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https://homotopical.wordpress.com/category/uncategorized/page/2/ | # Archive for the ‘Uncategorized’ Category
## Postdoc opportunities in France
Posted by Andreas Holmstrom on January 25, 2011
I found my current job in Bordeaux thanks to this blog post of Minhyong Kim, and will now try to make someone else a similar favour.
Firstly, there are postdoc positions at INRIA advertised here. The subject area is computer science and applied mathematics, but I know that in the past this has included computational arithmetic geometry. If anyone is interested, I can put you in touch with someone at the maths department here in Bordeaux who has hired math postdocs via INRIA before (am hesitant to post his name and email address here without his permission). Just leave a comment or send me an email.
Secondly, there is some European Union money for a number of postdoc positions in the Aquitaine region. As far as I understand, the first step towards an application is to contact a potential host researcher, for example at the IMB.
## Essay on Tate’s thesis
Posted by Andreas Holmstrom on June 14, 2010
Many years ago I wrote an essay on Tate’s thesis, which is now (finally) available here. This is the “baby case” of the global Langlands correspondence, and involves lots of interesting mathematics. Obviously there are many other introductions to Tate’s thesis on the web, for example this discussion on the blog of Terry Tao.
Posted in Uncategorized | 1 Comment »
## Happy New Year!
Posted by Andreas Holmstrom on January 16, 2010
A bit late, I know, but I would like to wish all blog readers a peaceful and fulfilling new year 2010! Due to holidays, job applications, and a stolen laptop, I have been rather silent for a while, but hopefully I will be able to post more often in the next few months. Today I don’t have much to say, except showing you a picture from the year that passed:
It’s a tiny picture taken with a bad mobile phone camera, but it shows the Academy of Motives in Granada, where I was attending the F1 workshop in November. Other mathematical-touristic experiences of 2009 included two trips to Germany; unfortunately I was not able to find the famous shop where they sell affine schemes.
Posted in Uncategorized | Tagged: | 3 Comments »
## Ordinary vs generalized cohomology theories
Posted by Andreas Holmstrom on December 10, 2009
(Post updated on 7 Jan 2010, based on some useful feedback from Tobias Barthel)
Introduction
When trying to classify or organize cohomology theories “found in nature” within (commutative) algebraic geometry, one realizes that there is a fundamental divide between generalized cohomology theories and the more restrictive notion of ordinary cohomology theories. This can result in confusion, for example when speaking of “universal” cohomology theories. Today I will try to give some explanation of what the difference is, although I am still very far from understanding this completely. These two notions of cohomology can be given precise definitions in topology, and there are several ways one could imagine making them precise also in algebraic geometry.
First a word about terminology: The phrase “generalized cohomology” has been used in several different ways in the literature. For example, the excellent article Motivic sheaves and filtrations on Chow groups by Jannsen, in the Motives volumes, uses a definition of generalized cohomology which corresponds to what I want to call ordinary cohomology. My choice of terminology seems more common nowadays, and it also corresponds to well-established practice in topology.
Cohomology theories in algebraic topology
In topology, a cohomology theory is by definition a sequence of functors on a suitable category of topological spaces, which satisfy the Eilenberg-Steenrod axioms. If we include the so called dimension axiom, we get the definition of ordinary cohomology, and if we exclude it, we get the definition of generalized cohomology. The classical Brown representability theorem says essentially that a generalized cohomology in the above sense is exactly the same thing as a functor represented by a spectrum. For precise statements, and details on the Eilenberg-Steenrod axioms and Brown representability, see Kono and Tamaki: Generalized cohomology (Google Books link), or May: A concise course in algebraic topology (pdf available here). Recall that for any abelian group G, we can define singular cohomology with coefficients in G; these cohomology theories are the only examples of ordinary cohomology theories in algebraic topology. There are many examples of generalized (non-ordinary) cohomology theories, for example complex cobordism, elliptic cohomology/topological modular forms, Brown-Peterson cohomology, and various forms of K-theory. Stable homotopy theory is the study of the category of spectra, i.e. the objects representing such generalized cohomology theories.
A very important class of generalized cohomology theories is the class of oriented theories. Roughly speaking, these are the cohomology theories which admit a reasonable theory of characteristic classes of line bundles. To any oriented cohomology theory one can associate a formal group, and there is a converse to this for formal groups which are “Landweber exact”. There is a “universal” oriented cohomology theory, namely complex cobordism. Some other examples: Singular cohomology with coefficients in any ring (or maybe Q-algebra) corresponds to the additive formal group. Complex K-theory corresponds to the multiplicative formal group. An elliptic cohomology theory corresponds to a formal group law coming from an elliptic curve. See Kono and Tamaki, or Lurie’s Survey of elliptic cohomology, for definitions and more details.
(I feel I should apologize for being so brief in this section, but there are already good references for algebraic topology, and today I want to get to some interesting algebraic geometry before I die. Hopefully I will find time to post in the future on things such as background on formal groups, and various approaches to defining the category of spectra.)
Algebraic geometry background
Although I did not give precise definitions in the algebraic topology discussion, such definitions can be found in the references, and with these definitions it is completely clear what one means by “ordinary” and “generalized” cohomology. In algebraic geometry, the same distinction clearly exists “in nature”, but to give precise definitions is more difficult. Roughly speaking, ordinary cohomology theories can be understood using only homological algebra, while generalized cohomology theories need the more flexible language of homotopical algebra.
Some examples of ordinary cohomology theories: Etale cohomology, Deligne cohomology, motivic cohomology, crystalline cohomology, de Rham cohomology, Betti cohomology. Most ordinary cohomology theories are defined as the sheaf cohomology of some sheaf of abelian groups (or more generally in terms of hypercohomology of some complex of sheaves of abelian groups). Here the notion of sheaf depends on some choice of Grothendieck topology. Many ordinary cohomology theories come in pairs of an “absolute” and a “geometric” theory (more about this in a future post!). Any Weil cohomology theory is ordinary, as well as any Bloch-Ogus theory. In algebraic topology, we have mentioned that ordinary theories correspond to abelian groups. The picture in algebraic geometry is more complicated, partly because we want to apply our cohomology theories to categories which are more complicated and more varied (see earlier posts on varieties and Weil cohomology for some examples).
Some examples of generalized (non-ordinary) cohomology theories: algebraic cobordism, algebraic K-theory, Witt groups. Theories of this kind are never defined in terms sheaf cohomology of abelian sheaves as above. However, there are more general notions of sheaf cohomology which do apply in most cases, using simplicial sheaves/presheaves in some form.
Remark 1: To speak of “universal” cohomology theories, it is necessary to specify what one means by “cohomology theory”. If we want to talk about all generalized cohomology theories, I guess the only thing that could be universal is some good notion of “stable homotopy type”. However, when it comes to more restrictive notions of cohomology, I am quite sure the following three statements can be made precise: (1) Algebraic cobordism is universal among oriented theories. (2) Pure motives is the universal ordinary (Weil) cohomology theory for smooth projective varieties over a field. (3) Motivic cohomology is the universal ordinary (Bloch-Ogus) cohomology for general varieties over a field.
Edit: Algebrac K-theory also has a universal property, at least when regarded as a functor on symmetric monoidal categories, but I am not sure about the details of this. There are some hints in Tyler Lawson’s answer to this MathOverflow question, and some more details in another answer of Clark Barwick.
Remark 2: It seems like the noun “motive” is used exclusively in connection with the world of ordinary cohomology theories (pure motives, mixed motives, triangulated categories of motives, etc). However, the adjective “motivic” is used in settings related to ordinary as well as generalized cohomology, e.g. motivic homotopy theory (generalized), motivic cohomology (ordinary).
Remark 3: There is a general heuristic principle which says that “any cohomology becomes ordinary after tensoring with Q” (i.e. killing all torsion). Some examples: (1) Algebraic K-theory cannot be defined in terms of homological algebra/abelian sheaf cohomology, but after tensoring with Q this becomes possible. (2) Homotopy groups in topology are very hard to compute in general, and homological algebra doesn’t help you at all, but after tensoring with Q, everything can be described in terms of (differential graded) homological algebra, thanks to rational homotopy theory. (3) The classical Grothendieck school in the 60s never really bothered about homotopical algebra – this seems related to the fact that they were always studying cohomology theories with coefficients in Q-algebras only. (4) In topology, and maybe also in algebraic geometry, any generalized cohomology theory $E$ has an associated Atiyah-Hirzebruch spectral sequence, which relates the ordinary cohomology with coefficients in $E^*(point)$ to $E$ itself, and I believe this spectral sequence tends to be complicated, but degenerate after tensoring with Q.
Edit: For oriented cohomology theories, this phenomenon is probably related to the fact that any formal group law is isomorphic to the additive one over the rationals.
Characterizing ordinary cohomology theories
I am not aware of any completely satisfactory definition of generalized cohomology theory in algebraic geometry (the best candidate would be “something represented by a spectrum in the sense of motivic homotopy theory”). However, we could pretend for a moment that such a definition exists, and then ask for a characterization/definition of ordinary cohomology theories. I can imagine four approaches to this question, but I have no idea if any of them can be made precise in any reasonable way.
Candidate 1: “A cohomology theory is ordinary if it is functorial not only with respect to maps in the classical sense, but also with respect to correspondences”. Recall that a correspondence from $X$ to $Y$ is a cycle on $X \times Y$, a special case being the graph of a map $X \to Y$. In his Motives volume article mentioned above, Jannsen remarks that any cohomology satisfying his axioms is functorial with respect to correspondences. Voevodsky also discusses this in the introduction to Homology of schemes I , claiming that in topology this functoriality property actually characterizes ordinary cohomology theories among all generalized theories. This surrounding discussion on what Voevodsky calls his underlying “simple topological intuition” was unfortunately not included in the preprint but only in the published version.
Candidate 2: “A cohomology theory is ordinary if it is oriented and its associated formal group is the additive formal group”. This definition makes sense if we have a notion of oriented theory in algebraic geometry, as well as a correspondence with formal group laws. There are definitions of oriented theories which might be suitable for our purpose here, but I am not sure about the formal groups bit. For closely related ideas, see for example this preprint of Naumann, Østvær, and Spitzweck.
Candidate 3: “A cohomology theory is ordinary if it factors through some suitable triangulated category of motives”. One reason for thinking that this might be a reasonable definition is that any theory I know of with this property (i.e. any theory which corresponds to a “realization functor”) should be thought of as being ordinary. Another reason is some very vague feeling that for a nice base scheme S, maybe the triangulated category DM(S) of motives relates to the motivic stable homotopy category SH(S) roughly as the derived category of abelian groups relates to the classical stable homotopy category (this might be complete nonsense though).
Edit: The right way of making this precise might be by using the motivic Eilenberg-MacLane functor. I hope to come back to this in a future post.
Candidate 4: Urs Schreiber advocates the viewpoint that every cohomology theory can be expressed in terms of a mapping space Map(X,K) in some higher topos in the sense of Lurie. Whenever this point of view is valid, one could probably define the cohomology to be ordinary if the target object K is in the essential image of some kind of Dold-Kan correspondence. I believe this idea is excellent, but it is not always clear which higher categories to work with in a concrete algebro-geometric problem. See the nLab pages on cohomology and generalized cohomology for more details.
## Blog silence because of Math Overflow…
Posted by Andreas Holmstrom on November 20, 2009
The last few weeks have been quite busy, and the spare moments that I would normally spend on blogging have been hi-jacked by Math Overflow. I wrote a few things there which I would normally have put on this blog, and since they might possibly be of interest to some blog readers, here are the links: Why are functional equations important, and What is the Yoga of Motives.
For quite a while, I have been trying (without much success) to understand finiteness properties for simplicial sheaves, and thanks to MO, I got an absolutely brilliant explanation from Denis-Charles Cisinski – something which simply could not have happened otherwise. Lots of credit to MO (and to Cisinski)!
## Intersection theory at Rigorous Trivialities
Posted by Andreas Holmstrom on November 3, 2009
Charles Siegel at Rigorous Trivialities is aiming to blog about intersection theory every day of November, essentially creating a minor book in the process. The first two posts are out, one on Chow groups and one on Manipulating cycles. These posts look promising, and I am very much looking forward to the rest of the series!
Posted in Uncategorized | Tagged: , , | 1 Comment »
## Semi-abelian categories
Posted by Andreas Holmstrom on November 1, 2009
The usual setting for doing homological algebra is abelian categories. However, many of the things one can do in abelian categories also make sense in more general settings. For example, the category of groups is not abelian, but one can still make sense of exact sequences, diagram lemmas, and so on.
A more general framework for doing homological algebra, which I first learnt about from Julia Goedecke, is given by the notion of semi-abelian categories. Some examples of semi-abelian categories are: groups, compact Hausdorff spaces, crossed modules, Lie algebras, any abelian category, and any category of algebras over a reduced operad (although I am not sure what it means for an operad to be reduced).
A very nice introduction and survey of semi-abelian categories can be found in the recent article of Hartl and Loiseau, on the arXiv. Other references include the nLab page and the thesis of Van der Linden.
The category of monoids is unfortunately not semi-abelian, but there was an interesting discussion on Math Overflow recently about making sense of homological algebra in the category of commutative monoids, which is interesting when trying to do algebraic geometry over the field with one element.
## Notes on p-adic Hodge theory
Posted by Andreas Holmstrom on October 15, 2009
For a long time I have been looking for a sensible introduction to p-adic Hodge theory, and I think I might finally have found one: these lecture notes of Conrad and Brinon, an expanded but still prelimary set of notes based on their CMI summer school lectures earlier this year. Thanks to David Brown for pointing out these notes on Math Overflow, as part of an answer to a question about models.
A much shorter survey is Berger: An introduction to the theory of p-adic representations, but Conrad and Brinon give a lot more background, which seems very helpful.
## Math Overflow!!
Posted by Andreas Holmstrom on October 15, 2009
An amazing new questions-and-answers site has been launched, and I believe it will be a huge success! I asked in a recent post for a place to post algebraic geometry questions, and now there is a wonderful place for this (and other mathematical questions as well). Check out the SBS blog post and the site itself!
## Young Researchers in Mathematics conference in Cambridge
Posted by Andreas Holmstrom on October 15, 2009
Registration is now open for the next Young Researchers in Mathematics conference in Cambridge, which will take place 25-27 March 2010. See the conference webpage for more information. | {"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": 0.7734136581420898, "perplexity": 447.94537252952983}, "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-2017-13/segments/1490218189313.82/warc/CC-MAIN-20170322212949-00633-ip-10-233-31-227.ec2.internal.warc.gz"} |
https://activecalculus.org/multi/S-11-1-Double-Integrals-Rectangles.html | Section3.1Double Riemann Sums and Double Integrals over Rectangles
Motivating Questions
• What is a double Riemann sum?
• How is the double integral of a continuous function $f = f(x,y)$ defined?
• What are two things the double integral of a function can tell us?
In single-variable calculus, recall that we approximated the area under the graph of a positive function $f$ on an interval $[a,b]$ by adding areas of rectangles whose heights are determined by the curve. The general process involved subdividing the interval $[a,b]$ into smaller subintervals, constructing rectangles on each of these smaller intervals to approximate the region under the curve on that subinterval, then summing the areas of these rectangles to approximate the area under the curve. We will extend this process in this section to its three-dimensional analogs, double Riemann sums and double integrals over rectangles.
Preview Activity3.1.1.
In this activity we introduce the concept of a double Riemann sum.
1. Review the concept of the Riemann sum from single-variable calculus. Then, explain how we define the definite integral $\int_a^b f(x) \ dx$ of a continuous function of a single variable $x$ on an interval $[a,b]\text{.}$ Include a sketch of a continuous function on an interval $[a,b]$ with appropriate labeling in order to illustrate your definition.
2. In our upcoming study of integral calculus for multivariable functions, we will first extend the idea of the single-variable definite integral to functions of two variables over rectangular domains. To do so, we will need to understand how to partition a rectangle into subrectangles. Let $R$ be rectangular domain $R = \{(x,y) : 0 \leq x \leq 6, 2 \leq y \leq 4\}$ (we can also represent this domain with the notation $[0,6] \times [2,4]$), as pictured in Figure 3.1.1.
To form a partition of the full rectangular region, $R\text{,}$ we will partition both intervals $[0,6]$ and $[2,4]\text{;}$ in particular, we choose to partition the interval $[0,6]$ into three uniformly sized subintervals and the interval $[2,4]$ into two evenly sized subintervals as shown in Figure 3.1.1. In the following questions, we discuss how to identify the endpoints of each subinterval and the resulting subrectangles.
1. Let $0=x_0 \lt x_1 \lt x_2 \lt x_3=6$ be the endpoints of the subintervals of $[0,6]$ after partitioning. What is the length $\Delta x$ of each subinterval $[x_{i-1},x_i]$ for $i$ from 1 to 3?
2. Explicitly identify $x_0\text{,}$ $x_1\text{,}$ $x_2\text{,}$ and $x_3\text{.}$ On Figure 3.1.1 or your own version of the diagram, label these endpoints.
3. Let $2=y_0 \lt y_1 \lt y_2=4$ be the endpoints of the subintervals of $[2,4]$ after partitioning. What is the length $\Delta y$ of each subinterval $[y_{j-1},y_j]$ for $j$ from 1 to 2? Identify $y_0\text{,}$ $y_1\text{,}$ and $y_2$ and label these endpoints on Figure 3.1.1.
4. Let $R_{ij}$ denote the subrectangle $[x_{i-1},x_i] \times [y_{j-1},y_j]\text{.}$ Appropriately label each subrectangle in your drawing of Figure 3.1.1. How does the total number of subrectangles depend on the partitions of the intervals $[0,6]$ and $[2,4]\text{?}$
5. What is area $\Delta A$ of each subrectangle?
Subsection3.1.1Double Riemann Sums over Rectangles
For the definite integral in single-variable calculus, we considered a continuous function over a closed, bounded interval $[a,b]\text{.}$ In multivariable calculus, we will eventually develop the idea of a definite integral over a closed, bounded region (such as the interior of a circle). We begin with a simpler situation by thinking only about rectangular domains, and will address more complicated domains in Section 3.3.
Let $f = f(x,y)$ be a continuous function defined on a rectangular domain $R = \{(x,y) : a \leq x \leq b, c \leq y \leq d\}\text{.}$ As we saw in Preview Activity 3.1.1, the domain is a rectangle $R$ and we want to partition $R$ into subrectangles. We do this by partitioning each of the intervals $[a,b]$ and $[c,d]$ into subintervals and using those subintervals to create a partition of $R$ into subrectangles. In the first activity, we address the quantities and notations we will use in order to define double Riemann sums and double integrals.
Activity3.1.2.
Let $f(x,y) = 100 - x^2-y^2$ be defined on the rectangular domain $R = [a,b] \times [c,d]\text{.}$ Partition the interval $[a,b]$ into four uniformly sized subintervals and the interval $[c,d]$ into three evenly sized subintervals as shown in Figure 3.1.2. As we did in Preview Activity 3.1.1, we will need a method for identifying the endpoints of each subinterval and the resulting subrectangles.
1. Let $a=x_0 \lt x_1 \lt x_2 \lt x_3 \lt x_4 =b$ be the endpoints of the subintervals of $[a,b]$ after partitioning. Label these endpoints in Figure 3.1.2.
2. What is the length $\Delta x$ of each subinterval $[x_{i-1},x_i]\text{?}$ Your answer should be in terms of $a$ and $b\text{.}$
3. Let $c=y_0 \lt y_1 \lt y_2 \lt y_3 =d$ be the endpoints of the subintervals of $[c,d]$ after partitioning. Label these endpoints in Figure 3.1.2.
4. What is the length $\Delta y$ of each subinterval $[y_{j-1},y_j]\text{?}$ Your answer should be in terms of $c$ and $d\text{.}$
5. The partitions of the intervals $[a,b]$ and $[c,d]$ partition the rectangle $R$ into subrectangles. How many subrectangles are there?
6. Let $R_{ij}$ denote the subrectangle $[x_{i-1},x_i] \times [y_{j-1},y_j]\text{.}$ Label each subrectangle in Figure 3.1.2.
7. What is area $\Delta A$ of each subrectangle?
8. Now let $[a,b] = [0,8]$ and $[c,d] = [2,6]\text{.}$ Let $(x_{11}^*,y_{11}^*)$ be the point in the upper right corner of the subrectangle $R_{11}\text{.}$ Identify and correctly label this point in Figure 3.1.2. Calculate the product
\begin{equation*} f(x_{11}^*,y_{11}^*) \Delta A. \end{equation*}
Explain, geometrically, what this product represents.
9. For each $i$ and $j\text{,}$ choose a point $(x_{ij}^*,y_{ij}^*)$ in the subrectangle $R_{i,j}\text{.}$ Identify and correctly label these points in Figure 3.1.2. Explain what the product
\begin{equation*} f(x_{ij}^*,y_{ij}^*) \Delta A \end{equation*}
represents.
10. If we were to add all the values $f(x_{ij}^*,y_{ij}^*) \Delta A$ for each $i$ and $j\text{,}$ what does the resulting number approximate about the surface defined by $f$ on the domain $R\text{?}$ (You don't actually need to add these values.)
11. Write a double sum using summation notation that expresses the arbitrary sum from part ($j$).
Subsection3.1.2Double Riemann Sums and Double Integrals
Now we use the process from the most recent activity to formally define double Riemann sums and double integrals.
Definition3.1.3.
Let $f$ be a continuous function on a rectangle $R = \{(x,y) : a \leq x \leq b, c \leq y \leq d\}\text{.}$ A double Riemann sum for $f$ over $R$ is created as follows.
• Partition the interval $[a, b]$ into $m$ subintervals of equal length $\Delta x = \frac{b-a}{m}\text{.}$ Let $x_0\text{,}$ $x_1\text{,}$ $\ldots\text{,}$ $x_m$ be the endpoints of these subintervals, where $a = x_0\lt x_1\lt x_2 \lt \cdots \lt x_m = b\text{.}$
• Partition the interval $[c, d]$ into $n$ subintervals of equal length $\Delta y = \frac{d-c}{n}\text{.}$ Let $y_0\text{,}$ $y_1\text{,}$ $\ldots\text{,}$ $y_n$ be the endpoints of these subintervals, where $c = y_0\lt y_1\lt y_2 \lt \cdots \lt y_n = d\text{.}$
• These two partitions create a partition of the rectangle $R$ into $mn$ subrectangles $R_{ij}$ with opposite vertices $(x_{i-1},y_{j-1})$ and $(x_i, y_j)$ for $i$ between $1$ and $m$ and $j$ between $1$ and $n\text{.}$ These rectangles all have equal area $\Delta A = \Delta x \cdot \Delta y\text{.}$
• Choose a point $(x_{ij}^*, y_{ij}^*)$ in each rectangle $R_{ij}\text{.}$ Then, a double Riemann sum for $f$ over $R$ is given by
\begin{equation*} \sum_{j=1}^n \sum_{i=1}^m f(x_{ij}^*, y_{ij}^*) \cdot \Delta A. \end{equation*}
If $f(x,y) \geq 0$ on the rectangle $R\text{,}$ we may ask to find the volume of the solid bounded above by $f$ over $R\text{,}$ as illustrated on the left of Figure 3.1.4. This volume is approximated by a Riemann sum, which sums the volumes of the rectangular boxes shown on the right of Figure 3.1.4.
As we let the number of subrectangles increase without bound (in other words, as both $m$ and $n$ in a double Riemann sum go to infinity), as illustrated in Figure 3.1.5, the sum of the volumes of the rectangular boxes approaches the volume of the solid bounded above by $f$ over $R\text{.}$ The value of this limit, provided it exists, is the double integral.
Definition3.1.6.
Let $R$ be a rectangular region in the $xy$-plane and $f$ a continuous function over $R\text{.}$ With terms defined as in a double Riemann sum, the double integral of $f$ over $R$ is
\begin{equation*} \iint_R f(x,y) \, dA = \lim_{m,n \to \infty} \sum_{j=1}^n \sum_{i=1}^m f(x_{ij}^*, y_{ij}^*) \cdot \Delta A. \end{equation*}
Some textbooks use the notation $\int_R f(x,y) \, dA$ for a double integral. You will see this in some of the WeBWorK problems.
Subsection3.1.3Interpretation of Double Riemann Sums and Double integrals.
At the moment, there are two ways we can interpret the value of the double integral.
• Suppose that $f(x,y)$ assumes both positive and negatives values on the rectangle $R\text{,}$ as shown on the left of Figure 3.1.7. When constructing a Riemann sum, for each $i$ and $j\text{,}$ the product $f(x_{ij}^*, y_{ij}^*) \cdot \Delta A$ can be interpreted as a “signed” volume of a box with base area $\Delta A$ and “signed” height $f(x_{ij}^*, y_{ij}^*)\text{.}$ Since $f$ can have negative values, this “height” could be negative. The sum
\begin{equation*} \sum_{j=1}^n \sum_{i=1}^m f(x_{ij}^*, y_{ij}^*) \cdot \Delta A \end{equation*}
can then be interpreted as a sum of “signed” volumes of boxes, with a negative sign attached to those boxes whose heights are below the $xy$-plane.
We can then realize the double integral $\iint_R f(x,y) \, dA$ as a difference in volumes: $\iint_R f(x,y) \, dA$ tells us the volume of the solids the graph of $f$ bounds above the $xy$-plane over the rectangle $R$ minus the volume of the solids the graph of $f$ bounds below the $xy$-plane under the rectangle $R\text{.}$ This is shown on the right of Figure 3.1.7.
• The average of the finitely many $mn$ values $f(x_{ij}^*, y_{ij}^*)$ that we take in a double Riemann sum is given by
\begin{equation*} \mbox{Avg} _{mn} = \frac{1}{mn} \sum_{j=1}^n \sum_{i=1}^m f(x_{ij}^*, y_{ij}^*). \end{equation*}
If we take the limit as $m$ and $n$ go to infinity, we obtain what we define as the average value of $f$ over the region $R\text{,}$ which is connected to the value of the double integral. First, to view $\text{ Avg } _{mn}$ as a double Riemann sum, note that
\begin{equation*} \Delta x = \frac{b-a}{m} \ \ \ \ \ \text{ and } \ \ \ \ \ \Delta y = \frac{d-c}{n}. \end{equation*}
Thus,
\begin{equation*} \frac{1}{mn} = \frac{\Delta x \cdot \Delta y}{(b-a)(d-c)} = \frac{\Delta A}{A(R)}, \end{equation*}
where $A(R)$ denotes the area of the rectangle $R\text{.}$ Then, the average value of the function $f$ over $R\text{,}$ $f_{\operatorname{AVG}(R)}\text{,}$ is given by
\begin{align*} f_{\operatorname{AVG}(R)} \amp = \lim_{m,n \to \infty} \frac{1}{mn} \sum_{j=1}^n \sum_{i=1}^m f(x_{ij}^*, y_{ij}^*)\\ \amp = \lim_{m,n \to \infty} \frac{1}{A(R)} \sum_{j=1}^n \sum_{i=1}^m f(x_{ij}^*, y_{ij}^*) \cdot \Delta A\\ \amp = \frac{1}{A(R)} \iint_R f(x,y) \, dA. \end{align*}
Therefore, the double integral of $f$ over $R$ divided by the area of $R$ gives us the average value of the function $f$ on $R\text{.}$ Finally, if $f(x, y) \geq 0$ on $R\text{,}$ we can interpret this average value of $f$ on $R$ as the height of the box with base $R$ that has the same volume as the volume of the surface defined by $f$ over $R\text{.}$
Activity3.1.3.
Let $f(x,y) = x+2y$ and let $R = [0,2] \times [1,3]\text{.}$
1. Draw a picture of $R\text{.}$ Partition $[0,2]$ into 2 subintervals of equal length and the interval $[1,3]$ into two subintervals of equal length. Draw these partitions on your picture of $R$ and label the resulting subrectangles using the labeling scheme we established in the definition of a double Riemann sum.
2. For each $i$ and $j\text{,}$ let $(x_{ij}^*, y_{ij}^*)$ be the midpoint of the rectangle $R_{ij}\text{.}$ Identify the coordinates of each $(x_{ij}^*, y_{ij}^*)\text{.}$ Draw these points on your picture of $R\text{.}$
3. Calculate the Riemann sum
\begin{equation*} \sum_{j=1}^n \sum_{i=1}^m f(x_{ij}^*, y_{ij}^*) \cdot \Delta A \end{equation*}
using the partitions we have described. If we let $(x_{ij}^*, y_{ij}^*)$ be the midpoint of the rectangle $R_{ij}$ for each $i$ and $j\text{,}$ then the resulting Riemann sum is called a midpoint sum.
4. Give two interpretations for the meaning of the sum you just calculated.
Activity3.1.4.
Let $f(x,y) = \sqrt{4-y^2}$ on the rectangular domain $R = [1,7] \times [-2,2]\text{.}$ Partition $[1,7]$ into 3 equal length subintervals and $[-2,2]$ into 2 equal length subintervals. A table of values of $f$ at some points in $R$ is given in Table 3.1.8, and a graph of $f$ with the indicated partitions is shown in Figure 3.1.9.
1. Sketch the region $R$ in the plane using the values in Table 3.1.8 as the partitions.
2. Calculate the double Riemann sum using the given partition of $R$ and the values of $f$ in the upper right corner of each subrectangle.
3. Use geometry to calculate the exact value of $\iint_R f(x,y) \, dA$ and compare it to your approximation. Describe one way we could obtain a better approximation using the given data.
We conclude this section with a list of properties of double integrals. Since similar properties are satisfied by single-variable integrals and the arguments for double integrals are essentially the same, we omit their justification.
Properties of Double Integrals.
Let $f$ and $g$ be continuous functions on a rectangle $R = \{(x,y) : a \leq x \leq b, c \leq y \leq d\}\text{,}$ and let $k$ be a constant. Then
1. $\iint_R (f(x,y) + g(x,y)) \, dA = \iint_R f(x,y) \, dA + \iint_R g(x,y) \, dA\text{.}$
2. $\iint_R kf(x,y) \, dA = k \iint_R f(x,y) \, dA\text{.}$
3. If $f(x,y) \geq g(x,y)$ on $R\text{,}$ then $\iint_R f(x,y) \, dA \geq \iint_R g(x,y) \, dA\text{.}$
Subsection3.1.4Summary
• Let $f$ be a continuous function on a rectangle $R = \{(x,y) : a \leq x \leq b, c \leq y \leq d\}\text{.}$ The double Riemann sum for $f$ over $R$ is created as follows.
• Partition the interval $[a, b]$ into $m$ subintervals of equal length $\Delta x = \frac{b-a}{m}\text{.}$ Let $x_0\text{,}$ $x_1\text{,}$ $\ldots\text{,}$ $x_m$ be the endpoints of these subintervals, where $a = x_0\lt x_1\lt x_2 \lt \cdots \lt x_m = b\text{.}$
• Partition the interval $[c, d]$ into $n$ subintervals of equal length $\Delta y = \frac{d-c}{n}\text{.}$ Let $y_0\text{,}$ $y_1\text{,}$ $\ldots\text{,}$ $y_n$ be the endpoints of these subintervals, where $c = y_0\lt y_1\lt y_2 \lt \cdots \lt y_n = d\text{.}$
• These two partitions create a partition of the rectangle $R$ into $mn$ subrectangles $R_{ij}$ with opposite vertices $(x_{i-1},y_{j-1})$ and $(x_i, y_j)$ for $i$ between $1$ and $m$ and $j$ between $1$ and $n\text{.}$ These rectangles all have equal area $\Delta A = \Delta x \cdot \Delta y\text{.}$
• Choose a point $(x_{ij}^*, y_{ij}^*)$ in each rectangle $R_{ij}\text{.}$ Then a double Riemann sum for $f$ over $R$ is given by
\begin{equation*} \sum_{j=1}^n \sum_{i=1}^m f(x_{ij}^*, y_{ij}^*) \cdot \Delta A. \end{equation*}
• With terms defined as in the Double Riemann Sum, the double integral of $f$ over $R$ is
\begin{equation*} \iint_R f(x,y) \, dA = \lim_{m,n \to \infty} \sum_{j=1}^n \sum_{i=1}^m f(x_{ij}^*, y_{ij}^*) \cdot \Delta A. \end{equation*}
• Two interpretations of the double integral $\iint_R f(x,y) \, dA$ are:
• The volume of the solids the graph of $f$ bounds above the $xy$-plane over the rectangle $R$ minus the volume of the solids the graph of $f$ bounds below the $xy$-plane under the rectangle $R\text{;}$
• Dividing the double integral of $f$ over $R$ by the area of $R$ gives us the average value of the function $f$ on $R\text{.}$ If $f(x, y) \geq 0$ on $R\text{,}$ we can interpret this average value of $f$ on $R$ as the height of the box with base $R$ that has the same volume as the volume of the surface defined by $f$ over $R\text{.}$
Exercises3.1.5Exercises
10.
The temperature at any point on a metal plate in the $xy$ plane is given by $T(x,y) = 100-4x^2 - y^2\text{,}$ where $x$ and $y$ are measured in inches and $T$ in degrees Celsius. Consider the portion of the plate that lies on the rectangular region $R = [1,5] \times [3,6]\text{.}$
1. Estimate the value of $\iint_R T(x,y) \, dA$ by using a double Riemann sum with two subintervals in each direction and choosing $(x_i^*, y_j^*)$ to be the point that lies in the upper right corner of each subrectangle.
2. Determine the area of the rectangle $R\text{.}$
3. Estimate the average temperature, $T_{\operatorname{AVG}(R)}\text{,}$ over the region $R\text{.}$
4. Do you think your estimate in (c) is an over- or under-estimate of the true temperature? Why?
11.
Let $f$ be a function of independent variables $x$ and $y$ that is increasing in both the positive $x$ and $y$ directions on a rectangular domain $R\text{.}$ For each of the following situations, determine if the double Riemann sum of $f$ over $R$ is an overestimate or underestimate of the double integral $\iint_R f(x,y) \, dA\text{,}$ or if it impossible to determine definitively. Provide justification for your responses.
1. The double Riemann sum of $f$ over $R$ where $f$ is evaluated at the lower left point of each subrectangle.
2. The double Riemann sum of $f$ over $R$ where $f$ is evaluated at the upper right point of each subrectangle.
3. The double Riemann sum of $f$ over $R$ where $f$ is evaluated at the midpoint of each subrectangle.
4. The double Riemann sum of $f$ over $R$ where $f$ is evaluated at the lower right point of each subrectangle.
12.
The wind chill, as frequently reported, is a measure of how cold it feels outside when the wind is blowing. In Table 3.1.10, the wind chill $w=w(v,T)\text{,}$ measured in degrees Fahrenheit, is a function of the wind speed $v\text{,}$ measured in miles per hour, and the ambient air temperature $T\text{,}$ also measured in degrees Fahrenheit. Approximate the average wind chill on the rectangle $[5,35] \times [-20,20]$ using 3 subintervals in the $v$ direction, 4 subintervals in the $T$ direction, and the point in the lower left corner in each subrectangle.
13.
Consider the box with a sloped top that is given by the following description: the base is the rectangle $R = [0,4] \times [0,3]\text{,}$ while the top is given by the plane $z = p(x,y) = 20 - 2x - 3y\text{.}$
1. Estimate the value of $\iint_R p(x,y) \, dA$ by using a double Riemann sum with four subintervals in the $x$ direction and three subintervals in the $y$ direction, and choosing $(x_i^*, y_j^*)$ to be the point that is the midpoint of each subrectangle.
2. What important quantity does your double Riemann sum in (a) estimate?
3. Suppose it can be determined that $\iint_R p(x,y) \, dA = 138\text{.}$ What is the exact average value of $p$ over $R\text{?}$
4. If you wanted to build a rectangular box (with the same base) that has the same volume as the box with the sloped top described here, how tall would the rectangular box have to be? | {"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": 0.9904295802116394, "perplexity": 188.32318592167223}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-51/segments/1575540529516.84/warc/CC-MAIN-20191210233444-20191211021444-00323.warc.gz"} |
https://espacemath.com/hex-calculator | # Hex calculator
#### RESULTS
Fill the calculator form and click on Calculate button to get result here
Get Hex calculator For Your Website
Table of Content
Our hexadecimal calculator allows you to perform the most famous 4 basic mathematical operations that are usually performed on decimal numbers. Here, you can perform addition, subtraction, multiplication and division on hex numerals as well.
It’s easier to do these operations on decimals but when it comes to hex symbols, the operations get trickier which an everyday person is not trained for.
Overview
The hex number system works virtually identically to the decimal and binary systems. Rather than making use of a base of 10 or 2 respectively, it has a base of 16 because it employs 16 digits with numbers from 0-9, just as the decimal system does, but also uses the letters A, B, C, D, E, and F (equivalent to a, b, c, d, e, f) to represent the numbers 10-15.
Every hex digit signifies 4 binary digits, called nibbles, which makes representing large binary numbers simpler. For instance, the binary value of $$011011100110011000011$$ can be characterized as $$DCCC3$$ in hex. This allows computing machines to compress huge binary values in a way that can be transformed between the two systems with ease.
Given below, are some general conversions between hexadecimal, binary, and decimal values:
Hex Binary Decimal
0 0 0
1 1 1
2 10 2
3 11 3
4 100 4
5 101 5
6 110 6
1 111 7
8 1000 8
9 1001 9
A 1010 10
B 1011 11
C 1100 12
D 1101 13
E 1110 14
F 1111 15
14 10100 20
3F 111111 63
Hex addition employs the same rules as decimal addition with the only distinction being the added symbols i.e. A, B, C, D, E, and F. It can be quite convenient to have the decimal equivalent values of A to F. Down below, is a sample of hex addition.
### Example:
18 1A B + B 7 8 = 1 4 2 3
In the example instance, B + 8 in decimal would be 11 + 8 = 19. 19 would be 13, since there is 1 set of 16, with 3 available. If you find it time-consuming, just use our calculator for hexadecimal addition.
## Hex Subtraction
The most important distinction between hexadecimal and decimal subtraction has to do with borrowing. When you borrow in hex, the "1" that is borrowed represents a base of 16 rather than that of 10.
The reason has to do with the column that is being borrowed from which is 16 times larger than the borrowing column in decimal subtraction.
### Example:
5 D 1C - 3 A F = 2 2 2
## Hex Multiplication
Hexadecimal multiplication can be a bit confusing as the conversions between hexadecimal and decimal demand more effort as the numerals happen to be larger.
Shown below is an example of hex multiplication. To the right of the example, each of the multiplication and steps for addition are given. Bear in mind that all of the numerals employed are hexadecimal.
### Example:
F A 3 × A = 1E; 1 carried down to F x C 3 3 × F = 2D, + 1 = 2E 2 E F C × A = 78; 7 carried down to F + B B 8 0 C × F = B4, + 7 = BB = B E 6 E
## Hex Division
Long division in hexadecimal is corresponding to long division in decimal, apart from the multiplication and subtraction that occur in hex.
For demonstrative purposes, the division example would be calculated in hexadecimal.
### Example:
$$\space\stackrel{DEF}{\stackrel{12\sqrt{FACE}}{\stackrel{\underline{EA}}{\stackrel{10C}{\space\stackrel{\underline{FC}}{\space\stackrel{10E}{\stackrel{\underline{10E}}{\stackrel{0}{}}}}}}}}$$
You can also check out our hex to binary and hex to decimal tools if you also want to convert data from one format to the other.
Other Languages
##### Not Available for Hex calculator
Related Calculators | {"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": 0.7475894093513489, "perplexity": 801.6157831846172}, "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-2021-49/segments/1637964363659.21/warc/CC-MAIN-20211209030858-20211209060858-00311.warc.gz"} |
https://brilliant.org/problems/clock-test/ | # Clock Test
Geometry Level pending
The hands of a clock are observed continuously from 12:45 p.m. onwards. They will be observed to point in the same direction some time between
× | {"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": 0.9807683229446411, "perplexity": 2314.039004255047}, "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-20170116095120-00107-ip-10-171-10-70.ec2.internal.warc.gz"} |
http://mathhelpforum.com/discrete-math/6878-please-help-me-set-theory.html | Attached Files
2. Originally Posted by m777
$B\times C=\{(a,m),(a,n),(b,m),(b,n)\}$
$A\times (B\times C)=\{ (1,(a,m)),(1,(a,n)),(1,(b,m)),(1,(b,n))$ $(2,(a,m)),(2,(a,n)),(2,(b,m)),(2,(b,n))$ $(3,(a,m)),(3,(a,n)),(3,(b,m)),(2,(b,n))\}$ | {"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": 0.9582127332687378, "perplexity": 24984.80654315487}, "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/1397609533121.28/warc/CC-MAIN-20140416005213-00039-ip-10-147-4-33.ec2.internal.warc.gz"} |
https://gitlab.mpcdf.mpg.de/ift/nifty/-/commit/b6fca36560db4e3aba25393f178e06bd21338bac?view=parallel | Commit b6fca365 by Philipp Arras
### Docstring fixups
parent 2f5ab8f3
... @@ -158,7 +158,7 @@ be extracted first, then changed, and a new field has to be created from the ... @@ -158,7 +158,7 @@ be extracted first, then changed, and a new field has to be created from the result. result. Fields defined on a MultiDomain Fields defined on a MultiDomain ------------------------------ ------------------------------- The :class:MultiField class can be seen as a dictionary of individual The :class:MultiField class can be seen as a dictionary of individual :class:Field s, each identified by a name, which is defined on a :class:Field s, each identified by a name, which is defined on a ... @@ -300,7 +300,7 @@ As an example one may consider the following combination of x, which is an o ... @@ -300,7 +300,7 @@ As an example one may consider the following combination of x, which is an o Basic operators Basic operators ------------ --------------- # FIXME All this is outdated! # FIXME All this is outdated! Basic operator classes provided by NIFTy are Basic operator classes provided by NIFTy are ... ...
... @@ -104,6 +104,7 @@ with :math:{R} the measurement response, which maps the continous signal field ... @@ -104,6 +104,7 @@ with :math:{R} the measurement response, which maps the continous signal field This is called a free theory, as the information Hamiltonian This is called a free theory, as the information Hamiltonian associate professor associate professor .. math:: .. math:: \mathcal{H}(d,s)= -\log \mathcal{P}(d,s)= \frac{1}{2} s^\dagger S^{-1} s + \frac{1}{2} (d-R\,s)^\dagger N^{-1} (d-R\,s) + \mathrm{const} \mathcal{H}(d,s)= -\log \mathcal{P}(d,s)= \frac{1}{2} s^\dagger S^{-1} s + \frac{1}{2} (d-R\,s)^\dagger N^{-1} (d-R\,s) + \mathrm{const} ... @@ -179,23 +180,22 @@ NIFTy takes advantage of this formulation in several ways: ... @@ -179,23 +180,22 @@ NIFTy takes advantage of this formulation in several ways: The reconstruction of a non-Gaussian signal with unknown covarinance from a non-trivial (tomographic) response is demonstrated in demos/getting_started_3.py. Here, the uncertainty of the field and the power spectrum of its generating process are probed via posterior samples provided by the MGVI algorithm. The reconstruction of a non-Gaussian signal with unknown covarinance from a non-trivial (tomographic) response is demonstrated in demos/getting_started_3.py. Here, the uncertainty of the field and the power spectrum of its generating process are probed via posterior samples provided by the MGVI algorithm. +-------------------------------------------------+ +----------------------------------------------------+ | .. image:: images/getting_started_3_setup.png | | **Output of tomography demo getting_started_3.py** | | :width: 30 % | +----------------------------------------------------+ +-------------------------------------------------+ | .. image:: images/getting_started_3_setup.png | | .. image:: images/getting_started_3_results.png | | | | :width: 30 % | +----------------------------------------------------+ +-------------------------------------------------+ | Non-Gaussian signal field, | | Output of tomography demo getting_started_3.py. | | data backprojected into the image domain, power | | **Top row:** Non-Gaussian signal field, | | spectrum of underlying Gausssian process. | | data backprojected into the image domain, power | +----------------------------------------------------+ | spectrum of underlying Gausssian process. | | .. image:: images/getting_started_3_results.png | | **Bottom row:** Posterior mean field signal | | | | reconstruction, its uncertainty, and the power | +----------------------------------------------------+ | spectrum of the process for different posterior | | Posterior mean field signal | | samples in comparison to the correct one (thick | | reconstruction, its uncertainty, and the power | | orange line). | | spectrum of the process for different posterior | +-------------------------------------------------+ | samples in comparison to the correct one (thick | | orange line). | +----------------------------------------------------+
... @@ -111,23 +111,27 @@ def _SlopePowerSpectrum(logk_space, sm, sv, im, iv): ... @@ -111,23 +111,27 @@ def _SlopePowerSpectrum(logk_space, sm, sv, im, iv): def AmplitudeOperator(s_space, Npixdof, ceps_a, ceps_k, sm, sv, im, iv, def AmplitudeOperator(s_space, Npixdof, ceps_a, ceps_k, sm, sv, im, iv, keys=['tau', 'phi'], zero_mode=True): keys=['tau', 'phi'], zero_mode=True): ''' ''' Operator for parametrizing smooth power spectra. Computes a smooth power spectrum. Computes a smooth power spectrum. Output is defined on a PowerSpace. Output is defined on a PowerSpace. Parameters Parameters ---------- ---------- Npixdof : int Npixdof : #pix in dof_space #pix in dof_space ceps_a : float ceps_a, ceps_k0 : Smoothness parameters in ceps_kernel Smoothness parameters in ceps_kernel eg. ceps_kernel(k) = (a/(1+(k/k0)**2))**2 a = ceps_a, k0 = ceps_k0 eg. ceps_kernel(k) = (a/(1+(k/k0)**2))**2 ceps_k0 : float a = ceps_a, k0 = ceps_k0 Smoothness parameters in ceps_kernel eg. ceps_kernel(k) = (a/(1+(k/k0)**2))**2 a = ceps_a, k0 = ceps_k0 sm : float sm, sv : slope_mean = expected exponent of power law (e.g. -4), slope_mean = expected exponent of power law (e.g. -4) slope_variance (default=1) sv : float slope_variance (default=1) im, iv : y-intercept_mean, y-intercept_variance of power_slope im : float y-intercept_mean iv : float y-intercept_variance of power_slope ''' ''' from ..operators.exp_transform import ExpTransform from ..operators.exp_transform import ExpTransform ... ...
... @@ -23,18 +23,18 @@ from .linear_operator import LinearOperator ... @@ -23,18 +23,18 @@ from .linear_operator import LinearOperator class DomainTupleFieldInserter(LinearOperator): class DomainTupleFieldInserter(LinearOperator): def __init__(self, domain, new_space, index, position): '''Writes the content of a field into one slice of a DomainTuple. '''Writes the content of a field into one slice of a DomainTuple. Parameters Parameters ---------- ---------- domain : Domain, tuple of Domain or DomainTuple domain : Domain, tuple of Domain or DomainTuple new_space : Domain, tuple of Domain or DomainTuple new_space : Domain, tuple of Domain or DomainTuple index : Integer index : Integer Index at which new_space shall be added to domain. Index at which new_space shall be added to domain. position : tuple position : tuple Slice in new_space in which the input field shall be written into. Slice in new_space in which the input field shall be written into. ''' ''' def __init__(self, domain, new_space, index, position): self._domain = DomainTuple.make(domain) self._domain = DomainTuple.make(domain) tgt = list(self.domain) tgt = list(self.domain) tgt.insert(index, new_space) tgt.insert(index, new_space) ... ...
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Finish editing this message first! | {"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": 0.9828960299491882, "perplexity": 13481.489259919977}, "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/1631780060882.17/warc/CC-MAIN-20210928184203-20210928214203-00404.warc.gz"} |
https://mathoverflow.net/questions/328335/why-central-isogeny-of-reductive-group-over-general-field-f-map-maximal-f-split/328620 | # Why central isogeny of reductive group over general field F map maximal F split torus onto a maximal split F torus
let $$f$$ be a central isogeny of reductive groups over a field F, why $$f$$ map a maximal split $$F$$ torus onto a maximal split $$F$$ torus.
• Because it induces an isomorphism of rational-ised character lattices (with Galois action). This question is not research level, and can be found in the part of any of the standard books dealing with rationality questions. Apr 18 '19 at 13:33
• @LSpice Thank you for the explanation. I only know how to show it if F is perfect field. The inverse image of a maximal torus defined over F is also maximal torus defined over F. But I don't know how to show it for reductive group over a non perfect field. Could you explain how to proved it in details. Apr 18 '19 at 22:11
• This is not the place to get detailed proofs of standard results. One approach (probably not optimal) is to notice that the character lattice of $f^{-1}(T_{F^{\text{alg}}})$ (which is certainly a torus) has the trivial Galois action, so that the $F$-algebra it generates is an $F$-structure for $f^{-1}(T_{F^{\text{alg}}})$. Apr 18 '19 at 23:05
• @LSpice, I think the pull back (in scheme sense) is not a smooth subgroup scheme over a non perfect field $F$ in general. The argument works when F is perfect field. Apr 19 '19 at 0:51
• Ah, I see. If you wish to work with pullbacks in the scheme-theoretic sense (not underlying reduced schemes), then the statement is not true. Let $k = \mathbb F_2((t))$, let $G$ and $G'$ be the group schemes underlying $\ker \mathrm N_{D/k}$ and $D^\times/k^\times$ where $D/k$ is the quaternionic division algebra, and let $f : G \to G'$ be the natural projection. Then the maximal split torus in $G'$ is trivial, but its pullback to $G$ is the non-smooth scheme $Z(G) = \mu_2$. Apr 19 '19 at 2:04
The image $$f(T)$$ of a maximal split torus $$T$$ is a split torus of the same dimension, which is contained in a maximal split torus $$T'$$. But the maximal split tori have the same dimension, and so $$f(T)=T'$$ (the maximal split tori are even conjugate, see, for example, Milne 2017, 25.10). [I am assuming that, as the question originally stated, $$f$$ maps a group to itself. Otherwise, you need to use that the two groups have the same split rank.]
@LSpice, I figured out how to show the pre-image of a maximal torus defined over $$F$$ is also defined over $$F$$( geometrical reduced subscheme of $$G_{F}$$). Let $$f: G\rightarrow G^{\prime}$$ be a central isogeny. By base change to $$F_{s}$$( separable closure of $$F$$), all $$U_{\alpha}$$ ( the unipotent group correspondents to the root $$\alpha$$) are defined over $$F_{s}$$. $$T(F_{s})$$ and all $$U_{\alpha}(F_s)$$ generates $$G(F_{s})$$ by Bruhat's decomposition. Central isogeny implies $$f$$ restricted to $$U_{\alpha}(F_{s})$$ is an isomorphism to $$U^{\prime}_{\alpha^{\prime}} (F_{s})$$. Therefore, two maximal torus defined over $$F_{s}$$ of $$G^{\prime}$$ are conjugate by an element in $$f(G(F_{s}))$$. This implies the preimage is defined over $$F_{s}$$. I think we essentially need it is a central isogeny. Do you think it still holds if it is only an isogeny? | {"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": 28, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9218525886535645, "perplexity": 143.04674756371446}, "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/1631780057091.31/warc/CC-MAIN-20210920191528-20210920221528-00691.warc.gz"} |
https://stats.stackexchange.com/questions/365825/finding-sample-size-with-known-sigma | # finding sample size with known $\sigma$
If the standard deviation of a normally distributed population is known to be 15, what size sample must be taken if 95% of the sample means are to differ from the population mean by less than 1?
I believe I can use $$\mathbb{P}\left(|\bar{X}-\mu|<\frac{2\sigma}{\sqrt{n}}=0.9544\right)$$ and I used $\frac{2\times 15}{\sqrt{n}}<1$ which yields $n=900$.
The correct answer is 865. Could anyone show me the correct way to solve this problem.
• Just want to add that this answer (including the one from @Don Walpola below) is only an estimate. It is entire possible to collect that many samples and still not achieve the desired precision (i.e. need more). – SecretAgentMan Sep 7 '18 at 16:23
Assuming your data are normally distributed, the formula you want to use is $n = \Big(\frac{z_{\alpha /2}\ \cdot \ \hat\sigma}{D} \Big)^{2}$, where $\alpha$ = $1 - \text{Confidence Level}$, $\hat\sigma$ is the estimate of the standard deviation, and $D$ is the desired level of accuracy for the estimate, i.e. the distance to the population mean. For your problem, $\alpha = 1 - 0.95 = 0.05$, $\hat\sigma = 15$, and $D = 1$. Then, after looking up the z-score for the $\alpha/2$ value of the probability in a z-table, will find that the z-score is $1.96$. Plugging these values into the formula will give you the desired result, after rounding up to the nearest whole number as fractional sample sizes are nonsensical. | {"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": 0.9582198858261108, "perplexity": 141.43231736647255}, "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/1614178363211.17/warc/CC-MAIN-20210302003534-20210302033534-00021.warc.gz"} |
http://mathhelpforum.com/advanced-math-topics/225345-function-fo-bounded-variation.html | # Thread: function fo bounded variation!
1. ## function fo bounded variation!
find $P_{f}= [-1,2], N_{f}= [-1, 2]$ and $T_{f}= [-1,2]$ if given that $f(x)= |x|+1$ for $-1\leq x \leq 2$
given that $f(x)=|x|+1$ for $-1\leq x \leq 2$
we have
f(-1) = 2
f(2) = 3
so
$P_{f}[-1,2]= \sum_{j=1}^{2}[3-2]^{+}$
$= [1]^{+}$ | {"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": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 8, "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": 0.9965891242027283, "perplexity": 6367.018858141594}, "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/1484560284429.99/warc/CC-MAIN-20170116095124-00109-ip-10-171-10-70.ec2.internal.warc.gz"} |
https://math24.net/optimization-problems-3d-geometry.html | Optimization Problems in 3D Geometry
This topic covers different optimization problems related to basic solid shapes (Pyramid, Cone, Cylinder, Prism, Sphere).
To solve such problems you can use the general approach discussed on the page Optimization Problems in 2D Geometry.
Solved Problems
Click or tap a problem to see the solution.
Example 1
A sphere of radius $$r$$ is inscribed in a right circular cone (Figure $$1a$$). Find the minimum volume of the cone.
Example 2
Find the cylinder with the smallest surface area (Figure $$2a$$).
Example 3
Given a cone with a slant height $$l$$ (Figure $$3a$$). Find the largest possible volume of the cone.
Example 4
Determine the largest volume of a cylinder inscribed in a cone with height $$H$$ and base radius $$R$$ (Figure $$4a$$).
Example 5
A coffee filter has a conical shape (Figure $$5a$$). It is made from a circle sector with the central angle $$\alpha$$ such that the volume of coffee held in the filter is maximized. Determine the central angle $$\alpha.$$
Example 6
Find a cone with the largest volume inscribed in a sphere of radius $$R$$ (Figure $$6a$$).
Example 7
A piece of cardboard is a rectangle of sides $$a$$ and $$b.$$ An equal square is cut out from each corner and the sides are folded up to make an open-top rectangular box (Figure $$7a$$). How large the square should be to make the box with the largest possible volume?
Example 8
A Chinese tea bowl has the shape of a spherical cap with the radius $$r$$ and the height $$h$$ (Figure $$8a$$). Determine the ratio $$\frac{h}{r}$$ that maximizes the volume of the bowl for a fixed surface area.
Example 1.
A sphere of radius $$r$$ is inscribed in a right circular cone (Figure $$1a$$). Find the minimum volume of the cone.
Solution.
The volume of a cone is given by the formula
${V = \frac{1}{3}\pi {R^2}H},$
where $$R$$ is the radius of the base and $$H$$ is the height.
The triangles $$\triangle CMO$$ and $$\triangle CKB$$ are similar. Then
$\frac{r}{R} = \frac{{\sqrt {{{\left( {H - r} \right)}^2} - {r^2}} }}{H},$
where $$r$$ is the radius of inscribed circle.
Hence
$\frac{r}{R} = \frac{{\sqrt {{H^2} - 2rH + \cancel{r^2} - \cancel{r^2}} }}{H},\;\; \Rightarrow rH = R\sqrt {{H^2} - 2rH} ,\;\; \Rightarrow {r^2}{H^2} = {R^2}\left( {{H^2} - 2rH} \right),\;\; \Rightarrow {r^2}{H^2} = {R^2}{H^2} - 2r{R^2}H,\;\; \Rightarrow \left( {{R^2} - {r^2}} \right){H^2} = 2r{R^2}H,\;\; \Rightarrow H = \frac{{2r{R^2}}}{{{R^2} - {r^2}}}.$
Now we can write the volume of the cone as a function of the base radius $$R:$$
$V = \frac{1}{3}\pi {R^2}H = \frac{1}{3}\pi {R^2} \cdot \frac{{2r{R^2}}}{{{R^2} - {r^2}}} = \frac{{2\pi r}}{3} \frac{{{R^4}}}{{{R^2} - {r^2}}} = V\left( R \right).$
Find the derivative $$V^\prime\left( R \right):$$
$V^{\prime}\left( R \right) = \left( {\frac{{2\pi r}}{3}\frac{{{R^4}}}{{{R^2} - {r^2}}}} \right)^{\prime} = \frac{{2\pi r}}{3} \cdot \frac{{4{R^3} \cdot \left( {{R^2} - {r^2}} \right) - {R^4} \cdot 2R}}{{{{\left( {{R^2} - {r^2}} \right)}^2}}} = \frac{{2\pi r}}{3} \cdot \frac{{4{R^5} - 4{r^2}{R^3} - 2{R^5}}}{{{{\left( {{R^2} - {r^2}} \right)}^2}}} = \frac{{2\pi r}}{3} \cdot \frac{{2{R^5} - 4{r^2}{R^3}}}{{{{\left( {{R^2} - {r^2}} \right)}^2}}} = \frac{{4\pi r{R^3}}}{3} \cdot \frac{{{R^2} - 2{r^2}}}{{{{\left( {{R^2} - {r^2}} \right)}^2}}}.$
Set the derivative equal to zero to calculate the critical point:
$V^{\prime}\left( R \right) = 0,\;\; \Rightarrow \frac{{4\pi r{R^3}}}{3} \cdot \frac{{{R^2} - 2{r^2}}}{{{{\left( {{R^2} - {r^2}} \right)}^2}}} = 0,\;\; \Rightarrow {R^2} - 2{r^2} = 0,\;\; \Rightarrow {R^2} = 2{r^2},\;\; \Rightarrow R = \sqrt 2 r.$
This point is a local minimum by the First Derivative Test.
The height of the cone is
$H = \frac{{2r{R^2}}}{{{R^2} - {r^2}}} = \frac{{2r \cdot 2{r^2}}}{{2{r^2} - {r^2}}} = \frac{{4{r^3}}}{{{r^2}}} = 4r.$
Hence, the minimum volume of the cone is given by
${V_{\min }} = \frac{1}{3}\pi {R^2}H = \frac{1}{3}\pi \cdot 2{r^2} \cdot 4r = \frac{8}{3}\pi {r^3}.$
Example 2.
Find the cylinder with the smallest surface area (Figure $$2a$$).
Solution.
The optimal shape of a cylinder at a fixed volume allows to reduce materials cost. Therefore, this problem is important, for example, in the construction of oil storage tanks (Figure $$2a$$).
Let $$H$$ be the height of the cylinder and $$R$$ be its base radius. The volume and total surface area of the cylinder are calculated by the formulas
$V = \pi {R^2}H,\;\;\;S = 2\pi {R^2} + 2\pi RH.$
We choose the base radius $$R$$ as an independent variable. Express $$H$$ in terms of $$R$$ (at a fixed volume $$V$$):
$H = \frac{V}{{\pi {R^2}}}.$
Investigate extreme values of the surface area $$S\left( R \right)$$.
$S\left( R \right) = 2\pi {R^2} + 2\pi RH = 2\pi {R^2} + 2\pi R \cdot \frac{V}{{\pi {R^2}}} = 2\pi {R^2} + \frac{{2V}}{R}.$
Calculate the derivative:
$S'\left( R \right) = {\left( {2\pi {R^2} + \frac{{2V}}{R}} \right)^\prime } = 4\pi R - \frac{{2V}}{{{R^2}}} = \frac{{4\pi {R^3} - 2V}}{{{R^2}}}.$
Find the stationary points:
$S'\left( R \right) = 0,\;\; \Rightarrow \frac{{4\pi {R^3} - 2V}}{{{R^2}}} = 0,\;\; \Rightarrow \left\{ {\begin{array}{*{20}{l}} {4\pi {R^3} - 2V = 0}\\ {{R^2} \ne 0} \end{array},} \right.\;\; \Rightarrow R = \sqrt[3]{{\frac{V}{{2\pi }}}}.$
This value of $$R$$ corresponds to the minimum surface area $$S\left( R \right),$$ as when passing through this point the derivative changes sign from minus to plus.
Calculate the height of the above cylinder:
$H = \frac{V}{{\pi {R^2}}} = \frac{V}{{\pi {{\left( {\sqrt[3]{{\frac{V}{{2\pi }}}}} \right)}^2}}} = \frac{{{2^{\frac{2}{3}}}{\pi ^{\frac{2}{3}}}V}}{{\pi {V^{\frac{2}{3}}}}} = \frac{{{2^{\frac{2}{3}}}{V^{\frac{1}{3}}}}}{{{\pi ^{\frac{1}{3}}}}} = \sqrt[3]{{\frac{{4V}}{\pi }}}.$
The ratio of the height to the base radius is
$\frac{H}{R} = \frac{{\sqrt[3]{{\frac{{4V}}{\pi }}}}}{{\sqrt[3]{{\frac{V}{{2\pi }}}}}} = \sqrt[3]{{\frac{{4V}}{\pi } \cdot \frac{{2\pi }}{V}}} = \sqrt[3]{8} = 2.$
In other words, the height of the cylinder with the smallest surface area should be equal to its diameter, that is an axial section of this cylinder has the form of a square.
Example 3.
Given a cone with a slant height $$l$$ (Figure $$3a$$). Find the largest possible volume of the cone.
Solution.
The volume of a cone is
$V = \frac{1}{3}\pi {R^2}H.$
By the Pythagorean theorem,
${H^2} + {R^2} = {l^2},\;\; \Rightarrow {R^2} = {l^2} - {H^2}.$
Hence
$V = \frac{\pi }{3}\left( {{l^2} - {H^2}} \right)H = \frac{\pi }{3}\left( {{l^2}H - {H^3}} \right) = V\left( H \right).$
Take the derivative of the function $$V\left( H \right):$$
$V^\prime\left( H \right) = \left( {\frac{\pi }{3}\left( {{l^2}H - {H^3}} \right)} \right)^\prime = \frac{\pi }{3}{l^2} - \pi {H^2}.$
Determine the critical value of $$H:$$
$V^\prime\left( H \right) = 0,\;\; \Rightarrow \frac{\pi }{3}{l^2} - \pi {H^2} = 0,\;\; \Rightarrow {H^2} = \frac{{{l^2}}}{3},\;\; \Rightarrow H = \frac{l}{{\sqrt 3 }}.$
Since
$V^{\prime\prime}\left( H \right) = - 9H \lt 0,$
then, by the Second Derivative Test, $$H = \frac{l}{{\sqrt 3 }}$$ is a point of local maximum.
The largest volume is equal
${V_{\max }} = \frac{\pi }{3}\left[ {{l^2} \cdot \frac{l}{{\sqrt 3 }} - {{\left( {\frac{l}{{\sqrt 3 }}} \right)}^3}} \right] = \frac{\pi }{3}\left( {\frac{{{l^3}}}{{\sqrt 3 }} - \frac{{{l^3}}}{{3\sqrt 3 }}} \right) = \frac{\pi }{3} \cdot \frac{{3{l^3} - {l^3}}}{{3\sqrt 3 }} = \frac{{2\pi {l^3}}}{{9\sqrt 3 }}.$
Example 4.
Determine the largest volume of a cylinder inscribed in a cone with height $$H$$ and base radius $$R$$ (Figure $$4a$$).
Solution.
We denote the base radius of the inscribed cylinder by $$x,$$ and its height by $$y$$ (Figure $$4b$$).
From the similarity of triangles $$SKD$$ and $$SOB$$ we get
$\frac{{KD}}{{OB}} = \frac{{SK}}{{SO}}\;\;\;\text{or}\;\;\;\frac{x}{R} = \frac{{H - y}}{H}.$
The last equation establishes a relationship between the variables $$x$$ and $$y.$$ Express $$y$$ in terms of $$x:$$
$\frac{x}{R} = \frac{{H - y}}{H},\;\; \Rightarrow HX = \left( {H - y} \right)R,\;\; \Rightarrow Hx = HR - Ry,\;\; \Rightarrow y = \frac{{HR - Hx}}{R} = H\left( {1 - \frac{x}{R}} \right).$
The volume of the inscribed cylinder is given by the formula
$V = \pi {x^2}y.$
Then
$V\left( x \right) = \pi {x^2}H\left( {1 - \frac{x}{R}} \right) = \pi H\left( {{x^2} - \frac{{{x^3}}}{R}} \right).$
Find the greatest value of the function $$V\left( x \right):$$
$V'\left( x \right) = \left[ {\pi H\left( {{x^2} - \frac{{{x^3}}}{R}} \right)} \right]^\prime = \pi H\left( {2x - \frac{{3{x^2}}}{R}} \right);$
$V'\left( x \right) = 0,\;\; \Rightarrow \pi H\left( {2x - \frac{{3{x^2}}}{R}} \right) = 0,\;\; \Rightarrow 2x - \frac{{3{x^2}}}{R} = 0,\;\; \Rightarrow x\left( {2 - \frac{{3x}}{R}} \right) = 0,\;\; \Rightarrow {x_1} = 0,\;{x_2} = \frac{{2R}}{3}.$
The solution $${x_1} = 0$$ corresponds to a zero-volume cylinder and has no physical meaning. When passing through the point $${x_2} = \frac{{2R}}{3}$$ the derivative changes sign from positive to negative. Therefore, $$x = \frac{{2R}}{3}$$ is the point of maximum of the function $$V\left( x \right).$$ For this base, the height of the cylinder is given by
$y = H\left( {1 - \frac{x}{R}} \right) = H\left( {1 - \frac{{2\cancel{R}}}{{3\cancel{R}}}} \right) = \frac{H}{3}.$
Consequently, the largest possible volume of the cylinder inscribed in the given cone is equal to
${V_{\max }} = \pi {x^2}y = \pi {\left( {\frac{{2R}}{3}} \right)^2} \cdot \frac{H}{3} = \frac{4}{{27}}\pi {R^2}H.$
It is $$\frac{4}{9}$$ of the volume of the cone.
Example 5.
A coffee filter has a conical shape (Figure $$5a$$). It is made from a circle sector with the central angle $$\alpha$$ such that the volume of coffee held in the filter is maximized. Determine the central angle $$\alpha.$$
Solution.
The arc length of the sector is given by
$P = l\alpha ,$
where $$l$$ is the radius of the sector, and the angle $$\alpha$$ is measured in radians.
Comparing the two figures we can write the relationship
$P = 2\pi R,$
where $$R$$ is the base radius of the cone.
It follows from these equations that
$P = 2\pi R,\;\; \Rightarrow l\alpha = 2\pi R,\;\; \Rightarrow R = \frac{{l\alpha }}{{2\pi }}.$
The height of the cone is given by
$H = \sqrt {{l^2} - {R^2}} = \sqrt {{l^2} - {{\left( {\frac{{l\alpha }}{{2\pi }}} \right)}^2}} = l\sqrt {1 - \frac{{{\alpha ^2}}}{{4{\pi ^2}}}} = \frac{l}{{2\pi }}\sqrt {4{\pi ^2} - {\alpha ^2}} .$
Then the volume of the cone is written as
$V = \frac{1}{3}\pi {R^2}H = \frac{\pi }{3} \cdot {\left( {\frac{{l\alpha }}{{2\pi }}} \right)^2} \cdot \frac{l}{{2\pi }}\sqrt {4{\pi ^2} - {\alpha ^2}} = \frac{\pi }{3} \cdot \frac{{{l^2}{\alpha ^2}}}{{4{\pi ^2}}} \cdot \frac{l}{{2\pi }}\sqrt {4{\pi ^2} - {\alpha ^2}} = \frac{{{l^3}{\alpha ^2}}}{{24{\pi ^2}}}\sqrt {4{\pi ^2} - {\alpha ^2}} = V\left( \alpha \right).$
Taking the derivative of the function $$V\left( \alpha \right)$$ and equating it to zero, we obtain the equation:
$\frac{{{l^3}}}{{24{\pi ^2}}} \cdot \frac{{8\alpha {\pi ^2} - 3{\alpha ^2}}}{{\sqrt {4{\pi ^2} - {\alpha ^2}} }} = 0,$
so the critical points are
$8\alpha {\pi ^2} - 3{\alpha ^2} = 0,\;\; \Rightarrow \alpha \left( {8{\pi ^2} - 3\alpha } \right) = 0,\;\; \Rightarrow \alpha = 0,\,\sqrt {\frac{8}{3}} \pi .$
The first solution $$\alpha = 0$$ is trivial. The second point $$\alpha = \sqrt {\frac{8}{3}} \pi$$ corresponds to the maximum of the function $$V\left( \alpha \right)$$ (by the First Derivative Test).
Hence,
$\alpha = \sqrt {\frac{8}{3}} \pi = 2\pi \sqrt {\frac{2}{3}} \approx 294^\circ.$
Example 6.
Find a cone with the largest volume inscribed in a sphere of radius $$R$$ (Figure $$6a$$).
Solution.
Consider the axial cross-section of the cone inscribed in the sphere (Figure $$6a$$).
We introduce the following notations: $$H$$ is the height of the cone, $$r$$ is the base radius of the cone, $$\alpha$$ is the angle between the radius of the sphere and the base of the cone. The base radius and height of the cone are connected with the radius of the sphere by the following relationships:
$r = R\cos \alpha ,\;\;\;H = R\sin \alpha + R.$
In such a case, the volume of the cone can be written as
$V = \frac{1}{3}\pi {r^2}H = \frac{1}{3}\pi {\left( {R\cos \alpha } \right)^2}\left( {R\sin \alpha + R} \right) = \frac{1}{3}\pi {R^3}{\cos ^2}\alpha \left( {\sin \alpha + 1} \right).$
where the angle $$\alpha$$ varies in the range $$0 \lt \alpha \lt {\frac{\pi }{2}}.$$ We differentiate the volume $$V$$ with respect to $$\alpha:$$
$V'\left( \alpha \right) = \left[ {\frac{1}{3}\pi {R^3}{{\cos }^2}\alpha \left( {\sin \alpha + 1} \right)} \right]^\prime = \frac{1}{3}\pi {R^3}{\left[ {{{\cos }^2}\alpha \left( {\sin \alpha + 1} \right)} \right]^\prime } = {\frac{1}{3}\pi {R^3}\cos \alpha \cdot \left[ {{{\cos }^2}\alpha - 2{{\sin }^2}\alpha - 2\sin \alpha } \right]};$
$V'\left( \alpha \right) = 0,\;\; \Rightarrow {\frac{1}{3}\pi {R^3}\cos \alpha} \cdot {\left[ {{{\cos }^2}\alpha - 2{{\sin }^2}\alpha - 2\sin \alpha } \right] = 0.}$
$1)\;\cos \alpha = 0,\;\; \Rightarrow \alpha = \frac{\pi }{2};$
$2)\;{\cos ^2}\alpha - 2{\sin ^2}\alpha - 2\sin \alpha = 0,\;\; \Rightarrow 1 - 3{\sin ^2}\alpha - 2\sin \alpha = 0,\;\; \Rightarrow 3{\sin ^2}\alpha + 2\sin \alpha - 1 = 0,\;\; \Rightarrow \sin \alpha = t,\;\; \Rightarrow 3{t^2} + 2t - 1 = 0,\;\; \Rightarrow D = 4 - 4 \cdot 3 \cdot \left( { - 1} \right) = 16,\;\; \Rightarrow {t_{1,2}} = \frac{{ - 2 \pm \sqrt {16} }}{6};$
${t_1} = - 1,\;\; \Rightarrow \sin\alpha = - 1,\;\; \Rightarrow \alpha = \frac{{3\pi }}{2},$
${t_2} = \frac{1}{3},\;\; \Rightarrow \sin \alpha = \frac{1}{3}.$
As it can be seen, the solution is $$\sin \alpha = \frac{1}{3}.$$ We can check that with increasing $$\alpha$$ and passing through this point the derivative changes sign from plus to minus, i.e. here we reach the maximum volume of the cone.
Calculate the cosine of the angle $$\alpha:$$
$\cos\alpha = \sqrt {1 - {{\left( {\frac{1}{3}} \right)}^2}} = \sqrt {1 - \frac{1}{9}} = \frac{{2\sqrt 2 }}{3}.$
Then the base radius and height of the cone of the largest volume have the following values:
$r = \frac{{2\sqrt 2 }}{3}R,\;\;\;{H = R \cdot \frac{1}{3} + R} = {\frac{4}{3}R.}$
The volume of this cone is equal to
$V = \frac{1}{3}\pi {r^2}H = \frac{\pi }{3} \cdot {\left( {\frac{{2\sqrt 2 }}{3}} \right)^2} \cdot \frac{4}{3}R = \frac{\pi }{3} \cdot \frac{8}{9}{R^2} \cdot \frac{4}{3}R = \frac{{32}}{{81}}\pi {R^3},$
which is $$\frac{{8}}{{27}}$$ of the volume of the sphere.
Example 7.
A piece of cardboard is a rectangle of sides $$a$$ and $$b.$$ An equal square is cut out from each corner and the sides are folded up to make an open-top rectangular box (Figure $$7a$$). How large the square should be to make the box with the largest possible volume?
Solution.
Let $$x$$ be the side of the square. The three sides of the rectangular box are equal to $$a - 2x,$$ $$b - 2x$$ and $$x$$. Then the volume of the box is given by
$V = \left( {a - 2x} \right)\left( {b - 2x} \right)x = \left( {ab - 2bx - 2ax + 4{x^2}} \right)x = abx - 2{x^2}\left( {a + b} \right) + 4{x^3} = V\left( x \right).$
Take the derivative of the function $$V\left( x \right):$$
$V^\prime\left( x \right) = ab - 4\left( {a + b} \right)x + 12{x^2}.$
To determine the critical point we need to solve the quadratic equation
$12{x^2} - 4\left( {a + b} \right)x + ab = 0.$
Calculate the discriminant:
$D = 16{\left( {a + b} \right)^2} - 48ab = 16\left( {{a^2} + 2ab + {b^2}} \right) - 48ab = 16{a^2} + 32ab + 16{b^2} - 48ab = 16\left( {{a^2} + ab + {b^2}} \right).$
The roots of the equations are
${x_{1,2}} = \frac{{4\left( {a + b} \right) \pm \sqrt {16\left( {{a^2} + ab + {b^2}} \right)} }}{{24}} = \frac{{a + b \pm \sqrt {{a^2} + ab + {b^2}} }}{6}.$
We should take the solution with the minus sign as $$x \lt a$$ and $$x \lt b.$$ Hence,
$x = \frac{{a + b - \sqrt {{a^2} + ab + {b^2}} }}{6}.$
Example 8.
