although it takes a fair bit of calculation to show it). • Interaction terms involve a product of three or more fields. They are of the form $$cA^2\eta$$, where $$c$$ is the coupling constant for the interaction. These terms represent fundamental interactions which are shown as individual vertices in Feynman diagrams. The term $$cA^2\eta$$, for example, would represent an interaction between two $$A$$ particles and one $$\eta$$ particle. Since we’re talking about the Higgs mechanism, the mass terms are of particular interest. Take a look at the two forms of the Lagrangian above. You’ll notice that both of them have a mass term for the field $$\eta$$ (or $$\phi$$). But in the first expression, there is no mass term for the field $$A$$, whereas in the second one, the mass term $$\frac{q^2\mu^2}{\lambda^2}A^2$$ has “magically” appeared! Just because of what amounts to a change of coordinates, a seemingly massless particle turns out to have a mass! That is the Higgs mechanism in a nutshell. In this example, $$\eta$$ is the Higgs field, and $$A$$ is a force carrier. It corresponds to the W and Z bosons which mediate the weak interaction. Notice that it’s actually the vacuum expectation value of the Higgs field, $$\frac{\mu}{\lambda}$$, that gives the field $$A$$ a mass. The terms which represent the Higgs boson, in particular its mass term $$-\mu^2\eta^2$$ and its kinetic term, are separate from the term that grants mass to the field $$A$$. So it’s not that the Higgs boson itself gives other particles masses; it’s a side effect of the mechanism as a whole. If you’re curious for more detail about how all this works, I’d recommend a good textbook on particle physics and/or quantum field theory. At the introductory level, Griffiths is a good choice, but for the real details, look at something like Peskin & Schroeder or Halzen & Martin, which I’ve most directly based this analysis on.	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 2, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8698732852935791, "perplexity": 196.5264059107559}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-30/segments/1500549426639.7/warc/CC-MAIN-20170726222036-20170727002036-00356.warc.gz"}