A Chinese tea bowl has the shape of a spherical cap with the radius $$r$$ and the height $$h$$ (Figure $$8a$$). Determine the ratio $$\frac{h}{r}$$ that maximizes the volume of the bowl for a fixed surface area.
Solution.
The outer surface area of the bowl is expressed in the form
$S = \pi \left( {{h^2} + {r^2}} \right).$
The volume is given by
$V = \frac{{\pi h\left( {3{r^2} + {h^2}} \right)}}{6}.$
We solve the first equation for $${r^2}:$$
${r^2} = \frac{S}{\pi } - {h^2}.$
Hence
$V = \frac{{\pi h}}{6}\left[ {3\left( {\frac{S}{\pi } - {h^2}} \right) + {h^2}} \right] = \frac{{\pi h}}{6}\left[ {\frac{{3S}}{\pi } - 2{h^2}} \right] = \frac{{3hS}}{6} - \frac{{2\pi {h^3}}}{6} = \frac{{hS}}{2} - \frac{{\pi {h^3}}}{3} = V\left( h \right).$
Find the derivative:
$V^\prime\left( h \right) = \left( {\frac{{hS}}{2} - \frac{{\pi {h^3}}}{3}} \right)^\prime = \frac{S}{2} - \pi {h^2}.$
There is one critical point
$h = \sqrt {\frac{S}{{2\pi }}} .$
Since the second derivative is negative for $$h \gt 0:$$
$V^{\prime\prime}\left( h \right) = \left( {\frac{S}{2} - \pi {h^2}} \right)^\prime = - 2\pi h \lt 0,$
the point $$h = \sqrt {\frac{S}{{2\pi }}}$$ corresponds to the maximum volume of the bowl.
Calculate the radius $$r:$$
${r^2} = \frac{S}{\pi } - {h^2} = \frac{S}{\pi } - {\left( {\sqrt {\frac{S}{{2\pi }}} } \right)^2} = \frac{S}{\pi } - \frac{S}{{2\pi }} = \frac{S}{{2\pi }};$
Then
$r = \sqrt {\frac{S}{{2\pi }}} ,$
so the ratio $$\frac{h}{r}$$ is equal to
$\frac{h}{r} = \frac{{\sqrt {\frac{S}{{2\pi }}} }}{{\sqrt {\frac{S}{{2\pi }}} }} = 1.$
See more problems on 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": 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": 0.9418414235115051, "perplexity": 187.99504659783264}, "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-2021-43/segments/1634323585025.23/warc/CC-MAIN-20211016200444-20211016230444-00426.warc.gz"} |
https://www.physicsforums.com/threads/newtons-law-friction-problem.294031/ | # Homework Help: Newton's Law Friction Problem
1. Feb 20, 2009
### MRGE
Ok, I was watching a physics lecture and there was an interesting example given
Heres the Example
"A rubber tire has a static coefficient of one, so at an angle of 45 degrees, the car will start to slide, which is independent of the area of the tires and mass of the car."
So i did the calculations real quick to see if this is true.
For the F (Friction Max) = Coefficient Friction x Normal Force
On an incline:
In the X direction, the Force can be measured in Mass(Gravity)Sin(Theta)
In the Y Direction, the force can be measured in Mass(Gravity)Cos(Theta)
(Correct me if i get any of this stuff wrong)
According to Newton's Law, The force that the car exerts on the ground, the ground as to exert an equal amount of force if the car has no acceleration in the y direction.
So: Mass(Gravity)Cos(Theta) Equals (=) Normal Force (Nf)
And at the Point of Breaking off toe Accelerate, the equation would be:
Mass(gravity)sin(Theta) - F(friction Max) = 0
Substitute F(friction Max) with (static friction = Ms)(Mass(gravity)Cos(Theta))
So you would get
Mass(gravity)sin(Theta) - Ms(M)gCos(theta) = 0
Deriving it from the equation, Than
Tan(theta) = Ms (Static Friction)
Than:
So I plugged Theta = 45 degrees
and 100 kg to those equations
F(Friction Max) = Mu x Normal Force
Tan(45)(100kg)(9.81m/s2)(Cos45) = 693.6717523
The Force in the X direction = (100kg)(9.81m/s2)Sin45 = 693.6717523 also
Since the forces are the same, how can the car move? The forces cancel each other out, granted a tiny force will able to make it slide down but if nothing touches is, the car will still be stationary. So, I can't quite figure out why the professor is saying the car will start to slide down at an angle of 45 degrees since both the Friction Max Force is equal to the X direction Force.
Anyone want to explain this for me?
2. Feb 20, 2009
### Delphi51
Seems to me you explained it yourself! Nice job, too.
Zero force holding it in place marks the point between sliding and not sliding, which you might call the beginning of the slide. | {"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": 0.893613874912262, "perplexity": 1088.6680569155674}, "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-2018-30/segments/1531676589932.22/warc/CC-MAIN-20180717222930-20180718002930-00564.warc.gz"} |
https://ch.mathworks.com/help/sps/ref/discretepicontroller.html;jsessionid=43b9f094647be3ab188070432011 | # Discrete PI Controller
Discrete-time PI controller with external anti-windup input
• Library:
• Simscape / Electrical / Control / General Control
## Description
The Discrete PI Controller block implements discrete PI control with external anti-windup input.
This diagram is the equivalent circuit for the controller with external anti-windup input.
### Equations
The Discrete PI Controller block calculates the control signal using the backward Euler discretization method:
`$u\left(k\right)=\left[{K}_{p}+\left({K}_{i}+du\left(k\right){K}_{aw}\right)\frac{{T}_{s}z}{z-1}\right]\text{e}\left(\text{k}\right),$`
where
• u is the control signal.
• Kp is the proportional gain coefficient.
• Ki is the integral gain coefficient.
• Kaw is the anti-windup gain coefficient.
• Ts is the sampling period.
• e is the error signal.
To prevent excessive overshoot, the block can use back calculation to implement an external anti-windup mechanism. It inputs du(k), the difference between the saturated control signal, usat(k), and the calculated unsaturated control signal, u(k). It then multiplies the difference by the anti-windup coefficient and adds the amplified signal from the integral gain.
## Ports
### Input
expand all
Error signal, e(k), obtained as the difference between the reference, r(k), and measurement, y(k), signals.
Data Types: `single` | `double`
Difference, du(k), between the saturated u^sat(k) and the unsaturated control signals, u(k). If du(k) is zero, the anti-windup is disabled.
Description
Data Types: `single` | `double`
External reset (rising edge) signal for the integrator.
Data Types: `single` | `double`
### Output
expand all
Control signal, u(k).
Data Types: `single` | `double`
## Parameters
expand all
Proportional gain, Kp, of the PI controller.
Integral gain,Ki, of the PI controller.
Anti-windup gain, Kaw, of the PI controller.
Value of the integrator at simulation start time.
Time interval between samples. If the block is inside a triggered subsystem, inherit the sample time by setting this parameter to `-1`. If this block is in a continuous variable-step model, specify the sample time explicitly. For more information, see What Is Sample Time? and Specify Sample Time.
## References
[1] Åström, K. and T. Hägglund. Advanced PID Control. Research Triangle Park, NC: ISA, 2005.
## Version History
Introduced in R2017b | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 1, "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": 0.8750453591346741, "perplexity": 16477.102734979915}, "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/1664030335254.72/warc/CC-MAIN-20220928113848-20220928143848-00582.warc.gz"} |
http://mathhelpforum.com/calculus/115451-simple-question-approximating-square-root.html | # Math Help - simple question - approximating a square root
1. ## simple question - approximating a square root
how do you approximate the differential of a square root? for example the square root of 23, something thats not as obvious.
2. Originally Posted by ayarfal40
how do you approximate the differential of a square root? for example the square root of 23, something thats not as obvious.
$f(x + h) \approx f(x) + h f'(x)$.
For the example you give, $f(x) = \sqrt{x}$, $x = 25$ and $h = -2$. | {"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": 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": 0.9018722176551819, "perplexity": 756.5781328379962}, "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-2015-27/segments/1435375098464.55/warc/CC-MAIN-20150627031818-00049-ip-10-179-60-89.ec2.internal.warc.gz"} |
http://physics.stackexchange.com/questions/27778/do-killing-spinors-know-global-information | # Do Killing spinors know global information?
The conformal Killing spinor equations on $R\times S^3$ in Minkowski signature are $$\nabla_\mu \epsilon=\pm \frac{i}{2}\gamma_\mu\gamma^0\gamma^5\epsilon$$ whose solution is $$\epsilon=e^{ix^0\gamma^5/2}\epsilon_0$$ where $\epsilon_0$ is a constant spinor. Note that we identify $S^3$ with $SU(2)$ and use the left-invariant vector fields of $SU(2)$ as an orthonormal frame. For more detail, please see around Eq.2.20 in the following paper.
http://arxiv.org/abs/hep-th/0605163v3
When the superconformal index is interpreted as a partition function on $S^1\times S^3$ in the Euclidean signature, the conformal Killing spinors are modified by the Wick rotation $\epsilon =e^{-x^0\gamma^5/2}\epsilon_0$ as in the following papers.
http://arxiv.org/pdf/1104.4482v3 http://arxiv.org/abs/1104.4470
However, $\epsilon =e^{-x^0\gamma^5/2}\epsilon_0$ is not well-defined on the temporal circle $S^1$.
This issue also happens on the Killing spinor on $AdS_3$. The metric of $AdS_3$ in the Minkowski signature can be written as $$ds^2=-\cosh^2 \rho dt^2 + \sinh^2\rho d\phi^2+d\rho^2~.$$ The Killing spinors on this coordinate takes the form $$e^{\frac 12\rho\gamma_3}e^{-\frac {i }2 (\phi+ t)\gamma_1}\epsilon_0$$ as in http://arxiv.org/abs/hep-th/9310194 . However, when you consider the elliptic genus $Tr(-1)^Fq^{L_{0}-c/24} \overline{q}^{\overline L_{0} -\overline c/24} y^{J}$, the bulk duals which satisfy the E.O.M of the supergravity theory are the Euclidean thermal $AdS_3$ and the family of its $SL(2,Z)$ transformations such as the BTZ BH. Then, again the Killing spinors on the Euclidean thermal $AdS_3$ take the form $$e^{\frac 12\rho\gamma_3}e^{(-\frac {i\phi }2 + \frac{t}{2})\gamma_1}\epsilon_0$$ which are also not well-defnined on the temporal circle.
The Killing spinor equations themselves are local, so does the Killing spinor know only local information? If so, how you distinguish the Killing spinors in the NS from in the R boundary condition on 2-torus?
-
Spinor fields are sections of a spinor bundle, so you have to be careful when you work with them as if they were functions. For a spinor field, the notions of being parallel, Killing, conformal Killing,... make perfect sense globally as equations on sections of the spinor bundle, but you have to specify which bundle.
Spinor bundles are associated vector bundles to a spin bundle, which is a lift of the oriented orthonormal frame bundle. Lifts need neither exist or, if they do exist, be unique, hence there are manifolds on which you cannot define a spin bundle and manifolds on which you have more than one such bundle. The obstruction for the existence of a spin structure is orientability and the vanishing of the second Stiefel-Whitney class of the tangent bundle. If a manifold M admits a spin structure, then it may admit more than one: they are classified by $H^1(M,\mathbb{Z}_2)$ which is isomorphic to the set of group homomorphisms from the fundamental group to $\mathbb{Z}_2$. Roughly speaking this measures how you can consistently assign signs to noncontractible loops.
The circle has fundamental group $\mathbb{Z}$ and since there are two homomorphisms $\mathbb{Z} \to \mathbb{Z}_2$, there are two different spin structures, which in string theory are usually called NS and R, much to the amusement of spin geometers everywhere.
Hence the lesson is that before you can even talk about <insert your favourite spinor equation> you need to say what your spinors are; that is, which spinor bundle they are sections of.
A rough analogy (which can be made precise in this case) is that you have equations and then boundary conditions and both are necessary in order to define the problem. The analogue of the boundary conditions is specifying the spinor bundle. This is indeed the case for the circle: where the spinor field will either change by a sign or not as you move along the circle.
It is not uncommon for manifolds admitting inequivalent spin structures, that there should be parallel, Killing,... spinor fields relative to one of the spin structures, but not relative to others. In fact, this is the generic situation.
In summary, the answer to the question in the title is emphatically Yes.
Further remarks
This may answer the OP's question in the comment to an earlier version of this answer.
One has to be careful to conclude that a spinor field does not obey the right periodicity conditions. Indeed, one must remember that there is a "gauge" symmetry whenever one deals with sections of associated vector bundles to principal bundles, and that is the freedom to perform a local $G$-transformation, where $G$ is structure group of the bundle. In the case of the spinor bundles, the structure group is the relevant Spin group. Hence it could be that the discrepancy in sign is simply an artefact of the choice of frame and can be cured by a local Spin transformation. With apologies for referring to my own work, an illustrative example of this occurs at the end of §3.2.2, particularly around equation (32), in my paper with Gutowski and Sabra on 4- and 5-dimensional preons: arXiv:0705.2778 [hep-th].
I hope that this helps.
-
Thank you very much for your comment. What if a solution of the Killing spinor equation does not satisfy the boundary condition you want to impose? Does it mean that the theory cannot be supersymmetric? But I think one can put the ${\cal N}=4$ SCFT on $S^1\times S^3$ in the Euclidean signature. In addition, does the existence of a solution depend on the signature of a metric? – Satoshi Nawata Oct 20 '11 at 18:13
Thank you very much for your further remarks. However, local G-transformations are allowed only in a local supersymmetric theory, namely supergravity. In the case of $S^1\times S^3$, the theory has rigid supersymmetry. So one cannot gauge away the factor in front of a constant spinor. – Satoshi Nawata Oct 21 '11 at 17:45
Satoshi-san, my statement has nothing to do with supergravity or gauge theories, it's a statement about spin geometry. When you write the (conformal) Killing spinor equation as you have done, you are trivialising the spinor bundle and thinking of spinor fields are functions with values in a spinor representation. You could choose a different trivialisation of the spinor bundle: the spinor field, as a section of the spinor bundle, does not change, but its description as a function with values in the spinor representation does. This clearly makes no reference to any underlying theory. – José Figueroa-O'Farrill Oct 21 '11 at 18:02
Perhaps the following simple example illustrates what I mean. Consider parallel spinors on flat euclidean space, say in two dimensions. If you choose to write them relative to the frame associated to the standard flat coordinates (write $ds^2 = dx^2 + dy^2$ and then the frame is $(\partial_x,\partial_y)$) parallel spinors are constant. However if you change coordinate to polar coordinates $ds^2 = dr^2 + r^2 d\theta^2$ and you choose the corresponding coordinate frame, then the parallel spinor is no longer constant, but is related to one by a local spin transformation. – José Figueroa-O'Farrill Oct 21 '11 at 18:07
(continued) The geometrical object (the parallel spinor) is the same, but its expression as a function with values in the spinor representation is different. Basically it comes down to the fact that sections are not really functions. – José Figueroa-O'Farrill Oct 21 '11 at 18:08 | {"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": 5, "x-ck12": 0, "texerror": 0, "math_score": 0.946516752243042, "perplexity": 244.7773431110398}, "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/1430455962510.77/warc/CC-MAIN-20150501045242-00065-ip-10-235-10-82.ec2.internal.warc.gz"} |
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# If m and n are non-zero integers, is m6-m5-m4 divisible by n? 1) m2
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If m and n are non-zero integers, is $$m^6-m^5-m^4$$ divisible by n?
1) $$m^2-1=m+n^2$$
2) $$m^4-2m^3+m^2=n^2+11$$
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Re: If m and n are non-zero integers, is m6-m5-m4 divisible by n? 1) m2 [#permalink]
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30 Mar 2017, 10:22
1
ziyuen wrote:
If m and n are non-zero integers, is $$m^6-m^5-m^4$$ divisible by n?
1) $$m^2-1=m+n^2$$
2) $$m^4-2m^3+m^2=n^2+11$$
m and n can either be positive or negative.
When m is negative
m^6+m^5-m^4. m4(m2+m-1)
When m is positive
m4(m2-m-1)
1) m2-m-1=n2
Divisible when m is negative but not when m is positive.
2)m2(m2-2m+1)=n2+11
Insuff.
IMO E
Please post the solution
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Re: If m and n are non-zero integers, is m6-m5-m4 divisible by n? 1) m2 [#permalink]
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30 Mar 2017, 15:48
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ziyuen wrote:
If m and n are non-zero integers, is $$m^6-m^5-m^4$$ divisible by n?
1) $$m^2-1=m+n^2$$
2) $$m^4-2m^3+m^2=n^2+11$$
OFFICIAL SOLUTION
If you modify the original condition and the question,$$m^6-m^5-m^4 = nt$$? (t = any non-zero integer), so you get $$m^4(m^2-m-1)=nt$$?. If you look at con 1), from $$m^2-m-1=n^2$$, if you substitute it to $$m^4(m^2-m-1)$$, you get $$m^4(m^2-m-1)=m^4*n^2=n(m^4n)$$, hence yes, it is sufficient. For con 2), it is difficult to approach the question, but if you apply CMT 4 (B: if you get A or B too easily, consider D), it is also sufficient. Therefore, the answer is D. If you actually solve it, for con 2), you get $$(m^2)^2-2m(m^2)+m^2=(m^2-m)^2=n^2+11$$, $$(m^2-m)^2-n^2=(m^2-m-n)(m^2-m+n)=11$$,
① When it becomes m^2-m-n=1 and m^2-m+n=11, from m^2-m-n=1, you get m^2-m-1=n, so m^4(m^2-m-1)=m^4*n, hence yes.
② When it becomes m2-m-n=11 and m^2-m+n=1, if you add the two equations, you get 2(m^2-m)=12, m^2-m=6 and n=-5, then m^2-m-1=6-1=5=(-1)(-5)=-n, so from m^4(m^2-m-1)=m^4(-n), it is also yes.
③ When it becomes m^2-m-n=-1 and m^2-m+n=-11, if you add the two equations, from 2(m^2-m)=-12, m^2-m=-6 and n=-5, integer m that satisfies this does not exist, so it is out of scope.
④ When it becomes m^2-m-n=-11 and m^2-m+n=-1, if you add the two equations, from 2(m^2-m)=-12, m^2-m=-6 and n=5, integer m that satisfies this does not exist, so it is out of scope.
Therefore, as ①, ② shown above, it always becomes yes, hence it is sufficient. Therefore, the answer is D.
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Re: If m and n are non-zero integers, is m6-m5-m4 divisible by n? 1) m2 [#permalink]
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31 Mar 2017, 08:02
How to solve this question in 2 minutes ?
Deriving option B takes a lot of time!
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Re: If m and n are non-zero integers, is m6-m5-m4 divisible by n? 1) m2 [#permalink]
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31 Mar 2017, 08:04
How to solve this question in 2 minutes ?
Deriving option B takes a lot of time!
Dear MathRevolution, Could you help to resolve this?
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Re: If m and n are non-zero integers, is m6-m5-m4 divisible by n? 1) m2 [#permalink]
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23 Jul 2019, 04:33
chetan2u can you solve option 2. I am unable to solve it.
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Re: If m and n are non-zero integers, is m6-m5-m4 divisible by n? 1) m2 [#permalink]
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25 Jul 2019, 19:15
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Re: If m and n are non-zero integers, is m6-m5-m4 divisible by n? 1) m2 [#permalink]
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25 Jul 2019, 20:05
Awesome! This is really good.
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Re: If m and n are non-zero integers, is m6-m5-m4 divisible by n? 1) m2 [#permalink]
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25 Jul 2019, 22:58
2
warrior1991 wrote:
m and n are non negative integers.
Ques: Is (m^6 - m^5 - m^4) divisible by n?
Stmnt 2:
$$m^2(m^2-2m+1)=n^2+11$$
$$m^2 (m - 1)^2 = n^2 + 11$$
Now note that LHS is a perfect square so RHS must be a perfect square too. n is an integer and its square is n^2.
n^2 + 11 needs to be a perfect square too. Two consecutive perfect squares with a difference of only 11 between them must be 25 and 36 (the difference between consecutive perfect squares keeps increasing)
So n must be 5 so that n^2 + 11 is 36 which is also a perfect square.
$$m^2 (m - 1)^2 = 36$$
$$(m(m-1))^2 = 6^2$$
$$m*(m-1) = 6$$
m = 2
We have the values for both m and n so we can find whether the given expression is divisible by n.
Sufficient.
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Re: If m and n are non-zero integers, is m6-m5-m4 divisible by n? 1) m2 [#permalink]
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26 Jul 2019, 08:35
warrior1991 wrote:
m and n are non negative integers.
Ques: Is (m^6 - m^5 - m^4) divisible by n?
Stmnt 2:
$$m^2(m^2-2m+1)=n^2+11$$
$$m^2 (m - 1)^2 = n^2 + 11$$
Now note that LHS is a perfect square so RHS must be a perfect square too. n is an integer and its square is n^2.
n^2 + 11 needs to be a perfect square too. Two consecutive perfect squares with a difference of only 11 between them must be 25 and 36 (the difference between consecutive perfect squares keeps increasing)
So n must be 5 so that n^2 + 11 is 36 which is also a perfect square.
$$m^2 (m - 1)^2 = 36$$
$$(m(m-1))^2 = 6^2$$
$$m*(m-1) = 6$$
m = 2
We have the values for both m and n so we can find whether the given expression is divisible by n.
Sufficient.
Honestly, I could not even think of a starting point. This explanation is just great.! Thank you!
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http://mathhelpforum.com/calculus/205019-differentiation-then-transposition.html | # Math Help - differentiation then transposition..
1. ## differentiation then transposition..
Hi all, I am new to this site and I'm just starting to get back into education. I need to figure out acceleration from speed then transpose for t to find out when accel reaches 0.
I'm given the formula for speed
v=12te-(t/2) +5
so my acceleration, a= dv/dt = -6te^-(0.5t) - 6e-(0.5t) which after 4.5s a= -3.48 m/s 2
if this is correct so far, I have no idea. If by some miracle it is, I need to transpose for t, to find the time when acceleration reaches zero. Any help would be greatly appreciated.
steve
2. ## Re: differentiation then transposition..
Your differentiation is incorrect.
The correct expression is $-6te^{-t/2} + 12e^{-t/2}$ (though I would have differentiated the product the other way round so as not to have a negative sign at the front).
There is no need to transpose for $t,$ you have $a = -6te^{-t/2} + 12e^{-t/2} = 6e^{-t/2}(2-t),$ and you simply have to ask yourself what value(s) of $t,$ will make this zero.
3. ## Re: differentiation then transposition..
thats great, thank you for the reply, I had used the product rule to differentiate, how should I have done it?
4. ## Re: differentiation then transposition..
You differentiated correctly, BobP is just saying that he would have written it as $12e^{-t}- 6t^{-t}= 6e^{-t}(2- t)$.
And to "transpose for t to find out when accel reaches 0" just means to solve $6e^{-t}(2- t)= 0$ for t.
(I have no idea why you calculated a when t= 4.5. Was there another part of the problem?)
5. ## Re: differentiation then transposition..
Suppose that you had to differentiate $x^{2}e^{-2x}$ (or $e^{-2x}x^{2})$ wrt $x.$
Using the product rule you could write the result as
$2xe^{-2x} - 2x^{2}e^{-2x},$
or
$-2x^{2}e^{-2x}+2xe^{-2x}.$
The results are identical but the first is preferable. It uses one fewer character, but more importantly, if you are writing this quickly on paper it's possible to lose the negative sign at the front of the expression, it can get tangled up with an equals sign. | {"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": 11, "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": 0.8944729566574097, "perplexity": 721.0164981060719}, "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-2014-10/segments/1393999650424/warc/CC-MAIN-20140305060730-00068-ip-10-183-142-35.ec2.internal.warc.gz"} |
https://link.springer.com/article/10.1007/s10657-022-09745-6 | 1 Introduction
This paper examines the relationship between the standardisation of goods and forms of rights, and the smooth functioning of markets. In particular, it focuses on the impact of the large-scale de-standardisation of digital goods. To do so, we start from a brief overview of the framework that applies to digital goods to provide the reader with an essential background of the legal state of the art. We point out that the transition from ownership-based circulation models to access-based circulation ones usually results in a loss of transactional clarity. This is because we all have, as members of a complex society, a basic yet solid understanding of the meaning of actions such as buying, owning, selling. This is not equally true for actions such as licensing and being licensed. We explain with some examples what this means in practice. Subsequently, we move to the economic analysis of the numerus clausus doctrine, which has been heralded as a viable solution for the phenomenon of idiosyncratic licensing by the law and economics literature. It is important to flag out from the beginning that we are not using the “numerus clausus” doctrine in its strictly legal meaning (that is, as a closed list of rights that can amount to proprietary effects), but rather in a more nuanced and economic sense, pointing to its standardisation-inducing and externality-reducing effects. Accordingly, we discuss the law and economics literature about the numerus clausus doctrine and then check its compatibility with the structural features of digital markets. In doing this, we discuss whether the numerus clausus doctrine might be of some use in digital markets. This is questionable, since the structure of licenses—in personam and generally not transferrable—differs greatly from the structure of property rights—in rem and alienable. Building on these elements, we argue that the traditional economic justifications for the numerus clausus doctrine do not suit digital markets in toto. This is because they are mostly focused on the problem of potential successor in titles, a situation that is less frequent in digital markets, because of the personal and non-transferrable nature of digital licenses. However, we also claim that some aspects of the numerus clausus rationale might apply to the practice of digital licensing, where the boundaries of the in personam and the in rem are blurred in a form of “ex re” enforcement.
Acknowledging the limitations coming from the in personam and eminently contractual structure of digital licensing markets (even if with some grey areas), we propose an often neglected rationale for the numerus clausus economic doctrine, whose benefits can be detected even in the absence of a ius sequelae and limited in scope to the privity of contract. This is the protective function of the numerus clausus, which is mainly based on its ‘competition effect’, i.e. on the possibility to achieve economically more efficient outcomes. It is indeed possible that, in markets with asymmetric information and uneven market power, the legal standardisation of objects increases competition and, by that, consumer welfare too. Also, we are aware that other legal tools and institutions might tackle the problem of standardisation and consumer deceipt (notably, standardisation of contracts in consumer law or the general law of torts). However, the embedding of legal remedies in the design of digital objects] which is frequent practice when digital licensing is involved—creates the space for a potential numerus clausus analysis. We conclude by modelling this situation, taking the negative effect of stricter standardisation into account too.
2 Legal background
Digital markets have grown rapidly in the last decades. Digital products, such as embedded goods and digital contents, represent a massive source of wealth. They are exceptional innovations that allow us to do things we now consider crucial for our well-being, professional and family lives. However, despite the crucial role they play in markets and everyday lives, the rules applying to them and their economic consequences are still mostly unclear to users.
The main issue is that both digital contents and embedded goods cannot be exchanged as properties in the technical sense. They cannot be bought, sold and owned. To summarise something that would require countless pages, this is because all property law systems in the Western legal tradition have requirements that things need to fulfil before being classifiable as properties and commercialised as such. This created considerable difficulties in the application of existing laws to the commerce of digital licensed goods (ALI-ELI, 2021) Germany, Greece, Italy, and France to some degree, require goods to be tangible in order to be classifiable as ‘property’.Footnote 1 Similarly, the common law of property, even if not asking for the tangibility of objects, demands some specific requirements, such as the transferability and separability of the right (Candian et al., 1992; Penner, 1997, 2013), which cannot be found in the commercialisation of digital entities. Other accounts of the common law of property provide an approach that is even more restrictive (Douglas 2011a, 2011b; Pretto-Sakmann, 2005; Rostill, 2021), requiring possession, and thus tangibility, to access the status of property and proprietary remedies (see, e.g., the tort of conversion or trespass for moveables). This applies mainly to the English common law of property, whereas in the United States some case-law differ by allowing conversion for intangible personal property (Network Sys. Architects Corp. v. Dimitruk, 2007; Thryoff v. Nationwide Mut. Ins. Co., 2007).
This means that, in general, proprietary rules for the circulation and protection of property rights cannot apply to digital products.Footnote 2 As a consequence, their regime is defined by the interplay between default IP law rules and their contractually-defined exceptions, which can be set up by parties on a case-by-case basis.Footnote 3 Unfortunately, this is not a mere legal technicality. It might well be said that what is at stake is nothing more than a legal label: of property law and ownership, or intellectual property and licenses. Surely, if the legal form changes in the face of an identical distribution of utilities in practice, there is no reason to be concerned.Footnote 4 However, this apparent technicality has several practical consequences.Footnote 5
Since proprerty law is generally not applicable to digital products, they cannot be bought and sold, but only licensed. Licenses are highly-customisable contracts among two parties, where the licensee, in exchange for consideration, benefits from the permission to use the protected IP in some ways that are contractually determined by the agreement with the licensor. Subsequently, when paying for a purely digital good or an embedded one, consumers are not buying it—they are merely acquiring the right to access it. Therefore, legally speaking, the actual object of this transaction is not the ownership of the product, but a mere license to use it (Kim, 2003; Loos et al., 2011, p. 14). Hence, with respect to digital products, we are never owners, but licensees,Footnote 6 whose access to the product depends on the contractually-given permission of the licensor (Wenderhost, 2016, p. 202), who is the IP-right holder. As Winston (2006) said, commenting on the commercialisation of embedded goods and digital contents, the «consumer […] exchanged consideration for a chattel without purchasing or receiving title to the chattel. Instead, each received a license to use the chattel» (p. 98). Thus, what the alleged buyer gets from the transaction is the permission to use the product in question, for a given period of time and in pre-determined ways (Perzanowski & Hoofnagle, 2017), which may range from more ‘classical’ uses to highly idiosyncratic ones.
This simple fact is crucial, as it reveals many things we are rarely aware of when interacting with digital products. The shift from ownership to licenses allows market-players to do something that rules of property law do not leave room for, that is customising the concrete object of the transaction on a contractual basis. This means that the utilities exchanged by parties can be crafted and customised by contract. It might be useful to formalise this situation with Honoré’s (1961) jargon.Footnote 7 Resorting to his conceptualisation, digital licensing implies that, when it comes to digital products, what is commercialised is not the bundle (i.e. all the utilities of the thing, all its incidents), but only some of its sticks (some of its utilities). What is more, bundles can be freely crafted by parties and there are no predetermined forms of rights to comply with, which is instead the case in property law. There, the relative stability and prevedibility of bundles are achieved thanks the numerus clausus principle. This doctrine underlies property law systems in both the civil and common law traditions, and limits the parties’ freedom to create new forms of property rights (Akkermans, 2017; Rudden, 1987). However, when the good is digital, in addition to defining the contractual terms of the agreement, parties have the power to design the object of the transaction itselfFootnote 8what they are selling and what they are buying. Indeed, they can contractually subtract one stick from the bundle to the point of leading some to talk about licesed digital objects as «things by design» (Madison, 2005).
On the contrary, with tangibles this is not generally possible. In this case, in fact, property law applies, which means that parties can adjust the contractual condition of the transaction according to their will (e.g. they may set up penalties, conditions, et cetera), but the entity they are bargaining on—the bundle—must be defined according to a plethora of legally-predetermined set of utilities. In other words, when bargaining under the shadow of property rights, parties can be reasonably sure about the set of rights they are bargaining on, because the possible forms of rights—possible bundles—are pre-determined by the law. For instance, when purchasing chattels, buyers can be sure that the bundle they are acquiring corresponds to all the possible utilities stemming from the product in accordance with its physical nature, since property rules for chattels prevent post-sale restrictions as well as servitudes (Madison, 2005, p. 410). This is, of course, a rule of thumb, as the legal regime for the acquisition of tangible property varies across jurisdictions, and it is well possible that a chattle might be burdened, after its sale, by another person’s legal title (see, for instance, the issue of sequential second bona fide purchases). However, these are only exceptional cases, and, most importantly, they modify the bundle ex post, not amounting to a proper burdening by “design” of the object traded.
In addition, not only are lawful bundles limited, but another significant facilitating factor intervenes, that is the fact that almost everyone shares a basic yet solid understanding of what ownership is and what rights it confers. This general undestanding exists even for ‘fancier’ forms of real rights—e.g. so that, when closing a mortgage, even laymen know with a resonable degree of certainty what will happen.
In conclusion, the shift from property to intellectual property law is not a mere technicality without practical economic consequences. On the contrary, its implications are quite far-reaching.As we show below, the shift from standardised objects of bargaining to totally unstandardised ones is likely to impact our relation with the objects that surround us more than we would expect. The fact that parties can contractually shape the object—the set of utilities—they are bargaining on (so as to subtract one or more sticks from the bundle) and do so without any legal limitation is not a neutral arrangement at all.
3 Some real world examples
It may be useful to go through a few examples, starting with embedded goods. Suppose someone is buying a coffee-maker. As an average consumer and current owner, she would expect to be able to use the coffee maker for all the purposes she deems appropriate. This would indeed be true if the coffee maker were a traditional one. In such a case, she would have bought the coffee maker in its entirety, including all its possible uses. This is no longer the case when the coffee maker is a ‘smart’ product.
In 2016, Keurig launched an updated version of its coffee maker, which was capable of recognising coffee pods, thanks to a built-in sensor. When users tried to brew coffee with generic capsules (i.e. capsules without the code as the licensed sellers’ ones), they were «greeted by a message on the device’s display that politely refused to make their cup of coffee, instructing them to buy Keurig-brand coffee instead» (Perzanowski & Schultz, 2016, p. 36). This is because consumers who bought the Keurig coffee-makers had—legally speaking—bought the hardware only, and not the control unit, which, being digital and immaterial, could not be sold, but licensed only. Looking at the economic side of the coin, this means that the object of the transaction was not the coffee-maker in its entirety (i.e. all the economic utilities stemming from it), but all its utilities minus the possibility to freely choose the brand of coffee-pods to insert in it. If the good were fully material, this would not be possible, not only due to the physical absence of the sensor, but also because property law forbids customising products with post-sale restrictionsFootnote 9rectius, it prevents removing that particular stick from the bundle. Given its intangibility and legal qualification under IP law, the coffee-maker can be lawfully burdened by post-sale restrictions instead, i.e. that very stick can be legitimately removed from the bundle.
While the coffee-maker case is the most striking one to get to the core of the problem, other examples are equally on the spot. For instance, John Deere tractors had a built-in DRM, set up to prevent farmers from repairing their own machinery or freely choosing a mechanic in lieu of authorised repairers (Perzanowski & Schultz, 2016, p. 144). To fix these tractors, access to their control units was needed. Considering that this access was precluded not only to non-authorised repairers, but also to the owners of the tractors themselves, we may argue that purchasers did not buy the tractor in its entirety. Other examples concern not lendable cameras (Winston, 2006, p. 96), not resellable smart watches (FitBit, 2018) and smart glasses (Kravets & Baldwin, 2013). Even seeds and woodworking tools have been the subject of similar claims from the seller/licensor (Mulligan, 2016, p. 1123; Winston, 2006, fn 20).
As explained above, the realm of digital products allows many more opportunities to apply the same logic. Think for instance of the case of Apple and Anders Goncalves Da Silva (Archer, 2018). Due to territorial copyright restrictions, this user was denied the access to three movies he had bought (paying for permanent access) on iTunes Store. When he got in touch with Apple’s customer service, they explained that he had lost the possibility to re-download those titles, even though he had paid for a permanent and all-inclusive license. This because the movies had been purchased from an iTunes Store of a different country than the one Da Silva was then located in (even if they were actually available on both stores). Da Silva’s is not an isolated case. Many people claim something similar happened to them (Archer, 2018). They bought ‘something digital’ and then discovered that some post-sale restrictions were in place, preventing them from enjoying the product they paid for. In sum, after the purchase they realised that they did not acquire the entitlement to all possible uses of the thing, but only the ones included by the interplay between IP law standards and EULAs. Furthermore, no general consensus exists on the minimum degree of freedom a user shall experience after having paid for an e-book, a PDF file, a MP3 file, a movie, a videogame, nor there is a minimum standard for their functionality. This leads to a great variety of rules and praxes. In the same legal context, «some e-books can be copied, printed and forwarded to friends; others will only play on selected devices, cannot be copied or borrowed or printed» (Loos et al., 2011, p. 15); the same is true for videogames, movies, music, and subscriptions to academic journals (with varying degrees of pdf functionality and different download policies).Footnote 10
What did Da Silva ‘buy’, then? To be precise, what he actually paid for was the permanent access to some contents, minus the possibility to access them in nations different from the one where the purchase took place. What about Keurig’s customers? They bought a coffee maker and all its utilities, exception made for the possibility to use different coffee pods from Keurig-certified ones. And John Deere tractors users? Not differently, they paid for something that is not the whole set of utilities of the tractor, since the access to the tractor’s control unit was excluded.
4 Is the standardisation of digital licensing a viable solution?
All the unpleasant situations described above could have been avoided if intellectual property law provided a mandatory limit to the legal customisation of contract objects, similarly to what the property law system does. For instance, if a mandatory right to repair had existed, the John Deere case would have never become ‘a case’. Similarly, if IP law stated that the set of licensed utilities must include the right to enjoy the content regardless of geographic location, the Da Silva case would have never happened. The same holds for the mandatory inclusion of the right to resell and the right to lend (Mulligan, 2013, pp. 275 ff.).Footnote 11
More generally in modern economies, how markets are born, function and evolve is shaped by the law (Deakin et al., 2017), and digital markets make no exception. The fact that the legal foundations of markets can create welcome outcomes together with perverse incentives at the same time is well documented, both outside and inside the digital sector (Chander, 2014; Giraudo, 2021; Pistor, 2019). We claim that the current legal framework of digital objects could be adjusted to correct some of its shortcomings.
The anecdotes we provided might suggest the introduction of some kind of standardisation for licenses in the digital market. If the law demanded a standard set of utilities to be necessarily licensed when bargaining on digital products, the task of «buying a bundle that is useful to own» (Van Houweling, 2008, p. 903) would be much easier. However, as we said, this is not a simple operation. IP law, differently from property law, is characterised by a so-called ‘numerus infinitus’ (Mulligan, 2013, p. 249). At the moment, the numerus clausus principle has no place in digital markets’ regulation,Footnote 12 even though «intellectual property may be the area of law where the justifications for numerus clausus are at their strongest» (Mulligan, 2013, p. 237).
This view is not widely shared, or at least it has not been investigated as thoroughly as the numerus clausus principle in property law. Accordingly, we briefly discuss below the main explanations for the limitation of parties’ freedom in the field of property law, in order to understand whether the same rationale can apply to digital licensing. For each explanation we try to highlight how they serve what in the law and economics literature is commonly called the lubricating function of the law. Subsequently, we consider whether the differences between the new context of digital licensing and the ‘normal’ context of property rights determine a structural incompatibility between the numerus clausus principle, as variously intended in law and economics, and the realm of licensing, or, alternatively, whether the principle simply requires some adjustments for the digital environment.
4.1 The ‘organisational’ view
The first economic doctrine rationalising the numerus clausus was the one by Michael Heller. He affirmed that property rights had to be limited in forms due to their potential to impair an efficient use of resources, arguing that, when more than one person is entitled to use a given resource and, contextually, to reciprocally exclude others from it, it is likely that the resource will suffer from underuse (Heller, 1998, 1999; Mahoney, 2001; Parisi, 2002; Parisi et al., 2005).
According to this theory, a legal limitation of property forms is necessary in order to minimise the social cost of a suboptimal level of use of wealth.Footnote 13 Coordinating co-owners might in fact be impossible and, even when possible, it is not a costless activity. Collecting the consent from all right-holders increases transaction costs and diminishes the surplus generated by the activity. Accordingly, the standardisation of property rights can avert the so-called ‘tragedy of anti-commons’, both by reducing the number of rights that may offer a hold-up opportunity and by sketching less costly ways to acquire consents. In this view, the numerus clausus is an organisational principle for markets and society as a whole, promoting an efficient use of resources via the standardisation of the forms for exercising decisional power (Heller, 1999; Mahoney, 2001; Mezzanotte, 2012).
4.2 The ‘informational’ view
An alternative justification for the numerus clausus is reducing transaction costs (some argue that this is the ultimate goal of property law itself, see Merril & Smith, 2020; Smith, 2011). There is a general consensus on the fact that lower transaction costs are preferable, as their presence decreases the volume of transactions both in terms of quantity and value (Niehans, 1989). However, ‘transaction costs’ is a wide and generic formula, an umbrella term that easily turns evanescent when applied to concrete situations. Usually, the formula covers at least three categories of costs, each corresponding to a different phase of a transaction: (1) search costs, (2) bargaining costs, and (3) enforcement and verification costs. Most of these fall into the broad ‘information costs’ category, and thus point to a departure from the frictionless benchmark of perfect information.
This classification somehow corresponds to different transaction costs-based theorisations of the numerus clausus.Footnote 14 In the first place, there is Merril and Smith’s (2001) theory, rationalising the numerus clausus with the goal of reducing measurement costs for bargaining parties and potential successors in interests. They believe that total freedom in legally customising the object of the transaction, given the ius sequelae of property rights, forces all parties (especially, second-hand transferees) to spend more time and efforts in measuring the object of their bargaining because of the acknowledged risk to transact on a bundle that is indeed limited, but not due to their contractual assent.Footnote 15 In the end, Merrill and Smith (2001) conclude that law should fulfil its lubricating function by setting up a numerus clausus that limits the ‘bundles’ parties can freely create up to an optimum point—which they single out thanks to a simple model—but not beyond that.
Usually depicted as opposed to the latter, Hansmann and Kraakman’s (2002) theory grounds the numerus clausus in enforcement and verification costs. They herald the numerus clausus as the solution to sunk cost deriving from the necessity to coordinate various right-holders on the same resource and to check opportunistic vindication of rights. Accordingly, they suggest that the law should shape “accommodating” (i.e. low-cost) verification rules for those rights that create big benefits for users, are likely to be amply used, have low system costs and pose small costs for non-users (pp. 396–397). They conclude that the goal of the numerus clausus is to maximise the amount resulting from the subtraction of non-user costs and system costs from users’ benefits, and that the law should explicate its lubricating function in this direction.
4.3 The ‘synthesis’ view
The ‘organisational’ and the ‘informational’ views are traditionally presented as opposite. However, along with others (Mulligan, 2013, 242 ff.), we believe this is too strong a conclusion. Whether focusing dynamically on ‘anticommons’ and the ‘problem of the future’ or on transaction costs, what really matters is that both theories claim that the true rationale of the numerus clausus of property rights is to reach efficiency. Their only—admittedly, not irrelevant—difference is how to achieve it. In the organisational view, this happens by materially reducing the choices of private parties; in the informational view, by reducing the efforts parties must put into measuring, negotiating, coordinating, and enforcing their rights. However, at a closer look, both views stand on common ground. On the one hand, transaction costs are somehow involved in the organisational approach; on the other, the efficient allocation of wealth is also the indirect goal of informational numerus clausus’ explanations. In a frictionless market—i.e. one without transaction costs—there would be no problem in fragmenting property rights according to the desires of the parties, as there would be no costs in renegotiating property rights and first-best efficiency would always be at hand (as an example, see Arruñada, 2003).
On this basis, we believe that the classical view, which pits organisational visions of numerus clausus against transaction costs-based explanations, is unsatisfactory insofar as it does not allow us to understand these theories as complementary. A more comprehensive approach might in fact enhance our understanding of the phenomenon and help us checking the compatibility of more classical numerus clausus rationales with the market of digital products (rectius, digital IP licenses). Combined, these theories claim that standardisation of property rights is a very good thing for resource allocation when markets are imperfect. Moreover, they also entail that no standardisation would be needed if markets were frictionless: in such a case, the possibility to renegotiate would be ensured, the collection of consents would not be costly and the erosion of welfare by measurement and verification costs would not happen.
5 The compatibility-check: in rem versus in personam rights.
It is now time to verify the compatibility of these theories of the numerus clausus with the practice of digital licensing. The theories are salient, but not entirely. The problem is that traditional property law justifications to the numerus clausus rely on two elements that are not present in the field of digital licensing. Both organisational and informational justifications are based on the in rem nature of property rights and the potential harms to successors in the idiosyncratic interests. Indeed, according to these theories, the main reason for limiting parties’ choices is the persistent nature of property rights, which results in limitations even after the transfer of these rights to third parties. On the contrary, licenses are, by definition, rights of contractual nature (i.e. in personam) and non-transferrable to third parties. This means that they are not persistent in character,Footnote 16 they cannot harm more people than the original parties, and they are not able to have a permanent impact.
The question, therefore, is whether these differences—inalienability and in personam nature—suffice to determine an incompatibility between the standard numerus clausus approach and the realm of digital licensing. Differently put, while traditional justifications for the numerus clausus are strongly based on the third-party dimension of property rights’ transactions (i.e. the alienability of property rights and their ius sequelae), the world of digital licensing is generally constrained within the an in personam dimension. The question, therefore, raises spontaneously: can the rationale of efficient resource allocation and minimal transaction costs (the latter meant as both measurement and verification costs) on potential transferees still justify a numerus clausus theory in a field where none of the aforementioned elements is present? This, of course, does not deny that other typical numerus clausus justifications might back the numerus clausus doctrine even in the field of digital licensing. Think, for instance, to the rationalisation of the legal design of rights and the outlawing of idiosyncratic and unfair/inefficient titles, or to the facilitative function that the numerus clausus has on reducing information costs even within the relative situations of contractual parties. However, the purpose of the following discussion will be to check whether, beyond these standard rationales, a justification based on externalities and the outside dimension of digital licensing transaction is available.
5.1 Chattels servitudes and the ‘new servitudes’
We believe that useful insights for answering this question might stem from the dated—but still applicable in its policy takeaway—doctrine of servitudes over chattels. As it turns out, in fact, the majority of arguments in favour of a numerus clausus standardisation on digital products are based on an analogy with the structure of chattels servitudes.Footnote 17
Simply put, servitudes on chattels are not allowed, and this holds valid in both the common law and civil law tradition. This means that, while it is possible to burden a portion of land with a legal restriction that is imprescriptible and enforceable against third parties, it is not possible to do so for pieces of personal property such as chattels. It is indeed possible to impose a contractual limitation on the use of a movable, but it cannot run with the thing, meaning that potential successors in interest have to expressly give their consent to the duty; otherwise, it will not be enforceable against them. Accordingly, the restriction can only be in personam, not in rem, since its enforcement is limited to the subjects who have agreed to it. This quite striaghfroward picture is complicated by the fact that for some chattels of higher value (e.g., work of art, racehorses, vehicles), the law has developed, in both civil law and common law jurisdictions, a plethora of institutions that allow burdens to run with the thing. However, this is not the case for objects that are the subject-matter of digital licensing transactions. Thus, this paragraph will stick to the standard baseline scenario where chattels servitudes are not allowed.
Examples of servitudes over movables can be various. Imagine a bag containing a warning that repairs can be made by authorised tailors only. Suppose this condition was not considered a ‘personal’—rectius, contractual—duty, but a real one (i.e. a duty that runs with the thing and passing to the secondary owner even in the lack of a specific contractual provision). In this case, the bag would have been burdened by a servitude. Similarly, a table whose height is not modifiable due to an in rem obligation is legally considered to be burdened by a servitude. If a bookmark comes with the duty to be used on Russian novels only, it is regarded as burdened by a servitude.
But why are servitudes over chattels forbidden by law? The reasons for this restriction are two. In the first place, burdens on chattels are notoriously more difficult to discover, especially when compared to burdens on lands. While, the legal state of affairs of lands is registered, the publicity function of possession cannot serve as signal of burdens that are not immediately perceivable from the physical features of the good.Footnote 18 Accordingly, to make sure that, when buying a material thing, the bundle perfectly matches the rerum natura features of the thing, property law limits the legal customisation of objects. The second reason is that exchanges upon them are usually less valuable than the ones upon lands. This means that transaction costs are more easily compensated when it comes to lands compared to when movables are involved.Footnote 19 In the case of a high-value deal, the threshold level of transaction costs that would make the deal too costly and thus inefficient is also likely to be comparatively higher than in the case of small purchases. Hence, the net value of land bargains and the overall surplus coming from them are more likely to be above zero even in the presence of significant transaction costs.
5.2 The supporting view: lack of publicity and transaction costs
Again, we are confronted with the question whether this policy rationale is applicable in a market, the digital one, that is structurally in personam and does not allow reselling.
Undoubtedly, the internal structure of a chattel servitude has a lot to share with the digital product examples mentioned above. After all, why should we give a different legal configuration to the coffee maker that comes with the duty to only buy a specific type of pods with respect to a ‘Russian novels only’ bookmark? Why should judges enforce the duty, coming with the tractor, of only choosing authorised mechanics and not the obligation to have a bag only repaired by licensed resellers? Not to mention the duty running on a wardrobe to substitute its shelves with the ones produced by a specific company (likely, the producer’s), which looks hardly different from the obligation to substitute the remote control of a garage door with the one made by the company that has manufactured the door itself. Indeed, the legal and economic structure of all these situations is remarkably similar.Footnote 20
In broad terms, digital markets and (what we might call) digital chattels might also be characterised by the same features that justify restrictions on chattels servitudes in comparable markets. Consider in the first place that digital goods account, on average, for low-value transactions. While in fact the overall revenue from digital products keeps growing, it is mainly composed of many everyday transactions of usually small value (especially when compared to, for instance, most transactions in real estate or finance).Footnote 21 Accordingly, the ‘critical threshold’ of transaction costs might be even lower in the case of digital chattels than for material ones (Van Houweling, 2008, p. 933). On top of this, allowing a high degree of legal customisation of objects would make the digital market even more uncertain than a hypotethical one of burdened chattels, because the digital realm lacks the minimum degree of publicity deriving from the objects’ physical features. This circumstance is reinforced by the so-called unreadness phenomenonFootnote 22 and by the fact that in the digital context consumers are mostly unable to evaluate the consequences of post-sale restrictions (Van Houweling, 2008, p. 921). In short, the two features backing the standardisation on bundles for chattels (lower critical threshold of transaction costs and lack of publicity) are present in the markets for digital products in an even stronger way.Several authors have recently pointed at the possibility to introduce restrictions on digital objects by the same principles applicable to chattels servitudes. Robinson (2004) states, for instance, that the «ubiquitous use of restrictive licensing agreements has created the functional equivalent of personal property servitudes» (p. 1452). Van Houweling (2008) affirms that the class of digital products «exhibits a different mix of problematically servitude-like features» (pp. 949–950) and that «these contemporary licensing practices […] resemble problematic chattels servitudes in several respects related to notice and information costs» (p. 934). Consequentially, she advises to use the chattels servitudes taxonomy to find solutions to the problems posed by what she calls the new servitudes. Not differently, Mulligan (2016), by comparing traditional servitudes to new ones, argues that IoT servitudes are more similar to chattels servitudes than not, and that they might create social and economic harm if not adequately limited, for reasons not too far from what servitudes on chattels could have done in the past.
Arguments for a numerus clausus for digital products exist too. Though not directly based on the chattels servitudes doctrine, they still advocate for a numerus clausus expansion due to a lack of publicity and information asymmetries in digital markets. For instance, Moringiello (2010) claims that the «justifications for [the numerus clausus] principle apply with special force to disputes over intangible assets» (p. 178). According to her view, the salience of the numerus clausus principle in the context of digital assets stems from the lack of publicity plaguing that market. The non-physical nature of digital objects, she argues, prevents a direct appreciation of the ‘boundaries’ of these objects—and of the bundles of rights upon them (p. 188). By predetermining the forms of rights, the numerus clausus then carries out a “notice function”, which might be «particularly useful in an environment in which the predominant method of contracting is by online terms of use» (p. 190). Similarly, Mulligan argues that a numerus clausus principle for intellectual property rights involving copies should be recognised in the digital world. She believes that «the numerus clausus principle could significantly benefit this area of intellectual property law by eliminating the licensing of copies of digital works and software and replacing them with ‘digital sales’», which would work similarly to chattels sales. In her view, this would be particularly important in the digital sector because of the information asymmetries characterising digital licensing.
5.3 The sceptical view: digital markets as personally-structured
In the previous subsections we have argued that the servitudes doctrine is still applicable today in the case of digital goods and that the numerus clausus rationale can also be found in the realm of digital linceses. Yet, there are good reasons to be somewhat pessimistic about such an assimilation, or at least to critically qualify it.
According to some authors, the in personam nature and inalienability of licenses determines a structural incompatibility between the numerus clausus doctrine and the world of digital licensing—which, it is remarked, affects parties in the original relationship only, i.e. IP holders and licensees. Akkermans (2008), for instance, states that the numerus clausus rationale can only be found in property law—the latter being defined as the domain of property rights (i.e. in rem and alienable ones). He argues that «only in a system where there is a distinction between property rights and personal rights and, connected to that, between the law of property and the law of obligations, does using such a filter [the numerus clausus] makes sense» (p. 409). This can be explained away by noting that Akkermans writes from a purely legal perspective, where the numerus clausus principle has a more restricted technical meaning, but Law and Economics scholars have similar doubts too. Mezzanotte (2012), for instance, claims that the loosening of the division between contract law and property law makes the numerus clausus more similar to mandatory clauses in contracts than to a principle regulating markets and enhancing their smooth functioning. Accordingly, it is necessary to draw a rigorous distinction between property rights and contractual rights on the basis of their ius sequelae and their alienability. When this boundary is blurred, and the proprietary character of an entitlement is weakened, Mezzanotte believes that «the limits on contractual freedom […] end up losing any possible rational justification» (p. 13). Similarly, Arruñada (2017, pp. 758–59, p. 760) states that, in principle, there is no reason nor plausible justification for the limitation of parties freedom in a market that is made of single, one-off transactions upon in personam rights, since all benefits and costs originating from the contract fall on contracting parties. According to him, traditional justifications for the numerus clausus doctrine only make sense in markets made of subsequential exchanges bounded by derivative acquisition, since sequential exchanges and in rem rights «drastically change the nature of transaction costs, including what in the single-exchange world would be a perplexing interaction with property rights» (p. 759).
The reasons for such scepticism are easy to grasp. The numerus clausus justifications that we have analysed above are largely based on the third-party dimension inherent to property rights. All affirm that the numerus clausus is beneficial to markets because it reduces transaction costs on third parties, makes verifying and enforcing rights easier for third parties, and smoothens procedures for future renegotiations of rights. Instead, in the world of digital products, no third parties dimension legally exists for the vast majority of cases, which means that the reasons to give up a fuller libertè contractuelle look far less cogent. First, the legal customisation of digital products happens through a license, which means that only the contracting parties will bear the costs of an idiosyncratic and unreasonable license (Arruñada, 2017). Secondly, digital licenses are not subsequently transferrable, which eliminates at the root the transaction costs problem on potential successors in interest. Finally, digital resources are by definition highly replicable and suffer from quick obsolescence, which might alleviate the so-called «problem of the future» (Mahoney, 2001).
In conclusion, when moving from sequential exchanges to the privity of contract, traditional justifications of the numerus clausus could really lose ground. This is valid even when recognising, as Merrill and Smith (2001) did, that there is a grey area between contract and property where the features of both show up (notice that they did not include digital licenses or other forms of IP rights in this category). After all, if the rationale of that doctrine can only be found in the third-party dimension of property rights, then it is simply reasonable that it cannot be of any help in the personally-structured field of licensing in general. This holds true even for digital licensing, where contractually-shaped restrictions are built in the object—they are part of the object—and are therefore automatically enforced against consumers. What makes a right proprietary, at least in the context of numerus clausus justifications, is its permanence in the face of different titleholders; the fact that a particular attempt to breach the contract is prevented by the object itself does not mean that it is enforced in rem, but rather that it is enforced ex re.Footnote 23
6 A simple economic model of enforced contract standardisation
The above-mentioned critiques sound convincing. Still, if the numerus clausus has no reason to exist in the privity of contract zone, why does allowing the marketing of non-reparable tractors sound so unreasonable? Why does «a coffee maker limiting your choice of grind seem as out of place as a frying pan dictating your egg» (Barrett, 2015)? We believe that a different rationale must exist for constraining the parties’ freedom to legally shape the bundle of rights they are transacting on, even in personally-structured markets.
To illustrate the intuition behind a new rationale for a numerus clausus in the privity of the contract zone with a simple economic model, where one consumer can purchase contracts from a firm with market power. Under the assumptions that (i) standardisation can reduce market power (call this the ‘competition effect’), and (ii) enforced standardisation can reduce a transaction’s total surplus (call this the ‘loss-in-diversification effect’), introducing stronger standardisation can result in an overall efficiency gain when market power is strong.
More in detail, we first show that in the market equilibrium without standardisation firms with market power will price by charging a markup on their cost, which leads to the textbook case of deadweight loss (inefficiency). We then show that this loss can be decreased by enforcing some degree of standardisation which decreases the market power of the firm. Finally we show that enforced standardisation is efficient (i.e. the competition effect is greatest compared to the loss-in-standardisation effect) when firms would otherwise charge high markups because they have considerable market power.
The economy is composed of two sectors. Each sector makes one offer to a representative consumer with CES preferences and endowed with $$W$$ resources.Footnote 24 Contracts provide the consumer with streams of utility, so the consumer simply chooses how many contracts to accept from each firm and pays the price. Contract $$a$$ is supplied competitively and its marginal cost is the numeraire (i.e., it is normalised to 1). Contract $$c$$ is supplied monopolistically by a firm that faces a constant marginal cost $$\psi$$.Footnote 25
The consumer maximises her utility by solving:
$$\begin{array}{*{20}c} {\mathop {\max }\limits_{a,c} F\left( \varepsilon \right)\left( {c^{{\frac{\varepsilon - 1}{\varepsilon }}} + a^{{\frac{\varepsilon - 1}{\varepsilon }}} } \right)^{{\frac{\varepsilon }{\varepsilon - 1}}} } \\ {s.t. \quad a + pc = W} \\ \end{array}$$
(1)
where $$\varepsilon >1$$ is the elasticity of substitution and $$p$$ is the price of contract $$c$$.Footnote 26$$F\left(\varepsilon \right)$$ is a normalizing function that ensures that, for any given $$\left(c,a\right)$$, the objective function takes the same value regardless of the $$\varepsilon$$. We assume that all agents take the value of $$F\left(\varepsilon \right)$$ as given. This normalizing function is needed because in the model we allow elasticity to change, but we do not want these changes to directly affect the consumer’s utility level. We set the price of offer $$a$$ equal to 1 since the offer is supplied competitively and its marginal cost is, as we said, the numeraire.
The monopolist maximises his profits by solvingFootnote 27:
$$\underset{p}{\mathit{max }}\left(p-\psi \right)c$$
(2)
The social planner has the option of introducing an arbitrary degree $$s\ge 1$$ of standardisation in the monopolistic sector (up to $$s \to \infty$$), where $$s=1$$ corresponds to minimum standardisation. Standardisation affects both costs and market power in the following ways:
$$\psi = \psi^{*} s$$
(3.1)
$$\varepsilon = \varepsilon^{*} s$$
(3.2)
In other words, standardisation has two effects: (i) it increases the marginal cost above its baseline $${\psi }^{*}$$; (ii) it decreases market power by increasing the elasticity of substitution faced by the consumer above its baseline $${\varepsilon }^{*}$$. This captures the idea that standardisation can benefit consumers by making transactions easier to understand and evaluate, thus reducing the market power of the supplier (since consumers are now more inclined to ditch his contracts). We called (3.2) the ‘competition effect’, which includes the protective effect for consumers. However, the benefits of the competition effect come at a cost, since standardisation potentially prevents parties from striking the optimal deal, thus reducing the transaction’s overall surplus. We called this the ‘loss-in-diversification effect’: in our model, it is captured by (3.1) as a cost increase.Footnote 28
The loss-in-diversification effect is modeled as a simple cost increase for analytical convenience. While it might even be argued that a standardised contract should cost less than a a tailored-to-customer one, results would be unaffected if, instead of increasing costs, we modeled standadisation as a decrease in the utility stream from $$c$$ by a corresponding factor. Economically-speaking, it is in fact indifferent to think of a given amount of ‘utility’ costing k times more (cost increase) or of the utility that can be acquired for some given resources decreasing by the same k times (utility decrease).Footnote 29 In practice, we may think about the loss-in-diversification effect as a decrease in the overall surplus of the transaction, regardless of whether this comes from less utility for the consumer or higher costs for the supplier. Economic analysis allows us to treat these alternatives as equivalent, so we can look at the loss-in-diversification effect as being a cost increase only, without loss of generality.
6.1 Market equilibrium
The market equilibrium is characterised by the quantities $$c$$, $$a$$ and the price $$p$$ that solve (1) and (2). Without action from the social planner we have $$s=1$$ (i.e. minimum standardisation), thus $$\psi ={\psi }^{*}$$ and $$\varepsilon ={\varepsilon }^{*}$$ (from (3)).
The CES properties of (1) yield the well known first order condition and conditional (on $$a$$) demand function:
$$c=a{p}^{-{\upvarepsilon }^{*}}$$
(4)
Substituting (4) into (2) yields the other well known first order condition of the firm problem:
$$p=\frac{{\varepsilon }^{*}}{{\varepsilon }^{*}-1}{\psi }^{*}$$
(5)
Condition (5) makes it clear that, given $$\varepsilon >1$$, the markup over marginal cost is decreasing in the elasticity of substitution. The underlying intuition is that, if it is easier for the consumer to substitute away from expensive products, the firm will be forced to charge a lower markup. So, if the monopolist could choose an arbitrary level of standardisation $$s \ge 1,$$ he would always go for $$s = 1$$, since this maximises his profit margin. In other words, it is not in the monopolist’s interest to encourage the competition effect, since this would affect his markup over marginal cost. Intuitively, more contractual flexibility allows suppliers with market power to make more profits by tailoring contracts to their clients.
In our context, the price $$p$$ is not just what is paid when the offer is chosen. $$p$$ represents all those transfers from the consumer to the firm that must take place when the buyer accepts a single contract $$c$$. In other words, $$p$$ accounts for all those additional (costly) obligations that consumers face. In the model we assume perfect knowledge of $$p$$ by the consumers. This captures the idea that consumers know they might be missing something costly when they sign a contract they have not read, but do it anyway.
To characterise the equilibrium, quantities $$c$$, $$a$$ can then be obtained by substituting (4) back into the consumer’s first order conditions and budget constraint. Note that this market equilibrium is not efficient because of the standard deadweight loss caused by monopoly pricing.
6.2 Social planner equilibrium
An equilibrium where the social planner sets $$s$$ is still characterised, in addition to a value $$s \ge 1$$, by quantities $$c$$, $$a$$ and by a price $$p$$ set by the monopolist, just like the market equilibrium. Yet, the social planner who maximises consumer utility faces a tradeoff: as $$s$$ increases, the monopolistic market gets closer to the optimal outcome (i.e. $$p={\psi }^{*}$$), but $$\psi$$ increases too, meaning that the welfare gain from the competition effect might be offset by the welfare loss from the loss-in-diversification effect.
Note that, while the welfare gains from decreasing the markup are bounded because the price cannot fall below marginal cost, the losses from increasing the marginal cost are unbounded.Footnote 30 Let’s visualise this in terms of an extreme case, where the law forces firms to offer only one specific contract (i.e. full standardisation, $$s \to \infty$$). In this scenario, the monopolist would have no room whatsoever to extract any additional surplus from the transaction (full competition effect), but many consumers would be very unsatisfied with the arrangement, either because this decreases what they get from the offer or—as in our preferred formalization—because it imposes such high costs on firms that prices become prohibitive.
Substituting (3) into (5) , and assuming that the social planner ‘moves first’, so that the firm and the consumer take $$s$$ as given, yields:
$$p=\frac{{\varepsilon }^{*}{s}^{2}}{{\varepsilon }^{*}s-1}{\psi }^{*}$$
(6)
Therefore, the social planner will choose $$s$$ such that $$p$$ from (5) is minimised, since, the lower $$p$$ is, the closer it will be to $${\psi }^{*}$$ (which is the first-best outcome). Note that, regardless of the value of $$s$$, the scenario where $$p={\psi }^{*}$$ is not attainable. In other words, the social planner can only achieve a second-best outcome, since the firm will never price below its actual marginal cost $$\psi ={\psi }^{*}s$$, which is clearly greater than $${\psi }^{*}$$.
The second-best outcome is achieved by solving:
$$\underset{s}{\mathit{min}}p$$
where $$p$$ is the same as in (5), which is a well-behaved objective function. The solution to this problem is (remember that $${\varepsilon }^{*}>1$$ by assumption):
$$s=\left\{ \begin{array}{ll}\frac{2}{{\varepsilon }^{*}}&\quad {\text{if}}\;1<{\varepsilon }^{*}\le 2\\ 0 &\quad {\text{otherwise}}\end{array}\right.$$
(7)
Condition (6) has an intuitive interpretation. If demand is very elastic (i.e. $${\varepsilon }^{*}>2$$), then the monopolist is weak, in the sense that he can only charge a low markup even in the market equilibrium, because the consumer can easily substitute away from an expensive contract. As a consequence, the benefit from standardisation (competition effect) is immediately offset by the increase in marginal cost (loss-in-diversification effect). Therefore, it is optimal not to enforce any additional standardisation. Instead, when the monopolist is strong and charges an high markup because demand is relatively inelastic (i.e. $$1<{\upvarepsilon }^{*}\le 2$$), setting $$s>0$$ increases overall welfare, because the benefit from the erosion of the monopolist’s markup can be greater than the cost of standardisation itself. In other words, standardisation is desirable when a party has considerable market (and bargaining) power over the other. In practice, as we said, this market power could arise from asymmetric information about the content of the offer and the features of the object, which incentivises rent extraction from the better informed party, making standardisation more needed.
The intuition behind the social planner’s optimal choice of $$s$$ when demand has low elasticy can be visualised in Fig. 1.
As Fig. 1 shows, when elasticity is low and thus the monopolist has a greater ability to extract rent, standardisation can improve overall welfare by inducing an allocation which is closer to the first-best equilibrium (although not as good, since $$p>{\psi }^{*}$$). Therefore, an optimal level of standardisation exists that achieves the second-best outcome. This corresponds to the pair (S, P) in Fig. 1, which is the point where the monopolist’s markup (from Eq. (5)), and thus his extra-profit, is minimised.
7 The protective function of the numerus clausus: a rationale for the ‘privity of contract zone’
Would the numerus clausus, at least theoretically, achieve the optimal level of standardisation implied by the model in the sectors mentioned in Sect. 2, i.e. digital licensing? When reflecting on the Keurigg case, the first thought in our minds is not a meditated concern for potential subsequent buyers of second-hand coffee-makers (which would be the case if we were talking of a hidden burden over lands), but a sense of imbalance in the relationship between the ‘seller’ and the ‘buyer’. It is true that the law has other tools and institutions than the numerus clausus to deal with the problem of deceived buyers. However, it is submitted here that this does not eliminate the need for the introduction of a numerus clausus-like principle in the market of digital licensing. This is because there is a relevant difference, in term of enforcement and verification costs, between taking care of deception through an ex post remedy (which would imply, depending on the jurisdiction of reference and the substantial relevance of the deception, to rescind or modify the transaction) and preventing it to occur through a careful ex ante design of legal entitlements and objects in a more consumer-friendly way.
One useful analogy might be the obligation to disclose some standard nutritional information on food labels. Without this, it would be too costly for buyers to acquire said information individually, leaving them with greater uncertainty about what they would buy anyway. The lack of information could be exploited by sellers, who might diversify their product lines to extract more surplus (e.g. by selling a selection of labeled food at a premium, in order to price discriminate between different types of consumers).
The urge for an alternative justification for the numerus clausus principle in the field of digital licensing also arises from the practical situation of digital markets. These markets do not in fact display any of the typical features of markets plagued by excessive transaction costs and resources’ underutilisation. Historically and theoretically, the numerus clausus has been heralded as a tool to smoothen bargaining and trade. The paramount example of this is the abolition of the dead hand, in order to facilitate land exchanges. However, digital markets do not appear to suffer from similar problems, which should translate into reduced sales volumes and constrained supply. On the contrary, they constitute an increasingly thriving and profitable part of today’s economies. Furthermore, transactions involving digital products are rather frequent for most consumers and represent a growing share of their spending. It is therefore hard to consider digital markets as critically affected by the issues that have justified the limitation of freedom of contract in the past.
All these considered, we believe that the numerus clausus might—indeed, should—have a secondary function, not alternative but complementary to the ones discussed above, which activates under particular circumstances. We will call it the ‘protective function’ of the numerus clausus. In this sense, we believe that the mandatory standardisation of licensed bundles of rights might be a handful tool to promote competition, reduce mark-ups, increase consumer surplus and generally enhance the functioning of markets. This would be especially true in markets that display some specific characteristics, such as wide information asymmetry, uneven bargaining power and high concentration of market power. More importantly, such justification holds true even if limiting the analysis to the ‘privity of contract zone’, thus considering neither the costs on potential successors in interest nor the anticommons problem.Footnote 31 A somehow similar intuition comes from Moringiello (2010) and Mulligan (2013), who both state that a numerus clausus for digital licensing is needed so that people can actually understand «the extent of the rights they are acquiring» (Moringiello, 2010, p. 190), something that would otherwise take «an inordinate and unrealistic amount of time» (Mulligan, 2013, 276). The following subsections discuss this hypothesis, i.e. that a protective rationale exists for the numerus clausus doctrine and that it comes in handy when specific circumstances occur.
7.1 The consequences of destandardisation
Suppose consumers live in an extreme version of the world described by Omri Ben-Shahar, where they receive ‘take it or leave it’ offers for objects that are so difficult and costly to measure and screen that they simply renounce to understand what sticks are in the bundle (Ben-Shahar, 2008). Everyday experience suggests that many, if not most, transactions concerning digital products and services are not that far from this description. Consumers rarely know what they are really buying and/or agreeing to, but they are aware that there is a not-so-remote possibility to eventually discover that they have accepted something that will somehow harm them in the future (Van Houweling, 2008, p. 940). Yet they accept the offers anyway. This is actually sensible: digital products play such a crucial role in so many aspects of their lives that they are willing to sustain additional costs that are not (a visible) part of the price they pay when the contract is signed. At the same time, the lack of valid alternatives, either because almost all competitors offer similar contracts or because there are almost no competitors in the first place (re the issue of high concentration: see below), forces consumers to decide whether to blindly accept or refuse the offer as a whole.
In short, screening costs for these offers are prohibitive and therefore rationally avoided. Hence customers are better-off by sticking with these products, even if the risk exists of finding out that the object is contractually-shaped differently from what it was reasonable to expect. The willigness to accept clearly means that the expected harm consumers face for not screening is not high enough to deter most of them from buying. This trivial conclusion is also backed by evidence: if this were not the case, we would not witness a booming digital sector. From an economic perspective this is very good news, since the fact that many are willing to keep buying means that some degree of mutual gain still exists in the agreements that firms propose.
However, this is no lucky coincidence. Technology firms are well aware of consumers’ preferences for their products and have considerable market power (Philippon, 2019). They are therefore in a favourable position to, at least potentially, exploit potential information asymmetries and increase their profits by extracting a big chunk of consumer surplus. In fact, the combination of high willingness to buy, low willingness to get information and the possibility to craft objects of contract leaves room for the behaviours we described in Sect. 2. Note that firms still walk a narrow path. They must be careful not to propose contracts with clauses that can ex post ‘scare’ customers away from future purchases by harming their reputation, as this would hurt future profits. Firms aim at elaborating offers—rectius, elaborating objects—that consumers will accept again, despite persisting uncertainty and despite they might have been damaged by some clauses in the license they did not know about.
These considerations are likely to hold in a dynamic setting too. Over time consumers might learn about products (assuming they are able to do so), and put some competitive pressure on firms to offer less extractive contracts. However, firms would ‘play’ the dynamic game too, by adjusting their offers over time with the objective of maximising profits. Since, in settings with asymmetric information, the informed party has the ability to extract some information rent, we would still detect some consumer harm. In addition, it is possible to imagine a dynamic game where firms keep updating the contracts that they offer (even by paying a cost) in order to keep their valuable information advantage over buyers.Footnote 32In some contexts entry could dampen these negative outcomes, but in the presence of endogenous sunk costs (such as the ones stemming from investmenting into the preservation of market power) there would still be market power in the dynamic equilibrium, even with completely free entry (Sutton, 1991).
The anecdotes of Sect. 2 suggest that technology firms are quite successful at this. Some harm to consumers is therefore inevitable: sellers can appropriate most of the surplus through direct transfers and obligations that strengthen their position. They create value for themselves not only through proper sales (i.e. exchanging products and services for a price), but also thanks to what customers unknowingly agree to, be it buying coffee capsules from one supplier only or not being able to repair their tractor autonomously (Mulligan, 2013, p. 264 argues that the issue of uniformed consumers is especially dangerous when digital licenses are traded). In practice, sellers exploit their market power by offering customers contracts with ‘hidden’ (since they are neither read nor understood) clauses, which, either directly or indirectly, grant them such additional value. When the Keurigg coffee machine is sold, the seller’s profit come not only from the sale itself, but also from the additional earnings stemming from the future (forced) purchases of brand coffee capsules.
But, why don’t sellers simply raise prices, without elaborating increasingly complicated contracts and restricted objects? The answer is that a contractual strategy is often preferable because it allows firms to insert clauses for multiple possibilities that need not arise every time the contract is accepted. For example, most e-reader users encounter minimal accessibility problems (thus face almost no additional costs) because their use of the product is compatible with the producer’s profit-maximising strategy. Thus, it is more efficient for the latter to charge relatively lower prices and extract as much value as possible when feasible, rather than distribute a uniform and visible price increase among all customers.Footnote 33 This, we claim, is the reason why firms are incentivised to make as much use as they can of de-standardisation of objects through idiosyncratic licensing.
7.2 The protective rationale: the ‘competition effect’
As we said, three elements appear necessary to make the above-mentioned rent extraction to happen: (1) market power, (2) asymmetric information, and (3) its exploitation through de-standardisation.Footnote 34 Market power is necessary because each seller needs to face soft competition to extract additional value from consumers. In the absence of it, consumers would easily switch to substitute products that are offered at more favourable conditions—which include more sticks of the bundle (or that offer the same sticks at a lower cost). Asymmetric information—with the customer being the uninformed party—is even more clearly necessary because, in the absence of it, consumers would not need any screening in the first place, leading to less market power and, thus, to a decreased ability to extract surplus. Finally, the possibility to de-standardise ensures that information stays asymmetric and that firms can contractually craft objects to maximise surplus extraction (in the given context).
Simply put, we argue that when these three elements are present, a numerus clausus doctrine might be helpful. More analytically, our claim is that standardisation, and in particular standardisation of objects, can be a costly but sometimes effective tool to decrease the extraction of consumer surplus by firms, taking as given the existence of significant market power and asymmetric information. Accordingly, in these last pages we show how a numerus clausus of licenses might be a useful tool to reduce some of the dysfunctional aspects of this situation, thus adding a new protective rationale to the numerus clausus doctrine as traditionally intended in the literature. The protective function arises when standardisation is conceived as a way to protect consumers from contractual situations that, given their factual features, would be likely to create a high risk of surplus extraction.
This new protective rationale works in the original contractual relation between parties (i.e. in the ‘privity of contract zone’) and thus perfectly applies in personally-structured markets as the digital ones. It is in fact based not on the costs beared by potential successors in interests, but rather on the generation of surplus within the single transaction and its distribution among parties. If some mandatory form of standardisation were enforced, consumers would be faced with more understandable offers and, therefore, with better chances to gain a larger share of the surplus. Moreover, our solution would allow the most extreme subtractions of essential utilities from a product—like e.g. choosing types of coffee, repairing tractors, lending cameras—to be directly outlawed, if so desired by law-makers. Mandatory rules concerning a hard core of sticks that must be necessarily included in the bundle—that is, licensed—when ‘selling’ an embedded good or a digital content would then empower consumers and push companies to make less extractive offers.Footnote 35
It is important to note, though, that our proposal is not just a matter of distributive effects. For sure, de facto outlawing the most damaging clauses and the subtraction of some essential sticks from the bundle would directly prevent the extraction by firms of (too much) consumer surplus. Yet, the fact that the numerus clausus works defensively in the privity of contract does not imply that its effects are limited to that zone and to parties directly involved in the transaction only. On the contrary, we argue that the numerus clausus of digital licensing would also positively impact overall market efficiency. This because, simply put, standardisation would enhance competition. While there are specific theoretical cases where the extraction of consumer surplus does not diminish overall welfare, the general result—and consensus—is that when firms earn supra-competitive rents, some deadweight loss ensues (see, for example, Mas-Colell et al., 1995, pp. 384–387). We group these beneficial consequences, for both consumers and markets, under the label ‘competition effect of standardisation’. Therefore, even without considering the specific competitive structure of digital markets, a higher degree of contract standardisation could generally improve competition and thus market efficiency.
That standardisation may exercise a beneficial effect is easy to show. It is for instance a well-known result in economics that legal restrictions on private contracts can improve economic efficiency when bargaining power and information are asymmetric (Aghion & Hermalin, 1990). On this basis, with respect to digital products, introducing a numerus clausus for digital licensing would diminish inefficient rent-extraction. Moreover, when contracts become more similar and are better understood, consumers would be able to make more informed and flexible choices among alternatives, forcing firms to compete by offering better objects at better contractual conditions.
7.3 The ‘loss-in-diversification effect’ and externalities
Needless to say, introducing a numerus clausus on licenses that involve digital products would have a negative aspect too.Footnote 36 Restricting the ability of parties to strike the optimal deal can obviously decrease the overall welfare of the transaction. Therefore, the positive ‘competition effect’ can be—partly or completely—offset by the ‘loss-in-diversification effect’ that would be automatically induced by mandatory standardisation.Footnote 37
The reason is not far from the «general scepticism shown by the traditional economic analysis of law towards any kind of authoritative restriction imposed on individuals’ ability to define the contents of their property transactions» (Mezzanotte, 2012, p. 14). In the majority of cases, the personalisation of products is actually beneficial (Perzanowski & Schultz, 2016, pp. 81 ff.), in that it allows parties to better refine the object of the contract so to adjust it to individual needs (Coase, 1990, p. 12). As it has been said from a legal theory standpoint (Gaus, 2012; Grey, 1980), contractual freedom inevitably leads to fragmenting bundles of rights, which are increasingly crafted to better match our interests and desires.
The fact that the competition effect and the loss-of-diversification effect go in opposite directions entails that from the point of view of market efficiency too much standardisation can eventually be worse than no standardisation at all. We capture the tradeoff between the two effects with our simple economic model in Sect. 5. The optimal level of standardisation, at least ideally, could be enforced through the introduction of a numerus clausus.
Yet, one last effect of standardisation (not considered in the model below) does exist. It is the ‘external effect’ of standardisation. In simple words, this is the effect of the well-known Monday-watch example by Merrill and Smith (2001). According to them, not only does destandardisation increase information and measurement costs for potential successors in interests, but it does so for other market participants as well. If market players are made aware that there is the risk to pay for a covertedly idiosyncratic ‘bundle’, they will spend more time and efforts in trying to understand what they are buying even if they do not buy from one of the parties of the original idiosyncratic transaction. Hansmann and Kraakman (2002) too are aware of this issue when they consider the costs of standardisation for «nonusers of the right» (p. 396). Dealing specifically with digital markets and ‘fancy’ licenses, Perzanowsky and Schulz (2016, pp. 8–9) also argue that the simple fact of being aware that some other people have suffered from the unresonable effects of idiosyncratic licensing makes information costs higher for all market participants. On the contrary, if all actors could be sure that no objects exists that is legally-crafted in some unreasonable way, their willingness to buy would be higher and the surplus generated by an eventual transaction would be greater, since screening costs would affect it to a much lesser extent.
What we have just described as the negative external effect of destandardisation is likely to be relevant only in those markets where the process of acquiring information is extremely costly—which is exactly the situation in digital markets, at least in relative terms. The effect is not limited to the ‘privity of contract zone’, nor it is directly connected to the third party dimension. This because it is referred neither to potential successors in interest nor to bargaining parties, but only to the negative externalities of destandardisation. As we said, our argument in the following model does not rely on this effect, though it is likely that some negative externalities are present in digital markets too. If they are indeed present, our economic argument in favor of the numerus clausus in the digital context is actually reinforced, because there is an additional source of inefficiency we are not accounting for. In other words, the protective rationale for the numerus clausus can be invoked even in the absence of externalities.
In summary, we think that striking a socially beneficial balance between the positive ‘competition effect’ and the negative ‘loss-in-diversification effect’ in digital markets is feasible by incresing standardisation. In terms of policy, the say ‘hell is in the details’ clearly applies: badly designed stadardisation can be more harmful than the current system of no standardisation (as our model shows). However, since digital markets generally involve indivisible goods and no active bargaining between individual consumers and firms (e.g. a coffe-maker sold through a take-it-or-leave-it offer), we are convinced that most decentralised alternatives—including the current situation—might not be enough to solve the underlying problem of information asymmetry and market power.
8 Conclusion
Digital markets pose considerable challenges to legal scholars and regulators. In this paper we argued that the introduction of a numerus clausus for digital licensing could yield some benefits if properly implemented.
Our argument stems from some real world evidence of the dysfunctionalities of the current arrangement in digital markets. These issues seem to arise because sellers can destandardise objects in ways that increase the information asymmetry between them and their customers, so that more consumer surplus can be extracted from every transaction. Since surplus extraction through information asymmetry is a rent, this outcome is likely to be economically inefficient compared to the competitive benchmark.
Most of the existing justifications of the numerus clausus rely on third-party arguments that are hard to apply to digital markets. For this reason, we propose a new rationale for a numerus clausus specific for this context. Unlike previous accounts, our alternative justification for the numerus clausus, the protective rationale, operates in the privity of contract, without relying so heavily on the third party dimension, which remains as an a fortiori argument at most. According to this new rationale, the numerus clausus can be an effective tool to reduce the exploitation of informational asymmetries by one of the parties, because it can enhance the understanding of the contract by the less informed party and, therefore, curtail the extraction opportunities of the other. As a consequence of protecting the uninformed party, the numerus clausus can also decrease inefficient rents.
Limiting contractual freedom entails a clear tradeoff, though . Drawing from standard arguments about the negative economic effects of imposing such limitations, we concluded that legislation should aim at striking a balance between the efficiency gains from reduced rent extraction and the welfare losses caused by decreased contractual freedom. | {"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": 0.28054818511009216, "perplexity": 2046.7306802833798}, "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-2023-14/segments/1679296943483.86/warc/CC-MAIN-20230320114206-20230320144206-00709.warc.gz"} |
https://www.maplesoft.com/support/help/maple/view.aspx?path=NumberTheory%2FNumberOfIrreduciblePolynomials | NumberTheory - Maple Programming Help
Home : Support : Online Help : Mathematics : Number Theory : NumberTheory/NumberOfIrreduciblePolynomials
NumberTheory
NumberOfIrreduciblePolynomials
number of monic irreducible polynomials
Calling Sequence NumberOfIrreduciblePolynomials(n, p) NumberOfIrreduciblePolynomials(n, p, m)
Parameters
n - non-negative integer p - power of prime number m - (optional) positive integer; defaults to $1$
Description
• The NumberOfIrreduciblePolynomials(n, p, m) command computes the number of monic irreducible univariate polynomials of degree n over a finite field of order ${p}^{m}$.
• An explicit formula for this function is $\frac{1}{n}\sum _{d|n}\mathrm{\mu }\left(d\right){\left({p}^{m}\right)}^{\frac{n}{d}}$ where the sum is over the divisors of n and $\mathrm{\mu }$ is the Moebius function.
Examples
> $\mathrm{with}\left(\mathrm{NumberTheory}\right):$
> $\mathrm{NumberOfIrreduciblePolynomials}\left(3,5\right)$
${40}$ (1)
> $\mathrm{NumberOfIrreduciblePolynomials}\left(1,{2}^{4}\right)$
${16}$ (2)
The number of linear, quadratic, cubic, and quartics over $\mathrm{GF}\left(p\right)$.
> $\mathrm{seq}\left(\mathrm{NumberOfIrreduciblePolynomials}\left(n,p\right),n=1..4\right)$
${p}{,}\frac{{1}}{{2}}{}{{p}}^{{2}}{-}\frac{{1}}{{2}}{}{p}{,}\frac{{1}}{{3}}{}{{p}}^{{3}}{-}\frac{{1}}{{3}}{}{p}{,}\frac{{1}}{{4}}{}{{p}}^{{4}}{-}\frac{{1}}{{4}}{}{{p}}^{{2}}$ (3)
The number of cubics over $\mathrm{GF}\left({p}^{m}\right)$.
> $\mathrm{NumberOfIrreduciblePolynomials}\left(3,p,m\right)$
$\frac{{\left({{p}}^{{m}}\right)}^{{3}}}{{3}}{-}\frac{{{p}}^{{m}}}{{3}}$ (4)
Compatibility
• The NumberTheory[NumberOfIrreduciblePolynomials] command was introduced in Maple 2016. | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 15, "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": 0.9954069256782532, "perplexity": 1657.8058039685193}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-47/segments/1573496670731.88/warc/CC-MAIN-20191121050543-20191121074543-00026.warc.gz"} |
http://math.stackexchange.com/users/5191/zhen-lin?tab=activity&sort=revisions&page=4 | # Zhen Lin
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# 432 Revisions
Dec17 revised Unprovable Equivalence in Type Theory edited tags Dec15 revised Proof that Beck-Chevalley holds for right adjoints iff it holds for left adjoints edited body Dec10 revised Right adjoint functor edited tags Dec9 revised Example of a functor which preserves all small limits but has no left adjoint deleted 1031 characters in body Dec9 revised Proving invariance of $ds^2$ from the invariance of the speed of light edited tags Dec9 revised Adjoint of forgetful functor edited tags Dec5 revised Why is the colimit over this filtered index category the object $F(i_0)$? added 209 characters in body Dec5 revised Why is the colimit over this filtered index category the object $F(i_0)$? added 460 characters in body Dec5 revised How Co-Comma Categories are constructed? deleted 8 characters in body Dec4 revised Pullback preserves cokernel edited tags Dec4 revised Showing that a functor is not representable. edited tags Dec2 revised Foundational theories, their uses, interactions and comparisons? edited tags Dec1 revised The set of discontinuous points is countable union of closed sets edited tags Nov29 revised Exact sequence in a category with zero morphisms added 263 characters in body Nov29 revised Every projective f. g. module is f. p. edited tags Nov28 revised Why $F^{+}$ is a monopresheaf? edited tags Nov28 revised What is a (the?) good starting point for learning the modern “higher” mathematics? edited tags Nov26 revised Properties of the internal language of the category of sheaves. edited tags Nov26 revised Deeper studies in Category Theory: suggestions and references. deleted 1 characters in body Nov26 revised Deeper studies in Category Theory: suggestions and references. deleted 1 characters in body | {"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": 0.45552968978881836, "perplexity": 5211.291575160731}, "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/1397609526102.3/warc/CC-MAIN-20140416005206-00058-ip-10-147-4-33.ec2.internal.warc.gz"} |
https://kb.osu.edu/dspace/handle/1811/28989 | # THE PHOTODISSOCIATION CAGE EFFECT IN VAN DER WAALS COMPLEXES: FLUORESCENCE SPECTRA OF $I_{2} B(^{1}E_{0})$ FROM THE HINDERED PHOTODISSOCIATION OF $I_{2}$ Ar AT 488 nm
Please use this identifier to cite or link to this item: http://hdl.handle.net/1811/28989
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1982-TC'-5.jpg 97.24Kb JPEG image
Title: THE PHOTODISSOCIATION CAGE EFFECT IN VAN DER WAALS COMPLEXES: FLUORESCENCE SPECTRA OF $I_{2} B(^{1}E_{0})$ FROM THE HINDERED PHOTODISSOCIATION OF $I_{2}$ Ar AT 488 nm Creators: Cross, J. B.; Valentini, J. J. Issue Date: 1982 Publisher: Ohio State University Abstract: The $B \rightarrow X$ fluorescence of $I_{2}$ produced in the hindered photodissociation of $I_{2}$ Ar at 488 nm has been resolved. The spectra show several vibrational progressions with low rotational energy, the most prominent of these is a $($\upsilon', D)$progression extending from$\upsilon'=49$to at least$\upsilon'=23$. The$I_{2}$Ar complexes were excited and the$I_{2}$fluorescence was observed under collisionfree conditions in a supersonic free-jet expansion. We attribute these observations to a one atom photodissociation cage effect in the$I_{2}$Ar complex, in which the molecular iodine, although excited more than$400 cm^{-1}$above the B state dissociation limit, is prevented from dissociating by energy transfer to the argon atom, resulting in the breaking of the van der Waals bond,$I_{2} Ar\stackrel{488 nm}{\longrightarrow}, I_{2} (B) + Ar,$leaving the iodine molecule in a bound level of the B electronic state,$386 cm^{-1}$to$1889 cm^{-1}\$ below the dissociation limit. Interpretation of the dynamics of the cage effect in terms of a simple impulsive energy transfer model will be presented. URI: http://hdl.handle.net/1811/28989 Other Identifiers: 1982-TC'-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": 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": 0.6118898391723633, "perplexity": 8266.834193395664}, "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/1500549425381.3/warc/CC-MAIN-20170725202416-20170725222416-00419.warc.gz"} |
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# How common is 4-10 schedule in US?
Crusader911 (Mechanical) (OP) 30 Mar 10 10:48
At our facility, we are allowed the option of working four 10-hour days and being off on Friday. Our company was sold to a much larger company that works a regular 5-8 schedule. We are continuing our schedule for now, but I was just wondering how common the 4-10 schedule is at other companies.
ctopher (Mechanical) 30 Mar 10 10:59
It is slowly catching on. More companies are going to 4-10, except those that need to communicate with sales/customers on Fridays.A lot of companies take every other Friday off. It depends on the company.Also just as common are employees working virtual from home or some type of satellite office. ChrisSolidWorks 09 SP4.1ctopher's homeSolidWorks Legion
BrunoPuntzJones (Materials) 30 Mar 10 11:08
I wish it was more common, I would jump at 4x10, but when we've brought it up with management, they've been very hestitant.
Yagonyonok (Mechanical) 30 Mar 10 11:58
We used to work 4x10's in the summers, but that was axed this year. The boss said that a customer complained about not being able to reach us on a Friday, but since we are an R&D facility, and don't really have customers, I'm not sure I buy it. I think she needed something and was annoyed that we weren't here. Either way, its her company and her choice. The three day weekends were really nice though. Engineering is the art of modelling materials we do not wholly understand, into shapes we cannot precisely analyse so as to withstand forces we cannot properly assess, in such a way that the public has no reason to suspect the extent of our ignorance. -A R Dykes
KENAT (Mechanical) 30 Mar 10 12:17
I work 4 X 10s, well more like 11+, 12+, 12+, 6+ and checking email on my Fridays, but it's a bit informal.We did have 9/80's officially for a while but they scrapped that for many departments a while back.In the UK we finished at lunch on Fridays so every week we got a 2.5 day weekend. Posting guidelines FAQ731-376: Eng-Tips.com Forum Policies http://eng-tips.com/market.cfm? (probably not aimed specifically at you)What is Engineering anyway: FAQ1088-1484: In layman terms, what is "engineering"?
Mr168 (Materials) 30 Mar 10 12:42
4/10's and 44/36 are increasingly common in corporate offices for EPC companies. I sure wish the job site was like that! From an economic standpoint, it can reduce overhead costs quite a bit.
mechengdude (Mechanical) 30 Mar 10 15:06
My company allows 4/10s during the summer. USA, medium to large defense contractor.
TDAA (Geotechnical) 30 Mar 10 19:27
Not common for a lot of firms, although I have seen it catching on a bit.Heck, I asked about doing it at my last job, during our winter slow time (ski days). I just wanted to do it a few weeks to get out more, and was immediately shot down. I think it was more to do with the fact that they wanted 45 hours out of you, while 4/10s limits you to a certain degree.
berkshire (Aeronautics) 30 Mar 10 20:01
4-10 has been catching on with some manufacturing plants since gasoline prices started getting high. However with work still being tight in So Cal some of these companies are currently working 3-8 with no idea when work is going to pick up.B.E.
cksh (Mechanical) 31 Mar 10 8:34
I have yet to work for a company that has considered it. It is usually frowned upon because of customer support.I have heard internal complaints if someone isn't there to help someone from another department. Personally I would not want 4 10's because of family. Sure, I would get an extra day off but then I would have no time during the week to spend with my son who is in bed by 7:30. And that extra day he would be in school anyways. If I didn't have a son I would probably try it out. But I am already here close to 10 hours a day anyways just to get out of here by 5. Would hate for them to tell me I have to stay until 7!I would rather have flex time and be done at 3:30 or 4.
moltenmetal (Chemical) 31 Mar 10 13:53
Not much in it for the business from what I can see, unless you only run the office 4 days per week- not very practical. Lots in it for the employee, especially if they have a bad commute.Alternating staff on 4-10s, or 9-9s (alternating Fridays off) can be done but generates a fair bit of confusion as to who is going to be around on what day.Personally I've never worked at a place that permitted it. Too much risk of the employees picking up a part-time job...not to mention all the lost uncompensated overtime. Working an extra couple hours isn't so attractive when it's on your day off, or after you've already put in 10...Working one day per week from home suits me fine. No commute, fewer interruptions etc.
cvg (Civil/Environmental) 31 Mar 10 18:18
not "technically" allowed at our multi-discipline, 10,000 employee A&E consulting firm. However, some do it.
berkshire (Aeronautics) 31 Mar 10 21:48
I think this 10-4 work schedule is more common with medium sized plants on the shop floor. Plant would work 5 am to 3 pm first shift, 3 pm to 1 am second shift. Plant would shut down completely lights out for 3 days. Office would be open 8 am to 4 pm or 9 am to 5 pm five days per week for customer support. Any overtime would be done on the Friday either a half day or full day depending on the load. I have worked for plants in Georgia and California using this schedule.B.E.
duck0601 (Electrical) 1 Apr 10 14:05
At the last place I worked for it was generally 5-10s, more if they could convince you. I didn't get convinced a lot, which may have led to my current condition of 0-10's. They asked and I was honest.
ewh (Aerospace) 1 Apr 10 15:20
I was told thet 4X 10 was fine, as long as I put in another 8 on Friday. "Good to know you got shoes to wear when you find the floor." - Robert Hunter
KENAT (Mechanical) 1 Apr 10 15:37
Only another 8, you lucky @#$%$%234. Posting guidelines FAQ731-376: Eng-Tips.com Forum Policies http://eng-tips.com/market.cfm? (probably not aimed specifically at you)What is Engineering anyway: FAQ1088-1484: In layman terms, what is "engineering"?
berkshire (Aeronautics) 1 Apr 10 18:00
That's it you guys need to get paid hourly!B.E.
brandoncdg (Civil/Environmental) 2 Apr 10 5:09
I worked at a 4.5 day work week job, that was really nice.For Civils it's not that common to get the full Friday off, because most cities/counties work either the 4 days or get every other Friday off. Civil Development Group, LLCLos Angeles Civil Engineering specializing in Hillside Gradinghttp://www.civildevelopmentgroup.comhttp://www.civildevelopmentgroup.com/blog
cvg (Civil/Environmental) 2 Apr 10 12:59
most civils work for both private and public clients. The clients call your cell phone on Saturdays and Sundays, so it is likely you will need to work at least 5 days per week plus OT. Laptops, Blackberries and VPN were made for this reason. Doors must remain unlocked on Fridays in case your client decides to pay you a visit. Perhaps some production staff such as drafters could work odd schedules as long as all the work gets done and somebody shows up on Friday to get the submittals out the door.
PeterStock (Mechanical) 5 Apr 10 9:06
You could set it up so some of the staff have Fridays off and some have Mondays off. Peter StockhausenSenior Design Analyst (Checker)Infotech Aerospace Serviceswww.infotechpr.net
HgTX (Civil/Environmental) 5 Apr 10 15:18
Technically allowed by my employer, but not by my particular office.Hg Eng-Tips policies: FAQ731-376: Eng-Tips.com Forum Policies
knight185 (Mechanical) 5 Apr 10 20:19
4-10's would be a dream for me. My normal schedule is 40 to 50 hours, Monday through Friday and on-call on weekends and holidays. Usually end up working a lot of weekends throughout the year.
PJones (Mechanical) 7 Apr 10 15:43
At a previous job, we worked 4-10s. I took Wednesday off. That solved the Friday coverage problem.Then we got busy and went to 6-10s, but that is a completely different problem.
plasgears (Mechanical) 7 Apr 10 16:09
During the VN war, I worked overtime in an aero plant. We did regular 10-12 hrs five days and half day on Sat. In that kind of schedule you will find yourself pacing yourself so that you have energy left at the end of the day. Saturday was all coffee and donuts and BS sessions.I have been able to work smarter and more efficient in an 8 hr day, five days. Proponents of the four day week find opposition from those who want to carry out the usual business and contacts on Fri.
Thedroid (Electrical) 10 Apr 10 12:26
I don't like 4 10's at all. I work 7-3:30 M-F, and it's great. I have plenty of time with the family everyday after work, and also have my weekends. Leaving at 5:30 everyday seems to cut short 4 days in exchange for 1 day off. I'm hourly and don't mind overtime, but I want to be making that premium after 8 hours not 10.
knight185 (Mechanical) 11 Apr 10 9:26
When I was an engineering intern one of my jobs was 7am to 3pm and that was the best. I lived only a few miles from the plant and was home everyday by 330pm. Now I am lucky to get home and be settled by 6pm.
NomLaser (Mechanical) 13 Apr 10 15:16
Starting to wish that we had a 4-10 week seeing as by the time I hit the bed Monday night that I already had in over 15hrs in for the week (counting time that I put in on Sunday).
npcannon (Mechanical) 13 Apr 10 15:21
I used to work 4-10's 4 miles from my house. I was in heaven, rode my bike into work every day, felt like I could work there forever... unfortunately the employer didn't have those same feelings. My days were shorter than other companies where I'd worked 8's or 9's with a long commute and a required hour lunch. I'm back on 5-8's. It's been almost a year and I find myself taking a friday off somewhat randomly once a month. It's amazing what a 3 day weekend can do for burnout relief. 9/80's is probably my favorite schedule. 10's are long days and with a commute could really wear you down. For customer issues a mon-thu and tue-fri 4/10 break down worked really well. Also staying in contact was required, but rarely needed. -Nate
spongebob007 (Military) 14 Apr 10 16:03
We have the 4-10 work schedule, but this so-called "benefit" is really a management scam to get uncompensated overtime. It is an unwritten rule around here that salaried employees are supposed to work at least a half day on Fridays. Some managers walk around their departments every Friday and keep a tally of who is in the office and who is not. I try to take at least every other Friday off. I don't play the overtime for the sake of overtime game. While it is nice to have a three day weekend, ten hours can be an awful long time, especially when things are kind of slow. Nothing worse than having been in the office for six hours and looking at the clock and realizing you still have four hours to go!
spongebob007 (Military) 14 Apr 10 16:06
The other way we get a little screwed with the 4-10 is that new employees only get 8 vacation days, instead of the two weeks most get in a 5-8 job. When the company went from 5-8 to 4-10 the vacation policy was changed from "two weeks" to "80 hours", hence the 8 vacation days. After five years, employees get 120 hours, or 12 days.
cvg (Civil/Environmental) 14 Apr 10 16:28
since you already get fridays off, you can still take a two week vacation - whats the problem?
KENAT (Mechanical) 15 Apr 10 10:06
Yeah, spongebob, while the '2 weeks' that most folks in the US get (at least initially) is a be meager however you look at it, I don't see that rating it in hours, as my place does too, makes it any worse. Posting guidelines FAQ731-376: Eng-Tips.com Forum Policies http://eng-tips.com/market.cfm? (probably not aimed specifically at you)What is Engineering anyway: FAQ1088-1484: In layman terms, what is "engineering"?
Gymmeh (Mechanical) 19 Apr 10 13:02
you mean 5-10 + 5hrs Sat. is not normal? I plan on working of first 40hr week and I am taking a full hour for lunch. I even took time to brows eng-tips!!!spongebob. Where are you that you get 8 days of vacation? I would love 8 days of vacation.
GregLocock (Automotive) 19 Apr 10 19:14
Oh. What would you do with 25 days +12 flex days? CheersGreg LocockNew here? Try reading these, they might help FAQ731-376: Eng-Tips.com Forum Policies http://eng-tips.com/market.cfm?
KENAT (Mechanical) 19 Apr 10 22:12
thread731-220498: Four tens? Posting guidelines FAQ731-376: Eng-Tips.com Forum Policies http://eng-tips.com/market.cfm? (probably not aimed specifically at you)What is Engineering anyway: FAQ1088-1484: In layman terms, what is "engineering"?
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Register now while it's still free! | {"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": 0.16350935399532318, "perplexity": 3695.759846507716}, "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-2014-42/segments/1414637900019.55/warc/CC-MAIN-20141030025820-00243-ip-10-16-133-185.ec2.internal.warc.gz"} |
https://scoop.eduncle.com/which-of-the-following-forms-of-dv-where-e-x-y-z-0szsx-y-x-sys-wx-0-sxs-1-are-possible-a-dz-dy-dx-dz | IIT JAM Follow
Rajat jain Asked a Question
June 25, 2020 4:03 pm 50 pts
Which of the following forms of dV Where E= {x. y. z) | 0szsx+y, x sys wx, 0 sxs 1) are possible? (A) dz dy dx dz "dz dx o dy (B) cX+x (C) dz dx dy (D) dy dz dx Jmax(z-x,x)
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• Deepak singh 1
option d is correct, see attached
• Deepak singh 1
i have attached solution, but its not showing in my side.. i think there is technical problem. .. Just equate first two equation simultaneously, u will get option d correct.
• Deepak singh 1
are u able to see attached solution..?
Rajat jain
no
• Deepak singh 1
yes option d is correct.. see attached solution .
• Deepak singh 1 Best Answer
option a is correct. see attached solution for detail | {"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": 0.9733443260192871, "perplexity": 20736.59841218551}, "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-2022-05/segments/1642320302706.62/warc/CC-MAIN-20220120220649-20220121010649-00532.warc.gz"} |
http://math.stackexchange.com/questions/777183/maximum-eigenvalue-of-a-special-m-matrix | Maximum eigenvalue of a special m-matrix
I have a set of matrix, which is:
1. Real symmetric positive definite. Very sparse.
2. Diagonal elements are positive while off-diagonal elements are negative.
3. $a_{ii}=-\sum^{n}_{j=1}a_{ij}$ when $i\neq j$
4. $a_{ii} \in (0,1]$
5. $a_{ij} \in (-1,0]$ when $i \neq j$
My experiments show that the largest eigenvalue of all the matrices I have are larger than 1. Can some one help me on proving that $\lambda_{max} >1$ for this matrix?
My first though is to prove that $Ax=\lambda x < x$ does not hold. But I couldn't get any break through. Thanks!
-
Your conjecture can't be true unless you put some constraints on the diagonal entries or something. If you have a matrix $A$ that has eigenvalue $\lambda$, then the matrix $kA$ has eigenvalue $k\lambda$ with the same eigenvector space. And your matrix conditions are invariant under multiplying the matrix by a positive constant. So given a matrix that satisfies your constraints, you can find an arbitrarily small matrix with arbitrarily small eigenvalues that satisfies the same constraints.
If there is always a '1' element in the diagonal element, can it be counted as the constraints you mentioned? Therefore the row the '1' appeared will be like: $x_{i} + \sum^{n}_{j=1} a_{ij}x_{j} < x_{i}$ for $Ax=\lambda_{max}x<x$. Thanks! – Jane Li May 1 at 17:01 | {"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": 0.9636304378509521, "perplexity": 263.9259099054136}, "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-2014-41/segments/1410657138980.37/warc/CC-MAIN-20140914011218-00166-ip-10-234-18-248.ec2.internal.warc.gz"} |
https://aperiodical.com/category/main/features/page/2/ | ### Everyone’s A Mathematician – Astronauts
We all know mathematicians are the coolest people on the planet. But it turns out that of all the people not on the planet, all of them are in fact either mathematicians, or have mathematical backgrounds or training. Astronauts – and Russian cosmonauts – are all super mathsy people, and if they weren’t already awesome enough, this really seals the deal for me.
### Carnival of Mathematics 145
Welcome to the 145th Carnival of Mathematics, hosted here at The Aperiodical.
If you’re not familiar with the Carnival of Mathematics, it’s a monthly blog post, hosted on some kind volunteer’s maths blog, rounding up their favourite mathematical blog posts (and submissions they’ve received through our form) from the past month, ish. If you think you’d like to host one on your blog, simply drop an email to katie@aperiodical.com and we can find an upcoming month you can do. On to the Carnival!
### “I own more maths books by Martin Gardner than by women, is that bad?”
Today is International Women’s Day, so we’ve taken a moment to think about the woman mathematicians in our lives.
We each have fairly sizeable collections of maths books, which prompted CLP to wonder how many of them are by female authors. A quick scan of our respective bookshelves later, here’s what we found.
### The maths of the Grime Cube
Not content with already having five cubes named after him, internet maths phenomenon James Grime has now developed a new Rubik’s cube-style puzzle for internet maths joy merchants Maths Gear. I’ve been slightly involved in the development process, so I thought I’d share some of the interesting maths behind it.
Another name for a Rubik’s cube is ‘the Magic Cube’ – and Dr James Grime wondered if you could make a Magic Cube which incorporates its 2D friend, the Magic Square.
### A more equitable statement of the jealous husbands puzzle
Every time I use the jealous husbands river crossing problem, I prefix it with a waffly apology about its formulation. You’ll see what I mean; here’s a standard statement of the puzzle:
Three married couples want to cross a river in a boat that is capable of holding only two people at a time, with the constraint that no woman can be in the presence of another man unless her (jealous) husband is also present. How should they cross the river with the least amount of rowing?
I’m planning to use this again next week. It’s a nice puzzle, good for exercises in problem-solving, particularly for Pólya’s “introduce suitable notation”. I wondered if there could be a better way to formulate the puzzle – one that isn’t so poorly stated in terms of gender equality and sexuality.
### Apéryodical: Roger Apéry’s Mathematical Story
This is a guest post by mathematician and maths communicator Ben Sparks.
## Roger Apéry: 14th November 1916 – 18th December 1994
100 years ago (on 14th November) was born a Frenchman called Roger Apéry. He died in 1994, is buried in Paris, and upon his tombstone is the cryptic inscription:
$1 + \frac{1}{8} + \frac{1}{27} +\frac{1}{64} + \cdots \neq \frac{p}{q}$
Apéry’s gravestone – Image from St. Andrews MacTutor Archive
Roger Apéry – Image from St. Andrews MacTutor Archive
The centenary of Roger Apéry’s birth is an appropriate time to unpack something of this mathematical story.
### Integer Sequence Reviews: A075771, A032799, A002717
It’s been almost two years since I last sat down with my friend David Cushing and did what God put us on this Earth to do: review integer sequences.
This week I lured David into my office with promises of tasty food and showed him some sequences I’d found. Thanks to (and also in spite of) my Windows 10 laptop, the whole thing was recorded for your enjoyment. Here it is:
I can only apologise for the terrible quality of the video – I was only planning on using it as a reminder when I did a write-up, but once we’d finished I decided to just upload it to YouTube and be done with it. | {"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": 0.42704370617866516, "perplexity": 2713.6831716471806}, "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-2020-40/segments/1600400187354.1/warc/CC-MAIN-20200918061627-20200918091627-00413.warc.gz"} |
https://chemistry.stackexchange.com/questions/114769/why-do-hydrogen-halideswith-the-exception-of-hf-form-mostly-strong-acids | # Why do Hydrogen Halides(with the exception of HF) form mostly strong acids? [duplicate]
Why do Hydrogen Halides(with the exception of HF) form mostly strong acids? My guess is that the negatively charged Halide part of the molecule is attracted by the partially positive part of the water molecule. Thus it is separated more easily. Although because it has one more electron it is more stable once it has dissociated
• Agree mostly but why "the halide part is not negatively charged"? What about $F^-$, $Cl^-$, $Br^-$ ,$I^-$ ...? – Buck Thorn May 3 '19 at 14:59 | {"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": 0.6449388861656189, "perplexity": 2210.1187267100513}, "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/1590347407001.36/warc/CC-MAIN-20200530005804-20200530035804-00006.warc.gz"} |
https://gasstationwithoutpumps.wordpress.com/2012/06/ | # Gas station without pumps
## 2012 June 30
I did some playing around with a simple op-amp amplifier to try to get an EKG signal, based on ideas like those in DIY ECG Machine On The Cheap, but I was unsuccessful in seeing anything other than 60Hz noise. I decided that it would be worthwhile to try building an instrumentation amplifier. Now, I can’t do as good a job at matching components as a laser-trimmed off-the-shelf instrumentation amp (like the TI INA126PA-ND, which costs $2.50 each in quantities of 10), but I’m more interested in concepts than high quality at the moment, and I have a bunch of MCP6002 op amp chips already. I decided to use the microphone input scaled down as my input source, as I can get a reliable signal from that. (The µV EKG signals are still eluding me.) I first tried thinking about instrumentation amplifiers from first principles: I knew that the input stages had to have no feedback to the input wires, and that the second stage had to do the differencing of the two inputs. I was having a hard time figuring out a reliable way to reject the common-mode noise and get just the differential signal, particularly at high gain. I finally broke down and read the Wikipedia article on instrumentation amplifiers. In that article, they give a classic design for a 3-op-amp instrumentation amplifier: I don’t have a particularly good assortment of resistors for my breadboard, but I managed to find enough pairs of resistors with nominally the same value to make a version of the circuit. I used a 10kΩ trimpot for the gain resistor, so I could adjust the gain. I initially set the trimpot to 2kΩ. Wikipedia reports the gain for this circuit as $\left(1+ \frac{2R_1}{R_{gain}}\right)\frac{R_3}{R_2}$, which matches my analysis of the circuit. Since I’m using single-power supply op amps, I also needed to make a bias voltage supply to act as “ground” for the feedback loop on the positive side of the differential amplifier. I’m wondering if we should have the students use a proper voltage reference (like the TI TL431ILP) instead of a voltage divider to get the bias voltage. The adjustable voltage references aren’t any more expensive (12.4¢ each in quantities of 10) than Zener diodes (12.6¢ each in quantities of 10). For an EKG circuit, the bias voltage would have to be connected to the body. Here is the final circuit as simulated and implemented: Microphone signal source and instrumentation amplifier. The signal source produces about a 140µV difference between Vin_plus and Vin_minus, which is nicely amplified. The amplifier appears to be working, amplifying the 140µV input to a 200mV signal (with a fair amount of noise added). Of course, with this signal source, I can’t really see whether the output is really a result of amplifying the differential signal, or a lesser gain amplification of the common-mode signal (since the differential signal is just 1/700th of the common-mode signal). The amplifier stops working if I set R_gain below about 1.8kΩ in this circuit. (I determined that by adjusting the potentiometer down to about 500Ω, seeing that the circuit produced no output, then gradually increasing the potentiometer until I got a signal again (albeit one that obviously had some clipping). If I want higher gain (which I probably do for an EKG), I’ll need to adjust the gain of the second stage, or add another stage. Hmm, if I swap the 24kΩ and 6.8kΩ resistors, I should be able to still set the trimpot to get about the same gain in the first stage and increase the gain in the second stage by a factor of 4. I might try that. Update: 2012 June 30 16:19, I tried that swap and couldn’t get the amplifier to work—the 10kΩ pot is probably not big enough. From a teaching standpoint, this instrumentation amplifier is relatively easy to construct and to understand, but for the students to test it reasonably we would need to use a signal source that has a low differential voltage and large common-mode signal. I think that the students would need a reliable source (not the rather iffy signal one gets from EKG, and not one cobbled together from a couple of benchtop signal generators). I might also want to try a 2-op-amp design, like the one used in the the TI INA126 instrumentation amp: Design for instrumentation amplifier used in the TI INA126 chip. Picture copied from data sheet MicroPOWER INSTRUMENTATION AMPLIFIER Single and Dual Versions SBOS062A – JANUARY 1996 – REVISED AUGUST 2005 I checked the gain for the 2 op-amp design using current flow equations for the two feedback inputs to the op amps, with R1 instead of 10kΩ and R2 instead of 40kΩ. It took me a while to fix all my typos, but I eventually got an old version (9.5) of Maple to agree with TI that the gain is $(R_1+R_2)/R_1 + 2 R_2/ R_G$. I’ll probably buy a couple of the INA126PA amplifiers to experiment with—using one with a gain of 1000 followed by an op amp to increase the gain more may be the only way I’ll get an EKG working. Update: 2012 June 30 16:20 I tried the 2-op amp instrumentation amp with feedback resistors of 24kΩ, 6.8kΩ, and R_G=330Ω, which should give a gain of about 150, but doesn’t seem to be. Hmm—removing the entire $V_{in-}$ part of the circuit, so that I just have an op amp with a 24kΩ feedback resistor, has essentially the same result. That is, I seem to be just doing a unity gain buffer of the $V_{in+}$ signal. That may have been all that was happening with the 3-op-amp instrumentation amplifier also. Time for some debugging! ## 2012 June 28 ### What sensors for circuits class? Filed under: Circuits course — gasstationwithoutpumps @ 22:33 Tags: , , , , What sensors are appropriate to use in a sensor-focused circuits class? I listed a bunch that I’ve been thinking about in Why teach circuits to bioengineers?, but in this post I want to focus a bit more on what criteria we should use for deciding which sensors to include or exclude. Some criteria: • Price. We want students to be able to buy a kit of parts for the course and take everything home with them when they are done. All sensors should be under$5 (ideally under $1) each in quantities of 10. • Variety of things sensed. I’d like for there to be at least 5 and preferably 8 or 9 different properties detected. • Variety of different electrical properties as sensor outputs (at least current, resistance, voltage, and capacitance, maybe also inductance or mutual inductance). • Some sensors should be rapidly varying (for oscilloscope output). • Some sensors should be slowly varying (for recording time course with Arduino). • Some sensors should require amplification. • Easy breadboarding. Students won’t have time to do a lot of soldering, particularly of SMD parts. We should do one or two labs where they do some soldering, but if we use SMD parts for other labs, we’ll need to design and assemble breakout boards for them. Device Senses Output Catalog Price Notes thermistor temperature resistance NTCLE413E2103F520L 35¢ non-linear, very sensitive, slowly time varying, no amplification needed RTD temperature resistance 480-2017-ND$1.94 slowly time varying, only 0.4% change/degree, similar to high-precision (which cost over $10 each) temp sensor temperature voltage MCP9700-E/TO-ND 25¢ slowly time varying, not very accurate, linear, not much challenge for circuitry electret mic sound current 102-1721-ND 75¢ rapidly time varying, can be amplified or not potentiometer angle resistance 987-1277-ND 66¢ slowly time varying, hard to connect to mechanically? potentiometer angle resistance 3382H-1-252$2.23 slowly time varying, easier to incorporate into a goniometer?, lead in for servos
breathalyzer alcohol resistance 605-00011-ND $4.50 fun for students? needs humidity and temperature correction. pH probe pH voltage SeroSystems pH probe$21 Too expensive and needs temperature correction.
humidity sensor humidity capacitance 480-2903-ND $3.61 pressure air pressure voltage MPXM2053GS-ND$6.51
gel electrodes EKG voltage SilveRest 22¢ (cheaper without snap), very low voltages and 60Hz noise requires good amplifier, time varying
gel electrodes GSR resistance SilveRest 22¢ (cheaper without snap), slowly time varying
CdS photoresistor visible light resistance PDV-P8104-ND 80¢
ambient light sensor visible light current 1080-1019-ND 46¢
phototransistor IR light current 754-1468-ND 19¢
reflectance sensor reflectance current QRE1113-ND 83¢ LED + phototransistor in same package, 5mm sensing distance
IR emitter 754-1600-ND 19¢ IR emitter and red LED needed for pulse oximeter
red LED 660nm 754-1218-ND ? IR emitter and red LED needed for pulse oximeter
green LED 754-1591-ND green LED needed for simple pulse sensor
conductance cell salinity bulk conductance ? ? May require student design and construction. Cheap with Al foil, expensive with Ag/AgCl electrodes.
touch sensor touch capacitance ? ? May require student design and construction. Al foil and plastic wrap?
Richard Hughey had an interesting idea for an air-flow sensor. Use one of the siren whistles for kids that cost about 50¢ each in quantity. They have a plastic turbine in them, and we could use an LED and light sensor (perhaps one of the reflectance sensors) to get a pulse stream from the turning of the turbine, timing the pulses with an Arduino.
I just noticed that I don’t have any switches, accelerometers, magnetic sensors, … on that list. A breath switch might be a useful sensor for those thinking of the rehabilitation concentration. A tilt switch is also a reasonable option. A lot of the sensors I have looked at are too expensive for their value in the course, though it might be worth spending a little lecture time going over how they work.
## 2012 June 27
### Bioinformatics in AP Bio, lessons released
Filed under: Uncategorized — gasstationwithoutpumps @ 11:03
Tags: , , , ,
As those who have been reading my blog for a while know, I’ve been working with UCSC grad students to develop materials for bioinformatics lessons for high school biology classes. I have a series of posts about Advanced Placement Biology courses and the AP Bio exam.
In a previous post about the project, I described our goals:
• The primary goal is to teach students biology, not computer science or bioinformatics. The bioinformatics should be good support for the underlying biology lesson.
• Whatever we produce should be made available on the web (but putting any answer keys behind password protection, should we end up producing anything that needs a key).
• The students will present the lessons to the class (both to expose the high school students to college student role models and to give the grad students practice teaching), but the lessons should be teachable by non-bioinformaticians. In particular, the high school teacher should be able to teach it himself next year.
• If things work out well, it might be worth presenting a paper explaining the project (and advertising the materials) at a high school biology teachers conference (perhaps an NABT conference?).
We have just released the two lessons we’ve developed so far: one on genetic diseases, the other on phyogenetic trees.
Each was tried at one school, in 3 sections of AP Bio (where AP bio is a required course for all students). The lessons took one block each (just under 2 hours for a block), with some sections finishing everything with time to spare and others not quite finishing. (Consistently the first section getting the lesson having trouble finishing and the third one having time to spare—I don’t know if the difference was in the speed of the initial presentation and our quickness in responding to problems or in the competence of the students. There was more assistance available to the students for the first two sections, which were also the slower two.
The resources can be accessed directly from http://compbio.soe.ucsc.edu/binf-in-AP/ They are released under a Creative Commons attribution/share-alike license.
Other resources people should know about include
## 2012 June 26
### Why teach circuits to bioengineers?
Filed under: Circuits course — gasstationwithoutpumps @ 17:48
Tags: , , , ,
I’ve been posting quite a bit on the design of the labs for the new applied circuits course we are designing for bioengineering (and other) students, but I’ve not yet clearly articulated why we require bioengineering students to take a circuits course. Without a clear justification, it could be just another arbitrary hoop for students to jump through—I’m sure many of the bioengineering majors see the current circuit theory class that way.
The justification for an electronics course for bioengineers can be summed up in one word: Sensors.
A sensor (in this context, anyway) is a device that converts some physical or chemical property of interest into an electrical parameter: a voltage, a current, a resistance, a capacitance, an inductance, … . The purpose of an electronic circuit is to convert this electrical parameter into a numeric value that we can record on a computer or in a lab notebook (which often means going through a voltage or time representation). There are, of course, other applications of electronics, but connecting to sensors is the one that matters for bioengineers.
It is very common in biological equipment these days to use a digital camera as a sensor, but the design of cameras and image processing software is outside the scope of this class. I think we want to concentrate on one-dimensional sensors that produce just a scalar value (or, more commonly, a value that varies as a function of time).
So in choosing labs, I want to focus on what sensors we are using and what processing we are doing in the electronics to get a numerical result at the end. Perhaps the course should be titled something like “Introductory circuits with applications to sensors” rather than what we were considering earlier, “Circuits with applications to bioengineering”.
Let’s go through the labs I’ve been thinking about so far and see how they fit with this theme:
• Potentiometer-based goniometer for joint angle measurement.
• Linear resistance-based measurement.
• Useful for lead in to servo motors?
• Useful for control and feedback in robotics.
• Thermistor-based temperature measurement.
• Resistance-based sensor.
• Non-linear response curve.
• Use of voltage divider to linearize curve and convert to voltage output.
• Electret microphone.
• Measuring current and voltage while varying series resistor to determine whether current source or resistance model is better.
• Using series resistance (voltage divider) to convert current or resistance value to a voltage value, which can be viewed on scope.
• Amplifying signal to make large enough to record with analog-to-digital converter.
• Electrical field measurements in an electrophoresis gel. This one doesn’t fit the new theme—I think that there may be several reasons for discarding this lab.
• Conductivity of saline solutions. Used for measuring ecosystems (like rivers).
• Useful for talking about conductivity of bulk materials.
• Requires thought about materials for electrodes.
• Skin conductance meter.
• Similar problems to conductivity of saline solution for measurement.
• Need recording of slowly time-varying signal.
• Do-it-yourself EKG
• Amplification of very weak signals (though not as weak as nanopipettes and nanopores)
• Can also be applied to other muscles (EMG) for control of robotics.
• Electrical noise
• May be too difficult to get good signals.
• Optical blood pulse detector
• Optical sensing very common in biosensors.
• About the simplest application of light sensing.
• Several different light sensors possible, with different circuits needed to convert to voltage.
• Pulse oximeter
• Expansion of optical pulse detector
• Uses two different light sources alternately.
• Gets into calibration questions.
• Breathalyzer
• Appears to be a resistance measurement.
• Relies on self heating.
• Should appeal to college students.
• Capacitance touch sensor.
• A different modality (not resistance, current, or voltage).
• Conversion to frequency instead of voltage.
It looks like I have enough labs here, but I don’t have any direct chemical detection (other than salinity by conductance). Also, I suspect that the EKG may be too difficult to get working, and skin conductance may vary too slowly, so we may need some other time-varying signals.
## 2012 June 25
### Op-amp lab
Since the thermistor lab seems to have worked fairly well (see More musings on circuits course: temperature lab, Buying parts for circuits course, Temperature lab, part2, and Temperature lab, part 3: voltage divider), I decided to try doing some op amp circuits today, to see how things worked. I want to get to the point where I can build a simple EKG, to see if that is feasible for a first circuits course.
My playing with the op amps today reminded me why I always hated breadboards: the components are always coming loose, and I spent a lot of the time trying to figure out why things weren’t working as I expected—most of the time it was a resistor or wire not making good contact, though occasionally I had an off-by-one error in inserting a wire.
Building a op amp circuit with MCP6002 chips was a little harder than I expected—the single power supply means that you need to bias the inputs to be in the middle of the range, to avoid clipping. My attempts to use the op amp to read EKG signals were a complete bust, so I went back to a simpler, stronger signal source: the electret microphone from the Oscilloscope practice lab.
I got amplification easily enough, but I had trouble with clipping. After a while, I realized that the electret mic was not acting like it was a 2.2kΩ resistor, like I thought it ought to from the 2.2kΩ output impedance spec. I did a series of measurements putting a potentiometer in series with the electret mic and measuring the resistance of the potentiometer and the voltage across it (being careful to remove power before switching to resistance measurement). I then fit both a constant-resistance model and a constant current model to the data. I think that modeling the electret mic as a constant current source is a much better model than treating it as a resistor, for DC analysis. This might be a useful exercise to have students do along with the oscilloscope practice lab, as multimeter practice.
The voltage across a resistor in series with the electret mic is much better modeled by treating the mic as a constant current source, rather than as a constant resistance.
Since the electret microphone behaves mostly like a current source, I wonder what the 2.2kΩ output impedance on the spec means. Are there any real electrical engineers reading this blog who can explain the output impedance of an electret microphone with an FET output stage?
If I want to have the output of the electret mic be in the middle of a 5.121v range (that is with a DC bias of 2.56v), I’d want a 13.8kΩ series resistor. I tried using a 12kΩ pullup resistor, and it put the voltage a little above the mid-point, as expected.
My initial efforts to use this signal as the input to an op-amp amplifier worked fine with a unity-gain amplifier (output directly fed back to the negative input), but whenever I tried to set a reasonable gain with a voltage divider, I got serious clipping. I finally realized that the voltage divider used for clipping had to have its bottom end tied to the center voltage, not ground (all the book examples use symmetric power supplies, so that ground is the center voltage). I made a bias voltage supply by using a voltage divider and a unity-gain amplifier, and hooked up the feedback voltage divider to the bias supply, rather than to ground. That worked fine, and I could even use AC coupling on the amplifier input with a blocking capacitor, if I added a large resistor to the bias supply for the positive input pin.
Working amplifier circuit with bias supply and AC coupling for the input.
The circuit also works with DC coupling (removing R5 and replacing C1 with a wire).
Circuit drawn and simulated with Circuit Lab.
Once I got all the biasing issues straightened out, the op amp worked as expected (except when I jostled a wire or component loose). I did not measure the gain carefully, but it does appear to be about 6.7, as expected from the design.
Next 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": 4, "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": 0.46444183588027954, "perplexity": 2391.073713692515}, "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-2015-22/segments/1432207927458.37/warc/CC-MAIN-20150521113207-00179-ip-10-180-206-219.ec2.internal.warc.gz"} |
https://cs.stackexchange.com/questions/45724/how-to-construct-a-grammar-that-generates-language-l/45725 | # How to construct a grammar that generates language L?
I'm in a Formal languages class and have a grammar quiz coming up. I'm assuming something like this will appear.
Consider the alphabet $\Sigma$ = {a, b, c}. Construct a grammar that generates the language $L = \{bab^nabc^na^p \mid n ≥ 0, p ≥ 1\}$. Assume that the start variable is $S$.
• and the problem is...? if there is no restriction on the grammar, there are many possible solution; I assume you meant a context-free grammar. – Ran G. Aug 31 '15 at 4:50
• What research have you done? What have you tried? Have you tried using the techniques in cs.stackexchange.com/q/18524/755? This question looks like it is answered by the answers there. – D.W. Aug 31 '15 at 6:21
One possible grammar is: $G = (N, \Sigma, P, S)$, where
$N = \{S,U,V\}$
$\Sigma = \{a,b,c\}$
$P = \{ S \to baUV, U \to ab|bUc, V \to a|aV \}$
The key observation here is breaking $bab^nabc^na^p$ into 3 parts, $ba$, $b^nabc^n$, and $a^p$, one fixed, one growing bidirectionally, and one simple repeatition. Express the growing patterns first, then merge them along with the fixed parts. | {"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": 0.6212227940559387, "perplexity": 700.8225953913263}, "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/1618039626288.96/warc/CC-MAIN-20210423011010-20210423041010-00113.warc.gz"} |
https://test-home.web.cern.ch/tags/telescope | # telescope
4 results
### A “muoscope” with CMS technology
Researchers from the CMS experiment at the Large Hadron Collider are developing a new application based on one of the experiment’s particle detectors
News
Knowledge sharing
22 March, 2019
### A “muoscope” with CMS technology
Knowledge sharing
News
22 March, 2019
### CALET docks on the International Space Station
The CALorimetric Electron Telescope reached the ISS on 24 August. It will perform long-exposure observations of high-energy cosmic radiation
News
Experiments
27 August, 2015
Experiments
News
27 August, 2015
### Neutrino telescopes point towards exotic physics
With the IceCube and ANTARES telescopes completed, there was plenty to discuss at the second Workshop on Exotic Physics with Neutrino Telescopes
News
Experiments
13 August, 2013
Experiments
News
13 August, 2013
Experiments
Experiments | {"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": 0.8098493814468384, "perplexity": 25924.578194060166}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-25/segments/1623488262046.80/warc/CC-MAIN-20210621025359-20210621055359-00364.warc.gz"} |
http://jrpr.org/journal/view.php?number=300 | J Radiat Prot > Volume 21(4);1996 > Article
NaI(T1) 섬광검출기를 이용한 공기 및 수중에서의 감마선 에너지스펙트럼 분석 김은숙;박재우; An Analysis of ${gamma}-ray$ Energy Spectra Using the NaI(T1) Scintillation Detector in the Air and Water Kim, Eun-Sug;Park, Jae-Woo; ABSTRACT The energy spectra in the air and water of several ${gamma}-ray$ sources such as Cr-51, Cs-137, Mn-54, Zn-65 have been investigated using the NaI(T1) scintillation detector. General response functions, which can curve fit the measured spectra, have been constructed. We have found that the constructed response functions can successfully represent the measured spectra in the water as well as in the air, It is possible, by comparing the relevant parameters of the response functions, to quantitatively characterize the changing features of the measured spectra as obtained with varying the water depth. Of the response function parameters, those which affect the shape of the full-energy Peak have most notably changed. Besides, those parameters which affect the shapes of the flat continuum, the Compton continuum and edge have also shown slight changes with varying the water depth.
TOOLS | {"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": 0.9757040143013, "perplexity": 2274.980582992935}, "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-2018-47/segments/1542039747369.90/warc/CC-MAIN-20181121072501-20181121094501-00457.warc.gz"} |
http://devmaster.net/posts/12741/glfrustum | 0
101 Jun 14, 2007 at 12:13
Hi,
When i use the glFrustum funtion to set up my projection matrix, it works fine. But as soon as I want to calculate the matrix myself, it does not work.
Following code works:
glViewport( 0, 0, (GLsizei)w, (GLsizei)h );
glMatrixMode( GL_PROJECTION );
glFrustum( -.4, .4, -.3, .3, 1., 1300. );
glMatrixMode( GL_MODELVIEW );
// continues
the following does not :(
glViewport( 0, 0, (GLsizei)w, (GLsizei)h );
glMatrixMode( GL_PROJECTION );
matrix4x4 projection;
projection = calculateFrustum(-.4, .4, -.3, .3, 1., 1300.);
glMatrixMode( GL_MODELVIEW );
// code continues
Some how my calculation of the Frustum matrix does not match that of the one calculated by the openGl. Can you please point out whats wrong in here.
I am using the defination given on the following page for “calculateFrsutum” funtions call:
http://msdn2.microsoft.com/en-us/library/ms537094.aspx | {"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": 0.400399386882782, "perplexity": 7102.119935050386}, "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/1394010832640/warc/CC-MAIN-20140305091352-00015-ip-10-183-142-35.ec2.internal.warc.gz"} |
http://tar.weatherson.org/2010/02/04/mixtures-of-conditional-probability-functions/ | # Mixtures of Conditional Probability Functions
It’s well known that it’s easy to ‘mix’ two unconditional probability functions and produce a third unconditional probability function. So if x ∈ [0, 1], and f1 and f2 are both unconditional probability functions, and for any proposition p in the domain of both f1 and f2, f3(p) = xf1(p) + (1-x)f2(p), then f3 will also be an unconditional probability function. (This is really immediate from the axioms for unconditional probability.) I thought the same kind of thing would work for conditional probability, but I can’t figure out how to do it.
It’s certainly not true that if f1 and f2 are both conditional probability functions, then the function f3 defined by f3(p|q) = xf1(p|q) + (1-x)f2(p|q) will be a conditional probability function. Here’s a counterexample.
• f1(A | BC) = 0.3
• f1(B | C) = 0.4
• f1(AB | C) = 0.12 (a consequence of previous two posits)
• f2(A | BC) = 0.5
• f2(B | C) = 0.6
• f2(AB | C) = 0.3 (again a consequence)
• x = 0.5
If we just apply the above formula, we get this
• f3(A | BC) = 0.4
• f3(B | C) = 0.5
• f3(AB | C) = 0.21 (inconsistent with previous two lines, if f3 is a probability function)
One natural move is to say that when f1(q) = f2(q) = 1, then f3(p|q) = xf1(p|q) + (1-x)f2(p|q). That will deliver something that is a conditional probability function as far as it goes, but it won’t tell us what f3(p|q) is when f1(q) = f2(q) = 0. And I can’t figure out a sensible way to handle that case that doesn’t run into a version of the inconsistency I just mentioned.
It feels like this is a simple problem that should have a simple solution, but I’m not sure just what it is. There’s a lot of information about mixing probability functions in this paper by David Jehle and Branden Fitelson, but it doesn’t, as far as I can see, touch on just this issue. Any suggestions would be appreciated!
## 2 Replies to “Mixtures of Conditional Probability Functions”
1. Gregory Wheeler says:
A quick thought: the def. of f3 defines a convex mixture of f1 and f2 but, owing (perhaps) to the nonmonotone character of the second coordinate of the conditional probability function, nothing constrains f1 or f2 simpliciter to yield values via the chain rule that must be in this convex hull defined by f3.
Notice that f3 will work just like the marginal case when the conditioning event, q, is fixed; the problem is that in one pair of cases we are conditioning on C, another pair the joint BC.
Not sure of what you want to do with the construction, but making sure convexity is satisfied might do the trick. This may mean that admissible values will be intervals, however. Another idea, again depending on what you’re after, is to restrict the conditional probability functions to the class of monotone functions (positive or negative), so that you can get a handle at least on which direction you’ll always go in when going from C to the joint BC.
2. It depends on what conditions you impose on conditional probability functions, and how you expect the mixture to behave. If you are talking about lexicographic functions (so that each one is given by a sequence of unconditional probability functions, and F(p|q) is defined as f(p and q)/f(q) for the first f in the sequence where f(q) is non-zero) then one natural way to do it would be to just mix the corresponding functions in the sequence. But this will have some strange effects on probabilities conditional on q, if q has a non-zero value somewhere earlier in one sequence than in the other. (I think the conditional probability in the mixture will just be equal to the conditional probability in the one that gives q its first non-zero value, and it will be a mixture of the conditional probabilities whenever the first non-zero value occurs at corresponding points in the sequence.)
Joe Halpern shows how to translate lexicographic probabilities and Popper functions into one another, though I think the translation might be non-unique in one direction, depending on what structural assumptions you make. | {"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": 0.8966673612594604, "perplexity": 533.0992183552423}, "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/1508187823153.58/warc/CC-MAIN-20171018214541-20171018234541-00622.warc.gz"} |
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https://pandasthumb.org/archives/2008/05/gamblers-ruin-i.html | # Gambler's Ruin is Darwin's Gain
by Joe Felsenstein
http://www.gs.washington.edu/faculty/felsenstein.htm
Over at Uncommon Descent Sal Cordova has opened a dramatic new thread “Gambler’s Ruin is Darwin’s Ruin”. Apparently improvement of a population by natural selection is now shown to be essentially impossible. He invokes the example of Edward Thorp, who developed the winning system for blackjack fictionalized in the movie 21.
Cordova uses the stochastic theory of gene frequency change of citing Motoo Kimura and Tomoko Ohta’s well-known 1971 monograph “Theoretical Aspects of Population Genetics”, and argues that
Without going into details, I’ll quote the experts who investigated the issues. Consider the probability a selectively advantaged trait will survive in a population a mere 7 generations after it emerges:
if a mutant gene is selectively neutral the probability is 0.79 that it will be lost from the population … if the mutant gene has a selective advantage of 1%, the probability of loss during the fist seven generations is 0.78. As compared with the neutral mutant, this probability of extinction [with natural selection] is less by only .01 [compared to extinction by purely random events]. (bracketing is by Cordova)
This means is that natural selection is only slightly better than random chance. Darwin was absolutely wrong to suggest that the emergence of a novel trait will be preserved in most cases. It will not! Except for extreme selection pressures (like antibiotic resistance, pesticide resistance, anti-malaria drug resistance), selection fails to make much of an impact.
The Kimura/Ohta quote in question is on page 1 of their book, and describes a mutant with a selective advantage of 1%.
This would be a shocking disproof of decades of work in population genetics—if it accurately reflected the ultimate fate of those mutants. Fortunately, we can turn to an equation seven pages later in Kimura and Ohta’s book, equation (10), which is Kimura’s famous 1962 formula for fixation probabilities. Using it we can compare three mutants, one advantageous (s = 0.01), one neutral (s = 0), and one disadvantageous (s = -0.01). Suppose that the population has size N = 1,000,000. Using equation (10) we find that
• The advantageous mutation has probability of fixation 0.0198013.
• The neutral mutation has probability of fixation 0.0000005.
• The disadvantageous mutation has probability of fixation 3.35818 x 10-17374
In other words, yes, in this case there is a lot of loss of advantageous mutations, about 49 being lost of every one that makes it to fixation. But they are each nearly 40,000 times as likely to fix as are individual neutral mutations, and deleterious mutations are essentially never going to fix in such a case.
Why does this give such a different result than the comparison of 0.78 to 0.79? It is because after 7 generations the surviving mutants in the case of selective advantage are at a higher frequency than are those in the neutral case, and the result is a much greater chance of fixation.
In fact, the Gambler’s Ruin shows a similar behavior—its mathematics is similar to (but not identical to) the population-genetic case. If you toss coins with a stake of $1 against a house which has$1,999,999 to wager, and you both keep playing until one holds the whole \$2,000,000, if the game is fair you will be the ultimate victor one time out of 2,000,000, and the rest of the times the house will win. But if you have a 1% advantage, so that on each toss you have a 50.5% chance of winning, you will be the ultimate victor nearly 1% of the time. Mostly you will be ruined, but you will bankrupt the house 20,000 times as often as you would if the toss were fair.
So yes, the mathematics of Gambler’s Ruin speaks to the issue of natural selection—but it confirms its effectiveness.
(The other issue raised by Cordova, that of interference between mutations at different loci, is the well-known Hill-Robertson effect. If the loci have more than a tiny amount of genetic recombination between them, the interference largely vanishes. Cordova and the other commenters there have forgotten this.) | {"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": 0.8084915280342102, "perplexity": 1480.5585126115782}, "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-2017-22/segments/1495463605188.47/warc/CC-MAIN-20170522151715-20170522171715-00414.warc.gz"} |
http://en.wikipedia.org/wiki/Pressure_measurement | # Pressure measurement
The construction of a bourdon tube gauge. Construction elements are made of brass
Many techniques have been developed for the measurement of pressure and vacuum. Instruments used to measure pressure are called pressure gauges or vacuum gauges.
A manometer is an instrument that uses a column of liquid to measure pressure, although the term is often used nowadays to mean any pressure measuring instrument.
A vacuum gauge is used to measure the pressure in a vacuum—which is further divided into two subcategories, high and low vacuum (and sometimes ultra-high vacuum). The applicable pressure range of many of the techniques used to measure vacuums have an overlap. Hence, by combining several different types of gauge, it is possible to measure system pressure continuously from 10 mbar down to 10−11 mbar.
## Absolute, gauge and differential pressures - zero reference
Everyday pressure measurements, such as for tire pressure, are usually made relative to ambient air pressure. In other cases measurements are made relative to a vacuum or to some other specific reference. When distinguishing between these zero references, the following terms are used:
• Absolute pressure is zero-referenced against a perfect vacuum, so it is equal to gauge pressure plus atmospheric pressure.
• Gauge pressure is zero-referenced against ambient air pressure, so it is equal to absolute pressure minus atmospheric pressure. Negative signs are usually omitted. To distinguish a negative pressure, the value may be appended with the word "vacuum" or the gauge may be labeled a "vacuum gauge."
• Differential pressure is the difference in pressure between two points.
The zero reference in use is usually implied by context, and these words are added only when clarification is needed. Tire pressure and blood pressure are gauge pressures by convention, while atmospheric pressures, deep vacuum pressures, and altimeter pressures must be absolute.
For most working fluids where a fluid exists in a closed system, gauge pressure measurement prevails. Pressure instruments connected to the system will indicate pressures relative to the current atmospheric pressure. The situation changes when extreme vacuum pressures are measured; absolute pressures are typically used instead.
Differential pressures are commonly used in industrial process systems. Differential pressure gauges have two inlet ports, each connected to one of the volumes whose pressure is to be monitored. In effect, such a gauge performs the mathematical operation of subtraction through mechanical means, obviating the need for an operator or control system to watch two separate gauges and determine the difference in readings.
Moderate vacuum pressure readings can be ambiguous without the proper context, as they may represent absolute pressure or gauge pressure without a negative sign. Thus a vacuum of 26 inHg gauge is equivalent to an absolute pressure of 30 inHg (typical atmospheric pressure) − 26 inHg = 4 inHg.
Atmospheric pressure is typically about 100 kPa at sea level, but is variable with altitude and weather. If the absolute pressure of a fluid stays constant, the gauge pressure of the same fluid will vary as atmospheric pressure changes. For example, when a car drives up a mountain, the (gauge) tire pressure goes up because atmospheric pressure goes down. The absolute pressure in the tire is essentially unchanged.
Using atmospheric pressure as reference is usually signified by a g for gauge after the pressure unit, e.g. 70 psig, which means that the pressure measured is the total pressure minus atmospheric pressure. There are two types of gauge reference pressure: vented gauge (vg) and sealed gauge (sg).
A vented gauge pressure transmitter for example allows the outside air pressure to be exposed to the negative side of the pressure sensing diaphragm, via a vented cable or a hole on the side of the device, so that it always measures the pressure referred to ambient barometric pressure. Thus a vented gauge reference pressure sensor should always read zero pressure when the process pressure connection is held open to the air.
A sealed gauge reference is very similar except that atmospheric pressure is sealed on the negative side of the diaphragm. This is usually adopted on high pressure ranges such as hydraulics where atmospheric pressure changes will have a negligible effect on the accuracy of the reading, so venting is not necessary. This also allows some manufacturers to provide secondary pressure containment as an extra precaution for pressure equipment safety if the burst pressure of the primary pressure sensing diaphragm is exceeded.
There is another way of creating a sealed gauge reference and this is to seal a high vacuum on the reverse side of the sensing diaphragm. Then the output signal is offset so the pressure sensor reads close to zero when measuring atmospheric pressure.
A sealed gauge reference pressure transducer will never read exactly zero because atmospheric pressure is always changing and the reference in this case is fixed at 1 bar.
An absolute pressure measurement is one that is referred to absolute vacuum. The best example of an absolute referenced pressure is atmospheric or barometric pressure.
To produce an absolute pressure sensor the manufacturer will seal a high vacuum behind the sensing diaphragm. If the process pressure connection of an absolute pressure transmitter is open to the air, it will read the actual barometric pressure.
## Units
Pressure units
Pascal Bar Technical atmosphere Standard atmosphere Torr Pounds per square inch
(Pa) (bar) (at) (atm) (Torr) (psi)
1 Pa ≡ 1 N/m2 10−5 1.0197×10−5 9.8692×10−6 7.5006×10−3 1.450377×10−4
1 bar 105 ≡ 106 dyn/cm2 1.0197 0.98692 750.06 14.50377
1 at 0.980665 ×105 0.980665 ≡ 1 kp/cm2 0.9678411 735.5592 14.22334
1 atm 1.01325 ×105 1.01325 1.0332 p0 ≡ 760 14.69595
1 Torr 133.3224 1.333224×10−3 1.359551×10−3 1.315789×10−3 ≈ 1 mmHg 1.933678×10−2
1 psi 6.8948×103 6.8948×10−2 7.03069×10−2 6.8046×10−2 51.71493 ≡ 1 lbF/in2
The SI unit for pressure is the pascal (Pa), equal to one newton per square metre (N·m−2 or kg·m−1·s−2). This special name for the unit was added in 1971; before that, pressure in SI was expressed in units such as N·m−2. When indicated, the zero reference is stated in parenthesis following the unit, for example 101 kPa (abs). The pound per square inch (psi) is still in widespread use in the US and Canada, for measuring, for instance, tire pressure. A letter is often appended to the psi unit to indicate the measurement's zero reference; psia for absolute, psig for gauge, psid for differential, although this practice is discouraged by the NIST.[1]
Because pressure was once commonly measured by its ability to displace a column of liquid in a manometer, pressures are often expressed as a depth of a particular fluid (e.g., inches of water). Manometric measurement is the subject of pressure head calculations. The most common choices for a manometer's fluid are mercury (Hg) and water; water is nontoxic and readily available, while mercury's density allows for a shorter column (and so a smaller manometer) to measure a given pressure. The abbreviation "W.C." or the words "water column" are often printed on gauges and measurements that use water for the manometer.
Fluid density and local gravity can vary from one reading to another depending on local factors, so the height of a fluid column does not define pressure precisely. So measurements in "millimetres of mercury" or "inches of mercury" can be converted to SI units as long as attention is paid to the local factors of fluid density and gravity. Temperature fluctuations change the value of fluid density, while location can affect gravity.
Although no longer preferred, these manometric units are still encountered in many fields. Blood pressure is measured in millimetres of mercury (see torr) in most of the world, and lung pressures in centimeters of water are still common, as in settings for CPAP machines. Natural gas pipeline pressures are measured in inches of water, expressed as "inches W.C." Scuba divers often use a manometric rule of thumb: the pressure exerted by ten meters depth of water is approximately equal to one atmosphere. In vacuum systems, the units torr, micrometre of mercury (micron),[citation needed] and inch of mercury (inHg) are most commonly used. Torr and micron usually indicates an absolute pressure, while inHg usually indicates a gauge pressure.
Atmospheric pressures are usually stated using kilopascal (kPa), or atmospheres (atm), except in American meteorology where the hectopascal (hPa) and millibar (mbar) are preferred. In American and Canadian engineering, stress is often measured in kip. Note that stress is not a true pressure since it is not scalar. In the cgs system the unit of pressure was the barye (ba), equal to 1 dyn·cm−2. In the mts system, the unit of pressure was the pieze, equal to 1 sthene per square metre.
Many other hybrid units are used such as mmHg/cm2 or grams-force/cm2 (sometimes as [[kg/cm2]] without properly identifying the force units). Using the names kilogram, gram, kilogram-force, or gram-force (or their symbols) as a unit of force is prohibited in SI; the unit of force in SI is the newton (N).
## Static and dynamic pressure
Static pressure is uniform in all directions, so pressure measurements are independent of direction in an immovable (static) fluid. Flow, however, applies additional pressure on surfaces perpendicular to the flow direction, while having little impact on surfaces parallel to the flow direction. This directional component of pressure in a moving (dynamic) fluid is called dynamic pressure. An instrument facing the flow direction measures the sum of the static and dynamic pressures; this measurement is called the total pressure or stagnation pressure. Since dynamic pressure is referenced to static pressure, it is neither gauge nor absolute; it is a differential pressure.
While static gauge pressure is of primary importance to determining net loads on pipe walls, dynamic pressure is used to measure flow rates and airspeed. Dynamic pressure can be measured by taking the differential pressure between instruments parallel and perpendicular to the flow. Pitot-static tubes, for example perform this measurement on airplanes to determine airspeed. The presence of the measuring instrument inevitably acts to divert flow and create turbulence, so its shape is critical to accuracy and the calibration curves are often non-linear.
## Instruments
Many instruments have been invented to measure pressure, with different advantages and disadvantages. Pressure range, sensitivity, dynamic response and cost all vary by several orders of magnitude from one instrument design to the next. The oldest type is the liquid column (a vertical tube filled with mercury) manometer invented by Evangelista Torricelli in 1643. The U-Tube was invented by Christiaan Huygens in 1661.
### Hydrostatic
Hydrostatic gauges (such as the mercury column manometer) compare pressure to the hydrostatic force per unit area at the base of a column of fluid. Hydrostatic gauge measurements are independent of the type of gas being measured, and can be designed to have a very linear calibration. They have poor dynamic response.
#### Piston
Piston-type gauges counterbalance the pressure of a fluid with a spring (for example tire-pressure gauges of comparatively low accuracy) or a solid weight, in which case it is known as a deadweight tester and may be used for calibration of other gauges.
#### Liquid column
The difference in fluid height in a liquid column manometer is proportional to the pressure difference. $h=\frac{P_a-P_o}{g \rho}$
By using Bernoulli's principle and the derived pressure head equation, liquids can be used for instrumentation where gravity is present. Liquid column gauges consist of a vertical column of liquid in a tube that has ends which are exposed to different pressures. The column will rise or fall until its weight (a force applied due to gravity) is in equilibrium with the pressure differential between the two ends of the tube (a force applied due to fluid pressure). A very simple version is a U-shaped tube half-full of liquid, one side of which is connected to the region of interest while the reference pressure (which might be the atmospheric pressure or a vacuum) is applied to the other. The difference in liquid level represents the applied pressure. The pressure exerted by a column of fluid of height h and density ρ is given by the hydrostatic pressure equation, P = hgρ. Therefore the pressure difference between the applied pressure Pa and the reference pressure P0 in a U-tube manometer can be found by solving PaP0 = hgρ. In other words, the pressure on either end of the liquid (shown in blue in the figure to the right) must be balanced (since the liquid is static) and so Pa = P0 + hgρ.
In most liquid column measurements, the result of the measurement is the height, h, expressed typically in mm, cm, or inches. The h is also known as the pressure head. When expressed as a pressure head, pressure is specified in units of length and the measurement fluid must be specified. When accuracy is critical, the temperature of the measurement fluid must likewise be specified, because liquid density is a function of temperature. So, for example, pressure head might be written "742.2 mmHg" or "4.2 inH2O at 59 °F" for measurements taken with mercury or water as the manometric fluid, respectively. The word "gauge" or "vacuum" may be added to such a measurement to distinguish between a pressure above or below the atmospheric pressure. Both mm of mercury and inches of water are common pressure heads which can be converted to S.I. units of pressure using unit conversion and the above formulas.
If the fluid being measured is significantly dense, hydrostatic corrections may have to be made for the height between the moving surface of the manometer working fluid and the location where the pressure measurement is desired except when measuring differential pressure of a fluid (for example across an orifice plate or venturi), in which case the density ρ should be corrected by subtracting the density of the fluid being measured.[2]
To measure the pressure of a fluid accurately using a liquid column, the fluid being measured should not be flowing for a static pressure measurement. A column connected to a flowing fluid will measure static plus dynamic pressure. So if a fluid is flowing, the liquid column will change due to dynamic pressure, proportional to the square of the fluid's velocity. This of course is precisely the desired measurement when a differential pressure measurement is needed for a venturi or an orifice plate. Measuring dynamic pressures is commonly used as an intermediary in determining a fluid's velocity or flow rate. See flow measurement.
As an example, an airplane flying through the air at sea level would experience the atmospheric pressure as a static pressure exerted on the skin of the aircraft. However, the forward surfaces of an aircraft in flight experience dynamic pressure in addition to the static pressure. To measure the static air pressure, we use a barometer in still air. To measure the dynamic pressure, imagine a mercury manometer like the U-tube above with an open end pointing in the direction of the airplane's travel and a closed end kept at the static air pressure. Mercury is pushed down the tube farther than it would if only measuring still air. For a plane traveling around 129 m/s, the dynamic pressure adds about 10% to the atmospheric pressure at sea level. A U-tube for measuring dynamic pressure on an airplane would be impractical, so a pitot tube is used instead that relies on a diaphragm rather than columns of fluid. Although dynamic pressure can be measured directly, fluid speed and air speed can be measured indirectly using the Bernoulli principle if both dynamic and static pressures are known.
Although any fluid can be used, mercury is preferred for its high density (13.534 g/cm3) and low vapour pressure. For low pressure differences well above the vapour pressure of water, water is commonly used (and "inches of water" or "Water Column" is a common pressure unit). Liquid-column pressure gauges are independent of the type of fluid being measured and have a highly linear calibration. They have poor dynamic response because the fluid in the column may react slowly to a pressure change.
When measuring vacuum, the working liquid may evaporate and contaminate the vacuum if its vapor pressure is too high. When measuring liquid pressure, a loop filled with gas or a light fluid can isolate the liquids to prevent them from mixing but this can be unnecessary, for example when mercury is used as the manometer fluid to measure differential pressure of a fluid such as water. Simple hydrostatic gauges can measure pressures ranging from a few Torr (a few 100 Pa) to a few atmospheres. (Approximately 1,000,000 Pa)
A single-limb liquid-column manometer has a larger reservoir instead of one side of the U-tube and has a scale beside the narrower column. The column may be inclined to further amplify the liquid movement. Based on the use and structure following type of manometers are used[3]
1. Simple Manometer
2. Micromanometer
3. Differential manometer
4. Inverted differential manometer
A McLeod gauge, drained of mercury
#### McLeod gauge
A McLeod gauge isolates a sample of gas and compresses it in a modified mercury manometer until the pressure is a few mmHg. The gas must be well-behaved during its compression (it must not condense, for example). The technique is slow and unsuited to continual monitoring, but is capable of good accuracy.
Useful range: above 10-4 torr [4] (roughly 10-2 Pa) as high as 10−6 Torr (0.1 mPa),
0.1 mPa is the lowest direct measurement of pressure that is possible with current technology. Other vacuum gauges can measure lower pressures, but only indirectly by measurement of other pressure-controlled properties. These indirect measurements must be calibrated to SI units via a direct measurement, most commonly a McLeod gauge.[5]
### Aneroid
Aneroid gauges are based on a metallic pressure sensing element that flexes elastically under the effect of a pressure difference across the element. "Aneroid" means "without fluid," and the term originally distinguished these gauges from the hydrostatic gauges described above. However, aneroid gauges can be used to measure the pressure of a liquid as well as a gas, and they are not the only type of gauge that can operate without fluid. For this reason, they are often called mechanical gauges in modern language. Aneroid gauges are not dependent on the type of gas being measured, unlike thermal and ionization gauges, and are less likely to contaminate the system than hydrostatic gauges. The pressure sensing element may be a Bourdon tube, a diaphragm, a capsule, or a set of bellows, which will change shape in response to the pressure of the region in question. The deflection of the pressure sensing element may be read by a linkage connected to a needle, or it may be read by a secondary transducer. The most common secondary transducers in modern vacuum gauges measure a change in capacitance due to the mechanical deflection. Gauges that rely on a change in capacitance are often referred to as capacitance manometers.
#### Bourdon
Membrane-type manometer
The Bourdon pressure gauge uses the principle that a flattened tube tends to straighten or regain its circular form in cross-section when pressurized. Although this change in cross-section may be hardly noticeable, and thus involving moderate stresses within the elastic range of easily workable materials, the strain of the material of the tube is magnified by forming the tube into a C shape or even a helix, such that the entire tube tends to straighten out or uncoil, elastically, as it is pressurized. Eugene Bourdon patented his gauge in France in 1849, and it was widely adopted because of its superior sensitivity, linearity, and accuracy; Edward Ashcroft purchased Bourdon's American patent rights in 1852 and became a major manufacturer of gauges. Also in 1849, Bernard Schaeffer in Magdeburg, Germany patented a successful diaphragm (see below) pressure gauge, which, together with the Bourdon gauge, revolutionized pressure measurement in industry.[6] But in 1875 after Bourdon's patents expired, his company Schaeffer and Budenberg also manufactured Bourdon tube gauges.
In practice, a flattened thin-wall, closed-end tube is connected at the hollow end to a fixed pipe containing the fluid pressure to be measured. As the pressure increases, the closed end moves in an arc, and this motion is converted into the rotation of a (segment of a) gear by a connecting link that is usually adjustable. A small-diameter pinion gear is on the pointer shaft, so the motion is magnified further by the gear ratio. The positioning of the indicator card behind the pointer, the initial pointer shaft position, the linkage length and initial position, all provide means to calibrate the pointer to indicate the desired range of pressure for variations in the behavior of the Bourdon tube itself. Differential pressure can be measured by gauges containing two different Bourdon tubes, with connecting linkages.
Bourdon tubes measure gauge pressure, relative to ambient atmospheric pressure, as opposed to absolute pressure; vacuum is sensed as a reverse motion. Some aneroid barometers use Bourdon tubes closed at both ends (but most use diaphragms or capsules, see below). When the measured pressure is rapidly pulsing, such as when the gauge is near a reciprocating pump, an orifice restriction in the connecting pipe is frequently used to avoid unnecessary wear on the gears and provide an average reading; when the whole gauge is subject to mechanical vibration, the entire case including the pointer and indicator card can be filled with an oil or glycerin. Tapping on the face of the gauge is not recommended as it will tend to falsify actual readings initially presented by the gauge. The Bourdon tube is separate from the face of the gauge and thus has no effect on the actual reading of pressure. Typical high-quality modern gauges provide an accuracy of ±2% of span, and a special high-precision gauge can be as accurate as 0.1% of full scale.[7]
In the following illustrations the transparent cover face of the pictured combination pressure and vacuum gauge has been removed and the mechanism removed from the case. This particular gauge is a combination vacuum and pressure gauge used for automotive diagnosis:
Indicator side with card and dial
Mechanical side with Bourdon tube
##### Mechanical details
Mechanical details
Stationary parts:
• A: Receiver block. This joins the inlet pipe to the fixed end of the Bourdon tube (1) and secures the chassis plate (B). The two holes receive screws that secure the case.
• B: Chassis plate. The face card is attached to this. It contains bearing holes for the axles.
• C: Secondary chassis plate. It supports the outer ends of the axles.
• D: Posts to join and space the two chassis plates.
Moving Parts:
1. Stationary end of Bourdon tube. This communicates with the inlet pipe through the receiver block.
2. Moving end of Bourdon tube. This end is sealed.
3. Pivot and pivot pin.
4. Link joining pivot pin to lever (5) with pins to allow joint rotation.
5. Lever. This is an extension of the sector gear (7).
6. Sector gear axle pin.
7. Sector gear.
8. Indicator needle axle. This has a spur gear that engages the sector gear (7) and extends through the face to drive the indicator needle. Due to the short distance between the lever arm link boss and the pivot pin and the difference between the effective radius of the sector gear and that of the spur gear, any motion of the Bourdon tube is greatly amplified. A small motion of the tube results in a large motion of the indicator needle.
9. Hair spring to preload the gear train to eliminate gear lash and hysteresis.
#### Diaphragm
A pile of pressure capsules with corrugated diaphragms in an aneroid barograph.
A second type of aneroid gauge uses deflection of a flexible membrane that separates regions of different pressure. The amount of deflection is repeatable for known pressures so the pressure can be determined by using calibration. The deformation of a thin diaphragm is dependent on the difference in pressure between its two faces. The reference face can be open to atmosphere to measure gauge pressure, open to a second port to measure differential pressure, or can be sealed against a vacuum or other fixed reference pressure to measure absolute pressure. The deformation can be measured using mechanical, optical or capacitive techniques. Ceramic and metallic diaphragms are used.
Useful range: above 10-2 Torr [8] (roughly 1 Pa)
For absolute measurements, welded pressure capsules with diaphragms on either side are often used.
shape:
• Flat
• corrugated
• flattened tube
• capsule
#### Bellows
In gauges intended to sense small pressures or pressure differences, or require that an absolute pressure be measured, the gear train and needle may be driven by an enclosed and sealed bellows chamber, called an aneroid, which means "without liquid". (Early barometers used a column of liquid such as water or the liquid metal mercury suspended by a vacuum.) This bellows configuration is used in aneroid barometers (barometers with an indicating needle and dial card), altimeters, altitude recording barographs, and the altitude telemetry instruments used in weather balloon radiosondes. These devices use the sealed chamber as a reference pressure and are driven by the external pressure. Other sensitive aircraft instruments such as air speed indicators and rate of climb indicators (variometers) have connections both to the internal part of the aneroid chamber and to an external enclosing chamber.
## Electronic pressure sensors
Main article: Pressure sensor
Piezoresistive Strain Gage
Uses the piezoresistive effect of bonded or formed strain gauges to detect strain due to applied pressure.
Capacitive
Uses a diaphragm and pressure cavity to create a variable capacitor to detect strain due to applied pressure.
Magnetic
Measures the displacement of a diaphragm by means of changes in inductance (reluctance), LVDT, Hall Effect, or by eddy current principal.
Piezoelectric
Uses the piezoelectric effect in certain materials such as quartz to measure the strain upon the sensing mechanism due to pressure.
Optical
Uses the physical change of an optical fiber to detect strain due applied pressure.
Potentiometric
Uses the motion of a wiper along a resistive mechanism to detect the strain caused by applied pressure.
Resonant
Uses the changes in resonant frequency in a sensing mechanism to measure stress, or changes in gas density, caused by applied pressure.
### Thermal conductivity
Generally, as a real gas increases in density -which may indicate an increase in pressure- its ability to conduct heat increases. In this type of gauge, a wire filament is heated by running current through it. A thermocouple or resistance thermometer (RTD) can then be used to measure the temperature of the filament. This temperature is dependent on the rate at which the filament loses heat to the surrounding gas, and therefore on the thermal conductivity. A common variant is the Pirani gauge, which uses a single platinum filament as both the heated element and RTD. These gauges are accurate from 10−3 Torr to 10 Torr, but their calibration is sensitive to the chemical composition of the gases being measured.
#### Pirani (one wire)
Main article: Pirani gauge
A Pirani gauge consist of a metal wire open to the pressure being measured. The wire is heated by a current flowing through it and cooled by the gas surrounding it. If the gas pressure is reduced, the cooling effect will decrease, hence the equilibrium temperature of the wire will increase. The resistance of the wire is a function of its temperature: by measuring the voltage across the wire and the current flowing through it, the resistance (and so the gas pressure) can be determined. This type of gauge was invented by Marcello Pirani.
#### Two-wire
In two-wire gauges, one wire coil is used as a heater, and the other is used to measure temperature due to convection. Thermocouple gauges and thermistor gauges work in this manner using thermocouple or thermistor, respectively, to measure the temperature of the heated wire.
### Ionization gauge
Ionization gauges are the most sensitive gauges for very low pressures (also referred to as hard or high vacuum). They sense pressure indirectly by measuring the electrical ions produced when the gas is bombarded with electrons. Fewer ions will be produced by lower density gases. The calibration of an ion gauge is unstable and dependent on the nature of the gases being measured, which is not always known. They can be calibrated against a McLeod gauge which is much more stable and independent of gas chemistry.
Thermionic emission generate electrons, which collide with gas atoms and generate positive ions. The ions are attracted to a suitably biased electrode known as the collector. The current in the collector is proportional to the rate of ionization, which is a function of the pressure in the system. Hence, measuring the collector current gives the gas pressure. There are several sub-types of ionization gauge.
Useful range: 10-10 - 10-3 torr (roughly 10-8 - 10-1 Pa)
Most ion gauges come in two types: hot cathode and cold cathode. A third type that is more sensitive and expensive known as a spinning rotor gauge exists, but is not discussed here. In the hot cathode version, an electrically heated filament produces an electron beam. The electrons travel through the gauge and ionize gas molecules around them. The resulting ions are collected at a negative electrode. The current depends on the number of ions, which depends on the pressure in the gauge. Hot cathode gauges are accurate from 10−3 Torr to 10−10 Torr. The principle behind cold cathode version is the same, except that electrons are produced in the discharge of a high voltage. Cold Cathode gauges are accurate from 10−2 Torr to 10−9 Torr. Ionization gauge calibration is very sensitive to construction geometry, chemical composition of gases being measured, corrosion and surface deposits. Their calibration can be invalidated by activation at atmospheric pressure or low vacuum. The composition of gases at high vacuums will usually be unpredictable, so a mass spectrometer must be used in conjunction with the ionization gauge for accurate measurement.[9]
#### Hot cathode
Bayard-Alpert hot-cathode ionization gauge
A hot-cathode ionization gauge is composed mainly of three electrodes acting together as a triode, wherein the cathode is the filament. The three electrodes are a collector or plate, a filament, and a grid. The collector current is measured in picoamps by an electrometer. The filament voltage to ground is usually at a potential of 30 volts, while the grid voltage at 180–210 volts DC, unless there is an optional electron bombardment feature, by heating the grid, which may have a high potential of approximately 565 volts. The most common ion gauge is the hot-cathode Bayard-Alpert gauge, with a small ion collector inside the grid. A glass envelope with an opening to the vacuum can surround the electrodes, but usually the Nude Gauge is inserted in the vacuum chamber directly, the pins being fed through a ceramic plate in the wall of the chamber. Hot-cathode gauges can be damaged or lose their calibration if they are exposed to atmospheric pressure or even low vacuum while hot. The measurements of a hot-cathode ionization gauge are always logarithmic.
Electrons emitted from the filament move several times in back and forth movements around the grid before finally entering the grid. During these movements, some electrons collide with a gaseous molecule to form a pair of an ion and an electron (Electron ionization). The number of these ions is proportional to the gaseous molecule density multiplied by the electron current emitted from the filament, and these ions pour into the collector to form an ion current. Since the gaseous molecule density is proportional to the pressure, the pressure is estimated by measuring the ion current.
The low-pressure sensitivity of hot-cathode gauges is limited by the photoelectric effect. Electrons hitting the grid produce x-rays that produce photoelectric noise in the ion collector. This limits the range of older hot-cathode gauges to 10−8 Torr and the Bayard-Alpert to about 10−10 Torr. Additional wires at cathode potential in the line of sight between the ion collector and the grid prevent this effect. In the extraction type the ions are not attracted by a wire, but by an open cone. As the ions cannot decide which part of the cone to hit, they pass through the hole and form an ion beam. This ion beam can be passed on to a:
#### Cold cathode
There are two subtypes of cold-cathode ionization gauges: the Penning gauge (invented by Frans Michel Penning), and the Inverted magnetron, also called a Redhead gauge. The major difference between the two is the position of the anode with respect to the cathode. Neither has a filament, and each may require a DC potential of about 4 kV for operation. Inverted magnetrons can measure down to 1x10−12 Torr.
Likewise, cold-cathode gauges may be reluctant to start at very low pressures, in that the near-absence of a gas makes it difficult to establish an electrode current - in particular in Penning gauges, which use an axially symmetric magnetic field to create path lengths for electrons that are of the order of metres. In ambient air, suitable ion-pairs are ubiquitously formed by cosmic radiation; in a Penning gauge, design features are used to ease the set-up of a discharge path. For example, the electrode of a Penning gauge is usually finely tapered to facilitate the field emission of electrons.
Maintenance cycles of cold cathode gauges are, in general, measured in years, depending on the gas type and pressure that they are operated in. Using a cold cathode gauge in gases with substantial organic components, such as pump oil fractions, can result in the growth of delicate carbon films and shards within the gauge that eventually either short-circuit the electrodes of the gauge or impede the generation of a discharge path.
## Calibration
Pressure gauges are either direct- or indirect-reading. Hydrostatic and elastic gauges measure pressure are directly influenced by force exerted on the surface by incident particle flux, and are called direct reading gauges. Thermal and ionization gauges read pressure indirectly by measuring a gas property that changes in a predictable manner with gas density. Indirect measurements are susceptible to more errors than direct measurements.
• McLeod
• mass spec + ionization
## Dynamic transients
When fluid flows are not in equilibrium, local pressures may be higher or lower than the average pressure in a medium. These disturbances propagate from their source as longitudinal pressure variations along the path of propagation. This is also called sound. Sound pressure is the instantaneous local pressure deviation from the average pressure caused by a sound wave. Sound pressure can be measured using a microphone in air and a hydrophone in water. The effective sound pressure is the root mean square of the instantaneous sound pressure over a given interval of time. Sound pressures are normally small and are often expressed in units of microbar.
• frequency response of pressure sensors
• resonance
## Standards
The American Society of Mechanical Engineers (ASME) has developed two separate and distinct standards on pressure Measurement, B40.100 and PTC 19.2. B40.100 provides guidelines on Pressure Indicated Dial Type and Pressure Digital Indicating Gauges, Diaphragm Seals, Snubbers, and Pressure Limiter Valves. PTC 19.2 provides instructions and guidance for the accurate determination of pressure values in support of the ASME Performance Test Codes. The choice of method, instruments, required calculations, and corrections to be applied depends on the purpose of the measurement, the allowable uncertainty, and the characteristics of the equipment being tested. The methods for pressure measurement and the protocols used for data transmission are also provides. Guidance is given for setting up the instrumentation and determining the uncertainty of the measurement. Information regarding the instrument type, design, applicable pressure range, accuracy, output, and relative cost is provided. Information is also provided on pressure-measuring devices that are used in field environments i.e., Piston Gauges, Manometers, and Low-Absolute-Pressure (Vacuum) Instruments. These methods are designed to assist in the evaluation of measurement uncertainty based on current technology and engineering knowledge, taking into account published instrumentation specifications and measurement and application techniques. This Supplement provides guidance in the use of methods to establish the pressure-measurement uncertainty.
## European (CEN) Standard
• EN 472 : Pressure gauge - Vocabulary.
• EN 837-1 : Pressure gauges. Bourdon tube pressure gauges. Dimensions, metrology, requirements and testing.
• EN 837-2 : Pressure gauges. Selection and installation recommendations for pressure gauges.
• EN 837-3 : Pressure gauges. Diaphragm and capsule pressure gauges. Dimensions, metrology, requirements, and testing.
## US ASME Standards
• B40.100-2013: Pressure gauges and Gauge attachments.
• PTC 19.2-2010 : Performance test code for pressure measurement. | {"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": 1, "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": 0.7356739640235901, "perplexity": 1509.3399732869225}, "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/1404776438382.45/warc/CC-MAIN-20140707234038-00087-ip-10-180-212-248.ec2.internal.warc.gz"} |
https://asmedigitalcollection.asme.org/solarenergyengineering/article-abstract/doi/10.1115/1.4055602/1146199/Wind-load-similarity-relations-for-parabolic?redirectedFrom=fulltext | ## Abstract
Large-scale parabolic trough collectors (PTCs) are generally installed in flat, open areas. Their specific costs are dependent on wind load-based structural design factors. To help estimate these wind loads, validated numerical simulations were used to develop similarity relations for large-scale PTCs. First, similarity relations were deduced between a full-sized model and a scaled-down experimental similarity model. Second, the wind loads on the similarity model were simulated with a computational model to analyze the pressure distributions and aerodynamic performance under different wind speeds and pitch angles. Third, the computational method was extended to compute wind loads on a LS-2 collector. The numerical results had a close agreement with the experiment results on the whole, achieving a mean relative error in the drag coefficients of 5.1%, 3.8% in the lift coefficients and 5.0% in the moment coefficients, which indicated that the simulation model was valid. Further, comparing with the other turbulence model, the ke turbulence model has a better accuracy. Finally, practical similarity equations were proposed which can be used to estimate the wind loads on a range of PTC designs in a wide range of conditions. The mean relative error of these practical similarity equations was found to be within 12.0%. Overall, this study reports a validated set of similarity equations which can be used to bypass costly numerical simulation and/or wind tunnel testing for the estimation of wind loads on the large-scale PTCs installed in flat, open areas.
This content is only available via PDF.
You do not currently have access to this content. | {"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": 0.8683450818061829, "perplexity": 1231.365652428799}, "config": {"markdown_headings": true, "markdown_code": false, "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-2022-40/segments/1664030335286.15/warc/CC-MAIN-20220928212030-20220929002030-00663.warc.gz"} |
https://www.autoitscript.com/forum/topic/148140-trouble-reading-file/ | ## Recommended Posts
Hi guys
Trring to get screen data off a console app. Which I have successfully done and then I write that data to a file successfully.
THen one I try to read the file it doesnt seem to work. I have tried _FileCountLines and it says the there is 14 lines but trying FileReadLine it doesreturn anything . The file its Saves is ANSI. Hope ppl can help
Here is my code:
#include <Constants.au3>
#include <File.au3>
Global $PID = Run("pdfinfo.exe IM_Rev4.pdf", @WorkingDir, @SW_MINIMIZE,$STDERR_MERGED)
Global $sStdOut = "" Do$sStdOut &= StdoutRead($PID) Until @error FileDelete(@ScriptDir & "\text.txt") If Not _FileCreate("test.txt") Then MsgBox(4096, "Error", " Error Creating/Resetting log. error:" & @error) EndIf Local$file = FileOpen("test.txt", 1)
If $file = -1 Then MsgBox(0, "Error", "Unable to open file.") Exit EndIf FileWrite($file, $sStdOut) Local$line = FileReadLine($file,8) MsgBox(0, "Line read:",$line)
FileClose(\$file)
Firefox's secret is the same as Jessica Simpson's: its effortless, glamorous style is the result of shhh extensions!
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the filehandle you used is only for writing operations use with flag 0 for read operations
My code:
PredictText: Predict Text of an Edit Control Like Scite. Remote Gmail: Execute your Scripts through Gmail. StringRegExp:Share and learn RegExp.
Run As System: A command line wrapper around PSEXEC.exe to execute your apps scripts as System (LSA). Database: An easier approach for _SQ_LITE beginners.
MathsEx: A UDF for Fractions and LCM, GCF/HCF. FloatingText: An UDF for make your text floating. Clipboard Extendor: A clipboard monitoring tool.
Custom ScrollBar: Scroll Bar made with GDI+, user can use bitmaps instead. Restrict text in an Edit Control through a Regular Expression.
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Thanks it didnt fix it but lead me to file what was wrong . Cheers !!!
Firefox's secret is the same as Jessica Simpson's: its effortless, glamorous style is the result of shhh extensions!
## Create an account
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http://stats.stackexchange.com/questions/89941/how-to-best-visualize-differences-in-many-proportions-across-three-groups | # How to best visualize differences in many proportions across three groups?
I'm trying to visually compare how three different news publications cover different topics (determined through an LDA topic model). I have two related methods for doing so, but have received lots of feedback from colleagues that this isn't very intuitive. I'm hoping someone out there has a better idea for visualizing this.
In the first graph, I show the proportions of each topic in each publication, like so:
This is pretty straightforward and intuitive to almost everyone I've talked to. However, it's difficult to see the differences between the publications. Which newspaper covers which topic more?
To get at this, I graphed the difference between the publication with the highest and second highest proportion of topics, colored by the publication with the highest. Like this:
So, the huge bar for football, for example, is really the distance between al-Ahram English and Daily News Egypt (#2 in football coverage), and it is colored red because Al-Ahram is #1. Similarly, trials is green because Egypt Independent has the highest proportion, and the bar size is the distance between Egypt Independent and Daily News Egypt (#2 again).
The fact that I have to explain that all in two paragraphs is a pretty sure sign that the graph fails the self-sufficiency test. It's hard to tell what's really going on by just looking at it.
Any general suggestions about how to visually highlight the dominant publication for each topic in a more intuitive way?
Edit: Data to play with: Here's dput output from R, as well as a CSV file.
Edit 2: Here's a preliminary dot plot version, with the diameters of the dots proportional to the proportion of the topic in the corpus (which is how the topics were originally sorted). Though I still need to tweak it a little more, it feels a lot more intuitive than what I was doing before. Thanks everyone!
-
I just added some data (for R and a CSV). I haven't finished choosing good colors yet (hence the Christmasy red/green), though I'm aware of the color blind issues :) – Andrew Mar 14 '14 at 1:31
The mention of "proportions" is a bit of a red herring here, as the data are not really proportions and more importantly, none of the graphical solutions so far depends on the data being proportions. This is good because the solutions have relevance to a wide range of data, but don't be misled. – Nick Cox Mar 14 '14 at 11:46
(+1) Nice question, including downloadable dataset and quick follow up! – chl Apr 23 '14 at 14:06
Andrew, regarding your latest edit, I think it would be better with the vertical grid lines. They create a checker pattern but don't add much value, assuming you don't care about reading precise values from the graph. – xan Apr 23 '14 at 17:30
Without the vertical lines? – Andrew Apr 23 '14 at 20:29
Thanks for making the data accessible and for an interesting dataset and graphical challenge.
My main suggestion is of a (Cleveland) dot chart.
The most important details I would like to emphasise:
1. Superimposition here allows and eases comparison.
2. The order of topics in your displays appears quite arbitrary. Absent a natural order (e.g. time, space, an ordered variable) I would always sort on one of the variables to provide a framework. Which to use could be a matter of whether one is particularly interesting or important, a researcher's decision. Another possibility is to order on some measure of the differences between papers, so that topics receiving similar coverage were at one end and those receiving different coverage at the other end.
3. Open markers or point symbols allow overlap or identity to be resolved better than closed or solid markers or symbols, which in the worst cases obscure or occlude each other. (An alternative that might work quite well here is letters such as A, D and I for the three newspapers.)
There is clearly much scope for improving my design. For example, is the lettering too large and/or too heavy? On the other hand, the headings must be easily readable, or else the graph is a failure.
Some smaller, pickier points:
a. Red and green on your graph is a colour combination to be avoided. When different markers are used, colour choices are a little less crucial.
b. The horizontal ticks on your graph are distracting. In contrast, grid lines on mine are needed, but I try to make them unobtrusive by using thin, light lines.
c. Your graph shows percents and the total is about 20 $\times$ 0.1% or 2%, so 98% of the papers is something else? I used the proportions directly in the .csv provided.
Cleveland dot charts owe most to
Cleveland, W.S. 1984. Graphical methods for data presentation: full scale breaks, dot charts, and multibased logging. American Statistician 38: 270-80.
Cleveland, W.S. 1985. Elements of graphing data. Monterey, CA: Wadsworth.
Cleveland, W.S. 1994. Elements of graphing data. Summit, NJ: Hobart Press.
One precursor (more famous statistically for quite different work!!!) was
Pearson, E.S. 1956. Some aspects of the geometry of statistics: the use of visual presentation in understanding the theory and application of mathematical statistics. Journal of the Royal Statistical Society A 119: 125-146.
For those interested, the graph was prepared in Stata after reading in the .csv with code
graph dot (asis) prop , over(pub) over(label, sort(1)) asyvars
marker(1, ms(Oh)) marker(2, ms(+)) marker(3, ms(Th)) linetype(line)
lines(lc(gs12) lw(vthin)) scheme(s1color)
-
This is awesome—thanks! The percents unfortunately don't add up to anything because the values are standardized means from a large corpus of documents (i.e. every document in each publication consists of some combination of the 20 topics, discovered by LDA—this shows the normalized means… hence the small numbers) – Andrew Mar 14 '14 at 3:20
Also, the topics are ordered by their proportion in the corpus. Egypt governance is the most commonly appearing topic, while miscellaneous is the rarest topic. But using that order here makes the dots/symbols slightly harder to visually follow. – Andrew Mar 14 '14 at 3:33
This is great! Thanks! I updated the original post to reflect your suggestions and add corpus proportions. – Andrew Mar 14 '14 at 15:13
(+6) Nice answer! And it's always nice to have references and reproducible code. – chl Apr 23 '14 at 14:08
@chl Many thanks for appreciative comments and the extra reputation. – Nick Cox Apr 24 '14 at 14:18
The dot plot from Nick Cox is probably best for the complete picture. If you really want to emphasize the first versus second relationship, here's a modification to your chart that offsets the difference bar with the length of the second bar.
And for a different big picture view, you can try something like a slope chart or parallel coordinates plot. The lines may be a bit too crowded here, but it may work if you want to highlight on a subset of the topics.
Also, you might try helpmeviz.com which is geared towards very specific data viz questions like this.
-
Interesting! Minute point: the axis title or label "proportion" does not match the units of %. – Nick Cox Mar 14 '14 at 8:54
Ooh, this is really interesting. I'm going to play with this to see if it can complement the dot chart. – Andrew Mar 14 '14 at 15:05
My first instict was to suggest a Mosaic plot; it graphs each sub-category as a rectangle, where one dimension represents the total count for the main category and the other dimension represents the sub-category's proportionate share. There's an R package to draw them, but it's also fairly straightforward to do with lower-level graphing tools.
However, mosaic plots (like percentage-based stacked bar graphs) work best if there are only 2 or 3 categories in the dimension in which you want to compare proportions. So they would work well if you wanted to compare differences between topics in the proportion of articles that were in each of three newspapers, but not so much for your intended use, comparing differences between three newspapers in the proportion of coverage for each topic. A subtle but important distinction!
For what you want to emphasize, I think the most effective graph is one of the simplest -- a grouped bar graph. More people understand bar graphs than dot charts; at a glance, you can see that you're comparing quantities of different size, and the values you want to compare are side-by-side.
However, if you really wanted to emphasize the differences in proportion, you could create a custom grouped bar graph, modified to position each group so that the median value per category is aligned with the axis, instead of the zero values:
Difference in proportion of coverage
per Newspaper,
relative to category median
(narrow bars)
____-0.1%____0_____0.1%____0.2%_____
|
|********|*****
A |~~~~~~~~|
|#### |
|
|****|**********
B |~~ |
|####|
|
|***** |
C |~~~~~~~|~~~~~
|#######|
|
|*** |
D |~~~~~~~~~~~|
|###########|##
|
0.2%_____0.1%____0_____
Median proportion of coverage
per category, all papers
(large bars)
Note that the bars in each group are still aligned for easy comparison of size, and that each group's baseline is now positioned to the left of the axis according to that group's median value, while the bars that project to the right of the axis are equivalent to your second bar graph showing the difference between the top two categories.
Regardless of whether you use a standard grouped bar graph or an offset-adjusted graph like the above, you could still take an idea from mosaic plots and make the width of each bar proportional to the total article count for that newspaper (so the size of the bar is proportional to the number of articles in that newspaper in that category).
Since your test statistic is a property of each comparison, not of individual values, I don't think it's useful to scale every data point according to the significance. Instead, I would have an icon next to each grouping representing significance. For academic publication, the standard */**/*** has the benefit of familiarity, but you could get creative if you wanted to show the full continuum of the statistic.
-
The main idea here is to group the bars vertically. That's a widely used design, but implies 60 bars vertically rather than 20 in the poster's original. Although you can clearly tweak bar width, I think you're going to need more space to do it well in this case, especially as you want to add space between groups. – Nick Cox Mar 15 '14 at 11:20
@NickCox That is a downside compared to the more compact original chart, although you could rotate the whole graph 90 degrees if a landscape-oriented figure suited your overall layout. – AmeliaBR Mar 15 '14 at 17:15
You could, but 60 bars is tough from left to right too, and 20 labels such as "Muslim Brotherhood and politics" would have to remain readable... – Nick Cox Mar 15 '14 at 17:26
You might be able to get it to work by having the bars in a group on top of each other instead of side-by-side. Hard to say without seeing a mockup (and my ASCII art isn't very good at conveying look and feel). It would be less intuitive since it's not as familiar a structure, and might lead to confusion if two bars are nearly the exact same height. But if the alternative is one-pixel wide bars... – AmeliaBR Mar 15 '14 at 18:43
So, you are approaching the suggestion in my answer of a dot chart. – Nick Cox Mar 15 '14 at 19:00
Have you tried a bubble chart? https://code.google.com/apis/ajax/playground/?type=visualization#bubble_chart
The individual topics could be circles and each circle could be pie chart of the percentage that each news outlet covers the topic. The size of the circle could indicate the relative coverage of the topic. e.g if more total articles are written about oil than culture then the oil circle has a bigger diameter.
-
What would the $[X,Y]$ coordinates be then? – Nick Stauner Mar 14 '14 at 8:30
@NickStauner I didn't see the edited question with the data set when I originally answered this. The co-ordinates wouldn't signify much but the number publications. The circles can be clustered by topic or by diameter size. I don't know why percentages were used in the first place since the numbers are extremely small. – rocinante Mar 15 '14 at 17:02 | {"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": 0.6161079406738281, "perplexity": 1303.2759174173311}, "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-2016-18/segments/1461860123840.94/warc/CC-MAIN-20160428161523-00094-ip-10-239-7-51.ec2.internal.warc.gz"} |
https://slicer.readthedocs.io/en/latest/developer_guide/modules/markups.html | # Markups¶
## Markups json file format (.mrk.json)¶
All markups node types (point list, line, angle, curve, etc.) can be saved to and loaded from json files. Detailed specification of all elements of the file is available in the JSON schema.
A simple example that specifies a markups point list with 3 points that can be saved to a myexample.mrk.json file and loaded into Slicer:
{"@schema": "https://raw.githubusercontent.com/slicer/slicer/master/Modules/Loadable/Markups/Resources/Schema/markups-schema-v1.0.0.json#",
"markups": [{"type": "Fiducial", "coordinateSystem": "LPS", "controlPoints": [
{ "label": "F-1", "position": [-53.388409961685827, -73.33572796934868, 0.0] },
{ "label": "F-2", "position": [49.8682950191571, -88.58955938697324, 0.0] },
{ "label": "F-3", "position": [-25.22749042145594, 59.255268199233729, 0.0] }
]}]}
## Markups fiducial point list file format (.fcsv)¶
vtkMRMLMarkupsFiducialStorageNode uses a comma separated value file with a custom header to store the control points on disk. A simple example:
# Markups fiducial file version = 4.13
# CoordinateSystem = LPS
# columns = id,x,y,z,ow,ox,oy,oz,vis,sel,lock,label,desc,associatedNodeID
0,-19.906699999999987,13.9347,29.442970822281154,0,0,0,1,1,1,0,F-1,,
1,-7.3939,-76.94990495817181,17.552540297898375,0,0,0,1,1,1,0,F-2,,
2,81.73332450520303,-42.9415,9.625586614976527,0,0,0,1,1,1,0,F-3,,
• Line 1: a comment line specifying the Slicer version that created the file
• Line 2: a comment line specifying the coordinate system (CoordinateSystem = LPS or CoordinateSystem = RAS). In earlier versions of Slicer, numeric codes were used: RAS = 0, LPS = 1.
• Line 3: a comment line explaining the fields in the csv (columns = id,x,y,z,ow,ox,oy,oz,vis,sel,lock,label,desc,associatedNodeID)
Each line after the header specifies a control point. Meaning of columns:
• id: a string giving a unique id for this control point, usually based on the class name
• x,y,z: the floating point coordinate of the control point
• ow,ox,oy,oz: the orientation quaternion of this control point, angle and axis, default 0,0,0,1 (or 0,0,0,0,0,0,1.0)
• vis: the visibility flag for this control point, 0 or 1, default 1
• sel: the selected flag for this control point, 0 or 1, default 1
• lock: the locked flag for this control point, 0 or 1, default 0
• label: the name for this control point, displayed beside the glyph, with quotes around it if there is a comma in the field
• desc: a string description for this control point, optional
• associatedNodeID = an id of a node in the scene with which the control point is associated, for example the volume or model on which the control point was placed, optional
## Markups control points table file format (.csv, .tsv)¶
Markups control points can be imported from and exported to a table node that can be written to/read from standard comma (or tab) separated file format. A simple example:
label,l,p,s,defined,selected,visible,locked,description
F-1,-19.9067,13.9347,29.443,1,1,1,0,
F-2,-7.3939,-76.9499,17.5525,1,1,1,0,
F-3,81.7333,-42.9415,9.62559,1,1,1,0,
Definition of columns:
• label: label that is displayed next to each control point
• l, p, s: coordinate values in LPS coordinate system (in this case, l and a columns should not be used)
• r, a, s: coordinate values in RAS coordinate system (in this case, r and a columns should not be used)
• defined: 0 = the position of the point is not defined (coordinate values can be ignored; useful for creating templates); 1: the position is defined
• selected: 0 = unselected; 1 = selected (the control point appears with different colors an may be used as additional input for analysis)
• visible: 0 = hidden; 1 = visible
• locked: 0 = the point can be interactively moved; 1 = the point position is locked
• description: text providing additional information for the point
## Examples¶
Examples for common operations on transform are provided in the script repository. | {"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": 0.36273401975631714, "perplexity": 7029.710557287777}, "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/1642320300343.4/warc/CC-MAIN-20220117061125-20220117091125-00147.warc.gz"} |
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# Which of the following equations has a root in common with x^2 - 6x +
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Which of the following equations has a root in common with x^2 - 6x + [#permalink]
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05 Feb 2011, 23:47
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Which of the following equations has a root in common with $$x^2 - 6x + 5 = 0$$?
A. $$x^2 + 1 = 0$$
B. $$x^2 - x - 2 = 0$$
C. $$2x^2 - 2 = 0$$
D. $$x^2 - 2x - 3 = 0$$
E. $$x^2 - 10x - 5 = 0$$
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Posts: 1901
Re: Which of the following equations has a root in common with x^2 - 6x + [#permalink]
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06 Feb 2011, 01:38
1
1
x^2-6x+5=0
(x-1)(x-5)=0
roots are 1 and 5.
Substitute these roots in all the equations;
1.x^2+1=0
x=1; 1^2+1=1+1=2!=0. Not a root.
x=5; 5^2+1=25+1=26!=0. Not a root.
2.x^2-x-2=0
x=1; 1^2-1-2=-2!=0. Not a root.
x=5; 5^2-5-2=25-7=18!=0. Not a root.
3.x^2-10x-5=0
x=1; 1^2-10*1-5=-14!=0. Not a root.
x=5; 5^2-10*5-5=25-55=-30!=0. Not a root.
4.2x^2-2=0
x=1; 2*1^2-2=2-2=0=0. 1 is a root. We can stop here.
x=5; 2*5^2-2=50-2=48!=0. Not a root.
5. x^2-2x-3=0
x=1; 1^2-2*1-3=-3!=0. Not a root.
x=5; 5^2-2*5-3=12!=0. Not a root.
Ans: "D"
Let's expand the correct answer algebraically;
2x^2-2=0
2*x^2=2
x^2=1
x=+1 and x=-1
(2x-2)(x+1) = 0
So; 2x-2=0; x=2/2=1. "1 is also one of the roots in the equation(x^2-6x+5=0)"
x+1=0; x=-1.
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Re: Which of the following equations has a root in common with x^2 - 6x + [#permalink]
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06 Feb 2011, 05:21
I like more -finding roots and further substitution as you explained first. I cant understand second solving algebraically, because other equations also share x=1 root.
I appreciate your help. Thanks a lot
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Re: Which of the following equations has a root in common with x^2 - 6x + [#permalink]
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06 Feb 2011, 06:18
Lolaergasheva wrote:
I like more -finding roots and further substitution as you explained first. I cant understand second solving algebraically, because other equations also share x=1 root.
I appreciate your help. Thanks a lot
None of the other equations has either 1 or 5 as root.
1.
x^2+1=0
was factored as
"(x-1)(x+1)", which is not correct
(x-1)(x+1) = x^2 - 1^2 = x^2 - 1 and not {x^2 + 1}
The correct way of factoring it is;
x^2 = -1
Well I see that; it cannot be factored because $$x = \sqrt{-1}$$ will result in some imaginary number.
So; x^2+1=0 has zero roots.
2.
x^2-x-2=0
x^2-2x+x-2=0
x(x-2)+1(x-2)=0
(x+1)(x-2)=0
So roots are;
x+1=0; x=-1 (Not 1)
x-2=0; x=2
3.
x^2-10x-5=0
This has two solutions but cannot be factored like other equations;
We will have to use discriminant approach to find roots;
The two roots are;
$$Roots=\frac{-b \pm sqrt{b^2-4*a*c}}{2*a}$$
x^2-10x-5=0
can be written as
1x^2+(-10)x+(-5)=0
a=1
b=-10
c=-5
Plug these values in the formula;
$$Roots = \frac{-(-10) \pm sqrt{(-10)^2-4*1*(-5)}}{2*1}$$
$$Roots = \frac{10 \pm sqrt{100+20}}{2*1}$$
$$Roots = \frac{10 \pm sqrt{120}}{2}$$
$$Roots=5 \pm \frac{sqrt{120}}{2}$$
###$$\frac{sqrt{120}}{2} \approx 5.5$$###
$$Root_1 \approx 5+5.5=10.5$$
$$Root_2 \approx 5-5.5=-0.5$$
Neither of the roots is 1 or 5.
4.
2x^2-2=0
2(x^2-1)=0
x^2-1=0
x^2=1
i.e. x=1(This is the only place where the root is 1) and x=-1
5.
x^2-2x-3=0
x^2-3x+x-3=0
x(x-3)+1(x-3)=0
(x+1)(x-3)=0
x+1=0; x=-1(Not 1)
x-3=0; x=3
http://gmatclub.com/forum/algebra-101576.html#p787276
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Re: Which of the following equations has a root in common with x^2 - 6x + [#permalink]
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06 Feb 2011, 07:58
Thank you for the link and for correcting my mistakes.
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Re: Which of the following equations has a root in common with x^2 - 6x + [#permalink]
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06 Feb 2011, 11:02
Roots of x^2-6x+5=0 are 1 and 5
After scanning the answer choices, I chose easy equation 2x^2-2=0 which gives x = 1 or -1 So D
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Re: Which of the following equations has a root in common with x^2 - 6x + [#permalink]
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14 Nov 2011, 08:53
1
1
Easy question. $$x^2 - 6x + 5 = 0$$ factors into $$(x-1)(x-5)=0$$. Thus, roots are x=1 and x=5.
Do the same for each option:
A. $$x^2 + 1 = 0$$
$$x^2 = -1$$
roots are imaginary
B. $$x^2 - x - 2 = 0$$
$$(x-2)(x+1) = 0$$
roots are x=2 and x=-1
none match question
C. $$2x^2 - 2 = 0$$
$$2(x^2-1)=0$$
$$(x^2-1) = 0$$
$$(x-1)(x+1) = 0$$
roots are x=1 and x=-1
x=1 matches the root of original equation
No need to do the rest, we have our answer. However, if you have lots of time you may want to do them anyway to make sure you didn't make a mistake above. You'll know you made a mistake somewhere if any of the questions below also yield a root in common.
D. $$x^2 - 2x - 3 = 0$$
$$(x-3)(x+1) = 0$$
roots are x=3 and x=-1, no roots in common
E. $$x^2 - 10x - 5 = 0$$
doesn't factor into integers, no roots in common
Kudos if you like the explanation and/or nice formatting.
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Re: Which of the following equations has a root in common with x^2 - 6x + [#permalink]
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14 Nov 2011, 15:20
ok here is how I approached the problem:
I solved the equation to get the x value
x=5, x=1
and I solved each of the equations to see if any of the equations has a common factor with the equation in the stem quation.
non of the had anything in common except for C, which has x=1,x=-1.
hope that helps
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Re: Which of the following equations has a root in common with x^2 - 6x + [#permalink]
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14 Nov 2011, 22:56
Stoneface wrote:
Which of the following equations has a root in common with x^2 - 6x + 5 = 0?
A. x^2 + 1 = 0
B. x^2 - x - 2 = 0
C. 2x^2 - 2 = 0
D. x^2 - 2x - 3 = 0
E. x^2 - 10x - 5 = 0
The given equation can be simplified to (x-1)(x-5)=0
Roots are 1 and 5.
You don't need to find roots of each equation give as options
Just simplify each option
After quick inspection only E can have 5 as a probable root. So only check whether or not 1 is a root.
A. No real root
B. (x-2)(x+1)=0 [x=1 does not make the left hand side zero]
C. 2(x^2-1)=0 [x=1 does make the left hand side zero]
D. (x-3)(x+1)=0 [x=1 does not make the left hand side zero]
E. Don't care... by observation neither 1 nor 5 can be a root
Hence C
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Re: Which of the following equations has a root in common with x^2 - 6x + [#permalink]
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28 Dec 2015, 13:58
Which of the following has "A" root common. Only C has one root common with the equation in the question.
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Re: Which of the following equations has a root in common with x^2 - 6x + [#permalink]
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08 Jul 2016, 02:00
Lolaergasheva wrote:
Which of the following equations has a root in common with x^2 - 6x + 5 = 0?
A. x^2 + 1 = 0
B. x^2 - x - 2 = 0
C. 2x^2 - 2 = 0
D. x^2 - 2x - 3 = 0
E. x^2 - 10x - 5 = 0
x^2 - 6x + 5 = 0
(x-5)(x-1) = 0
The roots are 1 and 5
We need to check for each option to calculate the roots. This can be done by plugging in the values in the equations
(A) x2 + 1 = 0. None of 1 or 5 satisfies this equation
(B) x2 - x - 2 =0. None of 1 or 5 satisfies this equation
(C) 2x2 - 2 =0. x = 1 satisfies this equation. Hence this has a common root
(D) x2 - 2x - 3 =0. None of 1 or 5 satisfies this equation
(E) x^2 - 10x - 5 = 0. None of 1 or 5 satisfies this equation
Correct Option: C
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Posts: 2561
Re: Which of the following equations has a root in common with x^2 - 6x + [#permalink]
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24 Jan 2018, 15:45
Top Contributor
Lolaergasheva wrote:
Which of the following equations has a root in common with $$x^2 - 6x + 5 = 0$$?
A. $$x^2 + 1 = 0$$
B. $$x^2 - x - 2 = 0$$
C. $$2x^2 - 2 = 0$$
D. $$x^2 - 2x - 3 = 0$$
E. $$x^2 - 10x - 5 = 0$$
Step 1: Solve the given equation: x² – 6x + 5 = 0
This is a quadratic set equal to zero, so let's factor to get:
(x-1)(x-5)=0
So, we have two solutions (roots): x=1 or x=5
Step 2: Solve the other 5 equations to see which one has a root (solution) of x=1 or x=5
IMPORTANT: It appears that the only way to answer this question is to keep checking every single answer choice until we find that one that has a solution of either x=1 or x=5. Given this, where do you think the test-maker would hide the correct answer? In these situations, I always start at E and work my way up. Is the answer to these questions always E (or perhaps D)? No, but it's more likely that the correct answer is near the bottom.
Okay, E: x² – 2x – 3 =0
Factor to get: (x-3)(x+1)=0
So, x=3 or x=-1
No shared solutions (roots) so keep moving.
D: 2x² – 2 =0
Factor: 2(x² - 1) = 0
Keep factoring: 2(x+1)(x-1)=0
So, x=1 or x=-1
We have a common solution, so the correct answer must be D
Cheers,
Brent
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Re: Which of the following equations has a root in common with x^2 - 6x + [#permalink]
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25 Mar 2018, 10:16
Lolaergasheva wrote:
Which of the following equations has a root in common with $$x^2 - 6x + 5 = 0$$?
A. $$x^2 + 1 = 0$$
B. $$x^2 - x - 2 = 0$$
C. $$2x^2 - 2 = 0$$
D. $$x^2 - 2x - 3 = 0$$
E. $$x^2 - 10x - 5 = 0$$
is my approach correct ?
so from here $$x^2 - 6x + 5 = 0$$ we have:
Root one = 1
Root two = 5
so i simply plugged one of these roots ( i took 1 ) in all answer choices and only C yielded ZERO
is it correct?
not sure about 5 though Am i just lucky to answer correctly?:)
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Joined: 12 Sep 2015
Posts: 2561
Re: Which of the following equations has a root in common with x^2 - 6x + [#permalink]
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25 Mar 2018, 10:27
1
Top Contributor
1
dave13 wrote:
Lolaergasheva wrote:
Which of the following equations has a root in common with $$x^2 - 6x + 5 = 0$$?
A. $$x^2 + 1 = 0$$
B. $$x^2 - x - 2 = 0$$
C. $$2x^2 - 2 = 0$$
D. $$x^2 - 2x - 3 = 0$$
E. $$x^2 - 10x - 5 = 0$$
is my approach correct ?
so from here $$x^2 - 6x + 5 = 0$$ we have:
Root one = 1
Root two = 5
so i simply plugged one of these roots ( i took 1 ) in all answer choices and only C yielded ZERO
is it correct?
not sure about 5 though Am i just lucky to answer correctly?:)
Perfect approach!
Cheers,
Brent
_________________
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Re: Which of the following equations has a root in common with x^2 - 6x + [#permalink] 25 Mar 2018, 10:27
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": 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": 0.721785306930542, "perplexity": 1980.1173807307428}, "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-2018-26/segments/1529267863489.85/warc/CC-MAIN-20180620065936-20180620085936-00507.warc.gz"} |
https://openstax.org/books/college-algebra-2e/pages/8-practice-test | College Algebra 2e
# Practice Test
College Algebra 2ePractice Test
### Practice Test
For the following exercises, write the equation in standard form and state the center, vertices, and foci.
1.
$x 2 9 + y 2 4 =1 x 2 9 + y 2 4 =1$
2.
$9 y 2 +16 x 2 −36y+32x−92=0 9 y 2 +16 x 2 −36y+32x−92=0$
For the following exercises, sketch the graph, identifying the center, vertices, and foci.
3.
$( x−3 ) 2 64 + ( y−2 ) 2 36 =1 ( x−3 ) 2 64 + ( y−2 ) 2 36 =1$
4.
$2 x 2 + y 2 +8x−6y−7=0 2 x 2 + y 2 +8x−6y−7=0$
5.
Write the standard form equation of an ellipse with a center at $( 1,2 ), ( 1,2 ),$ vertex at $( 7,2 ), ( 7,2 ),$ and focus at $( 4,2 ). ( 4,2 ).$
6.
A whispering gallery is to be constructed with a length of 150 feet. If the foci are to be located 20 feet away from the wall, how high should the ceiling be?
For the following exercises, write the equation of the hyperbola in standard form, and give the center, vertices, foci, and asymptotes.
7.
$x 2 49 − y 2 81 =1 x 2 49 − y 2 81 =1$
8.
$16 y 2 −9 x 2 +128y+112=0 16 y 2 −9 x 2 +128y+112=0$
For the following exercises, graph the hyperbola, noting its center, vertices, and foci. State the equations of the asymptotes.
9.
$( x−3 ) 2 25 − ( y+3 ) 2 1 =1 ( x−3 ) 2 25 − ( y+3 ) 2 1 =1$
10.
$y 2 − x 2 +4y−4x−18=0 y 2 − x 2 +4y−4x−18=0$
11.
Write the standard form equation of a hyperbola with foci at $( 1,0 ) ( 1,0 )$ and $( 1,6 ), ( 1,6 ),$ and a vertex at $( 1,2 ). ( 1,2 ).$
For the following exercises, write the equation of the parabola in standard form, and give the vertex, focus, and equation of the directrix.
12.
$y 2 +10x=0 y 2 +10x=0$
13.
$3 x 2 −12x−y+11=0 3 x 2 −12x−y+11=0$
For the following exercises, graph the parabola, labeling the vertex, focus, and directrix.
14.
$( x−1 ) 2 =−4( y+3 ) ( x−1 ) 2 =−4( y+3 )$
15.
$y 2 +8x−8y+40=0 y 2 +8x−8y+40=0$
16.
Write the equation of a parabola with a focus at $( 2,3 ) ( 2,3 )$ and directrix $y=−1. y=−1.$
17.
A searchlight is shaped like a paraboloid of revolution. If the light source is located 1.5 feet from the base along the axis of symmetry, and the depth of the searchlight is 3 feet, what should the width of the opening be?
For the following exercises, determine which conic section is represented by the given equation, and then determine the angle $θ θ$ that will eliminate the $xy xy$ term.
18.
$3 x 2 −2xy+3 y 2 =4 3 x 2 −2xy+3 y 2 =4$
19.
$x 2 +4xy+4 y 2 +6x−8y=0 x 2 +4xy+4 y 2 +6x−8y=0$
For the following exercises, rewrite in the $x ′ y ′ x ′ y ′$ system without the $x ′ y ′ x ′ y ′$ term, and graph the rotated graph.
20.
$11 x 2 +10 3 xy+ y 2 =4 11 x 2 +10 3 xy+ y 2 =4$
21.
$16 x 2 +24xy+9 y 2 −125x=0 16 x 2 +24xy+9 y 2 −125x=0$
For the following exercises, identify the conic with focus at the origin, and then give the directrix and eccentricity.
22.
$r= 3 2−sinθ r= 3 2−sinθ$
23.
$r= 5 4+6cosθ r= 5 4+6cosθ$
For the following exercises, graph the given conic section. If it is a parabola, label vertex, focus, and directrix. If it is an ellipse or a hyperbola, label vertices and foci.
24.
$r= 12 4−8sinθ r= 12 4−8sinθ$
25.
$r= 2 4+4sinθ r= 2 4+4sinθ$
26.
Find a polar equation of the conic with focus at the origin, eccentricity of $e=2, e=2,$ and directrix: $x=3. x=3.$
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As an Amazon Associate we earn from qualifying purchases. | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 34, "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": 0.5005343556404114, "perplexity": 620.2321889516461}, "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-2022-49/segments/1669446710974.36/warc/CC-MAIN-20221204140455-20221204170455-00079.warc.gz"} |
http://mathhelpforum.com/differential-equations/123627-find-inverse-laplace-1-a.html | # Thread: Find the inverse laplace of 1
1. ## Find the inverse laplace of 1
$\displaystyle l^{-1}(1)$ = ??!
2. Originally Posted by General
$\displaystyle l^{-1}(1)$ = ??!
It's the Dirac delta function.
$\displaystyle \mathcal{L} [\delta] = \int_0^{\infty} e^{-sx} \delta (x) dx = e^{-s . 0} = 1$ ,
since
$\displaystyle \int_{- \infty}^{\infty} \phi (x) \delta (x) dx = \phi(0)$
3. The question is a source of some little controversial... according to the definition of $\displaystyle \delta (*)$ given in Wolfram MathWorld , probably the most 'reliable' mathematical site in the Web, is...
http://mathworld.wolfram.com/DeltaFunction.html
$\displaystyle \delta (t)= \frac {d}{dt} \mathcal {H} (t)$ (1)
... where $\displaystyle \mathcal {H} (*)$ is the 'Heaviside Step Function' defined as...
http://mathworld.wolfram.com/HeavisideStepFunction.html
$\displaystyle \mathcal{H} (t)= \left\{\begin{array}{cc} 0,&\mbox { if } t<0\\ \frac{1}{2},&\mbox{ if } t=0\\1,&\mbox{ if } t>0\end{array}\right.$ (2)
Now, according to the basic properties of the Laplace Transform...
http://mathworld.wolfram.com/LaplaceTransform.html
..., we have...
$\displaystyle \mathcal{L} \{\mathcal{H} (t)\}= \frac {1}{s}$ (3)
... and for every $\displaystyle f(*)$ ...
$\displaystyle \mathcal{L} \{\frac{d}{dt} f(t)\}= s\cdot \mathcal{L} \{f(t)\} - f(0)$ (4)
Now if we combine (1), (2), (3) and (4) we obtain...
$\displaystyle \mathcal {L} \{\delta(t)\}= s\cdot \frac{1}{s} -\frac{1}{2} = \frac{1}{2}$ (5)
... so that it would be...
$\displaystyle \mathcal {L}^{-1} \{1\}= 2\cdot \delta(t)$ (6)
... just a little surprising! ...
Kind regards
$\displaystyle \chi$ $\displaystyle \sigma$
4. Originally Posted by chisigma
... so that it would be...
$\displaystyle \mathcal {L}^{-1} \{1\}= 2\cdot \delta(t)$ (6)
... just a little surprising! ...
All you're proving here, is that delta can not be considered as a function. The inverse laplace transform of 1 does not exist as a function. However, the laplace inverse of 1 is $\displaystyle \delta$, which is the Dirac distribution, in the sense of distributions.
When you say:
... and for every $\displaystyle f(*)$ ...
$\displaystyle \mathcal{L} \{\frac{d}{dt} f(t)\}= s\cdot \mathcal{L} \{f(t)\} - f(0)$ (4)
this is not true for distributions, where the formula doesn't have the $\displaystyle -f(0)$ term: $\displaystyle \mathcal{L}(T')(s)=s \mathcal{L}(T)$. Indeed, this border term is included in the differentiation: steps in the function $\displaystyle f$ give Dirac terms in the differential of $\displaystyle f$ in the sense of distributions. If you use distributions in the result, you must use a derivative in the sense of distributions for everything to make sense.
By the way, as a distribution, the Heaviside function doesn't have a specific value at 0. It is customary to choose it to be 0 for symmetry reasons, but it could be anything when we consider $\displaystyle \mathcal{H}$ as a distribution (for instance, when we differentiate it).
And Pomp's justification was also correct (except for the use of the word "function" and a slight abuse of notation in writing delta in an integral like physicists do...)
5. Originally Posted by Laurent
And Pomp's justification was also correct (except for the use of the word "function" and a slight abuse of notation in writing delta in an integral like physicists do...)
Actually I don't think it is, he ought to more careful since $\displaystyle 0$ is one of the limits of integration and what one thinks:
$\displaystyle \int_0^{\infty} e^{-st}\delta(t) \; dt$
is short hand for is now not at all clear. If we take it as the limit of integrals where $\displaystyle \delta$ is replaced by functions whose support becomes more and more concentrated near the origin and with integrals all $\displaystyle 1$ what we get depends on the form of these functions and in this case could give any value between $\displaystyle 0$ and $\displaystyle 1$.
The sort of intuitive use that physicists and engineers make of $\displaystyle \delta$ fails here and one has to be more careful.
CB
6. Originally Posted by CaptainBlack
what one thinks:
$\displaystyle \int_0^{\infty} e^{-st}\delta(t) \; dt$
is short hand for is now not at all clear.
Sure, that's the kind of thing I meant talking about "abuses of notation"... The integral should run from $\displaystyle -\infty$ (or any $\displaystyle -\varepsilon$) to $\displaystyle +\infty$ to be "a little" less controversial. Laplace transform is defined for distributions that are supported by $\displaystyle [0,\infty)$ (but not for any of these) hence the values on the negative axis don't matter. In fact, it is really not easy to define the Laplace transform of distributions properly; formally, it should be $\displaystyle \mathcal{L}(T)(z)=\langle T, t\mapsto e^{-tz}\rangle$ when one is able to make this make sense.
7. Seems I inadvertently opened a can of worms!
The notation I used was for convenience. Thanks for the pointers, I'll be more careful in future. | {"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": 0.9716771245002747, "perplexity": 389.39837376514834}, "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-2018-22/segments/1526794867254.84/warc/CC-MAIN-20180525235049-20180526015049-00353.warc.gz"} |
https://kb.osu.edu/dspace/handle/1811/19747 | # Knowledge Bank
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# EXPERIMENTAL MANIFESTATIONS OF THE JAHN-TELLER EFFECT
Please use this identifier to cite or link to this item: http://hdl.handle.net/1811/19747
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Title: EXPERIMENTAL MANIFESTATIONS OF THE JAHN-TELLER EFFECT Creators: Barckholtz, Timothy A. Issue Date: 2000 Abstract: Molecules in orbitally degenerate states are subject to a number of effects that typical molecules are not. One such effect is Jahn-Teller coupling, which is the coupling between the vibrational and electronic angular momenta. This talk will review how Jahn-Teller coupling is manifested in the spectroscopy of molecules in degenerate electronic states. Both the vibronic and rovibronic structure of these states will be covered, with particular emphasis on the additional complications that occur when spin-orbit coupling is significant. The electronic spectra of the methoxy radicals ($CH_{3}O, CH_{3}S, CF_{3}O$, and $CF_{3}S$) and of the Cp radical ($C_{5}H_{5}$) will be used to illustrate how the Jahn-Teller effect can be observed experimentally. Lastly, it will be shown how recently developed ab initio methods can be used to aid in the interpretation of the experimental spectra of Jahn-Teller molecules. URI: http://hdl.handle.net/1811/19747 Other Identifiers: 2000-RD-01 | {"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": 0.611899197101593, "perplexity": 2823.4358242018566}, "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/1397609535745.0/warc/CC-MAIN-20140416005215-00001-ip-10-147-4-33.ec2.internal.warc.gz"} |
https://worldwidescience.org/topicpages/r/reported+close+relations.html | Sample records for reported close relations
1. The relation between anorexic symptoms in women and their reports of trustworthiness in interactions with close persons.
Science.gov (United States)
Rotenberg, Ken J; Edwards, Kelley
2017-08-01
The study examined the relation between women's anorexic symptoms and their reports of trustworthiness in interactions with close persons. Ninety-eight females (mean age=24years-10months) completed the anorexic symptom subscale of the SEDS and reported (ascribed) the extent to which they showed reliability, emotional, and honesty trustworthiness behaviors in interactions with their mother, father, and close friend. Negative linear relations were found between anorexic symptoms and ascribed: (a) trustworthiness with close friends; (b) reliability trustworthiness; and (c) at a trend level, honesty trustworthiness. These were qualified by curvilinear relations and by elevated anorexic vs normative group comparisons. It was found that women with elevated anorexic symptoms ascribed lower trustworthiness than did women with the normal range of anorexic symptoms. The findings were interpreted as supporting the conclusion that women with elevated levels of anorexic symptoms are inclined to believe that they are deceptive in their interactions with close persons, primarily friends. Copyright © 2017 Elsevier Ltd. All rights reserved.
2. FINAL CLOSE-OUT REPORT
Energy Technology Data Exchange (ETDEWEB)
Mark A. Carl
2004-08-03
The Interstate Oil and Gas Compact Commission (IOGCC) engaged in numerous projects outlined under the scope of work discussed in the United States Department of Energy (DOE) grant number DE-FG26-01BC15336 awarded to the IOGCC. Numerous projects were completed that were extremely valuable to state oil and gas agencies as a result of work performed utilizing resources provided by the grant. There are numerous areas in which state agencies still need assistance. This additional assistance will need to be addressed under another grant because funding resources have been exhausted under The scope of work objectives for the eight projects covered under this grant is as follows: (1) Improve uniformity within state oil and gas data management efforts. (2) Conduct environmental compliance workshops and related educational projects on natural gas and oil exploration and production. (3) Improve regulatory efficiency through partnering opportunities provided by the Appalachian Illinois Basin Directors. (4) Promote the development and implementation of risk-based environmental regulation at the state level through an expertise-sharing program that brings stakeholders together to develop guidelines and models to meet regulatory challenges. (5) Support the IOGCC's regulatory streamlining efforts, including the identification and elimination of unnecessary duplications of effort between state and federal programs dealing with exploration and production on public lands, and identify the need to enhance and regionalize regulatory coordination and cooperation among the states. (6) Involve states and provinces of Canada that have offshore petroleum exploration and production in a regulatory sharing alliance to identify areas of concern that may be incorporated into standard practices for offshore environmental and regulatory compliance. (7) Coordinate efforts with the U.S. Environmental Protection Agency (EPA) to ensure that adequate information is available to the public
3. Pooling ASR data for closely related languages
CSIR Research Space (South Africa)
Van Heerden, C
2010-05-01
Full Text Available We describe several experiments that were conducted to assess the viability of data pooling as a means to improve speech-recognition performance for under-resourced languages. Two groups of closely related languages from the Southern Bantu language...
4. Sexual disclosures: connections to relational satisfaction and closeness.
Science.gov (United States)
Coffelt, Tina A; Hess, Jon A
2014-01-01
This study examines sexual communication by describing the content of sexual disclosures within marital relationships and assessing the association between sexual disclosures and relational outcomes, specifically relational satisfaction and closeness. A survey administered to 293 married individuals (58% female) who had an average age of 40 years (range = 20-73), 13.7 years of marriage (range = 1 month to 54 years), and who reported high levels of relational satisfaction assessed the relation between the content of sexual disclosures and satisfaction and closeness. While sexual disclosures are made infrequently, positive affect and sexual preferences are disclosed more than negative topics and disclosing sexual information is positively related to relationship satisfaction, rρ(280) =.26, p sexual information and relationship satisfaction and closeness, as reported by individuals experiencing relationship satisfaction.
5. Social comparison orientation as related to two types of closeness
NARCIS (Netherlands)
Buunk, Abraham P.; Dijkstra, Pieternel; Bosch, Zwenneke A.; Dijkstra, Arie; Barelds, Dick P. H.
Two studies examined the relationship between social comparison orientation (SCO) and two types of closeness (dimensional closeness and psychological closeness) in the context of appearance-related comparisons among women. A pilot study showed that these two types were relatively independent
6. 12 CFR 225.123 - Activities closely related to banking.
Science.gov (United States)
2010-01-01
... 12 Banks and Banking 3 2010-01-01 2010-01-01 false Activities closely related to banking. 225.123 Section 225.123 Banks and Banking FEDERAL RESERVE SYSTEM (CONTINUED) BOARD OF GOVERNORS OF THE FEDERAL... Holding Companies Interpretations § 225.123 Activities closely related to banking. (a) Effective June 15...
7. 12 CFR 225.129 - Activities closely related to banking.
Science.gov (United States)
2010-01-01
... 12 Banks and Banking 3 2010-01-01 2010-01-01 false Activities closely related to banking. 225.129 Section 225.129 Banks and Banking FEDERAL RESERVE SYSTEM (CONTINUED) BOARD OF GOVERNORS OF THE FEDERAL... Holding Companies Interpretations § 225.129 Activities closely related to banking. Courier activities. The...
8. Tonal bilingualism : the case of two closely related Chinese dialects
NARCIS (Netherlands)
Wu, Junru
2015-01-01
Tonal bilinguals of two closely related Chinese dialects handle two tonal systems in their mind; their two vocabularies are from closely related dialects; and they write translation equivalents with common Chinese characters. Their unique language situation makes their mind special. This thesis inve
9. Close pairs of relative equilibria for identical point vortices
DEFF Research Database (Denmark)
Dirksen, Tobias; Aref, Hassan
2011-01-01
Numerical solution of the classical problem of relative equilibria for identical point vortices on the unbounded plane reveals configurations that are very close to the analytically known, centered, symmetrically arranged, nested equilateral triangles. New numerical solutions of this kind are found...... also has this property, and new relative equilibria close to the nested, symmetrically arranged, regular heptagons have been found. The centered regular nonagon is also marginally stable. Again, a new family of close relative equilibria has been found. The closest relative equilibrium pairs occur...
10. 46 CFR 308.533 - Closing report, Form MA-313.
Science.gov (United States)
2010-10-01
... 46 Shipping 8 2010-10-01 2010-10-01 false Closing report, Form MA-313. 308.533 Section 308.533 Shipping MARITIME ADMINISTRATION, DEPARTMENT OF TRANSPORTATION EMERGENCY OPERATIONS WAR RISK INSURANCE War Risk Cargo Insurance Ii-Open Policy War Risk Cargo Insurance § 308.533 Closing report, Form...
11. Competitive strategies differentiate closely related species of marine actinobacteria
National Research Council Canada - National Science Library
Patin, Nastassia V; Duncan, Katherine R; Dorrestein, Pieter C; Jensen, Paul R
2016-01-01
... to the functional traits and evolutionary processes that led to their divergence. Here we show that two closely related marine actinomycete species can be differentiated based on competitive strategies...
12. Differentiation of closely related fungi by electronic nose analysis
DEFF Research Database (Denmark)
Karlshøj, Kristian; Nielsen, Per Væggemose; Larsen, Thomas Ostenfeld
2007-01-01
In this work the potential of electronic nose analysis for differentiation of closely related fun has been described. A total of 20 isolates of the cheese-associated species Geotrichum candidum, Penicillium camemberti, P.nordicum, and Proqueford and its closely related species P paneum, P carneum...... as well as the noacheese ociated P. expansum have been investigated by electronic nose, GC-MS, and LGMS analysis. The isolates were inoculated on yeast extract sucroseagar in 20-mL headspace flasks and electronicnose analysis was performed daily for a-74period. To assess which volatile metabolites...... by high pressure liquid chromatography, coupled-to a diode array detector and a time of flight mass spectrometer. Several mycotoxins were detected in samples from the specles P.nordicum, P.roqueforti, P.paneum, P.carneum, and P.expansum. Differentiation of closely related mycotoxin producing fungi...
13. Ulnar nerve palsy after closed forearm fracture: a case report
Directory of Open Access Journals (Sweden)
Levent Kucuk
2012-04-01
Full Text Available Closed double bone forearm fractures are among the most common fractures of childhood. These fractures often heal without problems with closed reduction and casting. The leading complications are known as malunion and compartment syndrome. The reports about nerve injuries related with these fractures are very limited. We present an eight years old boy who admitted to our hospital with ulnar nerve palsy symptomps three months after his initial trauma. His initial trauma was a simple fall which caused radius and ulna fractures. Radiological assessment showed proper union of the fractures. We performed surgical exploration to the ulnar nerve. We found a trapped and damaged nerve in the fracture region. Even though the rate of complications about nerve injuries are extremely rare in forearm fractures, neurologic examinations should be performed before and after the reduction maneuvers. Neurologic examination will be not only a guide for fracture management but also an important point for medicolegal problems. [Hand Microsurg 2012; 1(1.000: 30-32
14. Comparative Genomics via Wavelet Analysis for Closely Related Bacteria
Directory of Open Access Journals (Sweden)
Jiuzhou Song
2004-01-01
Full Text Available Comparative genomics has been a valuable method for extracting and extrapolating genome information among closely related bacteria. The efficiency of the traditional methods is extremely influenced by the software method used. To overcome the problem here, we propose using wavelet analysis to perform comparative genomics. First, global comparison using wavelet analysis gives the difference at a quantitative level. Then local comparison using keto-excess or purine-excess plots shows precise positions of inversions, translocations, and horizontally transferred DNA fragments. We firstly found that the level of energy spectra difference is related to the similarity of bacteria strains; it could be a quantitative index to describe the similarities of genomes. The strategy is described in detail by comparisons of closely related strains: S.typhi CT18, S.typhi Ty2, S.typhimurium LT2, H.pylori 26695, and H.pylori J99.
15. Comparative Genomics via Wavelet Analysis for Closely Related Bacteria
Science.gov (United States)
Song, Jiuzhou; Ware, Tony; Liu, Shu-Lin; Surette, M.
2004-12-01
Comparative genomics has been a valuable method for extracting and extrapolating genome information among closely related bacteria. The efficiency of the traditional methods is extremely influenced by the software method used. To overcome the problem here, we propose using wavelet analysis to perform comparative genomics. First, global comparison using wavelet analysis gives the difference at a quantitative level. Then local comparison using keto-excess or purine-excess plots shows precise positions of inversions, translocations, and horizontally transferred DNA fragments. We firstly found that the level of energy spectra difference is related to the similarity of bacteria strains; it could be a quantitative index to describe the similarities of genomes. The strategy is described in detail by comparisons of closely related strains: S.typhi CT18, S.typhi Ty2, S.typhimurium LT2, H.pylori 26695, and H.pylori J99.
16. School Counselors: Closing Achievement Gaps and Writing Results Reports
Science.gov (United States)
Hartline, Julie; Cobia, Debra
2012-01-01
Charged with closing the achievement gap for marginalized students, school counselors need to be able to identify gaps, develop interventions, evaluate effectiveness, and share results. This study examined 100 summary results reports submitted by school counselors after having received four days of training on the ASCA National Model. Findings…
17. Rations of Closely Related Elements in Soil and Their Inplications
Institute of Scientific and Technical Information of China (English)
XINGGUANG－XI; HOUWEN－HUA; 等
1991-01-01
This paper has investigated the ratios of closely related elements such as Mn,Cr,V,Ni,Co,Cu,Pb,Cd,Ba,Sr,La and Ce in the major soils of China,and the factors affecting them,and explored their use as indicators in soil formation,material transport and environmental pollution.Results show that the effect of soil-forming processes on the ratios of closely related elements varied with different elements,and became greater in the sequence of Ce/La grassland soils>desert soils and increasing gradually from the semi-arid subhumid zone soils>the temperate zone neutral soils>the north subtropic zone soils>tropical and subtropical acid soils.
18. Extracted facial feature of racial closely related faces
Science.gov (United States)
Liewchavalit, Chalothorn; Akiba, Masakazu; Kanno, Tsuneo; Nagao, Tomoharu
2010-02-01
Human faces contain a lot of demographic information such as identity, gender, age, race and emotion. Human being can perceive these pieces of information and use it as an important clue in social interaction with other people. Race perception is considered the most delicacy and sensitive parts of face perception. There are many research concerning image-base race recognition, but most of them are focus on major race group such as Caucasoid, Negroid and Mongoloid. This paper focuses on how people classify race of the racial closely related group. As a sample of racial closely related group, we choose Japanese and Thai face to represents difference between Northern and Southern Mongoloid. Three psychological experiment was performed to study the strategies of face perception on race classification. As a result of psychological experiment, it can be suggested that race perception is an ability that can be learn. Eyes and eyebrows are the most attention point and eyes is a significant factor in race perception. The Principal Component Analysis (PCA) was performed to extract facial features of sample race group. Extracted race features of texture and shape were used to synthesize faces. As the result, it can be suggested that racial feature is rely on detailed texture rather than shape feature. This research is a indispensable important fundamental research on the race perception which are essential in the establishment of human-like race recognition system.
19. MHC adaptive divergence between closely related and sympatric African cichlids.
Directory of Open Access Journals (Sweden)
Jonatan Blais
Full Text Available BACKGROUND: The haplochromine cichlid species assemblages of Lake Malawi and Victoria represent some of the most important study systems in evolutionary biology. Identifying adaptive divergence between closely-related species can provide important insights into the processes that may have contributed to these spectacular radiations. Here, we studied a pair of sympatric Lake Malawi species, Pseudotropheus fainzilberi and P. emmiltos, whose reproductive isolation depends on olfactory communication. We tested the hypothesis that these species have undergone divergent selection at MHC class II genes, which are known to contribute to olfactory-based mate choice in other taxa. METHODOLOGY/PRINCIPAL FINDINGS: Divergent selection on functional alleles was inferred from the higher genetic divergence at putative antigen binding sites (ABS amino acid sequences than at putatively neutrally evolving sites at intron 1, exon 2 synonymous sequences and exon 2 amino acid residues outside the putative ABS. In addition, sympatric populations of these fish species differed significantly in communities of eukaryotic parasites. CONCLUSIONS/SIGNIFICANCE: We propose that local host-parasite coevolutionary dynamics may have driven adaptive divergence in MHC alleles, influencing odor-mediated mate choice and leading to reproductive isolation. These results provide the first evidence for a novel mechanism of adaptive speciation and the first evidence of adaptive divergence at the MHC in closely related African cichlid fishes.
20. eShadow: A tool for comparing closely related sequences
Energy Technology Data Exchange (ETDEWEB)
Ovcharenko, Ivan; Boffelli, Dario; Loots, Gabriela G.
2004-01-15
Primate sequence comparisons are difficult to interpret due to the high degree of sequence similarity shared between such closely related species. Recently, a novel method, phylogenetic shadowing, has been pioneered for predicting functional elements in the human genome through the analysis of multiple primate sequence alignments. We have expanded this theoretical approach to create a computational tool, eShadow, for the identification of elements under selective pressure in multiple sequence alignments of closely related genomes, such as in comparisons of human to primate or mouse to rat DNA. This tool integrates two different statistical methods and allows for the dynamic visualization of the resulting conservation profile. eShadow also includes a versatile optimization module capable of training the underlying Hidden Markov Model to differentially predict functional sequences. This module grants the tool high flexibility in the analysis of multiple sequence alignments and in comparing sequences with different divergence rates. Here, we describe the eShadow comparative tool and its potential uses for analyzing both multiple nucleotide and protein alignments to predict putative functional elements. The eShadow tool is publicly available at http://eshadow.dcode.org/
1. Climate-induced range overlap among closely related species
Science.gov (United States)
Krosby, Meade; Wilsey, Chad B.; McGuire, Jenny L.; Duggan, Jennifer M.; Nogeire, Theresa M.; Heinrichs, Julie A.; Tewksbury, Joshua J.; Lawler, Joshua J.
2015-09-01
Contemporary climate change is causing large shifts in biotic distributions, which has the potential to bring previously isolated, closely related species into contact. This has led to concern that hybridization and competition could threaten species persistence. Here, we use bioclimatic models to show that future range overlap by the end of the century is predicted for only 6.4% of isolated, congeneric species pairs of New World birds, mammals and amphibians. Projected rates of climate-induced overlap are higher for birds (11.6%) than for mammals (4.4%) or amphibians (3.6%). As many species will have difficulty tracking shifting climates, actual rates of future overlap are likely to be far lower, suggesting that hybridization and competition impacts may be relatively modest.
2. Carbapenem resistance in a human clinical isolate identified to be closely related to Acinetobacter indicus.
Science.gov (United States)
Bonnin, Rémy A; Poirel, Laurent; van der Reijden, Tanny J K; Dijkshoorn, Lenie; Lescat, Mathilde; Nordmann, Patrice
2014-10-01
Here we report a case of carbapenem resistance in a human clinical isolate that was found to be closely related to the newly described environmental species Acinetobacter indicus. This strain harboured the blaOXA-23 carbapenemase gene located on a conjugative plasmid. Partial sequencing of 16S rDNA and rpoB genes, together with matrix-assisted laser desorption/ionisation time-of-flight (MALDI-TOF) analysis, showed that this strain was distantly related to the Acinetobacter baumannii-calcoaceticus complex and was closely related to A. indicus.
3. Detecting Horizontal Gene Transfer between Closely Related Taxa.
Directory of Open Access Journals (Sweden)
2015-10-01
Full Text Available Horizontal gene transfer (HGT, the transfer of genetic material between organisms, is crucial for genetic innovation and the evolution of genome architecture. Existing HGT detection algorithms rely on a strong phylogenetic signal distinguishing the transferred sequence from ancestral (vertically derived genes in its recipient genome. Detecting HGT between closely related species or strains is challenging, as the phylogenetic signal is usually weak and the nucleotide composition is normally nearly identical. Nevertheless, there is a great importance in detecting HGT between congeneric species or strains, especially in clinical microbiology, where understanding the emergence of new virulent and drug-resistant strains is crucial, and often time-sensitive. We developed a novel, self-contained technique named Near HGT, based on the synteny index, to measure the divergence of a gene from its native genomic environment and used it to identify candidate HGT events between closely related strains. The method confirms candidate transferred genes based on the constant relative mutability (CRM. Using CRM, the algorithm assigns a confidence score based on "unusual" sequence divergence. A gene exhibiting exceptional deviations according to both synteny and mutability criteria, is considered a validated HGT product. We first employed the technique to a set of three E. coli strains and detected several highly probable horizontally acquired genes. We then compared the method to existing HGT detection tools using a larger strain data set. When combined with additional approaches our new algorithm provides richer picture and brings us closer to the goal of detecting all newly acquired genes in a particular strain.
4. Competitive strategies differentiate closely related species of marine actinobacteria.
Science.gov (United States)
Patin, Nastassia V; Duncan, Katherine R; Dorrestein, Pieter C; Jensen, Paul R
2016-02-01
Although competition, niche partitioning, and spatial isolation have been used to describe the ecology and evolution of macro-organisms, it is less clear to what extent these principles account for the extraordinary levels of bacterial diversity observed in nature. Ecological interactions among bacteria are particularly challenging to address due to methodological limitations and uncertainties over how to recognize fundamental units of diversity and link them to the functional traits and evolutionary processes that led to their divergence. Here we show that two closely related marine actinomycete species can be differentiated based on competitive strategies. Using a direct challenge assay to investigate inhibitory interactions with members of the bacterial community, we observed a temporal difference in the onset of inhibition. The majority of inhibitory activity exhibited by Salinispora arenicola occurred early in its growth cycle and was linked to antibiotic production. In contrast, most inhibition by Salinispora tropica occurred later in the growth cycle and was more commonly linked to nutrient depletion or other sources. Comparative genomics support these differences, with S. arenicola containing nearly twice the number of secondary metabolite biosynthetic gene clusters as S. tropica, indicating a greater potential for secondary metabolite production. In contrast, S. tropica is enriched in gene clusters associated with the acquisition of growth-limiting nutrients such as iron. Coupled with differences in growth rates, the results reveal that S. arenicola uses interference competition at the expense of growth, whereas S. tropica preferentially employs a strategy of exploitation competition. The results support the ecological divergence of two co-occurring and closely related species of marine bacteria by providing evidence they have evolved fundamentally different strategies to compete in marine sediments.
5. Evolution of transcriptional regulation in closely related bacteria
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Tsoy Olga V
2012-10-01
Full Text Available Abstract Background The exponential growth of the number of fully sequenced genomes at varying taxonomic closeness allows one to characterize transcriptional regulation using comparative-genomics analysis instead of time-consuming experimental methods. A transcriptional regulatory unit consists of a transcription factor, its binding site and a regulated gene. These units constitute a graph which contains so-called “network motifs”, subgraphs of a given structure. Here we consider genomes of closely related Enterobacteriales and estimate the fraction of conserved network motifs and sites as well as positions under selection in various types of non-coding regions. Results Using a newly developed technique, we found that the highest fraction of positions under selection, approximately 50%, was observed in synvergon spacers (between consecutive genes from the same strand, followed by ~45% in divergon spacers (common 5’-regions, and ~10% in convergon spacers (common 3’-regions. The fraction of selected positions in functional regions was higher, 60% in transcription factor-binding sites and ~45% in terminators and promoters. Small, but significant differences were observed between Escherichia coli and Salmonella enterica. This fraction is similar to the one observed in eukaryotes. The conservation of binding sites demonstrated some differences between types of regulatory units. In E. coli, strains the interactions of the type “local transcriptional factor gene” turned out to be more conserved in feed-forward loops (FFLs compared to non-motif interactions. The coherent FFLs tend to be less conserved than the incoherent FFLs. A natural explanation is that the former imply functional redundancy. Conclusions A naïve hypothesis that FFL would be highly conserved turned out to be not entirely true: its conservation depends on its status in the transcriptional network and also from its usage. The fraction of positions under selection in
6. Elucidation of operon structures across closely related bacterial genomes.
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Chuan Zhou
Full Text Available About half of the protein-coding genes in prokaryotic genomes are organized into operons to facilitate co-regulation during transcription. With the evolution of genomes, operon structures are undergoing changes which could coordinate diverse gene expression patterns in response to various stimuli during the life cycle of a bacterial cell. Here we developed a graph-based model to elucidate the diversity of operon structures across a set of closely related bacterial genomes. In the constructed graph, each node represents one orthologous gene group (OGG and a pair of nodes will be connected if any two genes, from the corresponding two OGGs respectively, are located in the same operon as immediate neighbors in any of the considered genomes. Through identifying the connected components in the above graph, we found that genes in a connected component are likely to be functionally related and these identified components tend to form treelike topology, such as paths and stars, corresponding to different biological mechanisms in transcriptional regulation as follows. Specifically, (i a path-structure component integrates genes encoding a protein complex, such as ribosome; and (ii a star-structure component not only groups related genes together, but also reflects the key functional roles of the central node of this component, such as the ABC transporter with a transporter permease and substrate-binding proteins surrounding it. Most interestingly, the genes from organisms with highly diverse living environments, i.e., biomass degraders and animal pathogens of clostridia in our study, can be clearly classified into different topological groups on some connected components.
7. Elucidation of operon structures across closely related bacterial genomes.
Science.gov (United States)
Zhou, Chuan; Ma, Qin; Li, Guojun
2014-01-01
About half of the protein-coding genes in prokaryotic genomes are organized into operons to facilitate co-regulation during transcription. With the evolution of genomes, operon structures are undergoing changes which could coordinate diverse gene expression patterns in response to various stimuli during the life cycle of a bacterial cell. Here we developed a graph-based model to elucidate the diversity of operon structures across a set of closely related bacterial genomes. In the constructed graph, each node represents one orthologous gene group (OGG) and a pair of nodes will be connected if any two genes, from the corresponding two OGGs respectively, are located in the same operon as immediate neighbors in any of the considered genomes. Through identifying the connected components in the above graph, we found that genes in a connected component are likely to be functionally related and these identified components tend to form treelike topology, such as paths and stars, corresponding to different biological mechanisms in transcriptional regulation as follows. Specifically, (i) a path-structure component integrates genes encoding a protein complex, such as ribosome; and (ii) a star-structure component not only groups related genes together, but also reflects the key functional roles of the central node of this component, such as the ABC transporter with a transporter permease and substrate-binding proteins surrounding it. Most interestingly, the genes from organisms with highly diverse living environments, i.e., biomass degraders and animal pathogens of clostridia in our study, can be clearly classified into different topological groups on some connected components.
8. Regulated aggregative multicellularity in a close unicellular relative of metazoa
Science.gov (United States)
Sebé-Pedrós, Arnau; Irimia, Manuel; del Campo, Javier; Parra-Acero, Helena; Russ, Carsten; Nusbaum, Chad; Blencowe, Benjamin J; Ruiz-Trillo, Iñaki
2013-01-01
The evolution of metazoans from their unicellular ancestors was one of the most important events in the history of life. However, the cellular and genetic changes that ultimately led to the evolution of multicellularity are not known. In this study, we describe an aggregative multicellular stage in the protist Capsaspora owczarzaki, a close unicellular relative of metazoans. Remarkably, transition to the aggregative stage is associated with significant upregulation of orthologs of genes known to establish multicellularity and tissue architecture in metazoans. We further observe transitions in regulated alternative splicing during the C. owczarzaki life cycle, including the deployment of an exon network associated with signaling, a feature of splicing regulation so far only observed in metazoans. Our results reveal the existence of a highly regulated aggregative stage in C. owczarzaki and further suggest that features of aggregative behavior in an ancestral protist may had been co-opted to develop some multicellular properties currently seen in metazoans. DOI: http://dx.doi.org/10.7554/eLife.01287.001 PMID:24368732
9. Retrotranspositions in orthologous regions of closely related grass species
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Swigoňová Zuzana
2006-08-01
Full Text Available Abstract Background Retrotransposons are commonly occurring eukaryotic transposable elements (TEs. Among these, long terminal repeat (LTR retrotransposons are the most abundant TEs and can comprise 50–90% of the genome in higher plants. By comparing the orthologous chromosomal regions of closely related species, the effects of TEs on the evolution of plant genomes can be studied in detail. Results Here, we compared the composition and organization of TEs within five orthologous chromosomal regions among three grass species: maize, sorghum, and rice. We identified a total of 132 full or fragmented LTR retrotransposons in these regions. As a percentage of the total cumulative sequence in each species, LTR retrotransposons occupy 45.1% of the maize, 21.1% of the rice, and 3.7% of the sorghum regions. The most common elements in the maize retrotransposon-rich regions are the copia-like retrotransposons with 39% and the gypsy-like retrotransposons with 37%. Using the contiguous sequence of the orthologous regions, we detected 108 retrotransposons with intact target duplication sites and both LTR termini. Here, we show that 74% of these elements inserted into their host genome less than 1 million years ago and that many retroelements expanded in size by the insertion of other sequences. These inserts were predominantly other retroelements, however, several of them were also fragmented genes. Unforeseen was the finding of intact genes embedded within LTR retrotransposons. Conclusion Although the abundance of retroelements between maize and rice is consistent with their different genome sizes of 2,364 and 389 Mb respectively, the content of retrotransposons in sorghum (790 Mb is surprisingly low. In all three species, retrotransposition is a very recent activity relative to their speciation. While it was known that genes re-insert into non-orthologous positions of plant genomes, they appear to re-insert also within retrotransposons, potentially
10. Aliens on Earth. Are reports of close encounters correct?
CERN Document Server
Sobkowicz, Pawel
2012-01-01
Popular culture (movies, SF literature) and witness accounts of close encounters with extraterrestrials provide a rather bizarre image of Aliens behavior on Earth. It is far from stereotypes of human space exploration. The reported Aliens are not missions of diplomats, scientists nor even invasion fleets; typical encounters are with lone ETs (or small groups), and involve curious behavior: abductions and experiments (often of sexual nature), cattle mutilations, localized killing and mixing in human society using various methods. Standard scientific explanations of these social memes point to influence of cultural artifacts (movies, literature) on social imagination, projection of our fears and observations of human society, and, in severe cases, psychic disorder of the involved individuals. In this work we propose an alternate explanation, claiming that the memes might be the result of observations of actual behavior of true Aliens, who, visiting Earth behave in a way that is then reproduced by such memes. Th...
11. The Pathogenomic Sequence Analysis of B. cereus and B. Thuringiensis isolates closely related to Bacillus anthracis
Energy Technology Data Exchange (ETDEWEB)
Han, C S; Xie, G; Challacombe, J F; Altherr, M R; Bhotika, S S; Bruce, D; Campbell, C S; Campbell, M L; Chen, J; Chertkov, O; Cleland, C; Dimitrijevic-Bussod, M; Doggett, N A; Fawcett, J J; Glavina, T; Goodwin, L A; Hill, K K; Hitchcock, P; Jackson, P J; Keim, P; Kewalramani, A R; Longmire, J; Lucas, S; Malfatti, S; McMurry, K; Meincke, L J; Misra, M; Moseman, B L; Mundt, M; Munk, A C; Okinaka, R T; Parson-Quintana, B; Reilly, L P; Richardson, P; Robinson, D L; Rubin, E; Saunders, E; Tapia, R; Tesmer, J G; Thayer, N; Thompson, L S; Tice, H; Ticknor, L O; Wills, P L; Gilna, P; Brettin, T S
2005-10-12
The sequencing and analysis of two close relatives of Bacillus anthracis are reported. AFLP analysis of over 300 isolates of B. cereus, B. thuringiensis and B. anthracis identified two isolates as being very closely related to B. anthracis. One, a B. cereus, BcE33L, was isolated from a zebra carcass in Nambia; the second, a B. thuringiensis, 97-27, was isolated from a necrotic human wound. The B. cereus appears to be the closest anthracis relative sequenced to date. A core genome of over 3,900 genes was compiled for the Bacillus cereus group, including B anthracis. Comparative analysis of these two genomes with other members of the B. cereus group provides insight into the evolutionary relationships among these organisms. Evidence is presented that differential regulation modulates virulence, rather than simple acquisition of virulence factors. These genome sequences provide insight into the molecular mechanisms contributing to the host range and virulence of this group of organisms.
12. Ventricular Septal Defect Spontaneous Close Induced by Transcatheter: A Case Report
Institute of Scientific and Technical Information of China (English)
Qilian Xie; Jun Wang; Lei Gao; Zhen Wang; Milin Zhang; Kunshen Liu
2007-01-01
Congenital ventricular septal defect (VSD) spontaneous close induced by transcatheter treatment is rare and has not yet been reported.We report on one case of VSD spontaneous close induced by transcatheter treatment in a 10 years old girl.
13. Significant divergence of sex-related non-coding RNA expression patterns among closely related species in Drosophila
Institute of Scientific and Technical Information of China (English)
YANG YongFei; LI Zheng; FAN QiChang; LONG ManYuan; ZHANG WenXia
2007-01-01
Whether or not non-coding RNA genes play a significant role in reproductive biology and evolution of sex determination systems is an important problem. We report identification of sex-related non-coding RNA (ncRNA) genes and an analysis of ncRNAs expression patterns among Drosophila species. We detected 12 candidate ncRNAs that are expressed in the gonads of D. melanogaster by an integrative approach of RT-PCR and computational analysis of sequence conservation across species. We experimentally analyzed these ncRNA gene transcripts in head, ovary and testis of closely related species D. simulans, D. yakuba, D. pseudoobscura and D. virilis. We observed that the occurrence and extent of expression of most ncRNA fragments among closely related species show significant divergence.
14. 46 CFR 308.534 - Certificate to be attached to closing report, Form MA-313-A.
Science.gov (United States)
2010-10-01
... 46 Shipping 8 2010-10-01 2010-10-01 false Certificate to be attached to closing report, Form MA... § 308.534 Certificate to be attached to closing report, Form MA-313-A. The standard form of Certificate to be attached to the closing report, Form MA-313-A, may be obtained from the American War...
15. Volatiles as Chemosystematic Markers for Distinguishing Closely Related Species within the Pinus mugo Complex.
Science.gov (United States)
2015-08-01
Headspace solid-phase microextraction (HS-SPME) coupled to GC/MS analysis was used to identify the constituents of pine-needle volatiles differentiating three closely-related pine species within the Pinus mugo complex, i.e., P. uncinata Ramond ex DC., P. uliginosa G.E.Neumann ex Wimm., and P. mugo Turra. Moreover, chemosystematic markers were proposed for the three analyzed pine species. The major constituents of the pine-needle volatiles were α-pinene (28.4%) and bornyl acetate (10.8%) for P. uncinata, δ-car-3-ene (21.5%) and α-pinene (16.1%) for P. uliginosa, and α-pinene (20%) and δ-car-3-ene (18.1%) for P. mugo. This study is the first report on the application of the composition of pine-needle volatiles for the reliable identification of closely-related pine species within the Pinus mugo complex.
16. SHARK a new concept in electrical machines. Closing report
Energy Technology Data Exchange (ETDEWEB)
Ritchie, E.; Omand Rasmussen, P.; Tataru Kjaer, A,M.
2004-10-01
The research is rooted in the effort to reduce the energy consumed by electric motors. This work explored the idea that the efficiency of a specific type of electric motor may be improved by replacing the usual cylindrical air gap by a non-linear air gap. This idea is not new, other reports addressing this subject having been published prior to this work. However, no systematic analysis has been reported previously. Previous publications tried to demonstrate that the concept could function. The commercial applicability of this concept, called SHARK, was not considered seriously, because of the assembly difficulties caused by the non-linear air gap. However, these problems may be overcome by recently reported technologies. Thus a detailed analysis of the effect of the SHARK air gap on the performance of electric motors became more interesting. The methodology of the study was aimed to provide an analysis tool for future SHARK air gap machines. A Switched Reluctance Machines was selected as vehicle for this study, due to its simple geometry. The study regarded the linear analysis and the Finite Element Analysis as the main tools capable of providing basic knowledge of the magnetic behaviour of various air gap shapes applied in SRM. Based on results obtained from these, an analytical model, describing the magnetisation characteristics of the SHARK SRM in the aligned and unaligned rotor positions, was proposed. The modelling principle was to adapt an existing model of the cylindrical air gap SRM to account for the influence of the SHARK profile in the air gap. The proposed model was used to generate families of characteristics showing the relative improvement in terms of converted energy of the SHARK SRM in comparison with a cylindrical air gap SRM having identical main dimensions. Calculations were verified by measurements on two machines having cylindrical and saw-toothed air gaps. In addition, the performance of an Induction Motor and a brushless DC motor were
17. A Close Examination of Jo Boaler's Railside Report
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Paul Clopton
2012-12-01
Full Text Available Jo Boaler, an Associate Professor at the Stanford School of Education has just published an already well known study of three high schools that she called Hillside, Greendale, and Railside. This study makes extremely strong claims for discovery style instruction in mathematics, and consequently has the potential to affect instruction and curriculum throughout the country.As is the case with much education research of this nature, Prof. Boaler has refused to divulge the identities of the schools to qualified researchers. Consequently, it would normally be impossible to independently check her work. However, in this case, the names of the schools were determined and a close examination of the actual outcomes in these schools shows that Prof. Boaler’s claims are grossly exaggerated and do not translate into success for her treatment students. We give the details in the following article.Other papers where the researchers have refused to divulge such details as the names of the schools to qualified researchers have affected and continue to affect education policy decisions at the school, state and even national levels. Among these papers are Standards, Assessments – and What Else? The Essential Elements of Standards-Based School Improvement, D. Briars - L. Resnick, CRESST Technical Report 528, (2000 which has been cited repeatedly as justification for the adoption of Everyday Mathematics in school districts throughout the country, and The impact of two standards-based mathematics curricula on student achievement in Massachusetts. D. Perda, P. Noyce, J. Riordan, J. for Research in Mathematics Education, 32(2001, p. 368-398. which has been used to justify the adoption of the mathematics program “Investigations,” developed by TERC. It is worth noting that currently about 19% of U.S. elementary students use Everyday Mathematics and between 6% and 9% use Investigations, including many of our inner city schools.If we are to reverse the woeful
18. Closing in on chemical bonds by opening up relativity theory.
Science.gov (United States)
Whitney, Cynthia K
2008-03-01
This paper develops a connection between the phenomenology of chemical bonding and the theory of relativity. Empirical correlations between electron numbers in atoms and chemical bond stabilities in molecules are first reviewed and extended. Quantitative chemical bond strengths are then related to ionization potentials in elements. Striking patterns in ionization potentials are revealed when the data are viewed in an element-independent way, where element-specific details are removed via an appropriate scaling law. The scale factor involved is not explained by quantum mechanics; it is revealed only when one goes back further, to the development of Einstein's special relativity theory.
19. Tão longe, tão perto: escrita de si em relatórios de viagens So far, so close: writings about oneself in travel reports
Directory of Open Access Journals (Sweden)
Ana Chrystina Venancio Mignot
2011-04-01
Full Text Available Explorar os sentidos de um tom autobiográfico inscrito em relatórios de viagens empreendidas por três professores que integravam a primeira missão oficial de educadores que visitaria o continente europeu, no alvorecer da República, com a finalidade de estudar o sistema educacional de vários países, é o horizonte deste texto. Tais experiências compunham as preocupações com as melhorias na instrução pública no país, em que as viagens para conhecer e estudar o outro, divulgadas e defendidas pela Revista Pedagógica, publicação do Pedagogium, revertiam-se em diferentes modos de intervir e propor mudanças na educação no Brasil. Procura-se, nesta análise, em meio à escrita obrigatória e fadada à impessoalidade, mais do que impressões, conclusões e proposições sobre a organização escolar, a organização do magistério, o material didático, a arquitetura das escolas e os aspectos relativos à remuneração dos professores, mas, sobretudo, os traços da intimidade e dos modos de ver o mundo dos professores viajantes.This text explores the meanings and senses of autobiographical travel reports written by three professors, members of the first official educators' committee visiting Europe at the dawn of the Brazilian Republican regime. Their goal was to study the national education systems of several countries. This experience reflected concerns regarding the improvement of Brazilian public education. At that time, trips organized by the "Revista Pedagógica" (Pedagogic Magazine, published by "Pedagogium", were organized in order to study the "other", resulting in different ways of intervention and change proposals for the Brazilian educational system. The present work examines - through the mandatory impersonal writing style - more than mere impressions, conclusions and proposals for school organization, or the organization of teaching staff, school material, school architecture and aspects relating to teaching staff wages
20. Use of Wild Relatives and Closely Related Species to Adapt Common Bean to Climate Change
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James D. Kelly
2013-05-01
Full Text Available Common bean (Phaseolus vulgaris L. is an important legume crop worldwide. However, abiotic and biotic stress limits bean yields to <600 kg ha−1 in low-income countries. Current low yields result in food insecurity, while demands for increased yields to match the rate of population growth combined with the threat of climate change are significant. Novel and significant advances in genetic improvement using untapped genetic diversity available in crop wild relatives and closely related species must be further explored. A meeting was organized by the Global Crop Diversity Trust to consider strategies for common bean improvement. This review resulted from that meeting and considers our current understanding of the genetic resources available for common bean improvement and the progress that has been achieved thus far through introgression of genetic diversity from wild relatives of common bean, and from closely related species, including: P. acutifolius, P. coccineus, P. costaricensis and P. dumosus. Newly developed genomic tools and their potential applications are presented. A broad outline of research for use of these genetic resources for common bean improvement in a ten-year multi-disciplinary effort is presented.
1. Centrin protein and genes in Trichomonas vaginalis and close relatives.
Science.gov (United States)
Brugerolle, G; Bricheux, G; Coffe, G
2000-01-01
Anti-centrin monoclonal antibodies 20H5 and 11B2 produced against Clamydomononas centrin decorated the group of basal bodies as well as very closely attached structures in all trichomonads studied and in the devescovinids Foaina and Devescovina. Moreover, these antibodies decorated the undulating membrane in Trichomonas vaginalis, Trichomitus batrachorum, and Tritrichomonas foetus, and the cresta in Foaina. Centrin was not demonstrated in the dividing spindle and paradesmosis. Immunogold labeling, both in pre- and post-embedding, confirmed that centrin is associated with the basal body cylinder and is a component of the nine anchoring arms between the terminal plate of flagellar bases and the plasma-membrane. Centrin is also associated with the hook-shaped fibers attached to basal bodies (F1, F3), the X-fiber, and along sigmoid fibers (F2) at the pelta-axostyle junction, which is the microtubule organizing center for pelta-axostyle microtubules. There was no labeling on the striated costa and parabasal fibers nor on microtubular pelta-axostyle, but the fibrous structure inside the undulating membrane was labeled in T. vaginalis. Two proteins of 22-20 kDa corresponding to the centrin molecular mass were recognized by immunoblotting using these antibodies in the three trichomonad species examined. By screening a T. vaginalis cDNA library with 20H5 antibody, two genes encoding identical protein sequences were found. The sequence comprises the 4 typical EF-hand Ca++-binding domains present in every known centrin. Trichomonad centrin is closer to the green algal cluster (70% identity) than to the yeast Cdc31 cluster (55% identity) or the Alveolata cluster (46% identity).
2. Molecular relationships between closely related strains and species of nematodes
Science.gov (United States)
Butler, M. H.; Wall, S. M.; Luehrsen, K. R.; Fox, G. E.; Hecht, R. M.
1981-01-01
Electrophoretic comparisons have been made for 24 enzymes in the Bergerac and Bristol strains of Caenorhabditis elegans and the related species, Caenorhabditis briggsae. No variation was detected between the two strains of C. elegans. In contrast, the two species, C. elegans and C. briggsae exhibited electrophoretic differences in 22 of 24 enzymes. A consensus 5S rRNA sequence was determined for C. elegans and found to be identical to that from C. briggsae. By analogy with other species with relatively well established fossil records it can be inferred that the time of divergence between the two nematode species is probably in the tens of millions of years. The limited anatomical evolution during a time period in which proteins undergo extensive changes supports the hypothesis that anatomical evolution is not dependent on overall protein changes.
3. Oviposition preferences for ethanol depend on spatial arrangement and differ dramatically among closely related Drosophila species.
Science.gov (United States)
Sumethasorn, Matt; Turner, Thomas L
2016-11-15
Recent work on the model fly Drosophila melanogaster has reported inconsistencies in their preference for laying eggs on intermediate concentrations of ethanol. In this study, we resolve this discrepancy by showing that this species strongly prefers ovipositing on ethanol when it is close to a non-ethanol substrate, but strongly avoids ethanol when options are farther apart. We also show fluidity of these behaviors among other Drosophila species: D. melanogaster is more responsive to ethanol than close relatives in that it prefers ethanol more than other species in the close-proximity case, but avoids ethanol more than other species in the distant case. In the close-proximity scenario, the more ethanol-tolerant species generally prefer ethanol more, with the exception of the island endemic D. santomea This species has the lowest tolerance in the clade, but behaves like D. melanogaster We speculate that this could be an adaptation to protect eggs from parasites or predators such as parasitoid wasps, as larvae migrate to non-toxic substrates after hatching. These natural differences among species are an excellent opportunity to study how genes and brains evolve to alter ethanol preferences, and provide an interesting model for genetic variation in preferences in other organisms, including humans.
4. Language Adaptation for Extending Post-Editing Estimates for Closely Related Languages
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Rios Miguel
2016-10-01
Full Text Available This paper presents an open-source toolkit for predicting human post-editing efforts for closely related languages. At the moment, training resources for the Quality Estimation task are available for very few language directions and domains. Available resources can be expanded on the assumption that MT errors and the amount of post-editing required to correct them are comparable across related languages, even if the feature frequencies differ. In this paper we report a toolkit for achieving language adaptation, which is based on learning new feature representation using transfer learning methods. In particular, we report performance of a method based on Self-Taught Learning which adapts the English-Spanish pair to produce Quality Estimation models for translation from English into Portuguese, Italian and other Romance languages using the publicly available Autodesk dataset.
5. Ethical Challenges embedded in qualitative research interviews with close relatives
DEFF Research Database (Denmark)
Haahr, Anita; Norlyk, Annelise; Hall, Elisabeth
2013-01-01
Nurse researchers engaged in qualitative interviews with patients and spouses in healthcare may often experience being in unforseen ethical dilemmas. Researchers are guided by the bioethical principles of justice, beneficence, non-maleficence respect for human rights and respect for autonomy...... through the entire research process. However, these principles are not sufficient to prepare researchers for unanticipated ethical dilemmas related to qualitative researchs interviews. We describe and discuss ethically challenging and difficult moments embedded in two cases from our own phenomenological...... interview studies. We argue that qualitative interviews involve navigation between being guided by bioethics as a researcher, being a therapist/nurse and being a fellow human being or even a friend. The researchers' premises to react to unexpected situations and act in a sound ethical manner must...
6. Ethical challenges embedded in qualitative research interviews with close relatives.
Science.gov (United States)
Haahr, Anita; Norlyk, Annelise; Hall, Elisabeth Oc
2014-02-01
Nurse researchers engaged in qualitative interviews with patients and spouses in healthcare may often experience being in unforeseen ethical dilemmas. Researchers are guided by the bioethical principles of justice, beneficence, non-maleficence, respect for human rights and respect for autonomy through the entire research process. However, these principles are not sufficient to prepare researchers for unanticipated ethical dilemmas related to qualitative research interviews. We describe and discuss ethically challenging and difficult moments embedded in two cases from our own phenomenological interview studies. We argue that qualitative interviews involve navigation between being guided by bioethics as a researcher, being a therapist/nurse and being a fellow human being or even a friend. The researchers' premises to react to unexpected situations and act in a sound ethical manner must be enhanced, and there is a need for an increased focus on the researchers' ethical preparation and to continually address and discuss cases from their own interviews.
7. Complete Genome Sequence of Ehrlichia mineirensis, a Novel Organism Closely Related to Ehrlichia canis with a New Host Association
OpenAIRE
Cabezas-Cruz, Alejandro; Zweygarth, Erich; Broniszweska, Marzena; Passos,Lygia M.F.; Ribeiro,Múcio Flávio Barbosa; Manrique, Marina; Tobes,Raquel; de la Fuente, José
2015-01-01
We report here the complete genome sequencing of Ehrlichia mineirensis, an Ehrlichia organism that was isolated from the hemolymph of Rhipicephalus microplus–engorged females. E. mineirensis is the best characterized Ehrlichia isolate from a novel cattle-related clade closely related to the monocytotropic pathogen E. canis.
8. Towards a more liveable life for close relatives of individuals diagnosed with bipolar disorder.
Science.gov (United States)
Rusner, Marie; Carlsson, Gunilla; Brunt, David; Nyström, Maria
2013-04-01
The life of close relatives of persons with bipolar disorder (BD) is associated with emotional distress, depression, and a high level of use of mental health care. Illness-related changes of their life situation endanger relationships, social life, finances, and occupational functioning. Understanding of facilitating conditions for close relatives is still a neglected research area. The aim of the present study thus was to explore what makes the life of close relatives of persons with BD more liveable. A lifeworld phenomenological approach was used. The findings reveal that keeping distance, having stability in everyday life, and strengthening equality through transparent communication are conditions that enable close relatives to influence the unpredictable and its consequences and thus make life more liveable. This implies contributions from close relatives, the person with BD, and the caring services. We propose that health-care support should not be divided in support for the patient and/or the close relatives but instead be designed as support for the 'patient and close relatives' as a unit. Professional caregivers need to take responsibility for creating intersubjective settings for the person with BD and their close relatives to share their needs and make joint plans for how to influence the illness-related life issues.
9. LS1 Report: As one door closes, another opens
CERN Multimedia
Katarina Anthony & Anaïs Schaeffer
2014-01-01
Across the PS complex - from Linac 2 to TT2 to the accelerator itself - teams have seen the closing of their retro-1980s entryways, and the opening of state-of-the-art access points in compliance with the highest nuclear safety standards. One of the new PS access points. The new PS access system provides more than just doors. Designed to protect against the radiation hazards and other risks caused by machine operation, the access system will monitor who goes into each zone, check whether or not the individual has the appropriate permissions to be entering, and even stop the beam if access is attempted during beam mode. "These new points provide automatic means to check that the right people are going in and in safe circumstances," says Pierre Ninin, project leader of the PS complex safety system. "All of these checks were previously done manually, so the burden on operators has been significantly reduced." The 19 new access points were successfully insta...
10. 12 CFR 225.126 - Activities not closely related to banking.
Science.gov (United States)
2010-01-01
... 12 Banks and Banking 3 2010-01-01 2010-01-01 false Activities not closely related to banking. 225.126 Section 225.126 Banks and Banking FEDERAL RESERVE SYSTEM (CONTINUED) BOARD OF GOVERNORS OF THE... Financial Holding Companies Interpretations § 225.126 Activities not closely related to banking. Pursuant to...
11. Fish and Wildlife report for the Closed Basin Division : San Luis Valley Project Colorado
Data.gov (United States)
US Fish and Wildlife Service, Department of the Interior — This report for the Closed Basin Division is a description of the project and the fish and wildlife resources associated with the project. The document also reports...
12. New criteria for selecting the origin of DNA replication in Wolbachia and closely related bacteria
Directory of Open Access Journals (Sweden)
Baldo Laura
2007-06-01
Full Text Available Abstract Background The annotated genomes of two closely related strains of the intracellular bacterium Wolbachia pipientis have been reported without the identifications of the putative origin of replication (ori. Identifying the ori of these bacteria and related alpha-Proteobacteria as well as their patterns of sequence evolution will aid studies of cell replication and cell density, as well as the potential genetic manipulation of these widespread intracellular bacteria. Results Using features that have been previously experimentally verified in the alpha-Proteobacterium Caulobacter crescentus, the origin of DNA replication (ori regions were identified in silico for Wolbachia strains and eleven other related bacteria belonging to Ehrlichia, Anaplasma, and Rickettsia genera. These features include DnaA-, CtrA- and IHF-binding sites as well as the flanking genes in C. crescentus. The Wolbachia ori boundary genes were found to be hemE and COG1253 protein (CBS domain protein. Comparisons of the putative ori region among related Wolbachia strains showed higher conservation of bases within binding sites. Conclusion The sequences of the ori regions described here are only similar among closely related bacteria while fundamental characteristics like presence of DnaA and IHF binding sites as well as the boundary genes are more widely conserved. The relative paucity of CtrA binding sites in the ori regions, as well as the absence of key enzymes associated with DNA replication in the respective genomes, suggest that several of these obligate intracellular bacteria may have altered replication mechanisms. Based on these analyses, criteria are set forth for identifying the ori region in genome sequencing projects.
13. Arterial blood pressure is closely related to ascites development in compensated HCV-related cirrhosis.
Directory of Open Access Journals (Sweden)
Eduardo Vilar Gomez
Full Text Available BACKGROUND: Arterial blood pressure (BP is a reliable marker of circulatory dysfunction in cirrhotic patients. There are no prospective studies evaluating the association between different levels of arterial BP and ascites development in compensated cirrhotic patients. Therefore, we evaluated the relationship between arterial BP and ascites development in compensated cirrhotic patients. MATERIALS AND METHODS: A total of 402 patients with compensated HCV-related cirrhosis were prospectively followed during 6 years to identify ascites development. At baseline, patients underwent systolic, diastolic and mean arterial pressure (MAP measurements. Any history of arterial hypertension was also recorded. The occurrence of events such as bleeding, hepatocellular carcinoma, death and liver transplantation prior to ascites development were considered as competing risk events. RESULTS: Over a median of 156 weeks, ascites occurred in 54 patients (13%. At baseline, MAP was significantly lower in patients with ascites development (75.9 mm/Hg [95%CI, 70.3-84.3] than those without ascites (93.6 mm/Hg [95% CI: 86.6-102.3]. After adjusting for covariates, the 6-year cumulative incidence of ascites was 40% (95%CI, 34%-48% for patients with MAP<83.32 mm/Hg. In contrast, cumulative incidences of ascites were almost similar among patients with MAP values between 83.32 mm/Hg and 93.32 mm/Hg (7% [95% CI: 4%-12%], between 93.32 mm/Hg and 100.31 mm/Hg (5% [95% CI: 4%-11%] or higher than 100.31 mm/Hg (3% [95% CI: 1%-6%]. The MAP was an independent predictor of ascites development. CONCLUSIONS: The MAP is closely related to the development of ascites in compensated HCV-related cirrhosis. The risk of ascites development increases in 4.4 fold for subjects with MAP values <83.32 mm/Hg.
14. A role of Bradyrhizobium elkanii and closely related strains in the degradation of methoxychlor in soil and surface water environments.
Science.gov (United States)
Satsuma, Koji; Masuda, Minoru; Sato, Kiyoshi
2013-01-01
15. Relationship of Dyadic Closeness with Work-Related Stress: A Daily Diary Study
Science.gov (United States)
2007-01-01
We examined the association between work-related stress of both spouses and daily fluctuations in their affective states and dyadic closeness. Daily diary data from 169 Israeli dual-earner couples were analyzed using multilevel modeling. The findings indicate that work stress has no direct effect on dyadic closeness but rather is mediated by the…
16. Relationship of Dyadic Closeness with Work-Related Stress: A Daily Diary Study
Science.gov (United States)
2007-01-01
We examined the association between work-related stress of both spouses and daily fluctuations in their affective states and dyadic closeness. Daily diary data from 169 Israeli dual-earner couples were analyzed using multilevel modeling. The findings indicate that work stress has no direct effect on dyadic closeness but rather is mediated by the…
17. Closely related freshwater macrophyte species, Ceratophyllum demersum and em>C. submersum, differ in temperature response
DEFF Research Database (Denmark)
Hyldgaard, Benita; Sorrell, Brian Keith; Brix, Hans
2014-01-01
1. The importance of temperature responses of photosynthesis and respiration in determining species distributions was compared in two closely related freshwater macrophytes, Ceratophyllum demersum and C. submersum. The two species differed significantly in response to temperature in the short and...
18. Studies on the closed-loop digital control of multi-modular reactors. Final report
Energy Technology Data Exchange (ETDEWEB)
Bernard, J.A. [Massachusetts Inst. of Tech., Cambridge, MA (United States). Nuclear Reactor Lab.; Henry, A.F.; Lanning, D.D.; Meyer, J.E. [Massachusetts Inst. of Tech., Cambridge, MA (United States). Dept. of Nuclear Engineering
1992-11-01
This report describes the theoretical development and the evaluation via both experiment and simulation of digital methods for the closed-loop control of power, temperature, and steam generator level in multi-modular reactors. The major conclusion of the research reported here is that the technology is currently available to automate many aspects of the operation of multi-modular plants. This will in turn minimize the number of required personnel and thus contain both operating and personnel costs, allow each module to be operated at a different power level thereby staggering the times at which refuelings would be needed, and maintain the competitiveness of US industry relative to foreign vendors who are developing and applying advanced control concepts. The technology described in this report is appropriate to the proposed multi-modular reactor designs and to present-generation pressurized water reactors. Its extension to boiling water reactors is possible provided that the commitment is made to create a real-time model of a BWR. The work reported here was performed by the Massachusetts Institute of Technology (MIT) under contract to the Oak Ridge National Laboratory (ORNL) and to the United States Department of Energy (Division of Industry and University Programs, Contract No. DE-FG07-90ER12930.)
19. Empathy and the expression and recognition of sarcasm by close relations or strangers.
Science.gov (United States)
Rockwell, Patricia
2003-08-01
This study examined how relational type and empathy affect the use of sarcasm. We paired interviewers of high and low empathy with either an interviewee who was closely related or a stranger. Interviewers were given 10 questions to ask the interviewee, alternating sarcastic questions with sincere questions. Following each interview, participants completed questionnaires to assess their understanding of how sarcasm affected the interview. Relationship (closely related vs stranger) was a significant factor in recognition of sarcasm but not in its use. Empathy (high vs low) did not significantly affect the production or recognition of sarcasm.
20. 31 CFR 515.561 - Persons visiting close relatives in Cuba.
Science.gov (United States)
2010-07-01
... Cuba. 515.561 Section 515.561 Money and Finance: Treasury Regulations Relating to Money and Finance... Cuba. (a) General license. (1) Persons subject to the jurisdiction of the United States and persons... close relative, as defined in § 515.339 of this part, who is a national of Cuba, as defined in §...
1. The effect of close relatives on unsupervised Bayesian clustering algorithms in population genetic structure analysis.
Science.gov (United States)
Rodríguez-Ramilo, Silvia T; Wang, Jinliang
2012-09-01
The inference of population genetic structures is essential in many research areas in population genetics, conservation biology and evolutionary biology. Recently, unsupervised Bayesian clustering algorithms have been developed to detect a hidden population structure from genotypic data, assuming among others that individuals taken from the population are unrelated. Under this assumption, markers in a sample taken from a subpopulation can be considered to be in Hardy-Weinberg and linkage equilibrium. However, close relatives might be sampled from the same subpopulation, and consequently, might cause Hardy-Weinberg and linkage disequilibrium and thus bias a population genetic structure analysis. In this study, we used simulated and real data to investigate the impact of close relatives in a sample on Bayesian population structure analysis. We also showed that, when close relatives were identified by a pedigree reconstruction approach and removed, the accuracy of a population genetic structure analysis can be greatly improved. The results indicate that unsupervised Bayesian clustering algorithms cannot be used blindly to detect genetic structure in a sample with closely related individuals. Rather, when closely related individuals are suspected to be frequent in a sample, these individuals should be first identified and removed before conducting a population structure analysis.
2. On Enumerating Frequent Closed Patterns with Key in Multi-relational Data
Science.gov (United States)
Seki, Hirohisa; Honda, Yuya; Nagano, Shinya
We study the problem of mining closed patterns in multi-relational databases. Garriga et al. (IJCAI'07) proposed an algorithm RelLCM2 for mining closed patterns (i.e., conjunctions of literals) in multi-relational data, which is an extension of LCM, an efficient enumeration algorithm for frequent closed itemsets mining proposed in the seminal paper by Uno et al. (DS'04). We assume that a database considered contains a special predicate called key (or target), which determines the entities of interest and what is to be counted. We introduce a notion of closed patterns with key (key-closedness for short), where variables in a pattern other than the one in a key predicate are considered to be existentially quantified, and they are linked to a given target object. We then define a closure operation (key-closure) for computing key-closed patterns, and show that the difference between the semantics of key-closed patterns and that of the closed patterns in RelLCM2 implies different properties of the closure operations; in particular, the uniqueness of closure does not hold for key-closure. Nevertheless, we show that we can enumerate key-closed patterns using the technique of ppc-extensions à la LCM, thereby making the enumeration possible without storage space for previously generated patterns. We also propose a literal order designed for mining key-closed patterns, which will require less search space. The correctness of our algorithm is shown, and its computational complexity is discussed. Some preliminary experimental results are also given.
3. "Close Readings" of Internet Corporate Financial Reporting: Towards a More Critical Pedagogy on the Information Highway.
Science.gov (United States)
Amernic, Joel H.
1998-01-01
Discusses a curriculum strategy based upon a hierarchy of four close readings of corporate financial reporting Web sites (described as (1) objective characteristics, (2) internet financial reporting as rhetoric, (3) metaphor and thought, and (4) deconstruction) that is proffered as part of a curriculum objective to encourage university business…
4. Differential regulation of two closely related integrative and conjugative elements from Streptococcus thermophilus
Directory of Open Access Journals (Sweden)
Carraro Nicolas
2011-10-01
, ICESt3 and closely related ICEs, which we identified by analysis of recently sequenced genomes of firmicutes. This is the first report of a partial shutdown of the activity of an ICE executed by a strain belonging to its primary host species. The sharp increase of ICESt3 copy number suggests an induction of replication; such conditional intracellular replication may be common among ICEs.
5. The Pathogenomic Sequence Analysis of B. cereus and B.thuringiensis Isolates Closely Related to Bacillus anthracis
Energy Technology Data Exchange (ETDEWEB)
Han, Cliff S.; Xie, Gary; Challacombe, Jean F.; Altherr, MichaelR.; Smriti, B.; Bruce, David; Campbell, Connie S.; Campbell, Mary L.; Chen, Jin; Chertkov, Olga; Cleland, Cathy; Dimitrijevic-Bussod, M.; Doggett, Norman A.; Fawcett, John J.; Glavina, Tijana; Goodwin, Lynne A.; Hill, Karen K.; Hitchcock, Penny; Jackson, Paul J.; Keim, Paul; Kewalramani, Avinash Ramesh; Longmire, Jon; Lucas, Susan; Malfatti,Stephanie; McMurry, Kim; Meincke, Linda J.; Misra, Monica; Moseman,Bernice L.; Mundt, Mark; Munk, A. Christine; Okinaka, Richard T.; Parson-Quintana, B.; Reilly, Lee P.; Richardson, Paul; Robinson, DonnaL.; Rubin, Eddy; Saunders, Elizabeth; Tapia, Roxanne; Tesmer, Judith G.; Thayer, Nina; Thompson, Linda S.; Tice, Hope; Ticknor, Lawrence O.; Wills, Patti L.; Gilna, Payl; Brettin, Thomas S.
2005-08-18
The sequencing and analysis of two close relatives of Bacillus anthracis are reported. AFLP analysis of over 300 isolates of B.cereus, B. thuringiensis and B. anthracis identified two isolates as being very closely related to B. anthracis. One, a B. cereus, BcE33L, was isolated from a zebra carcass in Nambia; the second, a B. thuringiensis, 97-27, was isolated from a necrotic human wound. The B. cereus appears to be the closest anthracis relative sequenced to date. A core genome of over 3,900 genes was compiled for the Bacillus cereus group, including Banthracis. Comparative analysis of these two genomes with other members of the B. cereus group provides insight into the evolutionary relationships among these organisms. Evidence is presented that differential regulation modulates virulence, rather than simple acquisition of virulence factors. These genome sequences provide insight into the molecular mechanisms contributing to the host range and virulence of this group of organisms.
6. Relatively recent evolution of pelage coloration in Colobinae: phylogeny and phylogeography of three closely related langur species.
Directory of Open Access Journals (Sweden)
Zhijin Liu
Full Text Available To understand the evolutionary processes leading to the diversity of Asian colobines, we report here on a phylogenetic, phylogeographical and population genetic analysis of three closely related langurs, Trachypithecus francoisi, T. poliocephalus and T. leucocephalus, which are all characterized by different pelage coloration predominantly on the head and shoulders. Therefore, we sequenced a 395 bp long fragment of the mitochondrial control region from 178 T. francoisi, 54 T. leucocephalus and 19 T. poliocephalus individuals, representing all extant populations of these three species. We found 29 haplotypes in T. francoisi, 12 haplotypes in T. leucocephalus and three haplotypes in T. poliocephalus. T. leucocephalus and T. poliocephalus form monophyletic clades, which are both nested within T. francoisi, and diverged from T. francoisi recently, 0.46-0.27 (T. leucocephalus and 0.50-0.25 million years ago (T. poliocephalus. Thus, T. francoisi appears as a polyphyletic group, while T. leucocephalus and T. poliocephalus are most likely independent descendents of T. francoisi that are both physically separated from T. francoisi populations by rivers, open sea or larger habitat gaps. Since T. francoisi populations show no variability in pelage coloration, pelage coloration in T. leucocephalus and T. poliocephalus is most likely the result of new genetic mutations after the split from T. francoisi and not of the fixation of different characters derived from an ancestral polymorphism. This case study highlights that morphological changes for example in pelage coloration can occur in isolated populations in relatively short time periods and it provides a solid basis for studies in related species. Nevertheless, to fully understand the evolutionary history of these three langur species, nuclear loci should be investigated as well.
7. Aspergillus oerlinghausenensis, a new mould species closely related to A. fumigatus.
Science.gov (United States)
Houbraken, Jos; Weig, Michael; Groß, Uwe; Meijer, Martin; Bader, Oliver
2016-02-01
Two isolates belonging to Aspergillus section Fumigati were recovered from German soil on itraconazole containing agar media. Phylogenetic analysis and phenotypic characterization of both isolates show that they represent a novel species named Aspergillus oerlinghausenensis (holotype CBS H-22119(HT), ex-type CBS 139183(T) = IBT 33878 = DTO 316-A3). The species is phylogenetically related to A. fischeri and A. fumigatus. Aspergillus oerlinghausenensis can be differentiated from A. fischeri by its higher growth rate at 50°C. Furthermore, A. oerlinghausenensis is protoheterothallic as only the MAT1-1 idiomorph was detected, while A. fischeri is homothallic. The species differs from A. fumigatus by a weak sporulation on malt extract agar at 25°C, a floccose colony texture on Czapek yeast extract agar and malt extract agar and subglobose instead of subclavate vesicles. The cyp51A promoter region of A. oerlinghausenensis deviates from the previously reported cyp51A promoter regions in A. fumigatus and potentially presents a novel azole resistance conferring modification. Due to the close relationship of A. oerlinghausenensis with A. fischeri and A. fumigatus, this species is placed in a good position for comparative studies involving these species.
8. Close monitoring as a contextual stimulator : How need for structure affects the relation between close monitoring and work outcomes
NARCIS (Netherlands)
Rietzschel, Eric F.; Slijkhuis, Marjette; Van Yperen, Nico W.
2014-01-01
In this article, we argue and demonstrate that employees' Personal Need for Structure (PNS) moderates the negative effects of close monitoring on job satisfaction, intrinsic work motivation, and innovative job performance (as rated by their supervisors). In a field study (N=295), we found that emplo
9. Taxonomy and nomenclature of three closely related species of Eleocharis subgenus Limnochloa (Cyperaceae)
NARCIS (Netherlands)
Rosen, D.J.; Hatch, S.L.; Carter, R.
2008-01-01
A taxonomic synopsis and review of nomenclature is provided for Eleocharis cellulosa, E. mutata, and E. spiralis, three closely related species belonging to subgenus Limnochloa. One heterotypic synonym of E. mutata and the basionym and a heterotypic synonym of E. spiralis are lectotypified. The taxo
10. Rule-based conversion of closely-related languages: a Dutch-to-Afrikaans convertor
CSIR Research Space (South Africa)
Van Huyssteen, GB
2009-11-01
Full Text Available For fast-tracking the development of resources for resource-scarce languages, one could transfer existing technologies from one language to another well-sourced, closely-related language. In this contribution, the authors describe the development...
11. Relation between non uniform magnetic field and close binary systems period
Directory of Open Access Journals (Sweden)
M Zahedi
2011-12-01
Full Text Available Magnetic activity of one or both components of close binary systems can cause orbital period variation of the systems.Variation in gravitational quadropole moment will change the orbital period of the systems. In this article, we suppose that magnetic field is poloidal-troidal according to dynamo theory, and finds its relation with period change in the systems.
12. The Psychosocial Impact of Closed-Circuit Televisions on Persons with Age-Related Macular Degeneration
Science.gov (United States)
Huber, Jessica G.; Jutai, Jeffrey W.; Strong, J. Graham; Plotkin, Ann D.
2008-01-01
Closed-circuit televisions (CCTVs) are used by many elderly people who have age-related macular degeneration (AMD). The functional vision of 68 participants, which was measured immediately after they adopted CCTVs, suggested successful outcomes, but the psychosocial impact of the use of CCTVs did not peak until a month later. The findings help…
13. Taxonomy and nomenclature of three closely related species of Eleocharis subgenus Limnochloa (Cyperaceae)
NARCIS (Netherlands)
Rosen, D.J.; Hatch, S.L.; Carter, R.
2008-01-01
A taxonomic synopsis and review of nomenclature is provided for Eleocharis cellulosa, E. mutata, and E. spiralis, three closely related species belonging to subgenus Limnochloa. One heterotypic synonym of E. mutata and the basionym and a heterotypic synonym of E. spiralis are lectotypified. The
14. Doing Close-Relative Research: Sticking Points, Method and Ethical Considerations
Science.gov (United States)
Degabriele Pace, Geraldine
2015-01-01
Doing insider research can raise many problematic issues, particularly if the insiders are also close relatives. This paper deals with complexities arising from research which is participatory in nature. Thus, this paper seeks to describe the various sticking points that were encountered by the researcher when she decided to embark on insider…
15. Family Communication Patterns and Relational Maintenance Behavior: Direct and Mediated Associations with Friendship Closeness
Science.gov (United States)
Ledbetter, Andrew M.
2009-01-01
In this study, both face-to-face and online relational maintenance behaviors were tested as mediators of family communication patterns and closeness with a same-sex friend. Participants included 417 young adults recruited from communication courses at a large university in the Midwestern United States. The obtained structural model demonstrated…
16. Interspecific competition, predation, and the coexistence of three closely related neotropical armoured catfishes (Siluriformes - Callichthyidae)
NARCIS (Netherlands)
Mol, J.H.A.
1995-01-01
Tropical ecosystems are renowned for their high biodiversity with many closely related species living together. Alpha diversity of tropical freshwater fishes is also extremely high, as exemplified by the cichlid fauna of the Great African lakes and the neotropical characins. Since
17. Interspecific competition, predation, and the coexistence of three closely related neotropical armoured catfishes (Siluriformes-Callichthyidae).
NARCIS (Netherlands)
Mol, J.H.A.
1995-01-01
Tropical ecosystems are renowned for their high biodiversity with many closely related species living together. Alpha diversity of tropical freshwater fishes is also extremely high, as exemplified by the cichlid fauna of the Great African lakes and the neotropical characins. Since Hutchinson in 1959
18. Closely related Wolbachia recovered from different genera of Mexican Thelytokous figitidae (Hymenoptera)
Science.gov (United States)
Closely related novel Wolbachia strains were recovered from the thelytokous figitids Odontosema anastrephae Borgmeier and Aganaspis alujai Ovruski et al. No Wolbachia were detected in a bi-sexual strain of O. anastrephae. While the presence or absence of Wolbachia does not demonstrate that Wolbachia...
19. Mammary-type myofibroblastoma of soft tissue: a tumor closely related to spindle cell lipoma.
Science.gov (United States)
McMenamin, M E; Fletcher, C D
2001-08-01
Mammary myofibroblastoma is a benign breast tumor, with a reported predilection for older men. It is composed of fascicles of spindle cells having features of myofibroblasts, with intervening hyalinized collagenous stroma and a variably prominent component of adipose tissue. The spindle cells characteristically express both CD34 and desmin. Herein, we report the clinicopathologic features of nine tumors that were morphologically and immunohistochemically identical to myofibroblastoma of breast; however, they arose in subcutaneous soft tissue at extramammary sites. The study group comprised seven men and two women with an age range of 35-67 years (median 53 years). Lesions presented as either a slowly growing painless mass or were incidental findings at the time of surgery. The site distribution was as follows: inguinal/groin area (five cases) and one case each in posterior vaginal wall, buttock, anterior abdominal wall, and mid-back. Tumor size ranged from 2 to 13 cm (median 6 cm), and all lesions were well circumscribed. Eight tumors had a component of adipose tissue (ranging from 10% to 60%), within which some variation in adipocyte size was often seen. One case showed epithelioid cytomorphology and three cases showed rare atypical or multinucleated cells. Focal myxoid stromal change was seen in four cases. Tumor cells were positive for desmin (9 of 9 cases), CD34 (8 of 9 cases), and occasionally positive for smooth muscle actin (3 of 9 cases). Lesions were marginally excised with no recurrences to date, although follow-up is very limited. Lesions with morphologic and immunophenotypic features similar to myofibroblastoma of breast can arise at extramammary sites, with an apparent predilection for the inguinal area of older men. Both mammary and extramammary lesions show morphologic overlap with spindle cell lipoma and are likely closely related.
20. Identifying mutation regions for closely related individuals without a known pedigree
Science.gov (United States)
2012-01-01
Background Linkage analysis is the first step in the search for a disease gene. Linkage studies have facilitated the identification of several hundred human genes that can harbor mutations leading to a disease phenotype. In this paper, we study a very important case, where the sampled individuals are closely related, but the pedigree is not given. This situation happens very often when the individuals share a common ancestor 6 or more generations ago. To our knowledge, no algorithm can give good results for this case. Results To solve this problem, we first developed some heuristic algorithms for haplotype inference without any given pedigree. We propose a model using the parsimony principle that can be viewed as an extension of the model first proposed by Dan Gusfield. Our heuristic algorithm uses Clark’s inference rule to infer haplotype segments. Conclusions We ran our program both on the simulated data and a set of real data from the phase II HapMap database. Experiments show that our program performs well. The recall value is from 90% to 99% in various cases. This implies that the program can report more than 90% of the true mutation regions. The value of precision varies from 29% to 90%. When the precision is 29%, the size of the reported regions is three times that of the true mutation region. This is still very useful for narrowing down the range of the disease gene location. Our program can complete the computation for all the tested cases, where there are about 110,000 SNPs on a chromosome, within 20 seconds. PMID:22731852
1. Angles-only relative navigation and closed-loop guidance for spacecraft proximity operations
Science.gov (United States)
Luo, Jianjun; Gong, Baichun; Yuan, Jianping; Zhang, Zhaofei
2016-11-01
This research investigates angles-only relative navigation and closed-loop guidance algorithm for spacecraft mid-range orbital proximity operations when the orbital maneuver allows for range observability. Emphasis and contribution are on developing angles-only relative navigation and guidance coupling algorithm in the context of Clohessy-Wiltshire and Tschauner-Hempel dynamics. Observability analysis of the relative state is done and the general mathematical expression of the observable condition is obtained. Coupling relationship between the angles-only relative navigation and the multi-pulse sliding guidance is discussed and its analytic expression is derived. A novel closed-loop guidance scheme is designed based on the coupling relationship and unscented kalman filter. Two-body Monte Carlo simulations are conducted to evaluate the validity and test the performance of the closed-loop system. The sensitivities of the navigation and guidance accuracy to the line-of-sight angles accuracy, initial separation and initial state uncertainties, number of pulses, and dynamics are presented and discussed.
2. Comparative Landscape Genetics of Three Closely Related Sympatric Hesperid Butterflies with Diverging Ecological Traits
Science.gov (United States)
Engler, Jan O.; Balkenhol, Niko; Filz, Katharina J.; Habel, Jan C.; Rödder, Dennis
2014-01-01
To understand how landscape characteristics affect gene flow in species with diverging ecological traits, it is important to analyze taxonomically related sympatric species in the same landscape using identical methods. Here, we present such a comparative landscape genetic study involving three closely related Hesperid butterflies of the genus Thymelicus that represent a gradient of diverging ecological traits. We analyzed landscape effects on their gene flow by deriving inter-population connectivity estimates based on different species distribution models (SDMs), which were calculated from multiple landscape parameters. We then used SDM output maps to calculate circuit-theoretic connectivity estimates and statistically compared these estimates to actual genetic differentiation in each species. We based our inferences on two different analytical methods and two metrics of genetic differentiation. Results indicate that land use patterns influence population connectivity in the least mobile specialist T. acteon. In contrast, populations of the highly mobile generalist T. lineola were panmictic, lacking any landscape related effect on genetic differentiation. In the species with ecological traits in between those of the congeners, T. sylvestris, climate has a strong impact on inter-population connectivity. However, the relative importance of different landscape factors for connectivity varies when using different metrics of genetic differentiation in this species. Our results show that closely related species representing a gradient of ecological traits also show genetic structures and landscape genetic relationships that gradually change from a geographical macro- to micro-scale. Thus, the type and magnitude of landscape effects on gene flow can differ strongly even among closely related species inhabiting the same landscape, and depend on their relative degree of specialization. In addition, the use of different genetic differentiation metrics makes it possible to
3. A hetero-micro-seeding strategy for readily crystallizing closely related protein variants.
Science.gov (United States)
2017-09-01
Protein crystallization remains difficult to rationalize and screening for optimal crystallization conditions is a tedious and time consuming procedure. Here, we report a hetero-micro-seeding strategy for producing high resolution crystals of closely related protein variants, where micro crystals from a readily crystallized variant are used as seeds to develop crystals of other variants less amenable to crystallization. We applied this strategy to Bovine Pancreatic Trypsin Inhibitor (BPTI) variants, which would not crystallize using standard crystallization practice. Out of six variants in our analysis, only one called BPTI-[5,55]A14G formed well behaving crystals; and the remaining five (A14GA38G, A14GA38V, A14GA38L, A14GA38I, and A14GA38K) could be crystallized only using micro-seeds from the BPTI-[5,55]A14G crystal. All hetero-seeded crystals diffracted at high resolution with minimum mosaicity, retaining the same space group and cell dimension. Moreover, hetero-micro-seeding did not introduce any biases into the mutant's structure toward the seed structure, as demonstrated by A14GA38I structures solved using micro-seeds from A14GA38G, A14GA38L and A14GA38I. Though hetero-micro-seeding is a simple and almost naïve strategy, this is the first direct demonstration of its workability. We believe that hetero-micro-seeding, which is contrasting with the popular idea that crystallization requires highly purified proteins, could contribute a new tool for rapidly solving protein structures in mutational analysis studies. Copyright © 2017 Elsevier Inc. All rights reserved.
4. Cooperativity and rapid evolution of cobound transcription factors in closely related mammals.
Science.gov (United States)
Stefflova, Klara; Thybert, David; Wilson, Michael D; Streeter, Ian; Aleksic, Jelena; Karagianni, Panagiota; Brazma, Alvis; Adams, David J; Talianidis, Iannis; Marioni, John C; Flicek, Paul; Odom, Duncan T
2013-08-01
To mechanistically characterize the microevolutionary processes active in altering transcription factor (TF) binding among closely related mammals, we compared the genome-wide binding of three tissue-specific TFs that control liver gene expression in six rodents. Despite an overall fast turnover of TF binding locations between species, we identified thousands of TF regions of highly constrained TF binding intensity. Although individual mutations in bound sequence motifs can influence TF binding, most binding differences occur in the absence of nearby sequence variations. Instead, combinatorial binding was found to be significant for genetic and evolutionary stability; cobound TFs tend to disappear in concert and were sensitive to genetic knockout of partner TFs. The large, qualitative differences in genomic regions bound between closely related mammals, when contrasted with the smaller, quantitative TF binding differences among Drosophila species, illustrate how genome structure and population genetics together shape regulatory evolution.
5. Usefulness of cpDNA markers for phylogenetic and phylogeographic analyses of closely related cactus species.
Science.gov (United States)
Bonatelli, I A S; Zappi, D C; Taylor, N P; Moraes, E M
2013-02-28
Although plastid DNA has been widely explored as a marker of choice for phylogeny and phylogeography studies, little is known about its utility for examining relationships between closely related species. The slow evolutionary rates inherent to chloroplast (cp) DNA make it difficult to perform lower level taxonomic analyses, particularly at the population level. We characterized the nucleotide variation and investigated the utility of eight noncoding cpDNA regions in four closely related species of the Pilosocereus aurisetus group (Cactaceae), an endemic taxon of eastern South America. The plastid intergenic spacers 5'-trnS-trnG, 3'-trnS-trnG and trnT-trnL were the most variable regions and were the most useful for lower level taxonomic comparisons, especially when used together. We conclude that an adequate combination of regions alongside indels as an additional character improves the usefulness of cpDNA for phylogenetic studies.
6. Cooperativity and Rapid Evolution of Cobound Transcription Factors in Closely Related Mammals
OpenAIRE
Stefflova, Klara,; Thybert, David; Wilson, Michael D.; Streeter, Ian; Aleksic, Jelena; Karagianni, Panagiota; Brazma, Alvis; Adams, David J.; Talianidis, Iannis; Marioni, John C.; Flicek, Paul; Odom, Duncan T.
2013-01-01
Summary To mechanistically characterize the microevolutionary processes active in altering transcription factor (TF) binding among closely related mammals, we compared the genome-wide binding of three tissue-specific TFs that control liver gene expression in six rodents. Despite an overall fast turnover of TF binding locations between species, we identified thousands of TF regions of highly constrained TF binding intensity. Although individual mutations in bound sequence motifs can influence ...
7. Algal culture studies related to a Closed Ecological Life Support System (CELSS)
Science.gov (United States)
Radmer, R.; Behrens, P.; Fernandez, E.; Ollinger, O.; Howell, C.; Venables, A.; Huggins, D.; Gladue, R.
1984-01-01
In many respects, algae would be the ideal plant component for a biologically based controlled life support system, since they are eminently suited to the closely coupled functions of atmosphere regeneration and food production. Scenedesmus obliquus and Spirulina platensis were grown in three continuous culture apparatuses. Culture vessels their operation and relative merits are described. Both light and nitrogen utilization efficiency are examined. Long term culture issues are detailed and a discussion of a plasmid search in Spirulina is included.
8. Identification of a cysteine protease closely related to interleukin-1 beta-converting enzyme.
Science.gov (United States)
Faucheu, C; Blanchet, A M; Collard-Dutilleul, V; Lalanne, J L; Diu-Hercend, A
1996-02-15
The present study describes the identification and molecular cloning of a new member of the interleukin-1 beta-converting enzyme (ICE) family denoted transcript Y (TY). TY is very closely related to both ICE (51% amino acid identity) and a protein named transcript X (TX) (75% amino acid identity) that we recently identified [Faucheu, C., Diu, A., Chan, A.W.E., Blanchet, A.-M., Miossec, C., Hervé, F.,Collard-Dutilleul, V., Gu, Y., Aldape, R., Lippke, J., Rocher, C., Su, M.S.-S., Livingston, D.J., Hercend, T. & Lalanne, J.-L. (1995) EMBO J. 14, 1914-1922]. The amino acids that are implicated in both the ICE catalytic site and in the PI aspartate-binding pocket are conserved in TY. Within the ICE gene family, TY belongs to a subfamily of proteins closely related to the prototype ICE protein. Using transfection experiments into mammalian cells, we demonstrate that TY has protease activity on its own precursor and that this activity is dependent on the presence of a cysteine residue at position 245. However, despite the close similarity between TY and ICE active sites, TY fails to process the interleukin-1 beta precursor. In addition, as already observed for ICE and TX, TY is able to induce apoptosis when overexpressed in COS cells. TY therefore represents a new member of the growing family of apoptosis-inducing ICE-related cysteine proteases.
9. Perspectives of patients, close relatives, nurses, and physicians on end-of-life medication management.
Science.gov (United States)
Dees, Marianne K; Geijteman, Eric C T; Dekkers, Wim J M; Huisman, Bregje A A; Perez, Roberto S G M; van Zuylen, Lia; van der Heide, Agnes; van Leeuwen, Evert
2017-08-14
Our aim was to gain insight into the perspectives of patients, close relatives, nurses, and physicians on medication management for patients with a life expectancy of less than 3 months. We conducted an empirical multicenter study with a qualitative approach, including in-depth interviews with patients, relatives, nurses, specialists, and general practitioners (GPs). We used the constant comparative method and ATLAS.ti (v. 7.1) software for our analysis. Saturation occurred after 18 patient cases (76 interviews). Some 5 themes covering 18 categories were identified: (1) priorities in end-of-life care, such as symptom management and maintaining hope; (2) appropriate medication use, with attention to unnecessary medication and deprescription barriers; (3) roles in decision making, including physicians in the lead, relatives' advocacy, and pharmacists as suppliers; (4) organization and communication (e.g., transparency of tasks and end-of-life conversations); and (5) prerequisites about professional competence, accessibility and quality of medical records, and financial awareness. Patients, relatives, nurses, specialists, and GPs varied in their opinions about these themes. This study adds to our in-depth understanding of the complex practice of end-of-life medication management. It provides knowledge about the diversity of the perspectives of patients, close relatives, nurses, and physicians regarding beliefs, attitudes, knowledge, skills, behavior, work setting, the health system, and cultural factors related to the matter. Our results might help to draw an interdisciplinary end-of-life medication management guide aimed at stimulating a multidisciplinary and patient-centered pharmacotherapeutic care approach.
10. Relational mobility explains between- and within-culture differences in self-disclosure to close friends.
Science.gov (United States)
Schug, Joanna; Yuki, Masaki; Maddux, William
2010-10-01
In the current research, we tested a novel explanation for previously demonstrated findings that East Asians disclose less personal information to other people than do Westerners. We propose that both between- and within-culture differences in self-disclosure to close friends may be explained by the construct of relational mobility, the general degree to which individuals in a society have opportunities to form new relationships and terminate old ones. In Study 1, we found that cross-cultural differences (Japan vs. United States) in self-disclosure to a close friend were mediated by individuals' perceptions of relational mobility. In Study 2, two separate measures of relational mobility predicted self-disclosure within a single culture (Japan), and this relationship was mediated by the motivation to engage in self-disclosure to strengthen personal relationships. We conclude that societies and social contexts higher in relational mobility (in which relationships can be formed and dissolved relatively easily) produce stronger incentives for self-disclosure as a social-commitment device.
11. Power, attraction, and reference in macrolevel social relations: An analysis of closed groups and closed societies based on the psychology of the “Soviet person”
Directory of Open Access Journals (Sweden)
2017-03-01
Full Text Available In this article the features of social-relationship systems are analyzed based on the data from a sociopsychological empirical study conducted in two stages (2002 and 2014 on a large sample with the help of g. Kelly’s Repertory grid Technique. A. V. Petrovsky’s three-factor interpersonal-relationships model as interpreted for closed groups by M. Yu. Kondratev and the concept of the closed society as described by Karl Popper provide the foundation for the theoretical hypothesis we tested. The empirical data obtained in 2002 came from 391 participants of different ages who were living in provincial towns in the Nizhny Novgorod region. The elderly respondents (232 people had lived almost all their lives under the Soviet regime; the middle-aged respondents (159 people got their education and started their careers in the USSR. Soviet society is considered to be closed because of its authoritarian and collectivist nature, static social structure, and dogmatic ideology. It is argued that both closed societies and closed groups are characterized by a rigid hierarchical social structure, isolation from other systems, and depersonalization of social relations. We have proved that members of a closed group and citizens of a closed society have similar social-relationship matrices.
12. SELECTION OF PHYLOGENETICALLY CLOSELY-RELATED YERSINIA PESTIS STRAINS DIFFERING IN THEIR VIRULENCE FOR GUINEA PIGS
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N. V. Anisimov
2015-01-01
Full Text Available Genomic, transcriptome or (and proteomic comparison of closely related virulent and avirulent microbial strains underlies the search for new pathogenicity factors, potential molecular targets for etiotropic therapy, vaccine prevention and immunotherapy of infectious diseases. This investigation was aimed in testing the ability of method of testicular animalization to select phylogenetically close pairs of Y. pestis strains, which dramatically differ in their pathogenicity for guinea pigs, from the populations of as a rule subcutaneously avirulent for guinea pigs “vole” strains of the plague pathogen. Animalization of Y. pestis cultures were performed on guinea pig males by fourfold testicular passage with reducing infective dose. There was no correlation between the ability to cause generalized infectious process (death after testicular and subcutaneous infection of guinea pigs, but testicular passages made it possible to enrich bacterial culture with a portion of microbes displaying high virulence after subcutaneous infection of this animal species. The methodical approach under study can be successfully applied for selection of pairs of phylogenetically closely related bacterial strains, dramatically differing in their degrees of selective virulence.
13. Origins and close relatives of a semi-domesticated neotropical fruit tree: Chrysophyllum cainito (Sapotaceae).
Science.gov (United States)
Petersen, Jennifer J; Parker, Ingrid M; Potter, Daniel
2012-03-01
Understanding patterns and processes associated with domestication has implications for crop development and agricultural biodiversity conservation. Semi-domesticated crops provide excellent opportunities to examine the interplay of natural and anthropogenic influences on plant evolution. The domestication process has not been thoroughly examined in many tropical perennial crop species. Chrysophyllum cainito (Sapotaceae), the star apple or caimito, is a semi-domesticated species widely cultivated for its edible fruits. It is known to be native to the neotropics, but the precise geographic origins of wild and cultivated forms are unresolved. We used nuclear ribosomal ITS sequences to infer phylogenetic relationships among C. cainito and close relatives (section Chrysophyllum). We employed phylogeographic approaches using ITS and plastid sequence data to determine geographic origins and center(s) of domestication of caimito. ITS data suggest a close relationship between C. cainito and C. argenteum. Plastid haplotype networks reveal several haplotypes unique to individual taxa but fail to resolve distinct lineages for either C. cainito or C. argenteum. Caimito populations from northern Mesoamerica and the Antilles exhibit a subset of the genetic diversity found in southern Mesoamerica. In Panama, cultivated caimito retains high levels of the diversity seen in wild populations. Chrysophyllum cainito is most closely related to a clade containing Central and South American C. argenteum, including subsp. panamense. We hypothesize that caimito is native to southern Mesoamerica and was domesticated from multiple wild populations in Panama. Subsequent migration into northern Mesoamerica and the Antilles was mediated by human cultivation.
14. Identifying the Best-Fitting Factor Structure of the Experience of Close Relations
DEFF Research Database (Denmark)
Esbjørn, Barbara Hoff; Breinholst, Sonja; Niclasen, Janni
2015-01-01
The aim of this study was to enhance the understanding of cultural and sample differences in the assessment of attachment by examining the factor structure of the Experiences in Close Relationships-Revised (ECR-R). The ECR-R is a self-report measure of adult roman- tic attachment dimensions....... The present study used a Danish sample with the purpose of addressing limitations in previous studies, such as the lack of diversity in cultural back- ground, restricted sample characteristics, and poorly fitting structure models. Participants consisted of 253 parents of children between the ages of 7 and 12...
15. Closed Hearts, Closed Minds: The Textbook Story of Marriage. A Report to the Nation from the Council on Families.
Science.gov (United States)
Glenn, Norval D.; Gallagher, Maggie; Blankenhorn, David, Ed.
This report is a summary opinion of current undergraduate marriage and family textbooks. The report suggests some textbooks are deficient, erroneous, and distorted in information given about marriage. Subheadings include: (1)"Why Textbooks Matter"; (2) "The Textbook Story of Marriage"; (3) "The Dangerous Institution"; (4) "People Who Love Too…
16. Transfusion-related acute lung injury: report of two cases.
Science.gov (United States)
Čermáková, Z; Kořískta, M; Blahutová, Š; Dvořáčková, J; Brát, R; Valkovský, I; Hrdličková, R
2012-01-01
Transfusion-related acute lung injury (TRALI) is a severe life-threatening complication of blood transfusion, characterized by acute lung injury developing within 2-6 h of transfusion. However, TRALI is difficult to diagnose, and the initial report or suspicion of TRALI depends on close collaboration between clinical departments and transfusion centres. A total of 17 adverse post-transfusion reactions were reported to the Blood Centre of the University Hospital Ostrava as suspected TRALI between 2005 and 2010. We report two cases of serious TRALI with different pathogenetic mechanisms.
17. Genome Annotation Transfer Utility (GATU: rapid annotation of viral genomes using a closely related reference genome
Directory of Open Access Journals (Sweden)
Upton Chris
2006-06-01
Full Text Available Abstract Background Since DNA sequencing has become easier and cheaper, an increasing number of closely related viral genomes have been sequenced. However, many of these have been deposited in GenBank without annotations, severely limiting their value to researchers. While maintaining comprehensive genomic databases for a set of virus families at the Viral Bioinformatics Resource Center http://www.biovirus.org and Viral Bioinformatics – Canada http://www.virology.ca, we found that researchers were unnecessarily spending time annotating viral genomes that were close relatives of already annotated viruses. We have therefore designed and implemented a novel tool, Genome Annotation Transfer Utility (GATU, to transfer annotations from a previously annotated reference genome to a new target genome, thereby greatly reducing this laborious task. Results GATU transfers annotations from a reference genome to a closely related target genome, while still giving the user final control over which annotations should be included. GATU also detects open reading frames present in the target but not the reference genome and provides the user with a variety of bioinformatics tools to quickly determine if these ORFs should also be included in the annotation. After this process is complete, GATU saves the newly annotated genome as a GenBank, EMBL or XML-format file. The software is coded in Java and runs on a variety of computer platforms. Its user-friendly Graphical User Interface is specifically designed for users trained in the biological sciences. Conclusion GATU greatly simplifies the initial stages of genome annotation by using a closely related genome as a reference. It is not intended to be a gene prediction tool or a "complete" annotation system, but we have found that it significantly reduces the time required for annotation of genes and mature peptides as well as helping to standardize gene names between related organisms by transferring reference genome
18. Genome Annotation Transfer Utility (GATU): rapid annotation of viral genomes using a closely related reference genome.
Science.gov (United States)
Tcherepanov, Vasily; Ehlers, Angelika; Upton, Chris
2006-06-13
Since DNA sequencing has become easier and cheaper, an increasing number of closely related viral genomes have been sequenced. However, many of these have been deposited in GenBank without annotations, severely limiting their value to researchers. While maintaining comprehensive genomic databases for a set of virus families at the Viral Bioinformatics Resource Center http://www.biovirus.org and Viral Bioinformatics - Canada http://www.virology.ca, we found that researchers were unnecessarily spending time annotating viral genomes that were close relatives of already annotated viruses. We have therefore designed and implemented a novel tool, Genome Annotation Transfer Utility (GATU), to transfer annotations from a previously annotated reference genome to a new target genome, thereby greatly reducing this laborious task. GATU transfers annotations from a reference genome to a closely related target genome, while still giving the user final control over which annotations should be included. GATU also detects open reading frames present in the target but not the reference genome and provides the user with a variety of bioinformatics tools to quickly determine if these ORFs should also be included in the annotation. After this process is complete, GATU saves the newly annotated genome as a GenBank, EMBL or XML-format file. The software is coded in Java and runs on a variety of computer platforms. Its user-friendly Graphical User Interface is specifically designed for users trained in the biological sciences. GATU greatly simplifies the initial stages of genome annotation by using a closely related genome as a reference. It is not intended to be a gene prediction tool or a "complete" annotation system, but we have found that it significantly reduces the time required for annotation of genes and mature peptides as well as helping to standardize gene names between related organisms by transferring reference genome annotations to the target genome. The program is freely
19. Phylogenomics Reveals Convergent Evolution of Lifestyles in Close Relatives of Animals and Fungi.
Science.gov (United States)
Torruella, Guifré; de Mendoza, Alex; Grau-Bové, Xavier; Antó, Meritxell; Chaplin, Mark A; del Campo, Javier; Eme, Laura; Pérez-Cordón, Gregorio; Whipps, Christopher M; Nichols, Krista M; Paley, Richard; Roger, Andrew J; Sitjà-Bobadilla, Ariadna; Donachie, Stuart; Ruiz-Trillo, Iñaki
2015-09-21
The Opisthokonta are a eukaryotic supergroup divided in two main lineages: animals and related protistan taxa, and fungi and their allies [1, 2]. There is a great diversity of lifestyles and morphologies among unicellular opisthokonts, from free-living phagotrophic flagellated bacterivores and filopodiated amoebas to cell-walled osmotrophic parasites and saprotrophs. However, these characteristics do not group into monophyletic assemblages, suggesting rampant convergent evolution within Opisthokonta. To test this hypothesis, we assembled a new phylogenomic dataset via sequencing 12 new strains of protists. Phylogenetic relationships among opisthokonts revealed independent origins of filopodiated amoebas in two lineages, one related to fungi and the other to animals. Moreover, we observed that specialized osmotrophic lifestyles evolved independently in fungi and protistan relatives of animals, indicating convergent evolution. We therefore analyzed the evolution of two key fungal characters in Opisthokonta, the flagellum and chitin synthases. Comparative analyses of the flagellar toolkit showed a previously unnoticed flagellar apparatus in two close relatives of animals, the filasterean Ministeria vibrans and Corallochytrium limacisporum. This implies that at least four different opisthokont lineages secondarily underwent flagellar simplification. Analysis of the evolutionary history of chitin synthases revealed significant expansions in both animals and fungi, and also in the Ichthyosporea and C. limacisporum, a group of cell-walled animal relatives. This indicates that the last opisthokont common ancestor had a complex toolkit of chitin synthases that was differentially retained in extant lineages. Thus, our data provide evidence for convergent evolution of specialized lifestyles in close relatives of animals and fungi from a generalist ancestor. Copyright © 2015 Elsevier Ltd. All rights reserved.
20. Comparative genomics and phylogenetic discordance of cultivated tomato and close wild relatives
Directory of Open Access Journals (Sweden)
Susan R. Strickler
2015-02-01
Full Text Available Background. Studies of ancestry are difficult in the tomato because it crosses with many wild relatives and species in the tomato clade that have diverged very recently. As a result, the phylogeny in relation to its closest relatives remains uncertain. By using the coding sequence from Solanum lycopersicum, S. galapagense, S. pimpinellifolium, S. corneliomuelleri, and S. tuberosum and the genomic sequence from S. lycopersicum ‘Heinz’, an heirloom line, S. lycopersicum ‘Yellow Pear’, and two of cultivated tomato’s closest relatives, S. galapagense and S. pimpinellifolium, we have aimed to resolve the phylogenies of these closely related species as well as identify phylogenetic discordance in the reference cultivated tomato.Results. Divergence date estimates suggest that the divergence of S. lycopersicum, S. galapagense, and S. pimpinellifolium happened less than 0.5 MYA. Phylogenies based on 8,857 coding sequences support grouping of S. lycopersicum and S. galapagense, although two secondary trees are also highly represented. A total of 25 genes in our analysis had sites with evidence of positive selection along the S. lycopersicum lineage. Whole genome phylogenies showed that while incongruence is prevalent in genomic comparisons between these genotypes, likely as a result of introgression and incomplete lineage sorting, a primary phylogenetic history was strongly supported.Conclusions. Based on analysis of these genotypes, S. galapagense appears to be closely related to S. lycopersicum, suggesting they had a common ancestor prior to the arrival of an S. galapagense ancestor to the Galápagos Islands, but after divergence of the sequenced S. pimpinellifolium. Genes showing selection along the S. lycopersicum lineage may be important in domestication or selection occurring post-domestication. Further analysis of intraspecific data in these species will help to establish the evolutionary history of cultivated tomato. The use of an
1. Comparative genomics and phylogenetic discordance of cultivated tomato and close wild relatives
Science.gov (United States)
Bombarely, Aureliano; Munkvold, Jesse D.; York, Thomas; Menda, Naama; Martin, Gregory B.; Mueller, Lukas A.
2015-01-01
Background. Studies of ancestry are difficult in the tomato because it crosses with many wild relatives and species in the tomato clade that have diverged very recently. As a result, the phylogeny in relation to its closest relatives remains uncertain. By using the coding sequence from Solanum lycopersicum, S. galapagense, S. pimpinellifolium, S. corneliomuelleri, and S. tuberosum and the genomic sequence from S. lycopersicum ‘Heinz’, an heirloom line, S. lycopersicum ‘Yellow Pear’, and two of cultivated tomato’s closest relatives, S. galapagense and S. pimpinellifolium, we have aimed to resolve the phylogenies of these closely related species as well as identify phylogenetic discordance in the reference cultivated tomato. Results. Divergence date estimates suggest that the divergence of S. lycopersicum, S. galapagense, and S. pimpinellifolium happened less than 0.5 MYA. Phylogenies based on 8,857 coding sequences support grouping of S. lycopersicum and S. galapagense, although two secondary trees are also highly represented. A total of 25 genes in our analysis had sites with evidence of positive selection along the S. lycopersicum lineage. Whole genome phylogenies showed that while incongruence is prevalent in genomic comparisons between these genotypes, likely as a result of introgression and incomplete lineage sorting, a primary phylogenetic history was strongly supported. Conclusions. Based on analysis of these genotypes, S. galapagense appears to be closely related to S. lycopersicum, suggesting they had a common ancestor prior to the arrival of an S. galapagense ancestor to the Galápagos Islands, but after divergence of the sequenced S. pimpinellifolium. Genes showing selection along the S. lycopersicum lineage may be important in domestication or selection occurring post-domestication. Further analysis of intraspecific data in these species will help to establish the evolutionary history of cultivated tomato. The use of an heirloom line is helpful
2. Comparative genomics and phylogenetic discordance of cultivated tomato and close wild relatives.
Science.gov (United States)
Strickler, Susan R; Bombarely, Aureliano; Munkvold, Jesse D; York, Thomas; Menda, Naama; Martin, Gregory B; Mueller, Lukas A
2015-01-01
Background. Studies of ancestry are difficult in the tomato because it crosses with many wild relatives and species in the tomato clade that have diverged very recently. As a result, the phylogeny in relation to its closest relatives remains uncertain. By using the coding sequence from Solanum lycopersicum, S. galapagense, S. pimpinellifolium, S. corneliomuelleri, and S. tuberosum and the genomic sequence from S. lycopersicum 'Heinz', an heirloom line, S. lycopersicum 'Yellow Pear', and two of cultivated tomato's closest relatives, S. galapagense and S. pimpinellifolium, we have aimed to resolve the phylogenies of these closely related species as well as identify phylogenetic discordance in the reference cultivated tomato. Results. Divergence date estimates suggest that the divergence of S. lycopersicum, S. galapagense, and S. pimpinellifolium happened less than 0.5 MYA. Phylogenies based on 8,857 coding sequences support grouping of S. lycopersicum and S. galapagense, although two secondary trees are also highly represented. A total of 25 genes in our analysis had sites with evidence of positive selection along the S. lycopersicum lineage. Whole genome phylogenies showed that while incongruence is prevalent in genomic comparisons between these genotypes, likely as a result of introgression and incomplete lineage sorting, a primary phylogenetic history was strongly supported. Conclusions. Based on analysis of these genotypes, S. galapagense appears to be closely related to S. lycopersicum, suggesting they had a common ancestor prior to the arrival of an S. galapagense ancestor to the Galápagos Islands, but after divergence of the sequenced S. pimpinellifolium. Genes showing selection along the S. lycopersicum lineage may be important in domestication or selection occurring post-domestication. Further analysis of intraspecific data in these species will help to establish the evolutionary history of cultivated tomato. The use of an heirloom line is helpful in
3. Two closely related species of Caloplaca (Teloschistaceae, Lichenes from the Namib Desert
Directory of Open Access Journals (Sweden)
I. Kärnefelt
1988-12-01
Full Text Available The anatomical and reproductive adaptations of two closely related lichen species. Caloplaca elegantissima (Nyl. Zahlbr. and C. namibensis Karnef., sp. nov., occurring in the outer Namib fog desert, are discussed. Both species belong to the cmstose forms, frequently found in the remarkably rich lichen communities, which largely depend on fog precipitation for their water supply. Both species are endemic to the Namib Desert. They are mainly distributed in South West Africa/Namibia but also extend into south-western Angola. The asexual isidiate species. C. namibensis Karnef., is described as new.
4. Species tree estimation for the late blight pathogen, Phytophthora infestans, and close relatives.
Directory of Open Access Journals (Sweden)
Jaime E Blair
Full Text Available To better understand the evolutionary history of a group of organisms, an accurate estimate of the species phylogeny must be known. Traditionally, gene trees have served as a proxy for the species tree, although it was acknowledged early on that these trees represented different evolutionary processes. Discordances among gene trees and between the gene trees and the species tree are also expected in closely related species that have rapidly diverged, due to processes such as the incomplete sorting of ancestral polymorphisms. Recently, methods have been developed for the explicit estimation of species trees, using information from multilocus gene trees while accommodating heterogeneity among them. Here we have used three distinct approaches to estimate the species tree for five Phytophthora pathogens, including P. infestans, the causal agent of late blight disease in potato and tomato. Our concatenation-based "supergene" approach was unable to resolve relationships even with data from both the nuclear and mitochondrial genomes, and from multiple isolates per species. Our multispecies coalescent approach using both Bayesian and maximum likelihood methods was able to estimate a moderately supported species tree showing a close relationship among P. infestans, P. andina, and P. ipomoeae. The topology of the species tree was also identical to the dominant phylogenetic history estimated in our third approach, Bayesian concordance analysis. Our results support previous suggestions that P. andina is a hybrid species, with P. infestans representing one parental lineage. The other parental lineage is not known, but represents an independent evolutionary lineage more closely related to P. ipomoeae. While all five species likely originated in the New World, further study is needed to determine when and under what conditions this hybridization event may have occurred.
5. Species Tree Estimation for the Late Blight Pathogen, Phytophthora infestans, and Close Relatives
Science.gov (United States)
Blair, Jaime E.; Coffey, Michael D.; Martin, Frank N.
2012-01-01
To better understand the evolutionary history of a group of organisms, an accurate estimate of the species phylogeny must be known. Traditionally, gene trees have served as a proxy for the species tree, although it was acknowledged early on that these trees represented different evolutionary processes. Discordances among gene trees and between the gene trees and the species tree are also expected in closely related species that have rapidly diverged, due to processes such as the incomplete sorting of ancestral polymorphisms. Recently, methods have been developed for the explicit estimation of species trees, using information from multilocus gene trees while accommodating heterogeneity among them. Here we have used three distinct approaches to estimate the species tree for five Phytophthora pathogens, including P. infestans, the causal agent of late blight disease in potato and tomato. Our concatenation-based “supergene” approach was unable to resolve relationships even with data from both the nuclear and mitochondrial genomes, and from multiple isolates per species. Our multispecies coalescent approach using both Bayesian and maximum likelihood methods was able to estimate a moderately supported species tree showing a close relationship among P. infestans, P. andina, and P. ipomoeae. The topology of the species tree was also identical to the dominant phylogenetic history estimated in our third approach, Bayesian concordance analysis. Our results support previous suggestions that P. andina is a hybrid species, with P. infestans representing one parental lineage. The other parental lineage is not known, but represents an independent evolutionary lineage more closely related to P. ipomoeae. While all five species likely originated in the New World, further study is needed to determine when and under what conditions this hybridization event may have occurred. PMID:22615869
6. RUGBY GAME-RELATED STATISTICS THAT DISCRIMINATE BETWEEN WINNING AND LOSING TEAMS IN IRB AND SUPER TWELVE CLOSE GAMES
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Luis Vaz
2010-03-01
Full Text Available The aim of the current study was to identify the Rugby game- related statistics that discriminated between winning and losing teams in IRB and S12 close games. Archival data reported to game-related statistics from 120 IRB games and 204 Super Twelve games played between 2003 and 2006. Afterwards, a cluster analysis was conducted to establish, according to game final score differences, three different match groups. Only the close games group was selected for further analysis (IRB n = 64 under 15 points difference and Super Twelve n = 95 under 11 points difference. An analysis to the structure coefficients (SC obtained through a discriminant analysis allowed to identify the most powerful game-related statistics in discriminating between winning and losing teams. The discriminant functions were statistically significant for Super Twelve games (Chi-square = 33.8, p < 0.01, but not for IRB games (Chi- square = 9.4, p = n.s.. In the first case, winners and losers were discriminated by possessions kicked (SC = 0.48, tackles made (SC = 0.45, rucks and pass (SC = -0.40, passes completed (SC = 0. 39, mauls won (SC = -0.36, turnovers won (SC = -0.33, kicks to touch (SC = 0.32 and errors made (SC = -0.32. The minus sign denotes higher values in losing teams. Rugby game-related statistics were able to discriminate between winners and losers in Super Twelve close games and suggest that a kicking based game supported by an effective defensive structure is more likely to win matches than a possession based one
7. Comparative genome analysis of the closely related Synechocystis strains PCC 6714 and PCC 6803.
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Kopf, Matthias; Klähn, Stephan; Pade, Nadin; Weingärtner, Christian; Hagemann, Martin; Voß, Björn; Hess, Wolfgang R
2014-06-01
Synechocystis sp. PCC 6803 is the most popular cyanobacterial model for prokaryotic photosynthesis and for metabolic engineering to produce biofuels. Genomic and transcriptomic comparisons between closely related bacteria are powerful approaches to infer insights into their metabolic potentials and regulatory networks. To enable a comparative approach, we generated the draft genome sequence of Synechocystis sp. PCC 6714, a closely related strain of 6803 (16S rDNA identity 99.4%) that also is amenable to genetic manipulation. Both strains share 2838 protein-coding genes, leaving 845 unique genes in Synechocystis sp. PCC 6803 and 895 genes in Synechocystis sp. PCC 6714. The genetic differences include a prophage in the genome of strain 6714, a different composition of the pool of transposable elements, and a ∼ 40 kb genomic island encoding several glycosyltransferases and transport proteins. We verified several physiological differences that were predicted on the basis of the respective genome sequence. Strain 6714 exhibited a lower tolerance to Zn(2+) ions, associated with the lack of a corresponding export system and a lowered potential of salt acclimation due to the absence of a transport system for the re-uptake of the compatible solute glucosylglycerol. These new data will support the detailed comparative analyses of this important cyanobacterial group than has been possible thus far. Genome information for Synechocystis sp. PCC 6714 has been deposited in Genbank (accession no AMZV01000000). © The Author 2014. Published by Oxford University Press on behalf of Kazusa DNA Research Institute.
8. Genetic basis of hybrid male sterility among three closely related species of Drosophila.
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Mishra, Paras Kumar; Singh, B N
2005-05-01
The genetic basis of hybrid male sterility among three closely related species, Drosophila bipectinata, D. parabipectinata and D. malerkotliana has been investigated by using backcross analysis methods. The role of Y chromosome, major hybrid sterility (MHS) genes (genetic factors) and cytoplasm (non-genetic factor) have been studied in the hybrids of these three species. In the species pair, bipectinata--parabipectinata, Y chromosome introgression of parabipectinata in the genomic background of bipectinata and the reciprocal Y chromosome introgression were unsuccessful as all males in second backcross generation were sterile. Neither MHS genes nor cytoplasm was found important for sterility. This suggests the involvement of X-Y, X-autosomes or polygenic interactions in hybrid male sterility. In bipectinata--malerkotliana and parabipectinata--malerkotliana species pairs, Y chromosome substitution in reciprocal crosses did not affect male fertility. Backcross analyses also show no involvement of MHS genes or cytoplasm in hybrid male sterility in these two species pairs. Therefore, X- autosome interaction or polygenic interaction is supposed to be involved in hybrid male sterility in these two species pairs. These findings also provide evidence that even in closely related species, genetic interactions underlying hybrid male sterility may vary.
9. Close relation between quantum interference in molecular conductance and diradical existence.
Science.gov (United States)
Tsuji, Yuta; Hoffmann, Roald; Strange, Mikkel; Solomon, Gemma C
2016-01-26
An empirical observation of a relationship between a striking feature of electronic transmission through a π-system, destructive quantum interference (QI), on one hand, and the stability of diradicals on the other, leads to the proof of a general theorem that relates the two. Subject to a number of simplifying assumptions, in a π-electron system, QI occurs when electrodes are attached to those positions of an N-carbon atom N-electron closed-shell hydrocarbon where the matrix elements of the Green's function vanish. These zeros come in two types, which are called easy and hard. Suppose an N+2 atom, N+2 electron hydrocarbon is formed by substituting 2 CH2 groups at two atoms, where the electrodes were. Then, if a QI feature is associated with electrode attachment to the two atoms of the original N atom system, the resulting augmented N+2 molecule will be a diradical. If there is no QI feature, i.e., transmission of current is normal if electrodes are attached to the two atoms, the resulting hydrocarbon will not be a diradical but will have a classical closed-shell electronic structure. Moreover, where a diradical exists, the easy zero is associated with a nondisjoint diradical, and the hard zero is associated with a disjoint one. A related theorem is proven for deletion of two sites from a hydrocarbon.
10. Do plant traits predict the competitive abilities of closely related species?
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Schwartz, Lauren M; Gibson, David J; Young, Bryan G
2015-12-31
Invasive species are a threat to every ecosystem. There is a strong incentive to predict which species will become invasive before they become too widespread and unmanageable. Different approaches have been advocated to assess invasive species potential. These include examining plant functional traits, quantifying competitive ability and phylogenetic comparison. In this study, we conducted experiments based on the above approaches in a multi-year, temporally replicated, set of experiments to compare these assessment methods to determine the invasive potential of Japanese chaff flower (Achyranthes japonica). We compared plant traits and competitive ability of Japanese chaff flower with two agricultural invasive species, Palmer amaranth (Amaranthus palmeri) and tall waterhemp (Amaranthus tuberculatus), and one endangered plant species, bloodleaf (Iresine rhizomatosa), in the Amaranthaceae. Additionally, we assessed the invasive potential based on each of these approaches and determined the degree of agreement between them. A relatively conservative assessment integrating all three approaches would be that the competitive ability of closely related individuals with similar functional traits would share invasive potential. In a greenhouse experiment, each of the study species and soya beans were grown as monocultures and were evaluated to assess the drawdown of an aboveground (light) and a belowground (nitrogen) resource. In a field experiment, each study species was grown at varying densities per 15-cm-diameter pot with or without one or two soya bean plants, to simulate relative densities for soya beans grown in 38- and 76-cm-wide row spacing, respectively. In addition, Japanese chaff flower seedlings were planted either as un-manipulated seedlings or as a seedling cut back to the soil surface at the four-node stage (cut Japanese chaff flower) at which point seedlings have reached a perennial growth stage. The greenhouse experiment showed that each species drew down
11. Summary report: Working group 5 on {open_quotes}Particle Beam Sources{close_quotes}
Energy Technology Data Exchange (ETDEWEB)
Serafini, L. [INFN-Milano and UCLA Dept. of Physics and Astronomy 405 Hilgard Ave., Los Angeles, California 90095-1547 (United States); Yeremian, A.D. [SLAC---Stanford, P.O. Box 4349, M/S 26, Stanford, California 94309 (United States)
1997-03-01
We report here on the activity carried in the working group on {open_quotes}Particle Beam Sources,{close_quotes} which was actually focused on electron beams and mostly covered the progress and future perspectives of laser driven RF photo-injectors. Recent experimental work on other types of electron sources were also presented: the pulsed power guns in our working group, while the plasma-based electron injectors in a joint session held with the working group on {open_quotes}Plasma-Based Accelerator Concepts.{close_quotes} Several beam dynamics issues of general interest in the field of high brightness beams production and manipulation have also been addressed by discussions and a number of communications in our working group. {copyright} {ital 1997 American Institute of Physics.}
12. 46 CFR 308.535 - Certificate to be attached to final closing report, Form MA-313-B.
Science.gov (United States)
2010-10-01
... MA-313-B. 308.535 Section 308.535 Shipping MARITIME ADMINISTRATION, DEPARTMENT OF TRANSPORTATION... § 308.535 Certificate to be attached to final closing report, Form MA-313-B. The Standard Form of Certificate, Form MA-313-B, shall be attached to the final closing report after cancellation of the...
13. Isolation and characterisation of a ruminant alphaherpesvirus closely related to bovine herpesvirus 1 in a free-ranging red deer
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Belák Sándor
2007-09-01
Full Text Available Abstract Background The genus Varicellovirus of the Herpesviridae subfamily Alphaherpesvirinae includes a cluster of viruses antigenically and genetically related to bovine herpesvirus 1 (BoHV-1: namely bovine herpesvirus 5 (BoHV-5, bubaline herpesvirus 1 (BuHV-1, caprine herpesvirus 1 (CpHV-1, cervid herpesviruses 1 (CvHV-1 and 2 (CvHV-2 and elk herpesvirus 1 (ElkHV-1. Considering the serological relationship between these ruminant alphaherpesviruses, several surveys have studied the occurrence of BoHV-1 related virus infection in wild and domestic ruminant species. In this way, a recent investigation has indicated, in Belgium, a high increase in the serological prevalence of BoHV-1 related virus infection in free-ranging red deer population. In this context, it has been decided to investigate the presence of an alphaherpesvirus spreading in the Belgian free-ranging red deer population. Results The current study reports the first isolation in a free-ranging red deer of a BoHV-1 closely related virus. The isolate was antigenically, genomically and genetically characterised by comparison with several ruminant alphaherpesvirus. Immunofluorescence assays revealed the isolate was antigenically distinct from bovine and caprine alphaherpesviruses. Similarly, BamHI and BstEII restriction analyses demonstrated the genomic difference between the isolate and the other ruminant alphaherpesviruses. Next, the sequencing of selected parts of UL27 and US8 genes showed a high degree of homologies between each BoHV-1 related ruminant alphaherpesvirus and the isolate. Besides the close relationship between all ruminant alphaherpesviruses, the phylogenetic analysis revealed that the isolate clustered with CvHV-1. Conclusion The first isolation of a virus closely related to BoHV-1 in a free-ranging red deer is reported. Data demonstrate that a CvHV-1 strain, named Anlier, circulates in wild red deer in continental Europe. Anlier strain show consistent differences
14. Closely related Campylobacter jejuni strains from different sources reveal a generalist rather than a specialist lifestyle
Science.gov (United States)
2011-01-01
Background Campylobacter jejuni and Campylobacter coli are human intestinal pathogens of global importance. Zoonotic transmission from livestock animals or animal-derived food is the likely cause for most of these infections. However, little is known about their general and host-specific mechanisms of colonization, or virulence and pathogenicity factors. In certain hosts, Campylobacter species colonize persistently and do not cause disease, while they cause acute intestinal disease in humans. Results Here, we investigate putative host-specificity using phenotypic characterization and genome-wide analysis of genetically closely related C. jejuni strains from different sources. A collection of 473 fresh Campylobacter isolates from Germany was assembled between 2006 and 2010 and characterized using MLST. A subset of closely related C. jejuni strains of the highly prevalent sequence type ST-21 was selected from different hosts and isolation sources. PCR typing of strain-variable genes provided evidence that some genes differed between these strains. Furthermore, phenotypic variation of these strains was tested using the following criteria: metabolic variation, protein expression patterns, and eukaryotic cell interaction. The results demonstrated remarkable phenotypic diversity within the ST-21 group, which however did not correlate with isolation source. Whole genome sequencing was performed for five ST-21 strains from chicken, human, bovine, and food sources, in order to gain insight into ST-21 genome diversity. The comparisons showed extensive genomic diversity, primarily due to recombination and gain of phage-related genes. By contrast, no genomic features associated with isolation source or host were identified. Conclusions The genome information and phenotypic data obtained in vitro and in a chicken infection model provided little evidence of fixed adaptation to a specific host. Instead, the dominant C. jejuni ST-21 appeared to be characterized by phenotypic
15. Identification of a fungi-specific lineage of protein kinases closely related to tyrosine kinases.
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Zhongtao Zhao
Full Text Available Tyrosine kinases (TKs specifically catalyze the phosphorylation of tyrosine residues in proteins and play essential roles in many cellular processes. Although TKs mainly exist in animals, recent studies revealed that some organisms outside the Opisthokont clade also contain TKs. The fungi, as the sister group to animals, are thought to lack TKs. To better understand the origin and evolution of TKs, it is important to investigate if fungi have TK or TK-related genes. We therefore systematically identified possible TKs across the fungal kingdom by using the profile hidden Markov Models searches and phylogenetic analyses. Our results confirmed that fungi lack the orthologs of animal TKs. We identified a fungi-specific lineage of protein kinases (FslK that appears to be a sister group closely related to TKs. Sequence analysis revealed that members of the FslK clade contain all the conserved protein kinase sub-domains and thus are likely enzymatically active. However, they lack key amino acid residues that determine TK-specific activities, indicating that they are not true TKs. Phylogenetic analysis indicated that the last common ancestor of fungi may have possessed numerous members of FslK. The ancestral FslK genes were lost in Ascomycota and Ustilaginomycotina and Pucciniomycotina of Basidiomycota during evolution. Most of these ancestral genes, however, were retained and expanded in Agaricomycetes. The discovery of the fungi-specific lineage of protein kinases closely related to TKs helps shed light on the origin and evolution of TKs and also has potential implications for the importance of these kinases in mushroom fungi.
16. Identification of a fungi-specific lineage of protein kinases closely related to tyrosine kinases.
Science.gov (United States)
Zhao, Zhongtao; Jin, Qiaojun; Xu, Jin-Rong; Liu, Huiquan
2014-01-01
Tyrosine kinases (TKs) specifically catalyze the phosphorylation of tyrosine residues in proteins and play essential roles in many cellular processes. Although TKs mainly exist in animals, recent studies revealed that some organisms outside the Opisthokont clade also contain TKs. The fungi, as the sister group to animals, are thought to lack TKs. To better understand the origin and evolution of TKs, it is important to investigate if fungi have TK or TK-related genes. We therefore systematically identified possible TKs across the fungal kingdom by using the profile hidden Markov Models searches and phylogenetic analyses. Our results confirmed that fungi lack the orthologs of animal TKs. We identified a fungi-specific lineage of protein kinases (FslK) that appears to be a sister group closely related to TKs. Sequence analysis revealed that members of the FslK clade contain all the conserved protein kinase sub-domains and thus are likely enzymatically active. However, they lack key amino acid residues that determine TK-specific activities, indicating that they are not true TKs. Phylogenetic analysis indicated that the last common ancestor of fungi may have possessed numerous members of FslK. The ancestral FslK genes were lost in Ascomycota and Ustilaginomycotina and Pucciniomycotina of Basidiomycota during evolution. Most of these ancestral genes, however, were retained and expanded in Agaricomycetes. The discovery of the fungi-specific lineage of protein kinases closely related to TKs helps shed light on the origin and evolution of TKs and also has potential implications for the importance of these kinases in mushroom fungi.
17. Final Close-Out Report for DE-FG02-93ER40764
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Gyulassy, Miklos [Columbia Univ., New York, NY (United States)
2016-02-12
This is a final close-out report for DOE contract DE-FG02-93ER40764 at Columbia University in New York that funded nuclear theory research at Columbia from 12/15/1992 to 12/14/2015. Highlight of research results from the last FY 2015 period, a list of all 12 PhD students trained through the whole grant, and a list of 201 original papers published from 1993-2015 with impact factor metrics are presented.
18. Phylogenetic reconstruction and DNA barcoding for closely related pine moth species (Dendrolimus in China with multiple gene markers.
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Qing-Yan Dai
Full Text Available Unlike distinct species, closely related species offer a great challenge for phylogeny reconstruction and species identification with DNA barcoding due to their often overlapping genetic variation. We tested a sibling species group of pine moth pests in China with a standard cytochrome c oxidase subunit I (COI gene and two alternative internal transcribed spacer (ITS genes (ITS1 and ITS2. Five different phylogenetic/DNA barcoding analysis methods (Maximum likelihood (ML/Neighbor-joining (NJ, "best close match" (BCM, Minimum distance (MD, and BP-based method (BP, representing commonly used methodology (tree-based and non-tree based in the field, were applied to both single-gene and multiple-gene analyses. Our results demonstrated clear reciprocal species monophyly for three relatively distant related species, Dendrolimus superans, D. houi, D. kikuchii, as recovered by both single and multiple genes while the phylogenetic relationship of three closely related species, D. punctatus, D. tabulaeformis, D. spectabilis, could not be resolved with the traditional tree-building methods. Additionally, we find the standard COI barcode outperforms two nuclear ITS genes, whatever the methods used. On average, the COI barcode achieved a success rate of 94.10-97.40%, while ITS1 and ITS2 obtained a success rate of 64.70-81.60%, indicating ITS genes are less suitable for species identification in this case. We propose the use of an overall success rate of species identification that takes both sequencing success and assignation success into account, since species identification success rates with multiple-gene barcoding system were generally overestimated, especially by tree-based methods, where only successfully sequenced DNA sequences were used to construct a phylogenetic tree. Non-tree based methods, such as MD, BCM, and BP approaches, presented advantages over tree-based methods by reporting the overall success rates with statistical significance. In
19. Phylogenetic reconstruction and DNA barcoding for closely related pine moth species (Dendrolimus) in China with multiple gene markers.
Science.gov (United States)
Dai, Qing-Yan; Gao, Qiang; Wu, Chun-Sheng; Chesters, Douglas; Zhu, Chao-Dong; Zhang, Ai-Bing
2012-01-01
Unlike distinct species, closely related species offer a great challenge for phylogeny reconstruction and species identification with DNA barcoding due to their often overlapping genetic variation. We tested a sibling species group of pine moth pests in China with a standard cytochrome c oxidase subunit I (COI) gene and two alternative internal transcribed spacer (ITS) genes (ITS1 and ITS2). Five different phylogenetic/DNA barcoding analysis methods (Maximum likelihood (ML)/Neighbor-joining (NJ), "best close match" (BCM), Minimum distance (MD), and BP-based method (BP)), representing commonly used methodology (tree-based and non-tree based) in the field, were applied to both single-gene and multiple-gene analyses. Our results demonstrated clear reciprocal species monophyly for three relatively distant related species, Dendrolimus superans, D. houi, D. kikuchii, as recovered by both single and multiple genes while the phylogenetic relationship of three closely related species, D. punctatus, D. tabulaeformis, D. spectabilis, could not be resolved with the traditional tree-building methods. Additionally, we find the standard COI barcode outperforms two nuclear ITS genes, whatever the methods used. On average, the COI barcode achieved a success rate of 94.10-97.40%, while ITS1 and ITS2 obtained a success rate of 64.70-81.60%, indicating ITS genes are less suitable for species identification in this case. We propose the use of an overall success rate of species identification that takes both sequencing success and assignation success into account, since species identification success rates with multiple-gene barcoding system were generally overestimated, especially by tree-based methods, where only successfully sequenced DNA sequences were used to construct a phylogenetic tree. Non-tree based methods, such as MD, BCM, and BP approaches, presented advantages over tree-based methods by reporting the overall success rates with statistical significance. In addition, our
20. A murine herpesvirus closely related to ubiquitous human herpesviruses causes T-cell depletion.
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Patel, Swapneel J; Zhao, Guoyan; Penna, Vinay R; Park, Eugene; Lauron, Elvin J; Harvey, Ian B; Beatty, Wandy L; Plougastel-Douglas, Beatrice; Poursine-Laurent, Jennifer; Fremont, Daved H; Wang, David; Yokoyama, Wayne M
2017-02-08
Mouse models of human herpesvirus infections The human roseoloviruses HHV6A, HHV6B, and HHV7 comprise the Roseolovirus genus of the human Betaherpesvirinae subfamily. Infections with these viruses have been implicated in many diseases; however, it has been challenging to establish infections with Roseoloviruses as direct drivers of pathology because they are nearly ubiquitous and display species-specific tropism. Furthermore, controlled study of infection has been hampered by the lack of experimental models, and until now, a mouse roseolovirus has not been identified. Herein we describe a virus that causes severe thymic necrosis in neonatal mice, characterized by a loss of CD4(+) T-cells. These phenotypes resemble those caused by the previously described mouse thymic virus (MTV), a putative herpesvirus that has not been molecularly characterized. By Next Generation sequencing of infected tissue homogenates, we assembled a contiguous 174Kb genome sequence encoding 128 unique predicted open reading frames (ORFs), many of which were most closely related to herpesvirus genes. Moreover, the structure of the virus genome and phylogenetic analysis of multiple genes strongly suggested that this virus is a betaherpesvirus more closely related to the roseoloviruses, HHV6A, HHV6B, and HHV7, than another murine betaherpesvirus, mouse cytomegalovirus (MCMV). As such, we have named this virus murine roseolovirus (MRV) because these data strongly suggest that MRV is a mouse homolog of HHV6A/HHV6B/HHV7.Importance: Herein we describe the complete genome sequence of a novel murine herpesvirus. By sequence and phylogenetic analyses, we show that it is a betaherpesvirus most closely related to the roseoloviruses, human herpesvirus 6A, 6B, and 7. These data combined with physiological similarities with human roseoloviruses collectively suggest that this virus is a murine roseolovirus (MRV), the first definitively described rodent roseolovirus, to our knowledge. Many biological and
1. Separation of human, bovine, and porcine insulins, three very closely related proteins, by micellar electrokinetic chromatography.
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Lamalle, Caroline; Roland, Diane; Crommen, Jacques; Servais, Anne-Catherine; Fillet, Marianne
2015-10-01
Human, bovine, and porcine insulins are small proteins with very closely related amino acid sequences, which makes their separation challenging. In this study, we took advantage of the high-resolution power of CE, and more particularly of micellar electrokinetic chromatography, to separate those biomolecules. Among several surfactants, perfluorooctanoic acid ammonium salt was selected. Then, using a design of experiments approach, the optimal BGE composition was found to consist of 50 mM ammonium acetate pH 9.0, 65 mM perfluorooctanoic acid ammonium salt, and 4% MeOH. The three insulins could be separated within 12 min with a satisfactory resolution. This method could be useful to detect possible counterfeit pharmaceutical formulations. Indeed, it would be easy to determine if human insulin was replaced by bovine or porcine insulin.
2. TB-infected deer are more closely related than non-infected deer.
Science.gov (United States)
Blanchong, Julie A; Scribner, Kim T; Kravchenko, Alexandra N; Winterstein, Scott R
2007-02-22
Identifying mechanisms of pathogen transmission is critical to controlling disease. Social organization should influence contacts among individuals and thus the distribution and spread of disease within a population. Molecular genetic markers can be used to elucidate mechanisms of disease transmission in wildlife populations without undertaking detailed observational studies to determine probable contact rates. Estimates of genealogical relationships within a bovine tuberculosis-infected white-tailed deer (Odocoileus virginianus) population indicated that infected deer were significantly more closely related than non-infected deer suggesting that contact within family groups was a significant mechanism of disease transmission. Results demonstrate that epidemiological models should incorporate aspects of host ecology likely to affect the probability of disease transmission.
3. [Duties of TB patients or suspected patients and their close relations].
Science.gov (United States)
2015-01-01
The effective laws impose the duty upon TB patients or persons suspected to have TB as well as their close relations to undergo compulsory sanitary and epidemiological examinations. Furthermore, treatment is also mandatory and in case of infective patients hospitalization and isolation. Duty does not however denote enforcement, which is required in certain particularly dangerous infectious diseases. Poland operates a system of mandatory TB vaccination applicable, today, only to infants. Persons suspected of TB have the obligation to provide necessary information helping in diagnosing the disease or helping to find the source of infection and transmission of the disease. TB patients are under obligation to discontinue performing their work to prevent the disease from spreading to other persons.
4. Cell wall swelling, fracture mode, and the mechanical properties of cherry fruit skins are closely related.
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Brüggenwirth, Martin; Knoche, Moritz
2017-04-01
Cell wall swelling, fracture mode (along the middle lamellae vs. across cell walls), stiffness, and pressure at fracture of the sweet cherry fruit skin are closely related. Skin cracking is a common phenomenon in many crops bearing fleshy fruit. The objectives were to investigate relationships between the mode of fracture, the extent of cell wall swelling, and the mechanical properties of the fruit skin using sweet cherry (Prunus avium) as a model. Cracking was induced by incubating whole fruit in deionised water or by fracturing exocarp segments (ESs) in biaxial tensile tests. The fracture mode of epidermal cells was investigated by light microscopy. In biaxial tensile tests, the anticlinal cell walls of the ES fractured predominantly across the cell walls (rather than along) and showed no cell wall swelling. In contrast, fruit incubated in water fractured predominantly along the anticlinal epidermal cell walls and the cell walls were swollen. Swelling of cell walls also occurred when ESs were incubated in malic acid, in hypertonic solutions of sucrose, or in water. Compared to the untreated controls, these treatments resulted in more frequent fractures along the cell walls, lower pressures at fracture (p fracture), and lower moduli of elasticity (E, i.e., less stiff). Conversely, compared to the untreated controls, incubating the ES in CaCl2 and in high concentrations of ethanol resulted in thinner cell walls, in less frequent fractures along the cell walls, higher E and p fracture. Our study demonstrates that fracture mode, stiffness, and pressure at fracture are closely related to cell wall swelling. A number of other factors, including cultivar, ripening stage, turgor, CaCl2, and malic acid, exert their effects only indirectly, i.e., by affecting cell wall swelling.
5. Mycorrhizal associations and reproductive isolation in three closely related Orchis species
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Jacquemyn, Hans; Brys, Rein; Cammue, Bruno P. A.; Honnay, Olivier; Lievens, Bart
2011-01-01
Background and Aims The maintenance of species boundaries in sympatric populations of closely related species requires some kind of reproductive isolation that limits gene flow among species and/or prevents the production of viable progeny. Because in orchids mycorrhizal fungi are needed for seed germination and subsequent seedling establishment, orchid–mycorrhizal associations may be involved in acting as a post-mating barrier. Methods We investigated the strength of post-mating barriers up to the seed germination stage acting between three closely related Orchis species (Orchis anthropophora, O. militaris and O. purpurea) and studied the role of mycorrhizal fungi in hybridization by burying seed packets of pure and hybrid seeds. After retrieval and assessment of seed germination, the fungi associating with protocorms originating from hybrid and pure seeds were determined and compared with those associating with adult individuals using DNA array technology. Results Whereas pre-zygotic post-mating barriers were rather weak in most crosses, post-zygotic post-mating barriers were stronger, particularly when O. purpurea was crossed with O. anthropophora. Germination trials in the field showed that seed germination percentages of hybrid seeds were in most cases lower than those originating from pure crosses. In all species pair combinations, total post-mating reproductive isolation was asymmetric. Protocorms associated with a smaller range of fungal symbionts than adult plants, but there was considerable overlap in mycorrhizal associations between protocorms and their respective parents. Conclusions Our results suggest that mycorrhizal associations contribute little to reproductive isolation. Pre-mating barriers are probably the main factors determining hybridization rates between the investigated species. PMID:21186239
6. Asymmetric gene introgression in two closely related Orchis species: evidence from morphometric and genetic analyses
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Jacquemyn Hans
2012-09-01
Full Text Available Abstract Background In food-deceptive orchids of the genera Anacamptis, Neotinea and Orchis floral isolation has been shown to be weak, whereas late-acting reproductive barriers are mostly strong, often restricting hybridization to the F1 generation. Only in a few species hybridization extends beyond the F1 generation, giving rise to hybrid swarms. However, little is known about the abundance of later-generation hybrids and what factors drive their occurrence in hybrid populations. In this study, molecular analyses were combined with detailed morphological measurements in a hybrid population of two closely related Orchis species (Orchis militaris and O. purpurea to investigate the hypothesis that the abundance of later-generation hybrids is driven by changes in floral characters after hybridization that exert selective pressures that in turn affect hybridization. Results Both the molecular and morphological data point to extensive genetic and morphological homogenization and asymmetric introgression. Estimating genomic clines from the multi-locus genotype data and testing for deviation from neutrality revealed that 30 out of 113 (27% AFLP markers significantly deviated from neutral expectations. Plants with large floral displays or plant with flowers that resembled more O. purpurea had higher female fitness than plants with small floral displays or plants with flowers resembling more O. militaris, suggesting that directional selection may have contributed to the observed patterns of introgression. Conclusions These results indicate that in closely related orchid species hybridization and gene introgression may be partly driven by selection for floral traits of one of the parental types. However, because some pure individuals were still present in the studied population, the parental species appeared to be sufficiently isolated to survive the challenge of sympatry.
7. Molecular survey and characterization of a novel Anaplasma species closely related to Anaplasma capra in ticks, northwestern China.
Science.gov (United States)
Yang, Jifei; Liu, Zhijie; Niu, Qingli; Liu, Junlong; Han, Rong; Liu, Guangyuan; Shi, Yaoxu; Luo, Jianxun; Yin, Hong
2016-11-25
Anaplasma spp. are tick-transmitted bacteria that infect a wide variety of wild and domestic animals. These pathogens exhibit a high degree of biological diversity, broad geographical distribution, and represent a serious threat to veterinary and public health worldwide. A novel Anaplasma species was identified in Haemaphysalis qinghaiensis (Ixodidae) in northwestern China and was molecularly characterized by comparison of 16S rRNA, gltA, and groEL gene sequences. Of the 414 samples tested, 24 (5.8%) were positive for this Anaplasma species. On the basis of the 16S rRNA gene, this organism has been found to be closely related to and exhibit the highest sequence similarity with A. capra (99.8-99.9%) that was identified in goats and humans in northern China, but was distinct from other known Anaplasma species. Sequence analysis of the gltA and groEL genes revealed that this Anaplasma species was distinct from A. capra considering the lower sequence identity (88.6-88.7% for gltA and 90.6-91.0% for groEL) and a divergent phylogenetic position. Therefore, we described this Anaplasma species as A. capra-like bacteria. The present study reports a potential novel Anaplasma species closely related to A. capra in H. qinghaiensis in northwestern China. The zoonotic potential of A. capra-like bacteria needs to be further determined.
8. Phenology, growth, and fecundity as determinants of distribution in closely related nonnative taxa
Science.gov (United States)
Marushia, Robin G.; Brooks, Matthew L.; Holt, Jodie S.
2012-01-01
Invasive species researchers often ask: Why do some species invade certain habitats while others do not? Ecological theories predict that taxonomically related species may invade similar habitats, but some related species exhibit contrasting invasion patterns. Brassica nigra, Brassica tournefortii, and Hirschfeldia incana are dominant, closely related nonnative species that have overlapping, but dissimilar, distributions. Brassica tournefortii is rapidly spreading in warm deserts of the southwestern United States, whereas B. nigra and H. incana are primarily limited to semiarid and mesic regions. We compared traits of B. tournefortii that might confer invasiveness in deserts with those of related species that have not invaded desert ecosystems. Brassica tournefortii, B. nigra and H. incana were compared in controlled experiments conducted outdoors in a mesic site (Riverside, CA) and a desert site (Blue Diamond, NV), and in greenhouses, over 3 yr. Desert and mesic B. tournefortii populations were also compared to determine whether locally adapted ecotypes contribute to desert invasion. Experimental variables included common garden sites and soil water availability. Response variables included emergence, growth, phenology, and reproduction. There was no evidence for B. tournefortii ecotypes, but B. tournefortii had a more rapid phenology than B. nigra or H. incana. Brassica tournefortii was less affected by site and water availability than B. nigra and H. incana, but was smaller and less fecund regardless of experimental conditions. Rapid phenology allows B. tournefortii to reproduce consistently under variable, stressful conditions such as those found in Southwestern deserts. Although more successful in milder, mesic ecosystems, B. nigra and H. incana may be limited by their ability to reproduce under desert conditions. Rapid phenology and drought response partition invasion patterns of nonnative mustards along a gradient of aridity in the southwestern United States
9. Migratory New World blackbirds (icterids are more neophobic than closely related resident icterids.
Directory of Open Access Journals (Sweden)
Claudia Mettke-Hofmann
Full Text Available Environments undergo short-term and long-term changes due to natural or human-induced events. Animals differ in their ability to cope with such changes which can be related to their ecology. Changes in the environment often elicit avoidance reactions (neophobia which protect animals from dangerous situations but can also inhibit exploration and familiarization with novel situations and thus, learning about new resources. Studies investigating the relationship between a species' ecology and its neophobia have so far been restricted to comparing only a few species and mainly in captivity. The current study investigated neophobia reactions to experimentally-induced changes in the natural environment of six closely-related blackbird species (Icteridae, including two species represented by two distinct populations. For analyses, neophobic reactions (difference in number of birds feeding and time spent feeding with and without novel objects were related to several measures of ecological plasticity and the migratory strategy (resident or migratory of the population. Phylogenetic relationships were incorporated into the analysis. The degree of neophobia was related to migratory strategy with migrants expressing much higher neophobia (fewer birds feeding and for a shorter time with objects present than residents. Furthermore, neophobia showed a relationship to diet breadth with fewer individuals of diet generalists than specialists returning when objects were present supporting the dangerous niche hypothesis. Residents may have evolved lower neophobia as costs of missing out on opportunities may be higher for residents than migrants as the former are restricted to a smaller area. Lower neophobia allows them approaching changes in the environment (e.g. novel objects quickly, thereby securing access to resources. Additionally, residents have a greater familiarity with similar situations in the area than migrants and the latter may, therefore, initially
10. The Relation of the Morse Index of Closed Geodesics with the Maslov-type Index of Symplectic Paths
Institute of Scientific and Technical Information of China (English)
Chun Gen LIU
2005-01-01
In this paper, we consider the relation of the Morse index of a closed geodesic with the Maslov-type index of a path in a symplectic group. More precisely, for a closed geodesic c on a Riemannian manifold M with its linear Poincare map P (a symplectic matrix), we construct a symplectic path γ(t) starting from identity I and ending at P, such that the Morse index of the closed geodesic c equals the Maslov-type index of γ. As an application of this result, we study the parity of the Morse index of any closed geodesic.
11. New species of Monepidosis Mamaev, 1966 and Antipodosis gen. nov., a closely related genus from New Zealand (Diptera, Cecidomyiidae
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Mathias Jaschhof
2016-04-01
Full Text Available Three new species of Monepidosis Mamaev, 1966, a Holarctic genus of Porricondylinae (Diptera, Cecidomyiidae, are described: M. heterocera sp. nov. from Sweden and Germany, M. scepteroides sp. nov. from Sweden, and M. shikokuensis sp. nov. from Japan. A new porricondyline genus, Antipodosis gen. nov., is introduced for eight new species from New Zealand, named A. australis gen. et sp. nov., A. elongata gen. et sp. nov., A. granvillensis gen. et sp. nov., A. pureora gen. et sp. nov., A. rakiura gen. et sp. nov., A. rotoiti gen. et sp. nov., A. rotoroa gen. et sp. nov., and A. waipapa gen. et sp. nov. Male genitalic morphology indicates that Monepidosis and Antipodosis gen. nov. are closely related, together forming the Monepidosis group of genera, which stands out from the other Porricondylini. Monepidosis spatulata Spungis, 2006, a species originally described from Latvia and Lithuania, is for the first time reported to occur in Sweden.
12. Comparative genomics of Japanese Erwinia pyrifoliae strain Ejp617 with closely related erwinias.
Science.gov (United States)
Thapa, Shree P; Park, Duck H; Kim, Won S; Choi, Beom S; Lim, Jong S; Choi, Ik Y; Hur, Jang H; Lim, Chun K
2013-02-01
Japanese Erwinia pyrifoliae strains cause bacterial shoot blight of pear (BSBP) in Japan. The genetics of Japanese Erwinia remains largely unknown relative to the abundant genomic information available for other Erwinia strains. We compared the genome of Japanese and Korean E. pyrifoliae strains along with those of E. amylovora and E. tasmaniensis. Comparisons with the Korean E. pyrifoliae strain revealed numerous gene insertions/deletions, rearrangements, and inversions in the central regions of the chromosomes. Approximately 80% (2843) of coding DNA sequences (CDSs) are shared by these two genomes which represent about three-quarters of the genome, and there are about 20% unique CDSs. Comparative analysis with closely related erwinias showed that 1942 (more than 50%) core open reading frames (ORF) are shared by all these strains. In addition to two type III secretion systems (hrp/dsp and inv/spa), the genome of Ejp617 encodes numerous virulence factors, including a type VI secretion system, an exopolysaccharide synthesis cluster, and another protein secretion system present in plant pathogenic Erwinia strains. The availability of whole genome sequence should provide a resource to further improve the understanding of pathogenesis in Japanese E. pyrifoliae Ejp617 and to facilitate evolutionary studies among the species of the genus Erwinia.
13. Genetic Comparison of B. Anthracis and its Close Relatives Using AFLP and PCR Analysis
Energy Technology Data Exchange (ETDEWEB)
Jackson, P.J.; Hill, K.K.; Laker, M.T.; Ticknor, L.O.; Keim, P.S.
1999-02-01
Amplified Fragment length Polymorphism (AFLP) analysis allows a rapid, relatively simple analysis of a large portion of a microbial genome, providing information about the species and its phylogenetic relationship to other microbes (Vos, et al., 1995). The method simply surveys the genome for length and sequence polymorphisms. The pattern identified can be used for comparison to the genomes of other species. Unlike other methods, it does not rely on analysis of a single genetic locus that may bias the interpretation of results and it does not require any prior knowledge of the targeted organism. Moreover, a standard set of reagents can be applied to any species without using species-specific information or molecular probes. The authors are using AFLP's to rapidly identify different bacterial species. A comparison of AFLP profiles generated from a large battery of B. anthracis strains shows very little variability among different isolates (Keim, et al., 1997). By contrast, there is a significant difference between AFLP profiles generated for any B. anthracis strain and even the most closely related Bacillus species. Sufficient variability is apparent among all known microbial species to allow phylogenetic analysis based on large numbers of genetically unlinked loci. These striking differences among AFLP profiles allow unambiguous identification of previously identified species and phylogenetic placement of newly characterized isolates relative to known species based on a large number of independent genetic loci. Data generated thus far show that the method provides phylogenetic analyses that are consistent with other widely accepted phylogenetic methods. However, AFLP analysis provides a more detailed analysis of the targets and samples a much larger portion of the genome. Consequently, it provides an inexpensive, rapid means of characterizing microbial isolates to further differentiate among strains and closely related microbial species. Such information
14. Work-related musculoskeletal disorders : prevention report
NARCIS (Netherlands)
Podniece, Z.; Heuvel, S. van den; Blatter, B.
2008-01-01
Work-related musculoskeletal disorders (MSDs) can interfere with activities at work and can lead to reduced productivity, sickness absence and chronic occupational disability. The aim of this report is to systematic evaluate the effectiveness of interventions at the workplace since 2002 and to
15. Genetic variability in apomictic mangosteen (Garcinia mangostana and its close relatives (Garcinia spp. based on ISSR markers
Directory of Open Access Journals (Sweden)
SOBIR
2011-04-01
Full Text Available Sobir, Poerwanto R, Santosa E, Sinaga S, Mansyah E (2011 Genetic variability in apomictic mangosteen (Garcinia mangostana and its close relatives (Garcinia spp. based on ISSR markers. Biodiversitas 12: 59-63. In order to reveal phylogenetic relationship of mangosteen and several close relatives (Garcinia spp., we employed seven ISSR dinucleotide primer systems on eleven close relatives of mangosteen and 28 mangosteen accessions from four islands in Indonesia (Sumatra, Java, Kalimantan and Lombok. ISSR analysis successfully amplified 43 bands on average 6.1 fragments for each primer system, and these all fragments were polymorphic. Seven close relatives of mangosteen were separated with mangosteen accessions at 0.22 level of dissimilarity, while other four including G. malaccensis, were clustered with mangosteen accessions, this results supported proposal that G. malaccensis was allopolyploid derivative of mangosteen. Clustering pattern among mangosteen accessions, however, not represented their origin, indicated that distribution of the accessions was not linked to their genetic properties.
16. Comparative genomics of four closely related Clostridium perfringens bacteriophages reveals variable rates of evolution within a core genome
Science.gov (United States)
Background: Biotechnological uses of bacteriophage gene products as alternatives to conventional antibiotics will require a thorough understanding of their genomic context. We sequenced and analyzed the genomes of four closely related phages isolated from Clostridium perfringens, an important agricu...
17. Contrasting Genomic Diversity in Two Closely Related Postharvest Pathogens: Penicillium digitatum and Penicillium expansum.
Science.gov (United States)
Julca, Irene; Droby, Samir; Sela, Noa; Marcet-Houben, Marina; Gabaldón, Toni
2015-12-14
Penicillium digitatum and Penicillium expansum are two closely related fungal plant pathogens causing green and blue mold in harvested fruit, respectively. The two species differ in their host specificity, being P. digitatum restricted to citrus fruits and P. expansum able to infect a wide range of fruits after harvest. Although host-specific Penicillium species have been found to have a smaller gene content, it is so far unclear whether these different host specificities impact genome variation at the intraspecific level. Here we assessed genome variation across four P. digitatum and seven P. expansum isolates from geographically distant regions. Our results show very high similarity (average 0.06 SNPs [single nucleotide polymorphism] per kb) between globally distributed isolates of P. digitatum pointing to a recent expansion of a single lineage. This low level of genetic variation found in our samples contrasts with the higher genetic variability observed in the similarly distributed P. expansum isolates (2.44 SNPs per kb). Patterns of polymorphism in P. expansum indicate that recombination exists between genetically diverged strains. Consistent with the existence of sexual recombination and heterothallism, which was unknown for this species, we identified the two alternative mating types in different P. expansum isolates. Patterns of polymorphism in P. digitatum indicate a recent clonal population expansion of a single lineage that has reached worldwide distribution. We suggest that the contrasting patterns of genomic variation between the two species reflect underlying differences in population dynamics related with host specificities and related agricultural practices. It should be noted, however, that this results should be confirmed with a larger sampling of strains, as new strains may broaden the diversity so far found in P. digitatum.
18. The γ-gliadin multigene family in common wheat (Triticum aestivum and its closely related species
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Chen Qing
2009-04-01
19. Closed gastroschisis, vanishing midgut and extreme short bowel syndrome: Case report and review of the literature.
Science.gov (United States)
Dennison, F A
2016-08-01
Gastroschisis alone has excellent survival rates. Occasionally reported is closed gastroschisis, leading to vanishing small bowel and extreme short bowel syndrome. It is believed that the abdominal wall defect can contract or close in utero, which leads to strangulation of the eviscerated bowel and the rare "vanishing gut syndrome." This has a very poor prognosis with mortality as high as 70%. An 18-year-old primigravid patient's 13 week scan diagnosed a large gastroschisis affecting the fetus. After counselling, she decided to continue with the pregnancy. Between 20 and 22 weeks, the gastroschisis disappeared, and the bowel within the abdomen became markedly dilated. Spontaneous labour occurred at 33 + 3 weeks gestation. There was no abdominal wall defect seen at delivery. Imaging and an exploratory laparotomy demonstrated absence of most of the midgut. Because available options for treatment would be very aggressive and risky, palliative care was thought to be the most feasible and practical option. He died at home on day 29 after birth. Extreme short gut syndrome (less than 25 cm of remaining small bowel) is rare. There are 13 reported cases in the literature from year 2000 to 2013. Treatment is aggressive and involves a bowel lengthening procedure or small bowel transplant. All require total parenteral nutrition and liver failure, and liver transplant is a common complication. Of these cases, 12 were born alive and 7 had aggressive treatment. Only two cases were confirmed to still be alive in infancy. If gastroschisis is seen to be reducing and "disappearing" antenatally, parents should be made aware of this rare complication so that they might be prepared if a poor outcome is anticipated.
20. Molecular characterization of a naturally occurring intraspecific recombinant begomovirus with close relatives widespread in southern Arabia
KAUST Repository
Al-Saleh, Mohammed A
2014-06-02
Background: Tomato leaf curl Sudan virus (ToLCSDV) is a single-stranded DNA begomovirus of tomato that causes downward leaf curl, yellowing, and stunting. Leaf curl disease results in significant yield reduction in tomato crops in the Nile Basin. ToLCSDV symptoms resemble those caused by Tomato yellow leaf curl virus, a distinct and widespread begomovirus originating in the Middle East. In this study, tomato samples exhibiting leaf curl symptoms were collected from Gezira, Sudan. The associated viral genome was molecularly characterized, analyzed phylogenetically, and an infectious clone for one isolate was constructed. Findings. The complete genomes for five newly discovered variants of ToLCSDV, ranging in size from 2765 to 2767-bp, were cloned and sequenced, and subjected to pairwise and phylogenetic analyses. Pairwise analysis indicated that the five Gezira isolates shared 97-100% nucleotide identity with each other. Further, these variants of ToLCSDV shared their highest nucleotide identity at 96-98%, 91-95%, 91-92%, and 91-92% with the Shambat, Gezira, Oman and Yemen strains of ToLCSDV, respectively. Based on the high maximum nucleotide identities shared between these ToLCSDV variants from Gezira and other previously recognized members of this taxonomic group, they are considered isolates of the Shambat strain of ToLCSDV. Analysis of the complete genome sequence for these new variants revealed that they were naturally occurring recombinants between two previously reported strains of ToLCSDV. Finally, a dimeric clone constructed from one representative ToLCSV genome from Gezira was shown to be infectious following inoculation to tomato and N. benthamiana plants. Conclusion: Five new, naturally occurring recombinant begomovirus variants (>96% shared nt identity) were identified in tomato plants from Gezira in Sudan, and shown to be isolates of the Shambat strain of ToLCSDV. The cloned viral genome was infectious in N. benthamiana and tomato plants, and symptoms
1. Sequence and characterization of six mitochondrial subgenomes from Globodera rostochiensis: multipartite structure is conserved among close nematode relatives.
Science.gov (United States)
Gibson, Tracey; Blok, Vivian C; Dowton, Mark
2007-09-01
Recently, a multipartite mitochondrial genome was characterized in the potato cyst nematode, Globodera pallida. Six subgenomic circles were detectable by PCR, while full-length genomes were not. We investigate here whether this subgenomic organization occurs in a close relative of G. pallida. We amplified and sequenced one entire mitochondrial subgenome from the cyst-forming nematode, Globodera rostochiensis. Comparison of the noncoding region of this subgenome with those reported previously for G. pallida facilitated the design of amplification primers for a range of subgenomes from G. rostochiensis. We then randomly sequenced five subgenomic fragments, each representative of a unique subgenome. This study indicates that the multipartite structure reported for G. pallida is conserved in G. rostochiensis. A comparison of subgenomic organization between these two Globodera species indicates a considerable degree of overlap between them. Indeed, we identify two subgenomes with an organization identical with that reported for G. pallida. However, other subgenomes are unique to G. rostochiensis, although some of these have blocks of genes comparable to those in G. pallida. Dot-plot comparisons of pairs of subgenomes from G. rostochiensis indicate that the different subgenomes share fragments with high sequence identity. We interpret this as evidence that recombination is operating in the mitochondria of G. rostochiensis.
2. Testing DNA barcodes in closely related species of Curcuma (Zingiberaceae) from Myanmar and China.
Science.gov (United States)
Chen, Juan; Zhao, Jietang; Erickson, David L; Xia, Nianhe; Kress, W John
2015-03-01
The genus Curcuma L. is commonly used as spices, medicines, dyes and ornamentals. Owing to its economic significance and lack of clear-cut morphological differences between species, this genus is an ideal case for developing DNA barcodes. In this study, four chloroplast DNA regions (matK, rbcL, trnH-psbA and trnL-F) and one nuclear region (ITS2) were generated for 44 Curcuma species and five species from closely related genera, represented by 96 samples. PCR amplification success rate, intra- and inter-specific genetic distance variation and the correct identification percentage were taken into account to assess candidate barcode regions. PCR and sequence success rate were high in matK (89.7%), rbcL (100%), trnH-psbA (100%), trnL-F (95.7%) and ITS2 (82.6%) regions. The results further showed that four candidate chloroplast barcoding regions (matK, rbcL, trnH-psbA and trnL-F) yield no barcode gaps, indicating that the genus Curcuma represents a challenging group for DNA barcoding. The ITS2 region presented large interspecific variation and provided the highest correct identification rates (46.7%) based on BLASTClust method among the five regions. However, the ITS2 only provided 7.9% based on NJ tree method. An increase in discriminatory power needs the development of more variable markers. © 2014 John Wiley & Sons Ltd.
3. Isolation and characterization of five lytic bacteriophages infecting a Vibrio strain closely related to Vibrio owensii.
Science.gov (United States)
Yu, Yan-Ping; Gong, Ting; Jost, Günter; Liu, Wen-Hua; Ye, De-Zan; Luo, Zhu-Hua
2013-11-01
Vibrio owensii is a potential bacterial pathogen in marine aquaculture system. In this study, five lytic phages specific against Vibrio strain B8D, closely related to V. owensii, were isolated from seawater of an abalone farm. The phages were characterized with respect to morphology, genome size, growth phenotype, as well as thermal, and pH stability. All phages were found to belong to the family Siphoviridae with long noncontractile tails and terminal fibers. Restriction analysis indicated that the five phages were dsDNA viruses with molecular weights ranging from c. 30 to 48 kb. One-step growth experiments revealed that the phages were heterogeneous in latent periods (10-70 min), rise periods (40-70 min), and burst sizes [23-331 plaque-forming units (PFU) per infected cell] at the same host strain. All phages were thermal stable and were tolerant to a wide range of pH. The results indicated that these phages could be potential candidates of a phage cocktail for biological control of V. owensii in aquaculture systems.
4. Host plant use among closely related Anaea butterfly species (Lepidoptera, Nymphalidae, Charaxinae
Directory of Open Access Journals (Sweden)
J. M. QUEIROZ
Full Text Available There is a great number of Charaxinae (Lepidoptera: Nymphalidae species in the tropics whose larvae feed on several plant families. However the genus Anaea is almost always associated with Croton species (Euphorbiaceae. This work describes patterns of host plant use by immature and adult abundance on different vertical strata of sympatric Anaea species in a forest of Southeastern Brazil. Quantitative samples of leaves were taken in April/1999 and May/2000 to collect eggs and larvae of four Anaea species on C.alchorneicarpus, C. floribundus and C. salutaris in a semideciduous forest. Sampled leaves were divided into three classes of plant phenological stage: saplings, shrubs and trees. The results showed that the butterfly species are segregating in host plant use on two scales: host plant species and plant phenological stages. C. alchorneicarpus was used by only one Anaea species, whereas C. floribundus was used by three species and C. salutaris by four Anaea species. There was one Anaea species concentrated on sapling, another on sapling/shrub and two others on shrub/tree leaves. Adults of Anaea were more frequent at canopy traps but there were no differences among species caught in traps at different vertical positions. This work supplements early studies on host plant use among Charaxinae species and it describes how a guild of closely related butterfly species may be organized in a complex tropical habitat.
5. Comparison of song frequency and receptor tuning in two closely related bushcricket species.
Science.gov (United States)
Kalmring, K; Rössler, W; Jatho, M; Hoffmann, E
1995-01-01
The songs and the structure and physiology of the auditory organs in the closely related bushcricket species Tettigonia viridissima and Tettigonia cantans were investigated comparatively using bioacoustical, histological and neurophysiological methods. The morphology of the crista acustica, the main auditory receptor organ, is very similar in the two species in respect to both the distribution of scolopidia along the length axis of the crista and the dimensions of corresponding scolopidia and attachment structures. The only obvious difference is that T. viridissima has one more scolopidium in the crista acustica and that the overall length of the crista is by about 50 microns larger than in T. cantans. In contrast, differences were found in the physiology of individual auditory receptor cells. Comparison of the threshold characteristics of all the receptor cells of the crista acustica in both species reveals a differential sensitivity of groups of auditory receptor cells at dominant frequencies of the song. In each species, the sensitivity of auditory receptor cells is method to the energy spectrum of the song. These differences in the physiology can partly be explained by differences in transmission characteristics of the acoustic trachea.
6. Trehalose 6-phosphate signal is closely related to sorbitol in apple (Malus domestica Borkh. cv. Gala)
Science.gov (United States)
Zhang, Wen; Lunn, John E.; Feil, Regina; Wang, Yufei; Zhao, Jingjing; Tao, Hongxia; Zhao, Zhengyang
2017-01-01
ABSTRACT Trehalose-6-phosphate (Tre6P) is a precursor of trehalose, which is widespread in nature and greatly influences plant growth and development. Tre6P acts as a signal of carbon availability in many plants, but little is known about the function of Tre6P in rosaceous plants, which have specific sorbitol biosynthesis and transportation pathways. In the present study, Tre6P levels and Sorbitol:Tre6P ratios were analyzed in apple (Malus domestica, Borkh. cv. Gala). Tre6P levels were positively correlated with sorbitol content but negatively correlated with sucrose, glucose, and fructose content in developing fruit. However, under sorbitol-limited conditions, Tre6P levels were positively correlated with both sorbitol and sucrose. In the presence of different exogenous sugar supply, Tre6P levels increased corresponding with sorbitol, but this was not the case with sucrose. In addition, Tre6P content and sorbitol:Tre6P ratios were more highly correlated with ADP-glucose levels under sorbitol-limited conditions and fruit development stages, respectively. These results suggest that Tre6P is more closely related to sorbitol than other soluble sugars and has an important role in influencing carbon metabolism in apple. PMID:28069587
7. Differences in metabolic costs of terrestrial mobility in two closely related species of albatross.
Science.gov (United States)
Kabat, Alexander P; Phillips, Richard A; Croxall, John P; Butler, Patrick J
2007-08-01
Black-browed albatrosses Thalassarche melanophrys typically colonise steeper habitats than grey-headed albatrosses T. chrysostoma. The present study investigated the effect of colony philopatry on terrestrial locomotory ability in these two species, to determine: (1) if there is a difference in terrestrial locomotory ability between these two closely related species, and (2) what physiological or behavioural adaptations may account for any differences identified. We examined the metabolic cost, mechanical efficiency on an incline, and gait characteristics of terrestrial locomotion of these two species on both level and inclined planes. T. chrysostoma were able to perform at a significantly greater speed than T. melanophrys without reaching a significantly different maximal rate of oxygen consumption (V(O(2))). Conversely, T. melanophrys were able to move up a significantly steeper incline than T. chrysostoma while maintaining a similar maximal V(O(2)). Each species demonstrates stride length, force production (behavioural) and leg length (morphological) adaptations that minimise the cost of traversing their chosen colonies, indicating a clear relationship between terrestrial performance and local topography. However, it is not possible to determine if the difference in locomotory ability results from differences in colony topography, or if choice of colony site is dictated by the ability of the species to traverse different terrain.
8. Binding site turnover produces pervasive quantitative changes in transcription factor binding between closely related Drosophila species.
Directory of Open Access Journals (Sweden)
2010-03-01
Full Text Available Changes in gene expression play an important role in evolution, yet the molecular mechanisms underlying regulatory evolution are poorly understood. Here we compare genome-wide binding of the six transcription factors that initiate segmentation along the anterior-posterior axis in embryos of two closely related species: Drosophila melanogaster and Drosophila yakuba. Where we observe binding by a factor in one species, we almost always observe binding by that factor to the orthologous sequence in the other species. Levels of binding, however, vary considerably. The magnitude and direction of the interspecies differences in binding levels of all six factors are strongly correlated, suggesting a role for chromatin or other factor-independent forces in mediating the divergence of transcription factor binding. Nonetheless, factor-specific quantitative variation in binding is common, and we show that it is driven to a large extent by the gain and loss of cognate recognition sequences for the given factor. We find only a weak correlation between binding variation and regulatory function. These data provide the first genome-wide picture of how modest levels of sequence divergence between highly morphologically similar species affect a system of coordinately acting transcription factors during animal development, and highlight the dominant role of quantitative variation in transcription factor binding over short evolutionary distances.
9. A chestnut seed cystatin differentially effective against cysteine proteinases from closely related pests.
Science.gov (United States)
Pernas, M; Sánchez-Monge, R; Gómez, L; Salcedo, G
1998-12-01
Cystatin CsC, a cysteine proteinase inhibitor from chestnut (Castanea sativa) seeds, has been purified and characterized. Its full-length cDNA clone was isolated from an immature chestnut cotyledon library. The inhibitor was expressed in Escherichia coli and purified from bacterial extracts. Identity of both seed and recombinant cystatin was confirmed by matrix-assisted laser desorption/ionization mass spectrometry analysis, two-dimensional electrophoresis and N-terminal sequencing. CsC has a molecular mass of 11,275 Da and pI of 6.9. Its amino acid sequence includes all three motifs that are thought to be essential for inhibitory activity, and shows significant identity to other phytocystatins, especially that of cowpea (70%). Recombinant CsC inhibited papain (Ki 29 nM), ficin (Ki 65 nM), chymopapain (Ki 366 nM), and cathepsin B (Ki 473 nM). By contrast with most cystatins, it was also effective towards trypsin (Ki 3489 nM). CsC is active against digestive proteinases from the insect Tribolium castaneum and the mite Dermatophagoides farinae, two important agricultural pests. Its effects on the cysteine proteinase activity of two closely related mite species revealed the high specificity of the chestnut cystatin.
10. Characterisation of a virus from Australia that is closely related to papaya mosaic potexvirus.
Science.gov (United States)
Geering, A D; Thomas, J E
1999-01-01
We have isolated a previously undescribed potexvirus from Alternanthera pungens (Amaranthaceae) in southern Queensland, Australia. This virus was shown to have a moderately wide experimental host range, infecting plants in nine of the twelve families tested. Using specific antibodies, a plate trapped antigen ELISA was developed, allowing detection of virions down to 0.8 microgram/ml of leaf extract. Virions averaged 554 nm long and had a capsid protein with a M(r) of 23.1 x 10(3). A portion of the genome containing the capsid protein ORF and 3' untranslated region was cloned and sequenced. From both serological and amino acid sequence comparisons, the virus was shown to be closely related to papaya mosaic potexvirus (PMV). To determine the taxonomic status of the virus, we assessed variation in the amino acid sequence of capsid proteins of distinct species within the potexvirus genus, as well as variation between strains of the same virus. When the core region of the capsid proteins were compared, distinct species had a maximum of 62.2% sequence identity, whereas strains had a minimum of 88.8% identity. By comparison, the core region of the capsid proteins of the Alternanthera virus and PMV had 79.8% identity. We have concluded that the Alternanthera virus is a different species from PMV, and its relationship with PMV resembles that of potyvirus subgroup members.
11. Creep performance of PVC aged at temperature relatively close to glass transition temperature
Institute of Scientific and Technical Information of China (English)
Zhi-hong ZHOU; Yao-long HE; Hong-jiu HU; Feng ZHAO; Xiao-long ZHANG
2012-01-01
In order to predict the mechanical performance of the polyvinyl chloride (PVC) at a high operating temperature,a series of short-term tensile creep tests (onetenth of the physical aging time) of the PVC are carried out at 63 ℃ with a small constant stress by a dynamic mechanical analyzer (DMA).The Struik-Kohlrausch (SK)formula and Struik shifting methods are used to describe these creep data for various physical aging time.A new phenomenological model based on the multiple relaxation mechanisms of an amorphous polymer is developed to quantitatively characterize the SK parameters (the initial creep compliance,the characteristic retardation time,and the shape factor) determined by the aging time.It is shown that the momentary creep compliance curve of the PVC at 63 ℃ can be very well fitted by the SK formula for each aging time.However,the SK parameters for the creep curves are not constant during the aging process at the elevated temperatures,and the evolution of these parameters and the creep rate versus aging time curves at the double logarithmic coordinates have shown a nonlinear phenomenon. Moreover,the creep master curves obtained by the superposition with the Struik shifting methods are unsatisfactory in such a case.Finally,the predicted results calculated from the present model incorporating with the SK formula are in excellent agreement with the creep experimental data for the PVC isothermally aged at the temperature relatively close to the glass transition temperature.
12. New Atglistatin closely related analogues: Synthesis and structure-activity relationship towards adipose triglyceride lipase inhibition.
Science.gov (United States)
Roy, Pierre-Philippe; D'Souza, Kenneth; Cuperlovic-Culf, Miroslava; Kienesberger, Petra C; Touaibia, Mohamed
2016-08-01
Adipose Triglyceride Lipase (ATGL) performs the first and rate-limiting step in lipolysis by hydrolyzing triacylglycerols stored in lipid droplets to diacylglycerols. By mediating lipolysis in adipose and non-adipose tissues, ATGL is a major regulator of overall energy metabolism and plasma lipid levels. Since chronically high levels of plasma lipids are linked to metabolic disorders including insulin resistance and type 2 diabetes, ATGL is an interesting therapeutic target. In the present study, fourteen closely related analogues of Atglistatin (1), a newly discovered ATGL inhibitor, were synthesized, and their ATGL inhibitory activity was evaluated. The effect of these analogues on lipolysis in 3T3-L1 adipocytes clearly shows that inhibition of the enzyme by Atglistatin (1) is due to the presence of the carbamate and N,N-dimethyl moieties on the biaryl central core at meta and para position, respectively. Mono carbamate-substituted analogue C2, in which the carbamate group was in the meta position as in Atglistatin (1), showed slight inhibition. Low dipole moment of Atglistatin (1) compared to the synthesized analogues possibly explains the lower inhibitory activities.
13. Host plant use among closely related Anaea butterfly species (Lepidoptera, Nymphalidae, Charaxinae
Directory of Open Access Journals (Sweden)
QUEIROZ J. M.
2002-01-01
Full Text Available There is a great number of Charaxinae (Lepidoptera: Nymphalidae species in the tropics whose larvae feed on several plant families. However the genus Anaea is almost always associated with Croton species (Euphorbiaceae. This work describes patterns of host plant use by immature and adult abundance on different vertical strata of sympatric Anaea species in a forest of Southeastern Brazil. Quantitative samples of leaves were taken in April/1999 and May/2000 to collect eggs and larvae of four Anaea species on C.alchorneicarpus, C. floribundus and C. salutaris in a semideciduous forest. Sampled leaves were divided into three classes of plant phenological stage: saplings, shrubs and trees. The results showed that the butterfly species are segregating in host plant use on two scales: host plant species and plant phenological stages. C. alchorneicarpus was used by only one Anaea species, whereas C. floribundus was used by three species and C. salutaris by four Anaea species. There was one Anaea species concentrated on sapling, another on sapling/shrub and two others on shrub/tree leaves. Adults of Anaea were more frequent at canopy traps but there were no differences among species caught in traps at different vertical positions. This work supplements early studies on host plant use among Charaxinae species and it describes how a guild of closely related butterfly species may be organized in a complex tropical habitat.
14. Intron Derived Size Polymorphism in the Mitochondrial Genomes of Closely Related Chrysoporthe Species.
Science.gov (United States)
Kanzi, Aquillah Mumo; Wingfield, Brenda Diana; Steenkamp, Emma Theodora; Naidoo, Sanushka; van der Merwe, Nicolaas Albertus
2016-01-01
In this study, the complete mitochondrial (mt) genomes of Chrysoporthe austroafricana (190,834 bp), C. cubensis (89,084 bp) and C. deuterocubensis (124,412 bp) were determined. Additionally, the mitochondrial genome of another member of the Cryphonectriaceae, namely Cryphonectria parasitica (158,902 bp), was retrieved and annotated for comparative purposes. These genomes showed high levels of synteny, especially in regions including genes involved in oxidative phosphorylation and electron transfer, unique open reading frames (uORFs), ribosomal RNAs (rRNAs) and transfer RNAs (tRNAs), as well as intron positions. Comparative analyses revealed signatures of duplication events, intron number and length variation, and varying intronic ORFs which highlighted the genetic diversity of mt genomes among the Cryphonectriaceae. These mt genomes showed remarkable size polymorphism. The size polymorphism in the mt genomes of these closely related Chrysoporthe species was attributed to the varying number and length of introns, coding sequences and to a lesser extent, intergenic sequences. Compared to publicly available fungal mt genomes, the C. austroafricana mt genome is the second largest in the Ascomycetes thus far.
15. Genomic comparison of closely related Giant Viruses supports an accordion-like model of evolution.
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Jonathan eFilée
2015-06-01
Full Text Available Genome gigantism occurs so far in Phycodnaviridae and Mimiviridae (order Megavirales. Origin and evolution of these Giant Viruses (GVs remain open questions. Interestingly, availability of a collection of closely related GV genomes enabling genomic comparisons offer the opportunity to better understand the different evolutionary forces acting on these genomes. Whole genome alignment for 5 groups of viruses belonging to the Mimiviridae and Phycodnaviridae families show that there is no trend of genome expansion or general tendency of genome contraction. Instead, GV genomes accumulated genomic mutations over the time with gene gains compensating the different losses. In addition, each lineage displays specific patterns of genome evolution. Mimiviridae (megaviruses and mimiviruses and Chlorella Phycodnaviruses evolved mainly by duplications and losses of genes belonging to large paralogous families (including movements of diverse mobiles genetic elements, whereas Micromonas and Ostreococcus Phycodnaviruses derive most of their genetic novelties thought lateral gene transfers. Taken together, these data support an accordion-like model of evolution in which GV genomes have undergone successive steps of gene gain and gene loss, accrediting the hypothesis that genome gigantism appears early, before the diversification of the different GV lineages.
16. Trehalose 6-phosphate signal is closely related to sorbitol in apple (Malus domestica Borkh. cv. Gala
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Wen Zhang
2017-02-01
Full Text Available Trehalose-6-phosphate (Tre6P is a precursor of trehalose, which is widespread in nature and greatly influences plant growth and development. Tre6P acts as a signal of carbon availability in many plants, but little is known about the function of Tre6P in rosaceous plants, which have specific sorbitol biosynthesis and transportation pathways. In the present study, Tre6P levels and Sorbitol:Tre6P ratios were analyzed in apple (Malus domestica, Borkh. cv. Gala. Tre6P levels were positively correlated with sorbitol content but negatively correlated with sucrose, glucose, and fructose content in developing fruit. However, under sorbitol-limited conditions, Tre6P levels were positively correlated with both sorbitol and sucrose. In the presence of different exogenous sugar supply, Tre6P levels increased corresponding with sorbitol, but this was not the case with sucrose. In addition, Tre6P content and sorbitol:Tre6P ratios were more highly correlated with ADP-glucose levels under sorbitol-limited conditions and fruit development stages, respectively. These results suggest that Tre6P is more closely related to sorbitol than other soluble sugars and has an important role in influencing carbon metabolism in apple.
17. Relational Systems: How Older Women with Chronic Health Problems Construct Close Relationships
Science.gov (United States)
McCann, Brandy Renee; Roberto, Karen A.
2012-01-01
Close relationships are important throughout life, but their dynamics may change as chronic health conditions permeate the lives of older women. To understand how older women (N = 36) manage their close relationships, this study was guided by two research questions: How do older women with chronic health conditions define meaningful relationships?…
18. Closed medial total subtalar joint dislocation without ankle fracture: a case report
Science.gov (United States)
2014-01-01
Introduction Total subtalar dislocation without fracture of the ankle is a rare clinical entity; it is usually due to a traumatic high-energy mechanism. Standard treatment is successful closed reduction under general anesthesia followed by non-weight bearing and ankle immobilization with a below-knee cast for 6 weeks. Case presentation We present the case of a 30-year-old Moroccan woman who was involved in a road traffic accident. She subsequently received a radiological assessment that objectified a total subtalar dislocation without fracture of her ankle. She was immediately admitted to the operating theater where an immediate reduction was performed under sedation, and immobilization in a plaster boot was adopted for 8 weeks. The management of this traumatic lesion is discussed in the light of the literature. Conclusions Medial subtalar dislocation is a rare dislocation and is not commonly seen as a sports injury because it requires transfer of a large amount of kinetic energy. The weaker talocalcaneal and talonavicular ligaments often bear the brunt of the energy and are more commonly disrupted, compared to the relatively stronger calcaneonavicular ligament. Urgent reduction is important, and closed reduction under general anesthesia is usually successful, often facilitated by keeping the knee in flexion to relax the gastrocnemius muscle. Long-term sequelae include talar avascular necrosis and osteochondral fracture, as well as chronic instability and pain. PMID:25240955
19. Report: Close-Out of Hotline Complaint on Unreasonable Cost Increase to the Wastewater Treatment Facility Improvements, Perkins, Oklahoma
Science.gov (United States)
Report #12-X-0161, December 29, 2011. We have closed a hotline complaint that project costs increased unreasonably due to American Recovery and Reinvestment Act of 2009 (Recovery Act) requirements because we found no evidence to support the complaint.
20. Comparative genomic analysis of phylogenetically closely related Hydrogenobaculum sp. isolates from Yellowstone National Park.
Science.gov (United States)
Romano, Christine; D'Imperio, Seth; Woyke, Tanja; Mavromatis, Konstantinos; Lasken, Roger; Shock, Everett L; McDermott, Timothy R
2013-05-01
We describe the complete genome sequences of four closely related Hydrogenobaculum sp. isolates (≥ 99.7% 16S rRNA gene identity) that were isolated from the outflow channel of Dragon Spring (DS), Norris Geyser Basin, in Yellowstone National Park (YNP), WY. The genomes range in size from 1,552,607 to 1,552,931 bp, contain 1,667 to 1,676 predicted genes, and are highly syntenic. There are subtle differences among the DS isolates, which as a group are different from Hydrogenobaculum sp. strain Y04AAS1 that was previously isolated from a geographically distinct YNP geothermal feature. Genes unique to the DS genomes encode arsenite [As(III)] oxidation, NADH-ubiquinone-plastoquinone (complex I), NADH-ubiquinone oxidoreductase chain, a DNA photolyase, and elements of a type II secretion system. Functions unique to strain Y04AAS1 include thiosulfate metabolism, nitrate respiration, and mercury resistance determinants. DS genomes contain seven CRISPR loci that are almost identical but are different from the single CRISPR locus in strain Y04AAS1. Other differences between the DS and Y04AAS1 genomes include average nucleotide identity (94.764%) and percentage conserved DNA (80.552%). Approximately half of the genes unique to Y04AAS1 are predicted to have been acquired via horizontal gene transfer. Fragment recruitment analysis and marker gene searches demonstrated that the DS metagenome was more similar to the DS genomes than to the Y04AAS1 genome, but that the DS community is likely comprised of a continuum of Hydrogenobaculum genotypes that span from the DS genomes described here to an Y04AAS1-like organism, which appears to represent a distinct ecotype relative to the DS genomes characterized.
1. Restricted variation in plant barcoding markers limits identification in closely related bryophyte species.
Science.gov (United States)
Hassel, Kristian; Segreto, Rossana; Ekrem, Torbjørn
2013-11-01
Species-level identification and delimitation of bryophytes using the proposed general barcode markers for land plants has been challenging. Bryophyta (mosses) is the second most species-rich group of land plants after angiosperms, and it is thus of great importance to find useful barcoding regions also for this group of plants. We investigated how the plastid regions atpF-atpH, rbcL and trnH-psbA and the nuclear ITS2 region performed as barcode markers on closely related bryophyte taxa of selected moss (Bartramia, Distichium, Fissidens, Meesia and Syntrichia) and liverwort (Blepharostoma) genera from boreal and arctic regions. We also evaluated how sequencing success of herbarium specimens is related to length of the sequenced fragment, specimen age and taxonomic group. Sequencing success was higher for shorter fragments and younger herbarium specimens, but was lower than expected in the genera Distichium and Fissidens, indicating imperfect universality of the primers used. None of the studied DNA barcode regions showed a consistent barcode gap across the studied genera. As a single locus, the region atpF-atpH performed slightly better than rbcL and ITS2 and much better than trnH-psbA in terms of grouping conspecific sequences in monophyletic groups. This marker also gave a higher percentage of correct hits when conducting blast searches on a local database of identified sequences. Concatenated data sets of two and three markers grouped more conspecific sequences in monophyletic groups, but the improvement was not great compared with atpF-atpH alone. A discussion of recent studies testing barcode regions for bryophytes is given. We conclude that atpF-atpH, rbcL and ITS2 are to be the most promising barcode markers for mosses.
2. Chloroplast gene arrangement variation within a closely related group of green algae (Trebouxiophyceae, Chlorophyta).
Science.gov (United States)
Letsch, Molly R; Lewis, Louise A
2012-09-01
The 22 published chloroplast genomes of green algae, representing sparse taxonomic sampling of diverse lineages that span over one billion years of evolution, each possess a unique gene arrangement. In contrast, many of the >190 published embryophyte (land plant) chloroplast genomes have relatively conserved architectures. To determine the phylogenetic depth at which chloroplast gene rearrangements occur in green algae, a 1.5-4 kb segment of the chloroplast genome was compared across nine species in three closely related genera of Trebouxiophyceae (Chlorophyta). In total, four distinct gene arrangements were obtained for the three genera Elliptochloris, Hemichloris, and Coccomyxa. In Elliptochloris, three distinct chloroplast gene arrangements were detected, one of which is shared with members of its sister genus Hemichloris. Both species of Coccomyxa examined share the fourth arrangement of this genome region, one characterized by very long spacers. Next, the order of genes found in this segment of the chloroplast genome was compared across green algae and land plants. As taxonomic ranks are not equivalent among different groups of organisms, the maximum molecular divergence among taxa sharing a common gene arrangement in this genome segment was compared. Well-supported clades possessing a single gene order had similar phylogenetic depth in green algae and embryophytes. When the dominant gene order of this chloroplast segment in embryophytes was assumed to be ancestral for land plants, the maximum molecular divergence was found to be over two times greater in embryophytes than in trebouxiophyte green algae. This study greatly expands information about chloroplast genome variation in green algae, is the first to demonstrate such variation among congeneric green algae, and further illustrates the fluidity of green algal chloroplast genome architecture in comparison to that of many embryophytes.
3. Summary report of working group 2 on {open_quotes}Beam Production{close_quotes}
Energy Technology Data Exchange (ETDEWEB)
Serafini, Luca [INFN and Universita di Milano Via Celoria 16, 20133Milano (Italy)] Cornacchia, Max [SSRL---Stanford Linear Accelerator Center, Stanford, California94309 (United States)
1997-06-01
We summarize here the discussions and the communications presented in the working group on {open_quotes}Beam Production{close_quotes}, whose main aim was actually focused on identification of main processes limiting the maximum achievable electron beam brightness at injection into the undulator of a generic linac-based X-Ray single pass FEL. These processes have been divided into three main categories: stochastic effects in the photoelectric emission at the cathode, emittance degradation due to space charge effects in the injector, coherent spontaneous emission in bends ({ital e.g.} magnetic compressors) and its related impact on the emittance and/or peak current budget. {copyright} {ital 1997 American Institute of Physics.}
4. Whole genome sequencing and comparative genomics of closely related Fusarium Head Blight fungi: Fusarium graminearum, F. meridionale and F. asiaticum.
Science.gov (United States)
Walkowiak, Sean; Rowland, Owen; Rodrigue, Nicolas; Subramaniam, Rajagopal
2016-12-09
The Fusarium graminearum species complex is composed of many distinct fungal species that cause several diseases in economically important crops, including Fusarium Head Blight of wheat. Despite being closely related, these species and individuals within species have distinct phenotypic differences in toxin production and pathogenicity, with some isolates reported as non-pathogenic on certain hosts. In this report, we compare genomes and gene content of six new isolates from the species complex, including the first available genomes of F. asiaticum and F. meridionale, with four other genomes reported in previous studies. A comparison of genome structure and gene content revealed a 93-99% overlap across all ten genomes. We identified more than 700 k base pairs (kb) of single nucleotide polymorphisms (SNPs), insertions, and deletions (indels) within common regions of the genome, which validated the species and genetic populations reported within species. We constructed a non-redundant pan gene list containing 15,297 genes from the ten genomes and among them 1827 genes or 12% were absent in at least one genome. These genes were co-localized in telomeric regions and select regions within chromosomes with a corresponding increase in SNPs and indels. Many are also predicted to encode for proteins involved in secondary metabolism and other functions associated with disease. Genes that were common between isolates contained high levels of nucleotide variation and may be pseudogenes, allelic, or under diversifying selection. The genomic resources we have contributed will be useful for the identification of genes that contribute to the phenotypic variation and niche specialization that have been reported among members of the F. graminearum species complex.
5. Medication errors: an analysis comparing PHICO's closed claims data and PHICO's Event Reporting Trending System (PERTS).
Science.gov (United States)
Benjamin, David M; Pendrak, Robert F
2003-07-01
Clinical pharmacologists are all dedicated to improving the use of medications and decreasing medication errors and adverse drug reactions. However, quality improvement requires that some significant parameters of quality be categorized, measured, and tracked to provide benchmarks to which future data (performance) can be compared. One of the best ways to accumulate data on medication errors and adverse drug reactions is to look at medical malpractice data compiled by the insurance industry. Using data from PHICO insurance company, PHICO's Closed Claims Data, and PHICO's Event Reporting Trending System (PERTS), this article examines the significance and trends of the claims and events reported between 1996 and 1998. Those who misread history are doomed to repeat the mistakes of the past. From a quality improvement perspective, the categorization of the claims and events is useful for reengineering integrated medication delivery, particularly in a hospital setting, and for redesigning drug administration protocols on low therapeutic index medications and "high-risk" drugs. Demonstrable evidence of quality improvement is being required by state laws and by accreditation agencies. The state of Florida requires that quality improvement data be posted quarterly on the Web sites of the health care facilities. Other states have followed suit. The insurance industry is concerned with costs, and medication errors cost money. Even excluding costs of litigation, an adverse drug reaction may cost up to $2500 in hospital resources, and a preventable medication error may cost almost$4700. To monitor costs and assess risk, insurance companies want to know what errors are made and where the system has broken down, permitting the error to occur. Recording and evaluating reliable data on adverse drug events is the first step in improving the quality of pharmacotherapy and increasing patient safety. Cost savings and quality improvement evolve on parallel paths. The PHICO data
6. Relation between premorbid adjustment, duration of untreated psychosis and close interpersonal trauma in first-episode psychosis
DEFF Research Database (Denmark)
Haahr, Ulrik Helt; Larsen, Tor Ketil; Simonsen, Erik
2016-01-01
AIM: Interpersonal traumas are highly prevalent in patients with psychotic disorders. Trauma caused by those close to the patient might have a more profound impact than other types of trauma and may influence early life social functioning. The aim is to investigate the associations between...... different types of trauma, in particular close interpersonal traumas experienced before the age of 18, premorbid factors and baseline clinical characteristics in a sample of first-episode psychosis patients. METHODS: A total of 191 patients from the 'TIPS' cohort completed assessment with the Brief Betrayal...... Trauma Survey at their 5 years follow-up interview. RESULTS: Half of the patients reported that they had experienced interpersonal trauma and one-third reported having experienced close interpersonal trauma before the age of 18. Women reported more sexual abuse, physical attacks and emotional...
7. Different patterns of oviposition learning in two closely related ectoparasitoid wasps with contrasting reproductive strategies
Science.gov (United States)
Sasakawa, Kôji; Uchijima, Kenta; Shibao, Harunobu; Shimada, Masakazu
2013-02-01
Many parasitoid wasps learn host-associated cues and use them in subsequent host-searching behavior. This associative learning, namely "oviposition learning," has been investigated in many studies. However, few studies have compared multiple species, and no comparative study has previously been conducted on ectoparasitoid species. We compared the effects of oviposition learning on host preference and offspring sex ratio in two closely related ectoparasitoid wasps with contrasting reproductive strategies, Anisopteromalus calandrae (r-strategist) and its sibling species (K-strategist). Using two bruchine hosts, Callosobruchus chinensis and Callosobruchus maculatus larvae infesting the cowpea Vigna unguiculata, oviposition choice experiments were performed at high and low host densities. In both species, no conspicuous effect on the offspring sex ratio was detected, but effects on host preference were found to differ between the species. In A. calandrae, the effects were detected only at high host density, suggesting that oviposition learning plays a role in host discrimination from a short distance but not from a long distance. In the sibling species, those effects were not detected in any of the cases, suggesting the absence of oviposition learning. These results are compatible with those of previous comparative studies of endoparasitoid wasps in that few lifetime oviposition experiences and/or low reward per foraging decision result in low or absent oviposition learning ability. This finding may indicate that ecological traits contributing to learning ability are similar between endoparasitoid and ectoparasitoid wasps. Thus, our species comparison of ectoparasitoids provides another model system for investigating learning and memory dynamics in parasitoid wasps.
8. Different patterns of oviposition learning in two closely related ectoparasitoid wasps with contrasting reproductive strategies.
Science.gov (United States)
Sasakawa, Kôji; Uchijima, Kenta; Shibao, Harunobu; Shimada, Masakazu
2013-02-01
Many parasitoid wasps learn host-associated cues and use them in subsequent host-searching behavior. This associative learning, namely "oviposition learning," has been investigated in many studies. However, few studies have compared multiple species, and no comparative study has previously been conducted on ectoparasitoid species. We compared the effects of oviposition learning on host preference and offspring sex ratio in two closely related ectoparasitoid wasps with contrasting reproductive strategies, Anisopteromalus calandrae (r-strategist) and its sibling species (K-strategist). Using two bruchine hosts, Callosobruchus chinensis and Callosobruchus maculatus larvae infesting the cowpea Vigna unguiculata, oviposition choice experiments were performed at high and low host densities. In both species, no conspicuous effect on the offspring sex ratio was detected, but effects on host preference were found to differ between the species. In A. calandrae, the effects were detected only at high host density, suggesting that oviposition learning plays a role in host discrimination from a short distance but not from a long distance. In the sibling species, those effects were not detected in any of the cases, suggesting the absence of oviposition learning. These results are compatible with those of previous comparative studies of endoparasitoid wasps in that few lifetime oviposition experiences and/or low reward per foraging decision result in low or absent oviposition learning ability. This finding may indicate that ecological traits contributing to learning ability are similar between endoparasitoid and ectoparasitoid wasps. Thus, our species comparison of ectoparasitoids provides another model system for investigating learning and memory dynamics in parasitoid wasps.
9. Rapid identification of closely related muscle foods by vibrational spectroscopy and machine learning.
Science.gov (United States)
Ellis, David I; Broadhurst, David; Clarke, Sarah J; Goodacre, Royston
2005-12-01
Muscle foods are an integral part of the human diet and during the last few decades consumption of poultry products in particular has increased significantly. It is important for consumers, retailers and food regulatory bodies that these products are of a consistently high quality, authentic, and have not been subjected to adulteration by any lower-grade material either by accident or for economic gain. A variety of methods have been developed for the identification and authentication of muscle foods. However, none of these are rapid or non-invasive, all are time-consuming and difficulties have been encountered in discriminating between the commercially important avian species. Whilst previous attempts have been made to discriminate between muscle foods using infrared spectroscopy, these have had limited success, in particular regarding the closely related poultry species, chicken and turkey. Moreover, this study includes novel data since no attempts have been made to discriminate between both the species and the distinct muscle groups within these species, and this is the first application of Raman spectroscopy to the study of muscle foods. Samples of pre-packed meat and poultry were acquired and FT-IR and Raman measurements taken directly from the meat surface. Qualitative interpretation of FT-IR and Raman spectra at the species and muscle group levels were possible using discriminant function analysis. Genetic algorithms were used to elucidate meaningful interpretation of FT-IR results in (bio)chemical terms and we show that specific wavenumbers, and therefore chemical species, were discriminatory for each type (species and muscle) of poultry sample. We believe that this approach would aid food regulatory bodies in the rapid identification of meat and poultry products and shows particular potential for rapid assessment of food adulteration.
10. Active ammonia oxidizers in an acidic soil are phylogenetically closely related to neutrophilic archaeon.
Science.gov (United States)
Wang, Baozhan; Zheng, Yan; Huang, Rong; Zhou, Xue; Wang, Dongmei; He, Yuanqiu; Jia, Zhongjun
2014-03-01
All cultivated ammonia-oxidizing archaea (AOA) within the Nitrososphaera cluster (former soil group 1.1b) are neutrophilic. Molecular surveys also indicate the existence of Nitrososphaera-like phylotypes in acidic soil, but their ecological roles are poorly understood. In this study, we present molecular evidence for the chemolithoautotrophic growth of Nitrososphaera-like AOA in an acidic soil with pH 4.92 using DNA-based stable isotope probing (SIP). Soil microcosm incubations demonstrated that nitrification was stimulated by urea fertilization and accompanied by a significant increase in the abundance of AOA rather than ammonia-oxidizing bacteria (AOB). Real-time PCR analysis of amoA genes as a function of the buoyant density of the DNA gradient following the ultracentrifugation of the total DNA extracted from SIP microcosms indicated a substantial growth of soil AOA during nitrification. Pyrosequencing of the total 16S rRNA genes in the "heavy" DNA fractions suggested that archaeal communities were labeled to a much greater extent than soil AOB. Acetylene inhibition further showed that (13)CO2 assimilation by nitrifying communities depended solely on ammonia oxidation activity, suggesting a chemolithoautotrophic lifestyle. Phylogenetic analysis of both (13)C-labeled amoA and 16S rRNA genes revealed that most of the active AOA were phylogenetically closely related to the neutrophilic strains Nitrososphaera viennensis EN76 and JG1 within the Nitrososphaera cluster. Our results provide strong evidence for the adaptive growth of Nitrososphaera-like AOA in acidic soil, suggesting a greater metabolic versatility of soil AOA than previously appreciated.
11. Visual perception can account for the close relation between numerosity processing and computational fluency
Directory of Open Access Journals (Sweden)
Xinlin eZhou
2015-09-01
Full Text Available Studies have shown that numerosity processing (e.g., comparison of numbers of dots in two dot arrays is significantly correlated with arithmetic performance. Researchers have attributed this association to the fact that both tasks share magnitude processing. The current investigation tested an visual perception hypothesis that visual perceptual ability (as measured by a figure-matching task can account for the close relation between numerosity processing and arithmetic performance (computational fluency. Four hundred and twenty four third- to fifth-grade children (220 boys and 204 girls, 8.0 to 11.0 years old; 120 third graders, 146 fourth graders, and 158 fifth graders were recruited from two schools (one urban and one suburban in Beijing, China. Six classes were randomly selected from each school, and all students in each selected class were asked to participate in the study. All children were given a series of cognitive and mathematical tests, including numerosity comparison, figure matching, forward verbal working memory, visual tracing, non-verbal matrices reasoning, mental rotation, choice reaction time, arithmetic tests and curriculum-based mathematical achievement test. Results showed that figure-matching ability had higher correlations with numerosity processing and computational fluency than did other cognitive factors (e.g., forward verbal working memory, visual tracing, non-verbal matrices reasoning, mental rotation, and choice reaction time. More important, hierarchical multiple regression showed that figure matching ability accounted for the well-established association between numerosity processing and computational fluency. The results suggest that visual perceptual ability, rather than magnitude processing, may be the shared component of numerosity processing and arithmetic performance.
12. Glycolysis Is Dynamic and Relates Closely to Respiration Rate in Stored Sugarbeet Roots
Directory of Open Access Journals (Sweden)
Clarice A. Megguer
2017-05-01
storage and that changes in glycolysis are closely related to changes in sugarbeet root respiration.
13. Initial data sets and the topology of closed three-manifolds in general relativity
Science.gov (United States)
Carfora, M.
1983-10-01
The interaction between the matter content of a closed physical space associated with a generic gravitational configuration and the topology of the underlying closed three-manifold is discussed. Within the context of the conformal approach to the initial value problem, it is shown that the presence of enough matter and radiation favors the three-sphere topology or the worm-hole topology. It is argued that such topologies leave more room for possible gravitational initial data sets for the field equations.
14. Treatment of cervical contractures utilising a closed platysmotomy like approach: Case report and review of the literature.
Science.gov (United States)
Haik, Josef; Prat, Daphna; Kornhaber, Rachel; Tessone, Ariel
2016-09-01
Contractures to the cervical region as a result of burns has the capacity to cause restrictions in range of movement, function of the lower face, cervical spine distortion and poor aesthetic outcomes that remain a surgical challenge. Consequently, physical and aesthetic deformities as a result of cervical contractures are reported to cause depression having implications for patients' quality of life and psychosocial wellbeing. At the time this research was conducted, there were no case reports describing a closed platysmotomy approach in burn patients. In this article, we review the literature surrounding closed platysmotomies and present what we believe to be the first reported case in the treatment of cervical contractures utilising a closed platysmotomy approach in a burns patient. A closed platysmotomy approach for the treatment of cervical contractures is a less invasive technique. Further investigation is warranted to determine the feasibility of this reconstructive approach in the area of burn scar management.
15. Negative aspects of close social relations and 10-year incident ischaemic heart disease hospitalization among middle-aged Danes
DEFF Research Database (Denmark)
Lund, Rikke; Rod, Naja Hulvej; Thielen, Karsten
2014-01-01
BACKGROUND: Little is known about the association between negative aspects of close social relations and development of ischaemic heart disease (IHD). We aim to address if the experience of worries/demands and conflicts with close social relations are related to risk of first-time hospitalization...... National Patient Registry. Cox regression analysis was used to analyse data and all analyses were adjusted for age, gender, social class, cohabitation, and depressive symptoms. RESULTS: Worries/demands from and conflicts with children were associated with IHD hospitalization in an exposure-dependent manner...... was found for conflicts with partner. High levels of worries/demands from or conflicts with family and friends were associated with a 40% higher risk of IHD. CONCLUSIONS: Negative aspects of close social relations are associated with higher risk of incident IHD hospitalization except for conflicts...
16. Identification of Traditional She Medicine Shi-Liang Tea Species and Closely Related Species Using the ITS2 Barcode
Directory of Open Access Journals (Sweden)
Shuangjiao Ma
2017-02-01
Full Text Available Traditional She medicine is part of China’s cultural heritage and has become remarkably popular worldwide. The Shi-Liang tea is made from the processed leaves of Chimonanthus salicifolius S. Y. Hu and Chimonanthus zhejiangensis M. C. Liu. To ensure the safety and efficacy of Shi-Liang tea, we used DNA barcoding based on the internal transcribed spacer 2 (ITS2 of nuclear ribosomal DNA to distinguish the original plant sources of Shi-Liang tea from closely related species. All 71 ITS2 sequences were aligned by Clustal-W, and genetic distances were computed using MEGA 6.0 according to the Kimura 2-parameter model. The results indicated that the sequence lengths of ITS2 regions of the original plants of Shi-Liang tea and closely related species ranged from 256 bp to 260 bp. Interspecific genetic distances ranged from 0 to 0.078. The neighbor-joining (NJ tree showed that the original plants of Shi-Liang tea species can be easily differentiated from closely related species. Distinct molecular differences were found between the secondary structures of ITS2 sequences from Shi-Liang tea and closely related species. The results in the present investigation suggested that the ITS2 could be an effective DNA marker to identify the original plants of Shi-Liang tea and their closely related species. These DNA barcodes can greatly benefit the supervision of the commercial circulation of She medicine.
17. Asexual reproduction in a close relative of Arabidopsis: a genetic investigation of apomixis in Boechera ( Brassicaceae).
NARCIS (Netherlands)
Schranz, M.E.; Kantama, L.; Jong, de J.H.S.G.M.; Mitchell-Olds, T.
2006-01-01
Understanding apomixis (asexual reproduction through seeds) is of great interest to both plant breeders and evolutionary biologists. The genus Boechera is an excellent system for studying apomixis because of its close relationship to Arabidopsis, the occurrence of apomixis at the diploid level, and
18. A modified nodal pressure method for calculating flow distribution in hydraulic circuits for the case of unconventional closing relations
Directory of Open Access Journals (Sweden)
Egor M. Mikhailovsky
2015-06-01
Full Text Available We proposed a method for numerically solving the problem of flow distribution in hydraulic circuits with lumped parameters for the case of random closing relations. The conventional and unconventional types of relations for the laws of isothermal steady fluid flow through the individual hydraulic circuit components are studied. The unconventional relations are presented by those given implicitly by the flow rate and dependent on the pressure of the working fluid. In addition to the unconventional relations, the formal conditions of applicability were introduced. These conditions provide a unique solution to the flow distribution problem. A new modified nodal pressure method is suggested. The method is more versatile in terms of the closing relation form as compared to the unmodified one, and has lower computational costs as compared to the known technique of double-loop iteration. The paper presents an analysis of the new method and its algorithm, gives a calculated example of a gas transportation network, and its results.
19. Closed suction drainage using Lichtenstein technique in preventing wound complications following inguinal hernioplasty: brief report
Directory of Open Access Journals (Sweden)
Hamid Reza Hemmati
2015-03-01
Results: No adverse event including hematoma, seroma or wound infection occurred in either group with or without closed suction drainage in the first 10 days after surgery. Only one patient carried wound infection during days 10 to 15 following operation who was in the group with closed drainage (P=1.00. Conclusion: In this study, Seroma and hematoma was not observed in patients with and without closed suction drainage. To avoid drains' complications, indiscriminate use of antibiotics, prolonged hospital stay, we do not recommend the use of drains in this type of surgery.
20. The closely related CD103+ dendritic cells (DCs) and lymphoid-resident CD8+ DCs differ in their inflammatory functions.
Science.gov (United States)
Jiao, Zhijun; Bedoui, Sammy; Brady, Jamie L; Walter, Anne; Chopin, Michael; Carrington, Emma M; Sutherland, Robyn M; Nutt, Stephen L; Zhang, Yuxia; Ko, Hyun-Ja; Wu, Li; Lew, Andrew M; Zhan, Yifan
2014-01-01
Migratory CD103+ and lymphoid-resident CD8+ dendritic cells (DCs) share many attributes, such as dependence on the same transcription factors, cross-presenting ability and expression of certain surface molecules, such that it has been proposed they belong to a common sub-lineage. The functional diversity of the two DC types is nevertheless incompletely understood. Here we reveal that upon skin infection with herpes simplex virus, migratory CD103+ DCs from draining lymph nodes were more potent at inducing Th17 cytokine production by CD4+ T cells than CD8+ DCs. This superior capacity to drive Th17 responses was also evident in CD103+ DCs from uninfected mice. Their differential potency to induce Th17 differentiation was reflected by higher production of IL-1β and IL-6 by CD103+ DCs compared with CD8+ DCs upon stimulation. The two types of DCs from isolated lymph nodes also differ in expression of certain pattern recognition receptors. Furthermore, elevated levels of GM-CSF, typical of those found in inflammation, substantially increased the pool size of CD103+ DCs in lymph nodes and skin. We argue that varied levels of GM-CSF may explain the contrasting reports regarding the positive role of GM-CSF in regulating development of CD103+ DCs. Together, we find that these two developmentally closely-related DC subsets display functional differences and that GM-CSF has differential effect on the two types of DCs.
1. The closely related CD103+ dendritic cells (DCs and lymphoid-resident CD8+ DCs differ in their inflammatory functions.
Directory of Open Access Journals (Sweden)
Zhijun Jiao
Full Text Available Migratory CD103+ and lymphoid-resident CD8+ dendritic cells (DCs share many attributes, such as dependence on the same transcription factors, cross-presenting ability and expression of certain surface molecules, such that it has been proposed they belong to a common sub-lineage. The functional diversity of the two DC types is nevertheless incompletely understood. Here we reveal that upon skin infection with herpes simplex virus, migratory CD103+ DCs from draining lymph nodes were more potent at inducing Th17 cytokine production by CD4+ T cells than CD8+ DCs. This superior capacity to drive Th17 responses was also evident in CD103+ DCs from uninfected mice. Their differential potency to induce Th17 differentiation was reflected by higher production of IL-1β and IL-6 by CD103+ DCs compared with CD8+ DCs upon stimulation. The two types of DCs from isolated lymph nodes also differ in expression of certain pattern recognition receptors. Furthermore, elevated levels of GM-CSF, typical of those found in inflammation, substantially increased the pool size of CD103+ DCs in lymph nodes and skin. We argue that varied levels of GM-CSF may explain the contrasting reports regarding the positive role of GM-CSF in regulating development of CD103+ DCs. Together, we find that these two developmentally closely-related DC subsets display functional differences and that GM-CSF has differential effect on the two types of DCs.
2. Spotted fever group rickettsia closely related to Rickettsia monacensis isolated from ticks in South Jeolla province, Korea.
Science.gov (United States)
Lee, Kyung-Min; Choi, Yeon-Joo; Shin, Sun-Hye; Choi, Min-Kyung; Song, Hyeon-Je; Kim, Heung-Chul; Klein, Terry A; Richards, Allen L; Park, Kyung-Hee; Jang, Won-Jong
2013-07-01
Rickettsia monacensis, a spotted fever group rickettsia, was isolated from Ixodes nipponensis ticks collected from live-captured small mammals in South Jeolla province, Korea in 2006. Homogenates of tick tissues were inoculated into L929 and Vero cell monolayers using shell vial assays. After several passages, Giemsa staining revealed rickettsia-like organisms in the inoculated Vero cells, but not the L929 cells. Sequencing analysis revealed that the ompA-small part (25-614 bp region), ompA-large part (2849-4455 bp region), nearly full-length ompB (58-4889 bp region) and gltA (196-1236 bp region) of the isolates had similarities of 100%, 99.8%, 99.3% and 99.5%, respectively, to those of R. monacensis. Furthermore, phylogenetic analysis showed that the isolate was grouped into the cluster in the same way as R. monacensis in the trees of all genes examined. These results strongly suggest that the isolate is closely related to R. monacensis. As far as is known, this is the first report of isolation of R. monacensis from ticks in Korea.
3. Genetically modified yeast of the species Issatchenkia orientalis and closely relates species, and fermentation processes using same
Science.gov (United States)
Suominen, Pirkko [Maple Grove, MN; Aristidou, Aristos [Highland Ranch, CO; Pentilla, Merja [Helsinki, FI; Ilmen, Marja [Helsinki, FI; Ruohonen, Laura [Helsinki, FI; Koivuranta, Kari [Vantaa, FI; Roberg-Perez, Kevin [Minneapolis, MN
2012-01-17
Cells of the species Issatchenkia orientalis and closely related yeast species are transformed with a vector to introduce an exogenous lactate dehydrogenase gene. The cells produce lactic acid efficiently and are resistant at low pH, high lactate titer conditions.
4. Whole-Genome Sequences of Two Closely Related Bacteria, Actinomyces sp. Strain Chiba101 and Actinomyces denticolens DSM 20671T
Science.gov (United States)
Ishige, Taichiro; Sekigawa, Yuriko; Kobayashi, Tomoko; Torii, Yasushi; Yokoyama, Eiji; Ishiwata, Hiroyuki; Hamada, Moriyuki; Tamura, Tomohiko; Azuma, Ryozo
2017-01-01
ABSTRACT Actinomyces sp. strain Chiba101, isolated from an arthritic leg joint of a pig raised in Japan, is a bacterium closely related to Actinomyces denticolens. Here, we deciphered the complete genome sequence of Actinomyces sp. Chiba101 and the high-quality draft genome sequence of A. denticolens DSM 20671T. PMID:28385845
5. Phylogeny Inference of Closely Related Bacterial Genomes: Combining the Features of Both Overlapping Genes and Collinear Genomic Regions
Science.gov (United States)
Zhang, Yan-Cong; Lin, Kui
2015-01-01
Overlapping genes (OGs) represent one type of widespread genomic feature in bacterial genomes and have been used as rare genomic markers in phylogeny inference of closely related bacterial species. However, the inference may experience a decrease in performance for phylogenomic analysis of too closely or too distantly related genomes. Another drawback of OGs as phylogenetic markers is that they usually take little account of the effects of genomic rearrangement on the similarity estimation, such as intra-chromosome/genome translocations, horizontal gene transfer, and gene losses. To explore such effects on the accuracy of phylogeny reconstruction, we combine phylogenetic signals of OGs with collinear genomic regions, here called locally collinear blocks (LCBs). By putting these together, we refine our previous metric of pairwise similarity between two closely related bacterial genomes. As a case study, we used this new method to reconstruct the phylogenies of 88 Enterobacteriale genomes of the class Gammaproteobacteria. Our results demonstrated that the topological accuracy of the inferred phylogeny was improved when both OGs and LCBs were simultaneously considered, suggesting that combining these two phylogenetic markers may reduce, to some extent, the influence of gene loss on phylogeny inference. Such phylogenomic studies, we believe, will help us to explore a more effective approach to increasing the robustness of phylogeny reconstruction of closely related bacterial organisms. PMID:26715828
6. Composition of the essential oils from underground parts of Valeriana officinalis L. s.l. and several closely related taxa
NARCIS (Netherlands)
Bos, Rein; Woerdenbag, Herman J.; Hendriks, Henk; Scheffer, Johannes J. C.
1997-01-01
The volatile constituents from roots and rhizomes of Valeriana officinalis L. s.l. and of several closely related Valeriana taxa were investigated by GC and GCMS (EI and NICI) analysis. Seeds were obtained from different botanical gardens in Europe, and the plants investigated were grown in an exper
7. Gender-related inequalities in the division of family work in close relationships: A social psychological perspective
NARCIS (Netherlands)
Kluwer, E.S.; Mikula, G.
2003-01-01
We offer a social psychological perspective on gender-related inequalities in close relationships and integrate two lines of research that have focused on the intrapersonal perceptions and interpersonal consequences respectively of the gendered division of labour. We start with a brief summary of
8. Microvariation artifacts introduced by PCR and cloning of closely related 16S rRNA gene sequences
NARCIS (Netherlands)
Speksnijder, A.G.C.L.; Kowalchuk, G.A.; Jong, S. de; Kline, E.; Stephen, J.R.; Laanbroek, H.J.
2001-01-01
A defined template mixture of seven closely related 16S-rDNA clones was used in a PCR-cloning experiment to assess and track sources of artifactual sequence variation in 16S rDNA clone libraries. At least 14% of the recovered clones contained aberrations. Artifact sources were polymerase errors, a m
9. Microvariation Artifacts Introduced by PCR and Cloning of Closely Related 16S rRNA Gene Sequences
NARCIS (Netherlands)
Speksnijder, A.G.C.L.; Kowalchuk, G.A.; Jong, de S.; Kline, E.; Stephen, J.R.; Laanbroek, H.J.
2001-01-01
A defined template mixture of seven closely related 16S-rDNA clones was used in a PCR-cloning experiment to assess and track sources of artifactual sequence variation in 16S rDNA clone libraries. At least 14% of the recovered clones contained aberrations. Artifact sources were polymerase errors, a m
10. Gender-related inequalities in the division of family work in close relationships: A social psychological perspective
NARCIS (Netherlands)
Kluwer, E.S.; Mikula, G.
2003-01-01
We offer a social psychological perspective on gender-related inequalities in close relationships and integrate two lines of research that have focused on the intrapersonal perceptions and interpersonal consequences respectively of the gendered division of labour. We start with a brief summary of re
11. Beauty is in the 'we' of the beholder: greater agreement on facial attractiveness among close relations.
Science.gov (United States)
2007-01-01
Scientific research on facial attractiveness has focused primarily on elucidating universal factors to which all raters respond consistently. However, recent work has shown that there is also substantial disagreement between raters, highlighting the importance of determining how attractiveness preferences vary among different individuals. We conducted a typical attractiveness ratings study, but took the unusual step of recruiting pairs of subjects who were spouses, siblings, or close friends. The agreement between pairs of affiliated friends, siblings, and spouses was significantly greater than between pairs of strangers drawn from the same race and culture, providing evidence that facial-attractiveness preferences are socially organized.
12. [Marks on clothing and skin in absolutely and relatively close distance gunshots with fright weapons].
Science.gov (United States)
Nadjem, H; Bohnert, M; Schley, K; Pollak, S
1996-01-01
Based on an actual case to be examined-the victim had sustained burning and powder tattooing of the abdominal skin--test shots were performed with blank cartridge guns (Mauser and Umarex revolvers, cal. 380) in order to study the changes occurring on textiles in the area of contact and close range shots. As expected, the extent of burning and smoke soiling depended on whether the propellant of the blank cartridges consisted of nitrocellulose (Nc) or black powder. At the same distance the smokeless nitro-powder caused less soot soiling and burning than black powder. Contact or near contact shots produced tear-like tissue damages due to the pressure of the discharged muzzle gases. When black powder cartridges were used, burn holes larger than the caliber were observed; with Nc blank cartridges the thermal effects were most pronounced if textiles made of thermolabile synthetics were shot at.
13. Large-Grain Superconducting Gun Cavity Testing Program Phase One Closing Report
Energy Technology Data Exchange (ETDEWEB)
Hammons, L. [Brookhaven National Lab. (BNL), Upton, NY (United States); Bellavia, S. [Brookhaven National Lab. (BNL), Upton, NY (United States); Belomestnykh, S. [Brookhaven National Lab. (BNL), Upton, NY (United States); Ben-Zvi, I. [Brookhaven National Lab. (BNL), Upton, NY (United States); Cullen, C. [Brookhaven National Lab. (BNL), Upton, NY (United States); Dai, J. [Brookhaven National Lab. (BNL), Upton, NY (United States); Degen, C. [Brookhaven National Lab. (BNL), Upton, NY (United States); Hahn, H. [Brookhaven National Lab. (BNL), Upton, NY (United States); Masi, L. [Brookhaven National Lab. (BNL), Upton, NY (United States); McIntyre, G. [Brookhaven National Lab. (BNL), Upton, NY (United States); Schultheiss, C. [Brookhaven National Lab. (BNL), Upton, NY (United States); Seda, T. [Brookhaven National Lab. (BNL), Upton, NY (United States); Kellerman, R. [Brookhaven National Lab. (BNL), Upton, NY (United States); Tallerico, T. [Brookhaven National Lab. (BNL), Upton, NY (United States); Todd, R. [Brookhaven National Lab. (BNL), Upton, NY (United States); Tuozzolo, S. [Brookhaven National Lab. (BNL), Upton, NY (United States); Xu, W. [Brookhaven National Lab. (BNL), Upton, NY (United States); Than, Y. [Brookhaven National Lab. (BNL), Upton, NY (United States)
2013-10-31
This report details the experimental configuration and RF testing results for the first phase of a large-grained niobium electron gun cavity testing program being conducted in the Small Vertical Testing Facility in the Collider-Accelerator Department. This testing is meant to explore multi-pacting in the cavity and shed light on the behavior of a counterpart cavity of identical geometry installed in the Energy Recovery LINAC being constructed in the Collider-Accelerator Department at Brookhaven National Laboratory. This test found that the Q of the large-grained cavity at 4 K reached ~6.5 × 108 and at 2 K reached a value of ~6 × 109. Both of these values are about a factor of 10 lower than would be expected for this type of cavity given the calculated surface resistance and the estimated geometry factor for this half-cell cavity. In addition, the cavity reached a peak voltage of 0.6 MV before there was sig-nificant decline in the Q value and a substantial increase in field emission. This relatively low volt-age, coupled with the low Q and considerable field emission suggest contamination of the cavity interior, possibly during experimental assembly. The results may also suggest that additional chemical etching of the interior surface of the cavity may be beneficial. Throughout the course of testing, various challenges arose including slow helium transfer to the cryostat and cable difficulties. These difficulties and others were eventually resolved, and the re-port discusses the operating experience of the experiment thus far and the plans for future work aimed at exploring the nature of multipacting with a copper cathode inserted into the cavity.
14. Shifts in patterns of microhabitat occupation by six closely related species of mosses along a complex altitudinal gradient.
Science.gov (United States)
Watson, Maxine A
1980-01-01
Changes in patterns of microhabitat occupation were examined for six closely related moss species (family Polytrichaceae) found growing together along a complex altitudinal gradient on the northeast face of Mount Washington, New Hampshire. Little evidence could be found to support the hypothesis that the relative distributions of these six moss species were determined by competitive interactions occurring among them. Instead, the data support the hypothesis that changing patterns in the relative distributions of these six moss species result from differences in microhabitat availability among sites. The moss species appear to behave in an opportunistic manner, occupying a wide array of microhabitats as these microhabitats become available to them.
15. Studies on two closely related species of octocorallians: biochemical and molecular characteristics of the organic matrices of endoskeletal sclerites.
Science.gov (United States)
Rahman, M Azizur; Isa, Y; Uehara, T
2006-01-01
Two species of alcyonarian corals, Lobophytum crassum and Sinularia polydactyla, are closely related to each other. It is reported that the calcified organic substances in the skeletons of both contain a protein-polysaccharide complex playing a key role in the regulation of biocalcification. However, information on the matrix proteins of endoskeletal sclerite has been lacking. Hence we studied the proteinaceous organic matrices of sclerites for both species, to analyze the sequences and the functional properties of the proteins present. Sodium dodecyl sulfate-polyacrylamide gel electrophoresis (SDS-PAGE) analysis of the preparations showed four bands of proteins with apparent molecular masses of 102, 67, 48, and 37 kDa for L. crassum and seven bands of 109, 83, 70, 63, 41, 30, and 22 kDa for S. polydactyla. A major protein band of about 67 kDa in L. crassum and two bands of proteins of about 70 and 63 kDa in S. polydactyla yielded N-terminal amino acid sequences. Periodic acid-Schiff staining indicated that the 67-kDa protein in L. crassum, and 83- and 63-kDa proteins in S. polydactyla were glycosylated. For detection of calcium binding proteins, a Ca(2+) overlay analysis was conducted in the extract via (45)Ca autoradiography. The 102- and 67-kDa calcium binding proteins in L. crassum, and the 109- and 63-kDa Ca(2+) binding proteins in S. polydactyla were found to be radioactive. An assay for carbonic anhydrase (CA), which is thought to play an important role in the process of calcification, revealed specific activities. Newly derived protein sequences were subjected to standard sequence analysis involving identification of similarities to other proteins in databases. The significantly different protein expressions and compositional analysis of sequences between two species were demonstrated.
16. A new vanilla species from Costa Rica closely related to V. planifolia (Orchidaceae
Directory of Open Access Journals (Sweden)
José B. Azofeifa-Bolaños
2017-02-01
Full Text Available We describe a new vanilla species growing in sympatry with Vanilla planifolia Jacks. ex Andrews (Orchidaceae in the province of Limón, Caribbean coast of Costa Rica. The morphology of the reproductive and vegetative organs observed on vines cultivated under shade-house, the nuclear (Internal Transcribed Spacer and plastid (matK nucleotide sequences, as well as the contents of aromatic compounds measured in ripe fruits, show that this species is close to but distinct from V. planifolia. The name V. sotoarenasii M.Pignal, Azofeifa-Bolaños & Grisoni sp. nov. is proposed for this new Vanilla species endemic in Costa Rica. It is especially distinguished from V. planifolia by a reduction of about 30% of the size of the fruits and flowers, by a divergence of ITS sequences for at least two species-conserved nucleotides compared to seven other species of the V. planifolia group, and by the presence of anisic compounds and low content of phenolic compounds (including vanillin in the fruits. These results confirmed the extension of the area of distribution of V. planifolia southward to Costa Rica, where a recent speciation process occurred. Because of its particular agronomic and aromatic properties, V. sotoarenasii sp. nov. could represent a valuable biological resource for the vanilla industry.
17. Adaptation and modification of three CRISPR loci in two closely related cyanobacteria.
Science.gov (United States)
Hein, Stephanie; Scholz, Ingeborg; Voß, Björn; Hess, Wolfgang R
2013-05-01
An RNA-based screen was performed to reveal a possible evolutionary scenario for the CRISPR-Cas systems in two cyanobacterial model strains. Following the analysis of a draft genome sequence of Synechocystis sp PCC6714, three different CRISPR-Cas systems were characterized that have different degrees of relatedness to another three CRISPR-Cas systems in Synechocystis sp PCC6803. A subtype III-B system was identified that is extremely conserved between both strains. Strong signals in northern hybridizations and the presence of different spacers (but identical repeats) indicated this system to be active, despite the absence of a known endonuclease candidate gene involved in the maturation of its crRNAs in the two strains. The other two systems were found to differ significantly from each other, with different sets of repeat-spacer arrays and different Cas genes. In view of the otherwise very close relatedness of the two analyzed strains, this is suggestive of an unknown mechanism involved in the replacement of CRISPR-Cas cassettes as a whole. Further RNA analyses revealed the accumulation of crRNAs to be impacted by environmental conditions critical for photoautotropic growth. All six systems are associated with a gene for a possible transcriptional repressor. Indeed, we identified one of these genes, sll7009, as encoding a negative regulator specific for the CRISPR1 subtype I-D system in Synechocystis sp PCC6803.
18. Asexual reproduction in a close relative of Arabidopsis: a genetic investigation of apomixis in Boechera (Brassicaceae).
Science.gov (United States)
Schranz, M Eric; Kantama, Laksana; de Jong, Hans; Mitchell-Olds, Thomas
2006-01-01
Understanding apomixis (asexual reproduction through seeds) is of great interest to both plant breeders and evolutionary biologists. The genus Boechera is an excellent system for studying apomixis because of its close relationship to Arabidopsis, the occurrence of apomixis at the diploid level, and its potentially simple inheritance by transmission of a heterochromatic (Het) chromosome. Diploid sexual Boechera stricta and diploid apomictic Boechera divaricarpa (carrying a Het chromosome) were crossed. Flow cytometry, karyotype analysis, genomic in situ hybridization, pollen staining and seed-production measurements were used to analyse the parents and resulting F1, F2 and selected F3 and test-cross (TC) generations. The F1 plant was a low-fertility triploid that produced a swarm of aneuploid and polyploid F2 progeny. Two of the F2 plants were fertile near-tetraploids, and analysis of their F3 and TC progeny revealed that they were sexual and genomically stabilized. The apomictic phenotype was not transmitted by genetic crossing as a single dominant locus on the Het chromosome, suggesting a complex genetic control of apomixis that has implications for future genetic and evolutionary analyses in this group.
19. Embarrassment When Illness Strikes A Close Relative: A World Mental Health Survey Consortium Multi-Site Study
Science.gov (United States)
Ahmedani, Brian K.; Kubiak, Sheryl Pimlott; Kessler, Ronald C.; de Graaf, Ron; Alonso, Jordi; Bruffaerts, Ronny; Zarkov, Zahari; Viana, Maria Carmen; Huang, Y.Q.; Hu, Chiyi; Posada-Villa, Jose A.; Lepine, Jean-Pierre; Angermeyer, Matthias C.; de Girolamo, Giovanni; Karam, Aimee N.; Medina-Mora, Maria Elena; Gureje, Oye; Ferry, Finola; Sagar, Rajesh; Anthony, James C.
2014-01-01
Background This global study seeks to estimate the degree to which a family member might feel embarrassed when a close relative is suffering from an alcohol, drug, or mental health condition (ADMC) versus a general medical condition (GMC). To date, most studies have considered embarrassment and stigma in society and internalized by the afflicted individual, but have not assessed family embarrassment in a large scale study. Method In 16 sites of the World Mental Health Surveys (WMHS), standardized assessments were completed including items on family embarrassment. Site matching was used to constrain local socially shared determinants of stigma-related feelings, enabling a conditional logistic regression model that estimates the embarrassment close relatives may hold in relation to family members affected by an ADMC, GMC, or both conditions. Results There was a statistically robust association such that subgroups with an ADMC-affected relative were more likely to feel embarrassed as compared to subgroups with a relative affected by a GMC (p<0.001), even with covariate adjustments for age and sex. Conclusions The pattern of evidence from this research is consistent with conceptual models for interventions that target individual- and family-level stigma-related feelings of embarrassment as might be part of the obstacles to effective early intervention and treatment for ADMC conditions. Macro-level interventions are underway, but micro-level interventions also may be required among family members, along with care for each person with an ADMC. PMID:23298443
20. A dimensionless relative trajectory estimation algorithm for autonomous imaging of a small astronomical body in a close distance flyby
Science.gov (United States)
Ariu, Kaito; Inamori, Takaya; Funase, Ryu; Nakasuka, Shinichi
2016-08-01
The world's first micro-spacecraft, "Proximate Object Close flYby with Optical Navigation" (PROCYON) has the advanced mission to approach an asteroid in dozen km (a one-order closer imaging distance compared with previous probes). In such a close distance encounter, the estimation of the relative trajectory of the target is necessary to perform autonomous imaging. However, the estimation is difficult owing to rapid changes of the line-of-sight direction of the target body. To overcome this problem, a novel dimensionless or direction only relative trajectory estimation algorithm, which uses a least square method, is proposed. The evaluation function for the least square method coincides with the error property of picture information to enable all of its calculations to be recursive and linear. It is suited for the implementation on the limited on-board computer. Numerical simulation results indicate that the proposed algorithm should enable the one-order closer flyby observation.
1. Students' perceptions of parent-adolescent closeness and communication about sexuality: relations with sexual knowledge, attitudes, and behaviors.
Science.gov (United States)
Somers, C L; Paulson, S E
2000-10-01
The main goal of this study was to explore how parent-adolescent closeness and communication about sexuality were associated with three aspects of adolescent sexuality (sexual knowledge, attitudes and behaviors). Participants were 157 boys and girls in grades 9 to 12 from two suburban high schools in the Midwest. Canonical correlation analyses revealed two significant combinations of variables. First, younger age and less maternal and paternal communication were related to less sexual behavior and less sexual knowledge. Second, being younger and female and receiving less maternal communication was related to less sexual knowledge and more conservative attitudes. Contrary to expectation, higher levels of parental closeness in conjunction with parental communication did not have a significant influence on these adolescents' sexuality. Given the importance of both age and parental communication in predicting adolescent's sexuality in this study, implications concerning the timing of communication become evident.
2. Closed hollow bulb obturator--one-step fabrication: a clinical report.
Science.gov (United States)
Buzayan, Muaiyed M; Ariffin, Yusnidar T; Yunus, Norsiah
2013-10-01
A method is described for the fabrication of a closed hollow bulb obturator prosthesis using a hard thermoforming splint material and heat-cured acrylic resin. The technique allowed the thickness of the thermoformed bulb to be optimized for weight reduction, while the autopolymerized seal area was covered in heat-cured acrylic resin, thus eliminating potential leakage and discoloration. This technique permits the obturator prosthesis to be processed to completion from the wax trial denture without additional laboratory investing, flasking, and processing.
3. Closed rhinoplasty：effects and changes on voice - a preliminary report
Institute of Scientific and Technical Information of China (English)
Giuseppe Guarro; Romano Mafifa; Barbara Rasile; Carmine Alfano
2016-01-01
Aim: Effects of rhinoplasty were already studied from many points of view: otherwise poor is scientific production focused on changes of voice after rhinoplasty. This preliminary study analyzed objectively and subjectively these potential effects on 19 patients who underwent exclusively closed rhinoplasty.Methods: This preliminary evaluation was conducted from September 2012 to May 2013 and 19 patients have undergone primary rhinoplasty with exclusively closed approach (7 males, 12 females). All patients were evaluated before and 6 months after surgery. Each of them answered to a questionnaire (Voice Handicap Index Score) and the voice was recorded for spectrographic analysis: this system allowed to perform the measurement of the intensity and frequency of vowels (“A” and “E”) and nasal consonants (“N” and “M”) before and after surgery. Data were analysed with the Mann-Whitney test.Results: Sixteen patients showed statistically significant differences after surgery. It was detected in 69% of cases an increased frequency of emission of the consonant sounds (P = 0.046), while in 74% of cases the same phenomenon was noticed for vowel sounds (P = 0.048).Conclusion: Many patients who undergo rhinoplasty think that the intervention only leads to anatomical changes and improvement of respiratory function. The surgeon should instead accurately inform patients about the potential effects on the voice. This preliminary study reveals the significant effects of closed rhinoplasty on the human voice.
4. Political market orientation and its commercial cousin: Close family or distant relatives?
DEFF Research Database (Denmark)
Ormrod, Robert P.
2007-01-01
the differences between the related terms of "market orientation" and "marketing orientation." Further, the article surveys the political market orientation literature and then discusses the perspective that each approach adopts, the extent to which a distinction is made between a "political market orientation...
5. New criteria for selecting the origin of DNA replication in Wolbachia and closely related bacteria
DEFF Research Database (Denmark)
Ioannidis, Panagiotis; Dunning Hotopp, Julie C; Sapountzis, Panagiotis
2007-01-01
, the origin of DNA replication (ori) regions were identified in silico for Wolbachia strains and eleven other related bacteria belonging to Ehrlichia, Anaplasma, and Rickettsia genera. These features include DnaA-, CtrA- and IHF-binding sites as well as the flanking genes in C. crescentus. The Wolbachia ori...
6. Two-component signal transduction in Bacillus cereus and closely related bacteria
NARCIS (Netherlands)
Been, de M.W.H.J.
2009-01-01
Bacillus cereus is a Gram-positive pathogen that is recognised as an important cause of food-borne disease worldwide. Within the genus Bacillus, B. cereus and its closest relatives form a homogeneous subdivision that has been termed the B. cereus group. This group includes B. anthracis, a pathogen
7. Gene regulations in HBV-related liver cirrhosis closely correlate with disease severity.
Science.gov (United States)
Lee, Seram; Kim, Soyoun
2007-09-30
Liver cirrhosis (LC) is defined as comprising diffuse fibrosis and regenerating nodules of the liver. The biochemical and anatomical dysfunction in LC results from both reduced liver cell number and portal vascular derangement. Although several studies have investigated dysregulated genes in cirrhotic nodules, little is known about the genes implicated in the pathophysiologic change of LC or about their relationship with the degree of decompensation. Here, we applied cDNA microarray analysis using 38 HBsAg-positive LC specimens to identify the genes dysregulated in HBV-associated LC and to evaluate their relation to disease severity. Among 1063 known cancer- and apoptosis-related genes, we identified 104 genes that were significantly up- (44) or down- (60) regulated in LC. Interestingly, this subset of 104 genes was characteristically correlated with the degree of decompensation, called the Pugh-Child classification (20 Pugh-Child A, 10 Pugh-Child B, and 8 Pugh-Child C). Patient samples from Pugh-Child C exhibited a distinct pattern of gene expression relative to those of Pugh-Child A and B. Especially in Pugh-Child C, genes encoding hepatic proteins and metabolizing enzymes were significantly down-regulated, while genes encoding various molecules related to cell replication were up-regulated. Our results suggest that subsets of genes in liver cells correspond to the pathophysiologic change of LC according to disease severity and possibly to hepatocarcinogenesis.
8. Closed-loop surface-related multiple elimination and its application to simultaneous data reconstruction
NARCIS (Netherlands)
Lopez Angarita, G.A.; Verschuur, D.J.
2015-01-01
Surface-related multiple elimination (SRME) is one of the most commonly used methods for suppressing surface multiples. However, to obtain an accurate surface multiple estimation, dense source and receiver sampling is required. The traditional approach to this problem is performing data interpolatio
9. Estrus Traits Derived from Activity Measurements are Heritable and Closely Related to Conventional
DEFF Research Database (Denmark)
Ismael, Ahmed Ismael Sayed; Kargo, Morten; Fogh, Anders
This study was aimed at assessing the genetic parameters for fertility-related traits, comparing the interval from calving to first insemination (ICF) to physical activity traits, especially days from calving to first high activity, DFHA. Data from commercial Holstein herds included insemination...
10. Specific molecular detection of Anaplasma sp. closely related to Anaplasma phagocytophilum in ixodid ticks and cattle in a pastureland in Hokkaido, Japan.
Science.gov (United States)
Ybañez, Adrian P; Tagawa, Michihito; Matsumoto, Kotaro; Kishimoto, Toshio; Yokoyama, Naoaki; Inokuma, Hisashi
2013-01-01
Recent molecular analyses of the Anaplasma sp. closely related to Anaplasma phagocytophilum (previously believed to be A. phagocytophilum) in Japan have clarified its distinct phylogenetic position. PCR methods relying on 16S rRNA- and P44/MSP2-based primers designed to detect this species have low sensitivity and specificity. In this study, a highly sensitive and specific nested PCR method using newly designed primers based on heat-shock operon gene (groEL) was developed to detect this species. The method was later used in an epidemiological study testing DNA samples from 85 Ixodid ticks (collected by flagging) and 50 cattle from the same pastureland in Nakaosobetsu, Hokkaido, Japan. Results revealed prevalence rates of 2.4% (2 of 85) in ticks and 2% (1 of 50) in cattle. The present study also reported the first molecular detection of the Anaplasma sp. closely related to A. phagocytophilum in Japan in H. douglasii, and established a new reliable PCR method that detects this Anaplasma sp. closely related to A. phagocytophilum in Japan.
11. Comparative genomics of four closely related Clostridium perfringens bacteriophages reveals variable evolution among core genes with therapeutic potential
Directory of Open Access Journals (Sweden)
Siragusa Gregory R
2011-06-01
Full Text Available Abstract Background Because biotechnological uses of bacteriophage gene products as alternatives to conventional antibiotics will require a thorough understanding of their genomic context, we sequenced and analyzed the genomes of four closely related phages isolated from Clostridium perfringens, an important agricultural and human pathogen. Results Phage whole-genome tetra-nucleotide signatures and proteomic tree topologies correlated closely with host phylogeny. Comparisons of our phage genomes to 26 others revealed three shared COGs; of particular interest within this core genome was an endolysin (PF01520, an N-acetylmuramoyl-L-alanine amidase and a holin (PF04531. Comparative analyses of the evolutionary history and genomic context of these common phage proteins revealed two important results: 1 strongly significant host-specific sequence variation within the endolysin, and 2 a protein domain architecture apparently unique to our phage genomes in which the endolysin is located upstream of its associated holin. Endolysin sequences from our phages were one of two very distinct genotypes distinguished by variability within the putative enzymatically-active domain. The shared or core genome was comprised of genes with multiple sequence types belonging to five pfam families, and genes belonging to 12 pfam families, including the holin genes, which were nearly identical. Conclusions Significant genomic diversity exists even among closely-related bacteriophages. Holins and endolysins represent conserved functions across divergent phage genomes and, as we demonstrate here, endolysins can have significant variability and host-specificity even among closely-related genomes. Endolysins in our phage genomes may be subject to different selective pressures than the rest of the genome. These findings may have important implications for potential biotechnological applications of phage gene products.
12. Integrative analysis of single nucleotide polymorphisms and gene expression efficiently distinguishes samples from closely related ethnic populations
Directory of Open Access Journals (Sweden)
Yang Hsin-Chou
2012-07-01
Full Text Available Abstract Background Ancestry informative markers (AIMs are a type of genetic marker that is informative for tracing the ancestral ethnicity of individuals. Application of AIMs has gained substantial attention in population genetics, forensic sciences, and medical genetics. Single nucleotide polymorphisms (SNPs, the materials of AIMs, are useful for classifying individuals from distinct continental origins but cannot discriminate individuals with subtle genetic differences from closely related ancestral lineages. Proof-of-principle studies have shown that gene expression (GE also is a heritable human variation that exhibits differential intensity distributions among ethnic groups. GE supplies ethnic information supplemental to SNPs; this motivated us to integrate SNP and GE markers to construct AIM panels with a reduced number of required markers and provide high accuracy in ancestry inference. Few studies in the literature have considered GE in this aspect, and none have integrated SNP and GE markers to aid classification of samples from closely related ethnic populations. Results We integrated a forward variable selection procedure into flexible discriminant analysis to identify key SNP and/or GE markers with the highest cross-validation prediction accuracy. By analyzing genome-wide SNP and/or GE markers in 210 independent samples from four ethnic groups in the HapMap II Project, we found that average testing accuracies for a majority of classification analyses were quite high, except for SNP-only analyses that were performed to discern study samples containing individuals from two close Asian populations. The average testing accuracies ranged from 0.53 to 0.79 for SNP-only analyses and increased to around 0.90 when GE markers were integrated together with SNP markers for the classification of samples from closely related Asian populations. Compared to GE-only analyses, integrative analyses of SNP and GE markers showed comparable testing
13. NEGLECTED POSTERIOR KNEE DISLOCATION TREATED WITH CLOSED MANIPULATION AND UNIPLANAR EXTERNAL FIXATOR : A CASE REPORT
Directory of Open Access Journals (Sweden)
Manikumar
2015-06-01
Full Text Available Neglected traumatic posterior knee dislocations were rare in orthopaedic literature more so after a surgical intervention . Majority of the injuries are associated with vascular trauma and distal or proximal fractures and complete disruption of anterior and posterior cruciate ligaments and nerve traction injuries. Traumatic knee dislocations are therefore treated as an orthopaedic emergency. There were no definitive guide lines to open reduction as well as conservative methods of treatment. The end results of functional recovery are still controversial with residual posterior subluxation. Here we present a case of neglected posterior knee dislocation treated with closed manipulation and uni planar external fixator
14. Summarizing knowledge about ethical considerations when conducting Joint Interviews with close relatives
DEFF Research Database (Denmark)
Voltelen, Barbara; Konradsen, Hanne; Østergaard, Birte
2016-01-01
was analyzed using thematic analysis with an inductive approach. Results In total 17 articles were located. Findings were divided into two main themes: Ethical challenges in conducting joint interviews and Ethical challenges when planning and reporting from joint interviews. Conclusions and implications Joint......Background and purpose Interviewing interrelated persons simultaneously might pose different ethical considerations than single interviews due to informants’ relationship. Studies indicate that conflict torn relationships are the strongest predictor for a negative health status which obligates...... the researcher not to jeopardize it doing joint interviews. Ethical considerations conducting joint interviews remain largely undescribed in the literature. Our purpose was to illuminate the literature regarding specific ethical challenges conducting joint interviews with interrelated people in order to avoid...
15. The evolution of different maternal investment strategies in two closely related desert vertebrates
Science.gov (United States)
Ennen, Joshua R.; Lovich, Jeffrey E.; Averill-Murray, Roy C.; Yackulic, Charles B.; Agha, Mickey; Loughran, Caleb; Tennant, Laura A.; Sinervo, Barry
2017-01-01
We compared egg size phenotypes and tested several predictions from the optimal egg size (OES) and bet-hedging theories in two North American desert-dwelling sister tortoise taxa, Gopherus agassizii and G. morafkai, that inhabit different climate spaces: relatively unpredictable and more predictable climate spaces, respectively. Observed patterns in both species differed from the predictions of OES in several ways. Mean egg size increased with maternal body size in both species. Mean egg size was inversely related to clutch order in G. agassizii, a strategy more consistent with the within-generation hypothesis arising out of bet-hedging theory or a constraint in egg investment due to resource availability, and contrary to theories of density dependence, which posit that increasing hatchling competition from later season clutches should drive selection for larger eggs. We provide empirical evidence that one species, G. agassizii, employs a bet-hedging strategy that is a combination of two different bet-hedging hypotheses. Additionally, we found some evidence for G. morafkai employing a conservative bet-hedging strategy. (e.g., lack of intra- and interclutch variation in egg size relative to body size). Our novel adaptive hypothesis suggests the possibility that natural selection favors smaller offspring in late-season clutches because they experience a more benign environment or less energetically challenging environmental conditions (i.e., winter) than early clutch progeny, that emerge under harsher and more energetically challenging environmental conditions (i.e., summer). We also discuss alternative hypotheses of sexually antagonistic selection, which arise from the trade-offs of son versus daughter production that might have different optima depending on clutch order and variation in temperature-dependent sex determination (TSD) among clutches. Resolution of these hypotheses will require long-term data on fitness of sons versus daughters as a function of
16. Ethical Challenges when Interviewing Close Relatives Together – An Integrative Review
DEFF Research Database (Denmark)
Voltelen, Barbara; Konradsen, Hanne; Østergaard, Birte
2015-01-01
. The purpose of this study is to describe the special ethical perspectives concerning joint interviews with interrelated persons. Method An integrative review was performed. A search was conducted in Pub Med, Cinahl, Philosophers Index and Academic Search from 1980 -2014. Data corpus from the 17 articles...... was analysed using thematic analysis with an inductive approach searching for themes about ethical considerations doing joint interviews. The SPIDER search tool was applied using keywords relatives, ethic, dyadic interview, challenges and qualitative methods created on the basis of relevant pseudonyms, Mesh...
17. Solvent-Induced Reversal of Activities between Two Closely Related Heterogeneous Catalysts in the Aldol Reaction
Energy Technology Data Exchange (ETDEWEB)
Kandel, Kapil [Ames Laboratory; Althaus, Stacey M [Ames Laboratory; Peeraphatdit, Chorthip [Ames Laboratory; Kobayashi, Takeshi [Ames Laboratory; Trewyn, Brian G [Ames Laboratory; Pruski, Marek [Ames Laboratory; Slowing, Igor I [Ames Laboratory
2013-01-11
The relative rates of the aldol reaction catalyzed by supported primary and secondary amines can be inverted by 2 orders of magnitude, depending on the use of hexane or water as a solvent. Our analyses suggest that this dramatic shift in the catalytic behavior of the supported amines does not involve differences in reaction mechanism, but is caused by activation of imine to enamine equilibria and stabilization of iminium species. The effects of solvent polarity and acidity were found to be important to the performance of the catalytic reaction. This study highlights the critical role of solvent in multicomponent heterogeneous catalytic processes.
18. Collecting close-contact social mixing data with contact diaries: reporting errors and biases.
Science.gov (United States)
Smieszek, T; Burri, E U; Scherzinger, R; Scholz, R W
2012-04-01
The analysis of contact networks plays a major role to understanding the dynamics of disease spread. Empirical contact data is often collected using contact diaries. Such studies rely on self-reported perceptions of contacts, and arrangements for validation are usually not made. Our study was based on a complete network study design that allowed for the analysis of reporting accuracy in contact diary studies. We collected contact data of the employees of three research groups over a period of 1 work week. We found that more than one third of all reported contacts were only reported by one out of the two involved contact partners. Non-reporting is most frequent in cases of short, non-intense contact. We estimated that the probability of forgetting a contact of ≤5 min duration is greater than 50%. Furthermore, the number of forgotten contacts appears to be proportional to the total number of contacts.
19. Closed loop chemical systems for energy storage and transmission (chemical heat pipe). Final report
Energy Technology Data Exchange (ETDEWEB)
Vakil, H.B.; Flock, J.W.
1978-02-01
The work documents the anlaysis of closed loop chemical systems for energy storage and transmission, commonly referred to as the Chemical Heat Pipe (CHP). Among the various chemical reaction systems and sources investigated, the two best systems were determined to be the high temperature methane/steam reforming reaction (HTCHP) coupled to a Very High Temperature Gas Cooled Reactor (VHTR) and the lower temperature, cyclohexane dehydrogenation reaction (LTCHP) coupled to existing sources such as coal or light water reactors. Solar and other developing technologies can best be coupled to the LTCHP. The preliminary economic and technical analyses show that both systems could transport heat at an incremental cost of approximately $1.50/GJ/160 km (in excess of the primary heat cost of$2.50/GJ), at system efficiencies above 80%. Solar heat can be transported at an incremental cost of 3/GJ/160 km. The use of the mixed feed evaporator concept developed in this work contributes significantly to reducing the transportation cost and increasing the efficiency of the system. The LTCHP shows the most promise of the two systems if the technical feasibility of the cyclic closed loop chemical reaction system can be established. An experimental program for establishing this feasibility is recommended. Since the VHTR is several years away from commercial demonstration and the HTCHP chemical technology is well developed, future HTCHP programs should be aimed at VHTR and interface problems. 20. Ethical Challenges when Interviewing Close Relatives Together – An Integrative Review DEFF Research Database (Denmark) Voltelen, Barbara; Konradsen, Hanne; Østergaard, Birte 2015-01-01 Background and purpose Interviewing two interrelated persons (or more) simultaneously might pose different ethical considerations than interviewing just one person. Such ethical considerations, however, remain largely undescribed in literature, challenging the researcher who wishes to conduct them...... was analysed using thematic analysis with an inductive approach searching for themes about ethical considerations doing joint interviews. The SPIDER search tool was applied using keywords relatives, ethic, dyadic interview, challenges and qualitative methods created on the basis of relevant pseudonyms, Mesh......: The researcher/interviewer, Planning of joint interviews and Participant well-being. Conclusions and implications The nature of joint interviews poses many ethical challenges as more people are involved. They provide insight into shared accounts and communication patterns between interviewees, highlighting... 1. Estrus Traits Derived from Activity Measurements are Heritable and Closely Related to Conventional DEFF Research Database (Denmark) Ismael, Ahmed Ismael Sayed; Kargo, Morten; Fogh, Anders This study was aimed at assessing the genetic parameters for fertility-related traits, comparing the interval from calving to first insemination (ICF) to physical activity traits, especially days from calving to first high activity, DFHA. Data from commercial Holstein herds included insemination...... dates of 11,363 cows for ICF. The activity traits were derived from electronic activity tags for 3533 Holstein cows. Estimates of heritability were 0.05 for ICF and 0.15 for DFHA. The genetic correlation between ICF and DFHA was strong (0.92). The high heritability estimate and the strong genetic...... correlation between ICF and DFHA suggest that genetic gain in ICF can be improved by including DFHA as a supplementary trait in the genetic evaluation of female fertility... 2. Genetic rescue of an endangered domestic animal through outcrossing with closely related breeds DEFF Research Database (Denmark) Strønen, Astrid Vik; Salmela, Elina; Baldursdottir, Birna K. 2017-01-01 Genetic rescue, outcrossing with individuals from a related population, is used to augment genetic diversity in populations threatened by severe inbreeding and extinction. The endangered Norwegian Lundehund dog underwent at least two severe bottlenecks in the 1940s and 1960s that each left only......: Norwegian Buhund, Icelandic Sheepdog, and Norrbottenspets. Examination of single nucleotide polymorphism (SNP) genotypes based on 165K loci in 48 dogs from the four breeds revealed substantially lower genetic diversity for the Lundehund (HE 0.035) than for other breeds (HE 0.209-0.284). Analyses of genetic...... structure with > 15K linkage disequilibrium-pruned SNPs showed four distinct genetic clusters. Pairwise FST values between Lundehund and the candidate breeds were highest for Icelandic Sheepdog, followed by Buhund and Norrbottenspets. We assessed the presence of outlier loci among candidate breeds... 3. Differential specificity between closely related corals and abundant Endozoicomonas endosymbionts across global scales KAUST Repository Neave, Matthew J. 2016-07-08 Reef-building corals are well regarded not only for their obligate association with endosymbiotic algae, but also with prokaryotic symbionts, the specificity of which remains elusive. To identify the central microbial symbionts of corals, their specificity across species and conservation over geographic regions, we sequenced partial SSU ribosomal RNA genes of Bacteria and Archaea from the common corals Stylophora pistillata and Pocillopora verrucosa across 28 reefs within seven major geographical regions. We demonstrate that both corals harbor Endozoicomonas bacteria as their prevalent symbiont. Importantly, catalyzed reporter deposition–fluorescence in situ hybridization (CARD–FISH) with Endozoicomonas-specific probes confirmed their residence as large aggregations deep within coral tissues. Using fine-scale genotyping techniques and single-cell genomics, we demonstrate that P. verrucosa harbors the same Endozoicomonas, whereas S. pistillata associates with geographically distinct genotypes. This specificity may be shaped by the different reproductive strategies of the hosts, potentially uncovering a pattern of symbiont selection that is linked to life history. Spawning corals such as P. verrucosa acquire prokaryotes from the environment. In contrast, brooding corals such as S. pistillata release symbiont-packed planula larvae, which may explain a strong regional signature in their microbiome. Our work contributes to the factors underlying microbiome specificity and adds detail to coral holobiont functioning. 4. Plant Virus Differentially Alters the Plant's Defense Response to Its Closely Related Vectors Science.gov (United States) Shi, Xiaobin; Pan, Huipeng; Xie, Wen; Wu, Qingjun; Wang, Shaoli; Liu, Yang; Fang, Yong; Chen, Gong; Gao, Xiwu; Zhang, Youjun 2013-01-01 Background The whitefly, Bemisia tabaci (Hemiptera: Aleyrodidae), is one of the most widely distributed agricultural pests. In recent years, B. tabaci Q has invaded China, and Q has displaced B in many areas now. In a number of regions of the world, invasion by B and/or Q has been followed by outbreaks of tomato yellow leaf curl virus (TYLCV). Our previous study showed TYLCV directly and indirectly modified the feeding behavior of B. tabaci in favor of Q rather than B. Methodology/Principal Findings In this study, we quantified the salicylic acid (SA) titers and relative gene expression of SA in tomato leaves that were infested with viruliferous or non-viruliferous B and Q. We also measured the impacts of exogenous SA on the performance of B and Q, including the effects on ovary development. SA titer was always higher in leaves that were infested with viruliferous B than with viruliferous Q, whereas the SA titer did not differ between leaves infested with non-viruliferous B and Q. The relative gene expression of SA signaling was increased by feeding of viruliferous B but was not increased by feeding of viruliferous Q. The life history traits of B and Q were adversely affected on SA-treated plants. On SA-treated plants, both B and Q had lower fecundity, shorter longevity, longer developmental time and lower survival rate than on untreated plants. Compared with whiteflies feeding on control plants, those feeding on SA-treated plants had fewer oocytes and slower ovary development. On SA-treated plants, viruliferous B had fewer oocytes than viruliferous Q. Conclusions/Significance These results indicate that TYLCV tends to induce SA-regulated plant defense against B but SA-regulated plant defense against Q was reduced. In other words, Q may have a mutualistic relationship with TYLCV that results in the reduction of the plant's defense response. PMID:24391779 5. Characterisation data of simple sequence repeats of phages closely related to T7M Directory of Open Access Journals (Sweden) Tiao-Yin Lin 2016-09-01 Full Text Available Coliphages T7M and T3, Yersinia phage ϕYeO3-12, and Salmonella phage ϕSG-JL2 share high homology in genomic sequences. Simple sequence repeats (SSRs are found in their genomes and variations of SSRs among these phages are observed. Analyses on regions of sequences in T7M and T3 genomes that are likely derived from phage recombination, as well as the counterparts in ϕYeO3-12 and ϕSG-JL2, have been discussed by Lin in “Simple sequence repeat variations expedite phage divergence: mechanisms of indels and gene mutations” [1]. These regions are referred to as recombinant regions. The focus here is on SSRs in the whole genome and regions of sequences outside the recombinant regions, referred to as non-recombinant regions. This article provides SSR counts, relative abundance, relative density, and GC contents in the complete genome and non-recombinant regions of these phages. SSR period sizes and motifs in the non-recombinant regions of phage genomes are plotted. Genomic sequence changes between T7M and T3 due to insertions, deletions, and substitutions are also illustrated. SSRs and nearby sequences of T7M in the non-recombinant regions are compared to the sequences of ϕYeO3-12 and ϕSG-JL2 in the corresponding positions. The sequence variations of SSRs due to vertical evolution are classified into four categories and tabulated: (1 insertion/deletion of SSR units, (2 expansion/contraction of SSRs without alteration of genome length, (3 changes of repeat motifs, and (4 generation/loss of repeats. 6. Different mechanics of snap-trapping in the two closely related carnivorous plants Dionaea muscipula and Aldrovanda vesiculosa CERN Document Server Poppinga, Simon 2011-01-01 The carnivorous aquatic Waterwheel Plant (Aldrovanda vesiculosa L.) and the closely related terrestrial Venus Flytrap (Dionaea muscipula SOL. EX J. ELLIS) both feature elaborate snap-traps, which shut after reception of an external mechanical stimulus by prey animals. Traditionally, Aldrovanda is considered as a miniature, aquatic Dionaea, an assumption which was already established by Charles Darwin. However, videos of snapping traps from both species suggest completely different closure mechanisms. Indeed, the well-described snapping mechanism in Dionaea comprises abrupt curvature inversion of the two trap lobes, while the closing movement in Aldrovanda involves deformation of the trap midrib but not of the lobes, which do not change curvature. In this paper, we present the first detailed mechanical models for these plants, which are based on the theory of thin solid membranes and explain this difference by showing that the fast snapping of Aldrovanda is due to kinematic amplification of the bending deforma... 7. Subacute autonomic and sensory neuropathy closely related to cytomegalovirus infection preceded by frequent syncopal attacks. Science.gov (United States) Nakao, Koichi; Namekawa, Michito; Kondo, Soichi; Ono, Sayaka; Nakano, Imaharu 2016-08-31 is the first report of subacute autonomic and sensory neuropathy caused by CMV infection. 8. Domestication and defence: Foliar tannins and C/N ratios in cassava and a close wild relative Science.gov (United States) Mondolot, Laurence; Marlas, Amandine; Barbeau, Damien; Gargadennec, Annick; Pujol, Benoît; McKey, Doyle 2008-09-01 Plant domestication is accompanied by shifts in resource allocation, as a result of farmer selection for genotypes that give high yields in agricultural habitats. Relaxed natural selection for chemical and physical defences in these habitats could facilitate resource allocation to yield. We compared the concentrations of tannins, and C/N ratios, which are often correlated with investment in cell-wall compounds, in leaves of landraces of domesticated cassava ( Manihot esculenta) and a close wild relative in French Guiana. Foliar concentrations of tannins were about 1.9 times higher in the wild relative than in domesticated cassava. Histochemical analyses showed that tannins were present in nearly all palisade and spongy parenchyma cells of the wild taxon, but in only some cells of these tissues in M. esculenta. C/N ratios were also 1.9 times higher in leaves of the wild relative than in those of domesticated cassava. Tannins accounted for only a small proportion of total carbon, and the higher C/N ratio in wild than in domesticated cassava may reflect higher investment in carbon-containing compounds additional to tannins, such as cell-wall compounds. The divergence in these traits between cassava and this close wild relative mirrors a broad pattern observed in wild plant species across habitats varying in resource availability. One explanation for our results is that domestication in cassava may have favoured a shift from a resource conservation strategy to a resource acquisition strategy. 9. Transposons play an important role in the evolution and diversification of centromeres among closely related species Directory of Open Access Journals (Sweden) Scott eJackson 2015-04-01 Full Text Available Centromeres are important chromosomal regions necessary for eukaryotic cell segregation and replication. Due to high amounts of tandem repeats and transposons, centromeres have been difficult to sequence in most multicellular organisms, thus their sequence structure and evolution are poorly understood. In this study, we analyzed transposons in the centromere 8 (Cen8 from the African cultivated rice (O. glaberrima and two subspecies of the Asian cultivated rice (O. sativa, indica and japonica. We detected much higher transposon contents (>69% in centromere regions than in the whole genomes of O. sativa ssp japonica and O. glaberrima (~35%. We compared the three Cen8s and identified numerous recent insertions of transposons that were frequently organized into multiple-layer nested blocks, similar to nested transposons in maize. Except for the Hopi retrotransposon, all LTR retrotransposons were shared but exhibit different abundances amongst the three Cen8s. Even though a majority of the transposons were located in intergenic regions, some gene-related transposons were found and may be involved in gene diversification. Chromatin immunoprecipitated (ChIP data analysis revealed that 165 families from both Class I and Class II transposons were found in CENH3-associated chromatin sequences. These results indicate essential roles for transposons in centromeres and that the rapid divergence of the Cen8 sequences between the two cultivated rice species was primarily caused by recent transposon insertions. 10. Locomotor performance of closely related Tropidurus species: relationships with physiological parameters and ecological divergence. Science.gov (United States) Kohlsdorf, Tiana; James, Rob S; Carvalho, José E; Wilson, Robbie S; Dal Pai-Silva, Maeli; Navas, Carlos A 2004-03-01 Tropidurid lizards have colonized a variety of Brazilian open environments without remarkable morphological variation, despite ecological and structural differences among habitats used. This study focuses on two Tropidurus sister-species that, despite systematic proximity and similar morphology, exhibit great ecological divergence and a third ecologically generalist congeneric species providing an outgroup comparison. We quantified jumping capacity and sprint speed of each species on sand and rock to test whether ecological divergence was also accompanied by differences in locomotor performance. Relevant physiological traits possibly associated with locomotor performance - metabolic scopes and fiber type composition, power output and activity of the enzymes citrate synthase, pyruvate kinase and lactate dehydrogenase of the iliofibularis muscle - were also compared among the three Tropidurus species. We found that the two sister-species exhibited remarkable differences in jumping performance, while Tropidurus oreadicus, the more distantly related species, exhibited intermediate values. Tropidurus psamonastes, a species endemic to sand dunes, exhibited high absolute sprint speeds on sand, jumped rarely and possessed a high proportion of glycolytic fibers and low activity of citrate synthase. The sister-species Tropidurus itambere, endemic to rocky outcrops, performed a large number of jumps and achieved lower absolute sprint speed than T. psamonastes. This study provides evidence of rapid divergence of locomotor parameters between sister-species that use different substrates, which is only partially explained by variation in physiological parameters of the iliofibularis muscle. 11. Rediscovery of Trypanosoma (Pycnomonas) suis, a tsetse-transmitted trypanosome closely related to T. brucei. Science.gov (United States) Hutchinson, Rachel; Gibson, Wendy 2015-12-01 The African tsetse-transmitted trypanosomes are considered to be a well-known group of parasitic protozoa, but in 2008 a novel and distinctive trypanosome related to Trypanosoma brucei was discovered among tsetse isolates from Msubugwe in Tanzania. The host range, distribution and potential pathogenicity of this new trypanosome remain to be elucidated; such studies would be facilitated by a sensitive and specific identification method. Here, we identified two highly repetitive elements in the genome of the new trypanosome: a 177 bp repeat, which was located predominantly on the highly abundant minichromosomes, and a 138 bp repeat, which was widely dispersed in the genome. A PCR test based on each repeat was specific for the new trypanosome and sensitive to Trypanosoma (Pycnomonas) suis. We also present data on the molecular karyotype and spliced leader (SL, miniexon) repeat of the new trypanosome, both of which distinguish T. suis from other, better-known African tsetse-transmitted trypanosomes. The rediscovery of T. suis opens new lines of research into the evolution and biology of the African trypanosomes. 12. Open and closed lip schizencephaly in Seckel syndrome: a case report. Science.gov (United States) Thapa, Rajoo; Mallick, Debkrishna; Biswas, Biswajit; Ghosh, Apurba 2010-04-01 Seckel syndrome (Online Mendelian Inheritance in Man database Number 210600) is the classic prototype of primordial bird-headed dwarfism. In addition to the characteristic craniofacial dysmorphism and skeletal defects, abnormalities of the cardiovascular, hematopoietic, endocrine, and central nervous systems are described. The full phenotypic spectrum of this clinically and genetically heterogeneous syndrome is yet to be delineated. Presented herein is a boy 2 years and 5 months old, with Seckel syndrome, born to second-degree consanguineous Muslim parents. In addition to the classic phenotype of the disorder, this patient had both, an open and a closed lip schizencephaly detected on cranial computed tomography (CT) scan. To our knowledge, the association of schizencephaly and Seckel syndrome is not described previously in the English language literature. In addition, presented briefly is a review of the anatomical cerebral cortical malformations associated with this syndrome. 13. USSR Report, International Economic Relations, No. 61 Science.gov (United States) 2007-11-02 INTERNATIONAL ECONOMIC RELATIONS No. 61 CONTENTS USSR- CEMA TRADE CEMA Progress in 1982 Spotlighted (APN DAILY REVIEW, 8 Aug 83) 1 Plant...Director Views Relations With CEMA Counterparts (V. P. Kabaidze Interview; PRAVDA, 27 Jun 83) 3 Soviet, CEMA Cooperation With Cuba (V. Morozov; APN...DAILY REVIEW, 29 Jul 83) 8 CEMA Specialization, Integration Noted (N. Syomin; APN DAILY REVIEW, 12 May 83) 12 TRADE WITH IDC’S 14. Closely related intertidal and deep-sea Halomonhystera species have distinct fatty acid compositions Science.gov (United States) Van Campenhout, Jelle; Vanreusel, Ann 2017-01-01 The deep-sea free-living nematode Halomonhystera hermesi, dominant in the sulphidic sediments of the Håkon Mosby mud volcano (1280 m, Barent sea slope), is part of the mainly estuarine Halomonhystera disjuncta species complex consisting of five cryptic species (GD1-GD5). Cryptic species have a very similar morphology raising questions on their specific environmental differences. This study analyzed total fatty acid (FA) compositions of H. hermesi and GD1, one of H. hermesi's closest relatives. Additionally, we experimentally investigated the effect of a temperature reduction, salinity increase and sulphide concentrations on GD1's FA composition. Because nematodes are expected to have low amounts of storage FA, total FA compositions most likely reflect FA contents of cellular membranes. The deep-sea nematode H. hermesi had significantly lower saturation levels and increased highly unsaturated fatty acid (HUFAs) proportions due to the presence of docosahexanoic acid (DHA—22:6ω3) and higher eicosapentaenoic acid (EPA—20:5ω3) proportions. HUFAs were absent in H. hermesi's food source indicating the ability and need for this nematode to synthesize HUFAs in a deep-sea environment. Our experimental data revealed that only a decrease in temperature resulted in lower saturated fatty acids proportions, indicating that the FA content of H. hermesi is most likely a response to temperature but not to sulphide concentrations or salinity differences. In experimental nematodes, EPA proportions were low and DHA was absent indicating that other factors than temperature, salinity and sulphides mediate the presence of these HUFAs in H. hermesi. 15. Transcriptomic Analyses Elucidate Adaptive Differences of Closely Related Strains of Pseudomonas aeruginosa in Fuel Energy Technology Data Exchange (ETDEWEB) Gunasekera, Thusitha S.; Bowen, Loryn L.; Zhou, Carol E.; Howard-Byerly, Susan C.; Foley, William S.; Striebich, Richard C.; Dugan, Larry C.; Ruiz, Oscar N.; Stams, Alfons J. M. 2017-03-17 Pseudomonas aeruginosacan utilize hydrocarbons, but different strains have various degrees of adaptation despite their highly conserved genome.P. aeruginosaATCC 33988 is highly adapted to hydrocarbons, whileP. aeruginosastrain PAO1, a human pathogen, is less adapted and degrades jet fuel at a lower rate than does ATCC 33988. We investigated fuel-specific transcriptomic differences between these strains in order to ascertain the underlying mechanisms utilized by the adapted strain to proliferate in fuel. During growth in fuel, the genes related to alkane degradation, heat shock response, membrane proteins, efflux pumps, and several novel genes were upregulated in ATCC 33988. Overexpression ofalkgenes in PAO1 provided some improvement in growth, but it was not as robust as that of ATCC 33988, suggesting the role of other genes in adaptation. Expression of the function unknown gene PA5359 from ATCC 33988 in PAO1 increased the growth in fuel. Bioinformatic analysis revealed that PA5359 is a predicted lipoprotein with a conserved Yx(FWY)xxD motif, which is shared among bacterial adhesins. Overexpression of the putative resistance-nodulation-division (RND) efflux pump PA3521 to PA3523 increased the growth of the ATCC 33988 strain, suggesting a possible role in fuel tolerance. Interestingly, the PAO1 strain cannot utilizen-C8andn-C10. The expression of green fluorescent protein (GFP) under the control ofalkBpromoters confirmed thatalkgene promoter polymorphism affects the expression ofalkgenes. Promoter fusion assays further confirmed that the regulation ofalkgenes was different in the two strains. Protein sequence analysis 16. Transcriptomic Analyses Elucidate Adaptive Differences of Closely-Related Strains of P. aeruginosa in Fuel. Science.gov (United States) Gunasekera, Thusitha S; Bowen, Loryn L; Zhou, Carol E; Howard-Byerly, Susan C; Foley, William S; Striebich, Richard C; Dugan, Larry C; Ruiz, Oscar N 2017-03-17 Pseudomonas aeruginosa can utilize hydrocarbons, but different strains have varying degrees of adaptation despite their highly conserved genome. P. aeruginosa ATCC 33988 is highly adapted to hydrocarbons while strain PAO1, a human pathogen, is less-adapted and degrades jet fuel at a slower rate than does ATCC 33988. We investigated fuel specific transcriptomic differences between these strains in order to ascertain the underling mechanisms utilized by the adapted strain to proliferate in fuel. During growth in fuel, the genes related to alkane degradation, heat-shock response, membrane proteins, efflux pumps and several novel genes were upregulated in ATCC 33988. Overexpression of alk genes in PAO1 provided some improvement in growth, but not as robust as that of ATCC 33988, suggesting the role of other genes in adaptation. Expression of the function unknown gene PA5359 from ATCC 33988 in PAO1 increased the growth in fuel. Bioinformatic analysis revealed that PA5359 is a predicted lipoprotein with a conserved 'Yx(FWY)xxD' motif, which is shared among bacterial adhesins. Overexpression of the putative RND-efflux pump PA3521-PA3523 increased the growth of ATCC 33988 strain suggesting a possible role in fuel tolerance. Interestingly the PAO1 strain cannot utilize nC8 and nC10. Expression of GFP under the control of alkB promoters confirmed that alk gene promoter polymorphism affects the expression of alk genes. Promoter fusion assays further confirmed that regulation of alk genes was different in the two strains. Protein sequence analysis showed low amino acid differences for many of the upregulated genes, further supporting transcriptional control as the main mechanism for enhanced adaptation.IMPORTANCE These results support that specific signal transduction, gene regulation and coordination of multiple biological responses are required to improve survival, growth and metabolism of fuel in adapted strains. This study provides new insight into the mechanistic 17. Poecilia picta, a Close Relative to the Guppy, Exhibits Red Male Coloration Polymorphism: A System for Phylogenetic Comparisons. Science.gov (United States) Lindholm, Anna K; Sandkam, Ben; Pohl, Kristina; Breden, Felix 2015-01-01 Studies on the evolution of female preference and male color polymorphism frequently focus on single species since traits and preferences are thought to co-evolve. The guppy, Poecilia reticulata, has long been a premier model for such studies because female preferences and orange coloration are well known to covary, especially in upstream/downstream pairs of populations. However, focused single species studies lack the explanatory power of the comparative method, which requires detailed knowledge of multiple species with known evolutionary relationships. Here we describe a red color polymorphism in Poecilia picta, a close relative to guppies. We show that this polymorphism is restricted to males and is maintained in natural populations of mainland South America. Using tests of female preference we show female P. picta are not more attracted to red males, despite preferences for red/orange in closely related species, such as P. reticulata and P. parae. Male color patterns in these closely related species are different from P. picta in that they occur in discrete patches and are frequently Y chromosome-linked. P. reticulata have an almost infinite number of male patterns, while P. parae males occur in discrete morphs. We show the red male polymorphism in P. picta extends continuously throughout the body and is not a Y-linked trait despite the theoretical prediction that sexually-selected characters should often be linked to the heterogametic sex chromosome. The presence/absence of red male coloration of P. picta described here makes this an ideal system for phylogenetic comparisons that could reveal the evolutionary forces maintaining mate choice and color polymorphisms in this speciose group. 18. Combining morphology, DNA sequences, and morphometrics: revising closely related species in the orb-weaving spider genus Araniella (Araneae, Araneidae). Science.gov (United States) Spasojevic, Tamara; Kropf, Christian; Nentwig, Wolfgang; Lasut, Liana 2016-05-17 The integration of independent data sets could solve problems in both traditional and DNA-based taxonomy. The aim of this study is to investigate the power of CO1 sequences and of morphometrics to distinguish closely related species in the spider genus Araniella. We put special emphasis on the species pair A. cucurbitina (Clerck, 1757) and A. opisthographa (Kulczyński, 1905) since the females are morphologically difficult to distinguish and often misidentified. A total of 216 sequences of eight Araniella species from seven European countries, North America and Asia were included in the molecular analysis. The results from both maximum likelihood and Bayesian phylogenetic inference indicate successful separation of six out of eight Araniella species, including A. cucurbitina and A. opisthographa. For the same six species, we detect no overlap of intra- and interspecific genetic divergence, leading to successful species identification with a threshold approach. In addition, morphometric analysis of the epigyna of A. cucurbitina and A. opisthographa supports species separation by two best explanatory ratios: receptaculum length and distance between receptaculum and copulatory duct. Although a small overlap in the ratios exists, the species identification rate increases when combining morphometric and molecular data, which demonstrates the efficiency of integrative approaches for distinguishing closely related species. However, none of the molecular approaches was able to separate closely related A. alpica (L. Koch, 1869) and A. inconspicua (Simon, 1874) due to shared CO1 haplotypes. Considering the clear morphological separation of the males and different habitat preferences, incomplete lineage sorting or introgressive hybridization could have led to identical CO1 sequences. Therefore, DNA-barcoding must be thoroughly tested even within small homogenous genera of spiders. 19. Two closely related species of desert carpenter ant differ in individual-level allocation to fat storage. Science.gov (United States) Hahn, Daniel A 2006-01-01 Comparison of closely related species that differ in their life histories is a powerful method for studying the underlying physiological mechanisms contributing to life-history variation. I investigated whether two closely related members of the Camponotus festinatus species complex of desert carpenter ants, C. nr. festinatus Desert Light and C. nr. festinatus Desert Dark, differed in their life-history tactics with respect to fat storage. Newly mated queens were collected in the field, and colonies were reared under common conditions in the laboratory for 2 yr before sampling. I show that the two species differ in fat storage at the individual level. While the basic scaling relationship between lean mass and fat content did not differ between the two species, Dark workers and soldiers stored significantly more fat per unit lean mass than Light workers or soldiers. There were no significant demographic differences in the proportions of workers or soldiers involved in fat storage between the two species, although there was a trend toward Light colonies having a greater proportion of soldiers storing large amounts of fat. There was also no significant difference in the total amount of fat stored by the two species at the colony level. The detection of strong individual-level effects but no colony-level effects was likely due to the low statistical power of colony-level analyses. Showing that these two closely related species differ in fat storage at the individual level in a common environment demonstrates their utility as a model for understanding the physiological and behavioral mechanisms regulating life-history variation in fat storage in ants. 20. Final Scientific/Technical Report. A closed path methane and water vapor gas analyzer Energy Technology Data Exchange (ETDEWEB) Xu, Liukang [LI-COR Inc., Lincoln, NE (United States); McDermitt, Dayle [LI-COR Inc., Lincoln, NE (United States); Anderson, Tyler [LI-COR Inc., Lincoln, NE (United States); Riensche, Brad [LI-COR Inc., Lincoln, NE (United States); Komissarov, Anatoly [LI-COR Inc., Lincoln, NE (United States); Howe, Julie [LI-COR Inc., Lincoln, NE (United States) 2012-02-01 Robust, economical, low-power and reliable closed-path methane (CH4), carbon dioxide (CO2), and water vapor (H2O) analyzers suitable for long-term measurements are not readily available commercially. Such analyzers are essential for quantifying the amount of CH4 and CO2 released from various ecosystems (wetlands, rice paddies, forests, etc.) and other surface contexts (e.g. landfills, animal husbandry lots, etc.), and for understanding the dynamics of the atmospheric CH4 and CO2 budget and their impact on climate change and global warming. The purpose of this project is to develop a closed-path methane, carbon dioxide gas and water vapor analyzer capable of long-term measurements in remote areas for global climate change and environmental research. The analyzer will be capable of being deployed over a wide range of ecosystems to understand methane and carbon dioxide exchange between the atmosphere and the surface. Measurements of methane and carbon dioxide exchange need to be made all year-round with limited maintenance requirements. During this Phase II effort, we successfully completed the design of the electronics, optical bench, trace gas detection method and mechanical infrastructure. We are using the technologies of two vertical cavity surface emitting lasers, a multiple-pass Herriott optical cell, wavelength modulation spectroscopy and direct absorption to measure methane, carbon dioxide, and water vapor. We also have designed the instrument application software, Field Programmable Gate Array (FPGA), along with partial completion of the embedded software. The optical bench has been tested in a lab setting with very good results. Major sources of optical noise have been identified and through design, the optical noise floor is approaching -60dB. Both laser modules can be temperature controlled to help maximize the stability of the analyzer. Additionally, a piezo electric transducer has been 1. The ectomycorrhizal morphotype Pinirhiza sclerotia is formed by Acephala macrosclerotiorum sp. nov., a close relative of Phialocephala fortinii. Science.gov (United States) Münzenberger, Babette; Bubner, Ben; Wöllecke, Jens; Sieber, Thomas N; Bauer, Robert; Fladung, Matthias; Hüttl, Reinhard F 2009-09-01 Relatively few ectomycorrhizal fungal species are known to form sclerotia. Usually, sclerotia are initiated at the extraradical mycelium. In this study, we present anatomical and ultrastructural evidence for the formation of sclerotia directly in the hyphal mantle of the mycorrhizal morphotype Pinirhiza sclerotia. A dark-pigmented fungal strain was isolated from Pinirhiza sclerotia and identified by molecular tools as Acephala macrosclerotiorum sp. nov., a close relative of Phialocephala fortinii s.l. As dark septate fungi are known to be mostly endophytic, resyntheses with Pinus sylvestris and A. macrosclerotiorum as well as Populus tremula x Populus tremuloides and A. macrosclerotiorum or P. fortinii s.l. were performed under axenic conditions. No mycorrhizas were found when hybrid aspen was inoculated with A. macrosclerotiorum or P. fortinii. However, A. macrosclerotiorum formed true ectomycorrhizas in vitro with P. sylvestris. Anatomical and ultrastructural features of this ectomycorrhiza are presented. The natural and synthesized ectomycorrhizal morphotypes were identical and characterized by a thin hyphal mantle that bore sclerotia in a later ontogenetic stage. The Hartig net was well-developed and grew up to the endodermis. To our knowledge, this is the first evidence at the anatomical and ultrastructural level that a close relative of P. fortinii s.l. forms true ectomycorrhizas with a coniferous host. 2. Conservative whole-organ scaling contrasts with highly labile suborgan scaling differences among compound eyes of closely related Formica ants. Science.gov (United States) Perl, Craig D; Rossoni, Sergio; Niven, Jeremy E 2017-03-01 Static allometries determine how organ size scales in relation to body mass. The extent to which these allometric relationships are free to evolve, and how they differ among closely related species, has been debated extensively and remains unclear; changes in intercept appear common, but changes in slope are far rarer. Here, we compare the scaling relationships that govern the structure of compound eyes of four closely related ant species from the genus Formica. Comparison among these species revealed changes in intercept but not slope in the allometric scaling relationships governing eye area, facet number, and mean facet diameter. Moreover, the scaling between facet diameter and number was conserved across all four species. In contrast, facet diameters from distinct regions of the compound eye differed in both intercept and slope within a single species and when comparing homologous regions among species. Thus, even when species are conservative in the scaling of whole organs, they can differ substantially in regional scaling within organs. This, at least partly, explains how species can produce organs that adhere to genus wide scaling relationships while still being able to invest differentially in particular regions of organs to produce specific features that match their ecology. 3. USSR Report, International Economic Relations, No. 57. Science.gov (United States) 2007-11-02 ECONOMIC RELATIONS No. 57 CONTENTS USSR WORLD TRADE Soviet Aid in Building Projects in CEMA , Less Developed Countries (I. Kapranov; EKONOMICHESKAYA...GAZETA, No 18, Apr 83) . 1 USSR- CEMA TRADE Coordinating CEMA Statistical Data (L. Antsiferovaj VESTNIK STATISTIKI, Jan 83) 9 USSR-EAST EUROPE...Meets (S. Nikolayevj EKONOMICHESKAYA GAZETA, No 11, Mar 83) UU b - USSR WORLD TRADE SOVIET AID IN BUILDING PROJECTS IN CEMA , LESS DEVELOPED 4. Complete cardiac rupture associated with closed chest cardiac massage: case report and review of the literature. Science.gov (United States) Tattoli, Lucia; Maselli, Eloisa; Romanelli, Maria Carolina; Di Vella, Giancarlo; Solarino, Biagio 2014-03-01 Chest skeletal injuries are the most frequent complications of external chest massage (ECM) during cardiopulmonary resuscitation, but heart and great vessels lacerations that are indeed very rare. We report the case of a 35-year-old workman who collapsed and underwent ECM by his co-workers for almost 30 min. At autopsy, no external injuries, fractures or bruises of the ribs or sternum, were observed. A hemopericardium with a rupture of the heart was found, with no signs of pre-existent cardiac disease. Bruises of thoracic aortic wall, lung petechiae, a contusion of the liver, and bruises of lumbar muscles were found. The cause of death was due to sudden cardiac death with an extensive cardiac rupture. This is an unusual report of massive heart damage without any skeletal or muscle chest injuries, secondary to cardiopulmonary resuscitation. This kind of cardiac lesions may be considered when thoracic–abdominal trauma, or medical history, is unclear. 5. Vacuum-assisted breast biopsy in close proximity to the skin: a case report Directory of Open Access Journals (Sweden) Zagouri Flora 2008-05-01 Full Text Available Abstract Introduction Vacuum-assisted breast biopsy is a minimally invasive technique used increasingly for the assessment of mammographically detected, non-palpable breast lesions. The effectiveness of vacuum-assisted breast biopsy has been demonstrated on lesions both with and without microcalcifications. Given that the position of the lesion represents a major factor in stereotactic vacuum-assisted breast biopsy, targeting lesions in close proximity to the skin (superficial lesions has been described as a problematic issue. Case presentation A 53-year-old woman presented with a newly developed, non-palpable lesion in her left breast. The lesion consisted of widely spread microcalcifications located approximately 5 mm from the skin. The lesion was isoechoic on ultrasound examination. Vacuum-assisted breast biopsy was scheduled (on the Fischer's table, using 11-gauge probes, under local anaesthesia. The vacuum-assisted breast biopsy probe was inserted antidiametrically into the breast, the probe reached the lesion and effort was made to excise the microcalcifications. As only a small proportion of the microcalcifications were excised an accurate diagnosis could not be expected. However, with the probe having entered the breast antidiametrically, the probe tip underlying the skin could be palpated. Following the palpation of the tip, the exact point was marked by a pen, the probe was removed and the patient was transferred to the surgery room to have the remaining lesion removed by a spindle-form excision under local anaesthesia. The mammogram of the removed specimen confirmed the total excision of the suspicious microcalcifications. Conclusion Isoechoic superficial lesions can be localized with a hook-wire and open breast biopsy under general or local anaesthesia can be performed. However, vacuum-assisted breast biopsy might offer an alternative solution and serve as an alternative approach to localize the lesion. The clinical significance of 6. Strong differences in chemical recognition cues between two closely related species of ants from the genus Lasius (Hymenoptera: Formicidae). Science.gov (United States) Morrison, W R; Witte, V 2011-11-01 Cuticular hydrocarbons (CHCs) are increasingly recognized as important to insects and are used for constructing taxonomies. However, multiple parameters affect the expression of CHCs besides a genetic component. We propose that selection may act differently on the expression of CHCs, depending on the evolutionary context. To explore the influence of selection, the CHCs of two closely related ant species, Lasius niger and Lasius platythorax, were studied in a multidisciplinary approach. We characterized (i) CHCs and (ii) niches (through baiting, activity observations and foraging analysis). The species were distinct in both measures, although to a varying degree. Although they showed moderate niche partitioning along diet and environmental preferences, chemical differences were unexpectedly pronounced. This may be explained by divergent selection on mate recognition cues or by other influences on CHCs. Such striking chemical differences among closely related species may not be the rule and suggest that taxonomies based on CHCs should be interpreted cautiously; though, they remain useful tools for differentiating among cryptic species. © 2011 The Authors. Journal of Evolutionary Biology © 2011 European Society For Evolutionary Biology. 7. Closely-related taxa influence woody species discrimination via DNA barcoding: evidence from global forest dynamics plots. Science.gov (United States) Pei, Nancai; Erickson, David L; Chen, Bufeng; Ge, Xuejun; Mi, Xiangcheng; Swenson, Nathan G; Zhang, Jin-Long; Jones, Frank A; Huang, Chun-Lin; Ye, Wanhui; Hao, Zhanqing; Hsieh, Chang-Fu; Lum, Shawn; Bourg, Norman A; Parker, John D; Zimmerman, Jess K; McShea, William J; Lopez, Ida C; Sun, I-Fang; Davies, Stuart J; Ma, Keping; Kress, W John 2015-10-12 To determine how well DNA barcodes from the chloroplast region perform in forest dynamics plots (FDPs) from global CTFS-ForestGEO network, we analyzed DNA barcoding sequences of 1277 plant species from a wide phylogenetic range (3 FDPs in tropics, 5 in subtropics and 5 in temperate zone) and compared the rates of species discrimination (RSD). We quantified RSD by two DNA barcode combinations (rbcL + matK and rbcL + matK + trnH-psbA) using a monophyly-based method (GARLI). We defined two indexes of closely-related taxa (Gm/Gt and S/G ratios) and correlated these ratios with RSD. The combination of rbcL + matK averagely discriminated 88.65%, 83.84% and 72.51% at the local, regional and global scales, respectively. An additional locus trnH-psbA increased RSD by 2.87%, 1.49% and 3.58% correspondingly. RSD varied along a latitudinal gradient and were negatively correlated with ratios of closely-related taxa. Successes of species discrimination generally depend on scales in global FDPs. We suggested that the combination of rbcL + matK + trnH-psbA is currently applicable for DNA barcoding-based phylogenetic studies on forest communities. 8. Coagulation and fibrinolysis in capybara (Hydrochaeris hydrochaeris), a close relative of the guinea-pig (Cavia porcellus). Science.gov (United States) Leitão, D P; Polizello, A C; Rothschild, Z 2000-01-01 Fibrinolytic and coagulation properties of capybara (Hydrochaeris hydrochaeris, LINNAEUS, 1766) plasma were analysed and the results compared to the guinea-pig (Cavia porcellus), a close relative. Capybara fibrinogen was isolated and fibrinolysis of its plasma was carried out in a homologous system and with bovine fibrin. Undiluted plasma did not have fibrinolytic activity on fibrin plates; euglobulins gave a dose-related response. Zymography of capybara and guinea-pig plasma gave the same patterns of activity as human or bovine plasma. Human urokinase (UK) and tissue plasminogen activator (t-PA) produced lysis in capybara fibrin plates. Streptokinase (SK) (500 IU/ml) did not activate capybara or guinea-pig plasma. In this system, human plasma was extensively activated. Coagulation tests for both species of rodent were prolonged. The capybara showed values for prothrombin time (PT) shorter than activated thromboplastin time (APTT). The guinea-pig, as already shown, had longer PT values. Factors X and VII were very low for capybara and guinea-pig when tested using reference curves and diagnostic kits for human plasma. It is suggested that the capybara could be a valuable laboratory animal considering its size and closeness to the guinea-pig, and this could allow for the provision of materials from one single animal when convenient or necessary. 9. Are the metabolomic responses to folivory of closely related plant species linked to macroevolutionary and plant-folivore coevolutionary processes? Energy Technology Data Exchange (ETDEWEB) Rivas-Ubach, Albert [Environmental Molecular Sciences Laboratory, Pacific Northwest National Laboratory, Richland Washington 99354 USA; CREAF, Cerdanyola del Vallès 08913 Catalonia Spain; Hódar, José A. [Grupo de Ecología Terrestre, Departamento de Biología Animal y Ecología, Facultad de Ciencias, Universidad de Granada, 18071 Granada Spain; Sardans, Jordi [CREAF, Cerdanyola del Vallès 08913 Catalonia Spain; CSIC, Global Ecology Unit CREAF-CEAB-CSIC-UAB, Cerdanyola del Vallès 08913 Catalonia Spain; Kyle, Jennifer E. [Biological Sciences Division, Pacific Northwest National Laboratory, Richland Washington 99354 USA; Kim, Young-Mo [Biological Sciences Division, Pacific Northwest National Laboratory, Richland Washington 99354 USA; Oravec, Michal [Global Change Research Centre, Academy of Sciences of the Czech Republic, Bĕlidla 4a CZ-603 00 Brno Czech Republic; Urban, Otmar [Global Change Research Centre, Academy of Sciences of the Czech Republic, Bĕlidla 4a CZ-603 00 Brno Czech Republic; Guenther, Alex [Department of Earth System Science, University of California, Irvine California 92697 USA; Peñuelas, Josep [CREAF, Cerdanyola del Vallès 08913 Catalonia Spain; CSIC, Global Ecology Unit CREAF-CEAB-CSIC-UAB, Cerdanyola del Vallès 08913 Catalonia Spain 2016-06-02 The debate whether the coevolution of plants and insects or macroevolutionary processes (phylogeny) is the main driver determining the arsenal of molecular defensive compounds of plants remains unresolved. Attacks by herbivorous insects affect not only the composition of defensive compounds in plants but the entire metabolome (the set of molecular metabolites), including defensive compounds. Metabolomes are the final products of genotypes and are directly affected by macroevolutionary processes, so closely related species should have similar metabolomic compositions and may respond in similar ways to attacks by folivores. We analyzed the elemental compositions and metabolomes of needles from Pinus pinaster, P. nigra and P. sylvestris to determine if these closely related Pinus species with different coevolutionary histories with the caterpillars of the processionary moth respond similarly to attacks by this lepidopteran. All pines had different metabolomes and metabolic responses to herbivorous attack. The metabolomic variation among the pine species and the responses to folivory reflected their macroevolutionary relationships, with P. pinaster having the most divergent metabolome. The concentrations of phenolic metabolites were generally not higher in the attacked trees, which had lower concentrations of terpenes, suggesting that herbivores avoid individuals with high concentrations of terpenes. Our results suggest that macroevolutionary history plays important roles in the metabolomic responses of these pine species to folivory, but plant-insect coevolution probably constrains those responses. Combinations of different evolutionary factors and trade-offs are likely responsible for the different responses of each species to folivory, which is not necessarily exclusively linked to plant-insect coevolution. 10. DNA barcoding in closely related species: A case study of Primula L.sect.Proliferae Pax (Primulaceae) in China Institute of Scientific and Technical Information of China (English) Hai-Fei YAN; Gang HAO; Chi-Ming HU; Xue-Jun GE 2011-01-01 DNA barcoding is a method of identifying species by analyzing one or a few short standardized DNA sequences. There are particular challenges in barcoding plants, especially for distinguishing closely related species. Hence, there is an urgent need to evaluate the performance of candidate loci for distinguishing between species, especially closely related species, to complement the rbcL + matK combination suggested as the core barcode for land plants. We sampled 48 individuals representing 12 species in Primula sect. Proliferae Pax in China to evaluate the performance of eight leading candidate barcode loci (matK, rbcL, rpoB, rpoCl, trnH-psbA, psbK-psbI, atpFatpH, and internal transcribed spacer (ITS)). The core combination rbcL + matK gave only 50% species resolution in sect. Proliferae. In terms of intraspecies and interspecies divergence, degree of monophyly, and sequence similarity, ITS, trnH-psbA, and psbK-psbI showed good performance as single-locus barcodes. Internal transcribed spacer displayed the highest genetic divergence and best discriminatory power, both alone and in combination with rbcL +matK (83.3% species resolution). We recommend evaluating the use of ITS for barcoding in other species. Low or single copy nuclear regions would provide more sophisticated barcoding tools in the long term, even though further research is required to find suitable loci. 11. Bacillus Strains Most Closely Related to Bacillus nealsonii Are Not Effectively Circumscribed within the Taxonomic Species Definition Directory of Open Access Journals (Sweden) K. Kealy Peak 2011-01-01 Full Text Available Bacillus strains with >99.7% 16S rRNA gene sequence similarity were characterized with DNA:DNA hybridization, cellular fatty acid (CFA analysis, and testing of 100 phenotypic traits. When paired with the most closely related type strain, percent DNA:DNA similarities (% S for six Bacillus strains were all far below the recommended 70% threshold value for species circumscription with Bacillus nealsonii. An apparent genomic group of four Bacillus strain pairings with 94%–70% S was contradicted by the failure of the strains to cluster in CFA- and phenotype-based dendrograms as well as by their differentiation with 9–13 species level discriminators such as nitrate reduction, temperature range, and acid production from carbohydrates. The novel Bacillus strains were monophyletic and very closely related based on 16S rRNA gene sequence. Coherent genomic groups were not however supported by similarly organized phenotypic clusters. Therefore, the strains were not effectively circumscribed within the taxonomic species definition. 12. Evolution of hydraulic traits in closely related species pairs from Mediterranean and nonMediterranean environments of North America. Science.gov (United States) Bhaskar, Radika; Valiente-Banuet, Alfonso; Ackerly, David D 2007-01-01 Chaparral shrubs in California experience cool, wet winters and hot, dry summers characteristic of mediterranean-type climates; by contrast, morphologically similar close relatives in central Mexico experience summer rainfall. A comparison of closely related species pairs was conducted to examine whether evolutionary divergences in plant hydraulic conductivity were associated with contrasting seasonality of precipitation. Six species pairs in Santa Barbara, California and Tehuacan, Mexico were chosen to test for repeated directional divergences across the habitat contrast. Additionally, evolutionary correlations were examined using phylogenetically independent contrasts (PICs) among a suite of hydraulic traits, including stem- and leaf-specific conductivity, resistance to embolism, wood density, inverse Huber value, and minimum seasonal water potential. Leaf-specific conductivity was generally higher in California, but for most hydraulic traits the species pairs exhibited varied evolutionary trajectories across the climate contrast. A significant correlation was found between divergences in xylem resistance to embolism and minimum seasonal water potential, but no evolutionary trade-off was found between resistance and stem conductivity. Higher leaf-specific conductivity may be adaptive in California, where soil and atmospheric droughts coincide during summer months. This response is consistent with a hydraulic strategy of high leaf water supply under high evaporative demand to prevent excessive drops in water potential. 13. Buried waste integrated demonstration fiscal year 1992 close-out report Energy Technology Data Exchange (ETDEWEB) Cannon, P.G.; Kostelnik, K.M.; Owens, K.J. 1993-02-01 The mission of the Buried Waste Integrated Demonstration Program (BWID) is to support the development and demonstration of a suite of technologies that when integrated with commercially-available baseline technologies form a comprehensive remediation system for the effective and efficient remediation of buried waste disposed of throughout the US Department of Energy complex. To accomplish this mission of identifying technological solutions for remediation deficiencies, the Office of Technology Development initiated the BWID at the Idaho National Engineering Laboratory in fiscal year (FY)-91. This report summarizes the activities of the BWID Program during FY-92. 14. Posttraumatic Stress Disorder After Bereavement: Early Psychological Sequelae of Losing a Close Relative Due to Terminal Cancer DEFF Research Database (Denmark) Kristensen, T. E.; Elklit, A.; Karstoft, K. I. 2012-01-01 Very few studies have investigated posttraumatic stress disorder (PTSD) as a consequence of bereavement from terminal illness. Therefore, knowledge on the traumatizing effects of bereavement and risk factors for traumatization from bereavement is rather sparse. This study investigated prevalence...... and predictors of PTSD in a group of people who had recently lost a close relative due to incurable cancer. The participants were 132 persons who were assessed with the Harvard Trauma Questionnaire, the Trauma Symptom Checklist, and the Crisis Support Scale. One month after the loss, 29.5% of the subjects had...... clinical PTSD and an additional 26.2% reached a subclinical PTSD level. Negative affectivity, social support, and locus of control in relation to the loss predicted 57% of the variance in PTSD severity. A focus on these risk factors in early assessment after bereavement will help identify subjects at risk... 15. The Cost of Mating: Influences of Life History Traits and Mating Strategies on Lifespan in Two Closely Related Yponomeuta Species Directory of Open Access Journals (Sweden) A. C. Bakker 2011-01-01 Full Text Available Theory predicts that in monandrous butterfly species males should not invest in a long lifespan because receptive females quickly disappear from the mating population. In polyandrous species, however, it pays for males to invest in longevity, which increases the number of mating opportunities and thus reproductive fitness. We tested an extension of this idea and compared male and female lifespan of two closely related Yponomeuta species with different degree of polyandry. Our results confirmed the theoretical prediction that male lifespan is fine-tuned to female receptive lifespan; once-mated males and females of both polyandrous species had an equal lifespan. However, the degree of polyandry was not reflected in male relative to female lifespan. The observed similar female and male lifespan could largely be attributed to a dramatic reduction of female lifespan after mating. 16. ”How do the patients and their close relatives experience The Coordinated Investigation Model of Dementia in the North Denmark Region?” DEFF Research Database (Denmark) Hulgaard, Hanne; Ottesen, Aase Marie How do the patients and their close relatives experience The Coordinated Investigation Model of Dementia in the North Denmark Region? The aim of the project was to investigate how the patients and their close relatives experienced the investigation and the subsequent social medicine intervention... 17. Buried waste integrated demonstration Fiscal Year 1993 close-out report Energy Technology Data Exchange (ETDEWEB) Owens, K.J.; Hyde, R.A. 1994-04-01 The Buried Waste Integrated Demonstration (BWID) supports the applied research, development, demonstration, and evaluation of a multitude of advanced technologies. These technologies are being integrated to form a comprehensive remediation system for the effective and efficient remediation of buried waste. These efforts are identified and coordinated in support of the U.S. Department of Energy Environmental Restoration and Waste Management needs and objectives. BWID works with universities and private industry to develop these technologies, which are being transferred to the private sector for use nationally and internationally. A public participation policy has been established to provide stakeholders with timely and accurate information and meaningful opportunities for involvement in the technology development and demonstration process. To accomplish this mission of identifying technological solutions for remediation deficiencies, the Office of Technology Development initiated BWID at the Idaho National Engineering Laboratory. This report summarizes the activities of the BWID program during FY-93. 18. Competing structures in nuclei near closed shells. Final report, September 1, 1993--November 30, 1996 Energy Technology Data Exchange (ETDEWEB) Robinson, S.J. 1999-02-01 This report summarizes the progress made during this period. A series of experiments on levels in {sup 144}Nd have led to the identification of quadrupole-octupole coupled states in the nucleus. These experiments included the measurement of excited level lifetimes using the GRID technique, the measurement of transition conversion coefficients and the measurement of weak transition intensities. A fast electronic timing system has been set-up at Tennessee Tech. This system can be used to measure nuclear excited state lifetimes in the range from 5 ps upward. A new variation of the centroid shift method has been developed which eliminates the need to determine a prompt position. This centroid difference method employs both forward and reverse gating of gamma cascades to generate two timing spectra. 19. Final report for LDRD project {open_quotes}A new approach to protein function and structure prediction{close_quotes} Energy Technology Data Exchange (ETDEWEB) Phillips, C.A. 1997-03-01 This report describes the research performed under the laboratory-Directed Research and Development (LDRD) grant {open_quotes}A new approach to protein function and structure prediction{close_quotes}, funded FY94-6. We describe the goals of the research, motivate and list our improvements to the state of the art in multiple sequence alignment and phylogeny (evolutionary tree) construction, but leave technical details to the six publications resulting from this work. At least three algorithms for phylogeny construction or tree consensus have been implemented and used by researchers outside of Sandia. 20. Final report for LDRD project {open_quotes}A new approach to protein function and structure prediction{close_quotes} Energy Technology Data Exchange (ETDEWEB) Phillips, C.A. 1997-03-01 This report describes the research performed under the laboratory-Directed Research and Development (LDRD) grant {open_quotes}A new approach to protein function and structure prediction{close_quotes}, funded FY94-6. We describe the goals of the research, motivate and list our improvements to the state of the art in multiple sequence alignment and phylogeny (evolutionary tree) construction, but leave technical details to the six publications resulting from this work. At least three algorithms for phylogeny construction or tree consensus have been implemented and used by researchers outside of Sandia. 1. Technical Area V (TA-V) transformation project close-out report. Energy Technology Data Exchange (ETDEWEB) 2010-07-01 Sandia National Laboratories (SNL) Technical Area V (TA-V) has provided unique nuclear experimental environments for decades. The technologies tested in TA-V facilities have furthered the United States Nuclear Weapons program and has contributed to the national energy and homeland security mission. The importance of TA-V working efficiently to produce an attractive and effective platform for experiments should not be underestimated. Throughout its brief history, TA-V has evolved to address multiple and diverse sets of requirements. These requirements evolved over many years; however, the requirements had not been managed nor communicated comprehensively or effectively. A series of programmatic findings over several years of external audits was evidence of this downfall. Today, these same requirements flow down through a new TA-V management system that produces consistently applied and reproducible approaches to work practices. In 2008, the TA-V department managers assessed the state of TA-V services and work activities to understand how to improve customer interfaces, stakeholders perceptions, and workforce efficiencies. The TA-V management team initiated the TA-V Transformation Project after they deemed the pre-June 2008 operational model to be ineffective in managing work and in providing integrated, continuous improvement to TA-V processes. This report summarizes the TA-V Transformation Project goals, activities, and accomplishments. 2. Air Force Research Laboratory Spacecraft Cryocooler Endurance Evaluation Facility Closing Report Science.gov (United States) Armstrong, J.; Martin, K. W.; Fraser, T. 2015-12-01 The Air Force Research Laboratory (AFRL) Spacecraft Component Thermal Research Group has been devoted to evaluating lifetime performance of space cryocooler technology for over twenty years. Long-life data is essential for confirming design lifetimes for space cryocoolers. Continuous operation in a simulated space environment is the only accepted method to test for degradation. AFRL has provided raw data and detailed evaluations to cryocooler developers for advancing the technology, correcting discovered deficiencies, and improving cryocooler designs. At AFRL, units of varying design and refrigeration cycles were instrumented in state-of-the-art experiment stands to provide spacelike conditions and were equipped with software data acquisition to track critical cryocooler operating parameters. This data allowed an assessment of the technology's ability to meet the desired lifetime and documented any long-term changes in performance. This paper will outline a final report of the various flight cryocoolers tested in our laboratory. The data summarized includes the seven cryocoolers tested during 2014-2015. These seven coolers have a combined total of 433,326 hours (49.5 years) of operation. 3. Organellar Genomes from a ∼5,000-Year-Old Archaeological Maize Sample Are Closely Related to NB Genotype Science.gov (United States) Pérez-Zamorano, Bernardo; Vallebueno-Estrada, Miguel; Martínez González, Javier; García Cook, Angel; Montiel, Rafael; Vielle-Calzada, Jean-Philippe 2017-01-01 The story of how preColumbian civilizations developed goes hand-in-hand with the process of plant domestication by Mesoamerican inhabitants. Here, we present the almost complete sequence of a mitochondrial genome and a partial chloroplast genome from an archaeological maize sample collected at the Valley of Tehuacán, México. Accelerator mass spectrometry dated the maize sample to be 5,040–5,300 years before present (95% probability). Phylogenetic analysis of the mitochondrial genome shows that the archaeological sample branches basal to the other Zea mays genomes, as expected. However, this analysis also indicates that fertile genotype NB is closely related to the archaeological maize sample and evolved before cytoplasmic male sterility genotypes (CMS-S, CMS-T, and CMS-C), thus contradicting previous phylogenetic analysis of mitochondrial genomes from maize. We show that maximum-likelihood infers a tree where CMS genotypes branch at the base of the tree when including sites that have a relative fast rate of evolution thus suggesting long-branch attraction. We also show that Bayesian analysis infer a topology where NB and the archaeological maize sample are at the base of the tree even when including faster sites. We therefore suggest that previous trees suffered from long-branch attraction. We also show that the phylogenetic analysis of the ancient chloroplast is congruent with genotype NB to be more closely related to the archaeological maize sample. As shown here, the inclusion of ancient genomes on phylogenetic trees greatly improves our understanding of the domestication process of maize, one of the most important crops worldwide. PMID:28338960 4. Vibrio vulnificus phage PV94 is closely related to temperate phages of V. cholerae and other Vibrio species. Science.gov (United States) Pryshliak, Mark; Hammerl, Jens A; Reetz, Jochen; Strauch, Eckhard; Hertwig, Stefan 2014-01-01 Vibrio vulnificus is an important pathogen which can cause serious infections in humans. Yet, there is limited knowledge on its virulence factors and the question whether temperate phages might be involved in pathogenicity, as is the case with V. cholerae. Thus far, only two phages (SSP002 and VvAW1) infecting V. vulnificus have been genetically characterized. These phages were isolated from the environment and are not related to Vibrio cholerae phages. The lack of information on temperate V. vulnificus phages prompted us to isolate those phages from lysogenic strains and to compare them with phages of other Vibrio species. In this study the temperate phage PV94 was isolated from a V. vulnificus biotype 1 strain by mitomycin C induction. PV94 is a myovirus whose genome is a linear double-stranded DNA of 33,828 bp with 5'-protruding ends. Sequence analysis of PV94 revealed a modular organization of the genome. The left half of the genome comprising the immunity region and genes for the integrase, terminase and replication proteins shows similarites to V. cholerae kappa phages whereas the right half containing genes for structural proteins is closely related to a prophage residing in V. furnissii NCTC 11218. We present the first genomic sequence of a temperate phage isolated from a human V. vulnificus isolate. The sequence analysis of the PV94 genome demonstrates the wide distribution of closely related prophages in various Vibrio species. Moreover, the mosaicism of the PV94 genome indicates a high degree of horizontal genetic exchange within the genus Vibrio, by which V. vulnificus might acquire virulence-associated genes from other species. 5. Vibrio vulnificus phage PV94 is closely related to temperate phages of V. cholerae and other Vibrio species. Directory of Open Access Journals (Sweden) Mark Pryshliak Full Text Available BACKGROUND: Vibrio vulnificus is an important pathogen which can cause serious infections in humans. Yet, there is limited knowledge on its virulence factors and the question whether temperate phages might be involved in pathogenicity, as is the case with V. cholerae. Thus far, only two phages (SSP002 and VvAW1 infecting V. vulnificus have been genetically characterized. These phages were isolated from the environment and are not related to Vibrio cholerae phages. The lack of information on temperate V. vulnificus phages prompted us to isolate those phages from lysogenic strains and to compare them with phages of other Vibrio species. RESULTS: In this study the temperate phage PV94 was isolated from a V. vulnificus biotype 1 strain by mitomycin C induction. PV94 is a myovirus whose genome is a linear double-stranded DNA of 33,828 bp with 5'-protruding ends. Sequence analysis of PV94 revealed a modular organization of the genome. The left half of the genome comprising the immunity region and genes for the integrase, terminase and replication proteins shows similarites to V. cholerae kappa phages whereas the right half containing genes for structural proteins is closely related to a prophage residing in V. furnissii NCTC 11218. CONCLUSION: We present the first genomic sequence of a temperate phage isolated from a human V. vulnificus isolate. The sequence analysis of the PV94 genome demonstrates the wide distribution of closely related prophages in various Vibrio species. Moreover, the mosaicism of the PV94 genome indicates a high degree of horizontal genetic exchange within the genus Vibrio, by which V. vulnificus might acquire virulence-associated genes from other species. 6. Specificity of herbivore-induced hormonal signaling and defensive traits in five closely related milkweeds (Asclepias spp.). Science.gov (United States) Agrawal, Anurag A; Hastings, Amy P; Patrick, Eamonn T; Knight, Anna C 2014-07-01 Despite the recognition that phytohormonal signaling mediates induced responses to herbivory, we still have little understanding of how such signaling varies among closely related species and may generate herbivore-specific induced responses. We studied closely related milkweeds (Asclepias) to link: 1) plant damage by two specialist chewing herbivores (milkweed leaf beetles Labidomera clivicolis and monarch caterpillars Danaus plexippus); 2) production of the phytohormones jasmonic acid (JA), salicylic acid (SA), and abscisic acid (ABA); 3) induction of defensive cardenolides and latex; and 4) impacts on Danaus caterpillars. We first show that A. syriaca exhibits induced resistance following monarch herbivory (i.e., reduced monarch growth on previously damaged plants), while the defensively dissimilar A. tuberosa does not. We next worked with a broader group of five Asclepias, including these two species, that are highly divergent in defensive traits yet from the same clade. Three of the five species showed herbivore-induced changes in cardenolides, while induced latex was found in four species. Among the phytohormones, JA and ABA showed specific responses (although they generally increased) to insect species and among the plant species. In contrast, SA responses were consistent among plant and herbivore species, showing a decline following herbivore attack. Jasmonic acid showed a positive quantitative relationship only with latex, and this was strongest in plants damaged by D. plexippus. Although phytohormones showed qualitative tradeoffs (i.e., treatments that enhanced JA reduced SA), the few significant individual plant-level correlations among hormones were positive, and these were strongest between JA and ABA in monarch damaged plants. We conclude that: 1) latex exudation is positively associated with endogenous JA levels, even among low-latex species; 2) correlations among milkweed hormones are generally positive, although herbivore damage induces a 7. New Techniques for Relating Dynamically Close Galaxy Pairs to Merger and Accretion Rates Application to the SSRS2 Redshift Survey CERN Document Server Patton, D R; Marzke, R O; Pritchet, C J; Da Costa, L N; Pellegrini, P S 2000-01-01 We introduce two new pair statistics, which relate close galaxy pairs to the merger and accretion rates. We demonstrate the importance of correcting these (and other) pair statistics for selection effects related to sample depth and completeness. In particular, we highlight the severe bias that can result from the use of a flux-limited survey. The first statistic, denoted N_c, gives the number of companions per galaxy, within a specified range in absolute magnitude. N_c is directly related to the galaxy merger rate. The second statistic, called L_c, gives the total luminosity in companions, per galaxy. This quantity can be used to investigate the mass accretion rate. Both N_c and L_c are related to the galaxy correlation function and luminosity function in a straightforward manner. We outline techniques which account for various selection effects, and demonstrate the success of this approach using Monte Carlo simulations. If one assumes that clustering is independent of luminosity (which is appropriate for re... 8. Mesophyll cells of C4 plants have fewer chloroplasts than those of closely related C3 plants. Science.gov (United States) Stata, Matt; Sage, Tammy L; Rennie, Troy D; Khoshravesh, Roxana; Sultmanis, Stefanie; Khaikin, Yannay; Ludwig, Martha; Sage, Rowan F 2014-11-01 The evolution of C(4) photosynthesis from C(3) ancestors eliminates ribulose bisphosphate carboxylation in the mesophyll (M) cell chloroplast while activating phosphoenolpyruvate (PEP) carboxylation in the cytosol. These changes may lead to fewer chloroplasts and different chloroplast positioning within M cells. To evaluate these possibilities, we compared chloroplast number, size and position in M cells of closely related C(3), C(3) -C(4) intermediate and C(4) species from 12 lineages of C(4) evolution. All C(3) species had more chloroplasts per M cell area than their C(4) relatives in high-light growth conditions. C(3) species also had higher chloroplast coverage of the M cell periphery than C(4) species, particularly opposite intercellular air spaces. In M cells from 10 of the 12 C(4) lineages, a greater fraction of the chloroplast envelope was pulled away from the plasmalemma in the C(4) species than their C(3) relatives. C(3) -C(4) intermediate species generally exhibited similar patterns as their C(3) relatives. We interpret these results to reflect adaptive shifts that facilitate efficient C(4) function by enhancing diffusive access to the site of primary carbon fixation in the cytosol. Fewer chloroplasts in C(4) M cells would also reduce shading of the bundle sheath chloroplasts, which also generate energy required by C(4) photosynthesis. 9. Different mechanics of snap-trapping in the two closely related carnivorous plants Dionaea muscipula and Aldrovanda vesiculosa Science.gov (United States) Poppinga, Simon; Joyeux, Marc 2011-10-01 The carnivorous aquatic waterwheel plant (Aldrovanda vesiculosa L.) and the closely related terrestrial venus flytrap (Dionaea muscipula Sol. ex J. Ellis) both feature elaborate snap-traps, which shut after reception of an external mechanical stimulus by prey animals. Traditionally, Aldrovanda is considered as a miniature, aquatic Dionaea, an assumption which was already established by Charles Darwin. However, videos of snapping traps from both species suggest completely different closure mechanisms. Indeed, the well-described snapping mechanism in Dionaea comprises abrupt curvature inversion of the two trap lobes, while the closing movement in Aldrovanda involves deformation of the trap midrib but not of the lobes, which do not change curvature. In this paper, we present detailed mechanical models for these plants, which are based on the theory of thin solid membranes and explain this difference by showing that the fast snapping of Aldrovanda is due to kinematic amplification of the bending deformation of the midrib, while that of Dionaea unambiguously relies on the buckling instability that affects the two lobes. 10. TSCA Chemical Data Reporting Fact Sheet: Reporting Manufactured Chemical Substances from Metal Mining and Related Activities Science.gov (United States) This fact sheet provides guidance on the Chemical Data Reporting (CDR) rule requirements related to the reporting of mined metals, intermediates, and byproducts manufactured during metal mining and related activities. 11. Leave for illness/accident or in the event of illness of a close relative - New medical certificate templates CERN Multimedia HR department 2016-01-01 Medical certificate templates are now available in the Admin e-guide (follow the “Forms and templates” link): Medical certificate for illness/accident Medical certificate for a medical examination or treatment Medical certificate in the event of illness of a close relative These templates are provided for the convenience of members of the personnel and their use is recommended but not compulsory. Other forms of medical certificates issued by a medical doctor may also be submitted, provided they contain the same items of information as those given in the templates. More information on the applicable rules and on the way leave is managed at CERN can be found in the Admin e-guide web pages. Human Resources department HR.leave@cern.ch 12. Shedding dynamics of Morogoro virus, an African arenavirus closely related to Lassa virus, in its natural reservoir host Mastomys natalensis. Science.gov (United States) Borremans, Benny; Vossen, Raphaël; Becker-Ziaja, Beate; Gryseels, Sophie; Hughes, Nelika; Van Gestel, Mats; Van Houtte, Natalie; Günther, Stephan; Leirs, Herwig 2015-05-29 Arenaviruses can cause mild to severe hemorrhagic fevers. Humans mainly get infected through contact with infected rodents or their excretions, yet little is known about transmission dynamics within rodent populations. Morogoro virus (MORV) is an Old World arenavirus closely related to Lassa virus with which it shares the same host species Mastomys natalensis. We injected MORV in its host, and sampled blood and excretions at frequent intervals. Infection in adults was acute; viral RNA disappeared from blood after 18 days post infection (dpi) and from excretions after 39 dpi. Antibodies were present from 7 dpi and never disappeared. Neonatally infected animals acquired a chronic infection with RNA and antibodies in blood for at least 3 months. The quantified excretion and antibody patterns can be used to inform mathematical transmission models, and are essential for understanding and controlling transmission in the natural rodent host populations. 13. [Genetic Connectivity Between Sympatric Populations of Closely Related Char Species, Dolly Varden Salvelinus malma and White Char Salvelinus albus]. Science.gov (United States) Salmenkova, E A 2016-01-01 The closely related chars Salvelinus malma and Salvelinus albus, which sympatrically inhabit the Kamchatka River basin and Kronotsky Lake (Kamchatka), attract the attention of the researchers because of their debated origin and taxonomic status. Previous studies of sympatric populations of these chars revealed small but statistically significant genetic differences between these species at a number of molecular markers, suggesting the presence of the genetic exchange and hybridization. In this study, based on genotypic characterization of nine microsatellite loci, a considerable level of historical and contemporary genetic migration between sympatric populations of these chars was demonstrated. At the individual level a high degree of hybridization was observed, mainly among the Dolly Varden individuals from the studied populations. The obtained evidence on the genetic connectivity between sympatric S. malma and S. albus do not support the separate species status of S. albus. 14. Mutations and/or close relatives? Six case work examples where 49 autosomal SNPs were used as supplementary markers. Science.gov (United States) Børsting, Claus; Morling, Niels 2011-06-01 Six case work examples are presented, where the individuals were typed for 15 autosomal short tandem repeats (STRs) and 49 autosomal single nucleotide polymorphisms (SNPs). The 15 STRs were typed with the AmpFlSTR Identifiler PCR Amplification Kit and the 49 SNPs were typed with the SNPforID multiplex assay. The six cases included two duos, two trios and two cases, where the alleged father was not available for testing and one or two of his close relatives were tested instead. The SNP investigation was more informative than the STR investigation in all six cases. In two cases, the alleged father would have been falsely included based on the STR results, while the SNP results showed that the alleged father was not the true parent. These case work examples underline the importance of performing supplementary investigations in selected cases and demonstrate the usefulness of the SNPforID multiplex assay. 15. Sampling strategy and potential utility of indels for DNA barcoding of closely related plant species: a case study in taxus. Science.gov (United States) Liu, Jie; Provan, Jim; Gao, Lian-Ming; Li, De-Zhu 2012-01-01 Although DNA barcoding has become a useful tool for species identification and biodiversity surveys in plant sciences, there remains little consensus concerning appropriate sampling strategies and the treatment of indels. To address these two issues, we sampled 39 populations for nine Taxus species across their entire ranges, with two to three individuals per population randomly sampled. We sequenced one core DNA barcode (matK) and three supplementary regions (trnH-psbA, trnL-trnF and ITS) for all samples to test the effects of sampling design and the utility of indels. Our results suggested that increasing sampling within-population did not change the clustering of individuals, and that meant within-population P-distances were zero for most populations in all regions. Based on the markers tested here, comparison of methods either including or excluding indels indicated that discrimination and nodal support of monophyletic groups were significantly increased when indels were included. Thus we concluded that one individual per population was adequate to represent the within-population variation in these species for DNA barcoding, and that intra-specific sampling was best focused on representing the entire ranges of certain taxa. We also found that indels occurring in the chloroplast trnL-trnF and trnH-psbA regions were informative to differentiate among for closely related taxa barcoding, and we proposed that indel-coding methods should be considered for use in future for closed related plant species DNA barcoding projects on or below generic level. 16. 16S-23S rRNA Gene Intergenic Spacer Region Variability Helps Resolve Closely Related Sphingomonads. Science.gov (United States) Tokajian, Sima; Issa, Nahla; Salloum, Tamara; Ibrahim, Joe; Farah, Maya 2016-01-01 Sphingomonads comprise a physiologically versatile group many of which appear to be adapted to oligotrophic environments, but several also had features in their genomes indicative of host associations. In this study, the extent variability of the 16S-23S rDNA intergenic spacer (ITS) sequences of 14 ATCC reference sphingomonad strains and 23 isolates recovered from drinking water was investigated through PCR amplification and sequencing. Sequencing analysis of the 16S-23S rRNA gene ITS region revealed that the ITS sizes for all studied isolates varied between 415 and 849 bp, while their G+C content was 42.2-57.9 mol%. Five distinct ITS types were identified: ITS(none) (without tRNA genes), ITS(Ala(TGC)), ITS(Ala(TGC)+Ile(GAT)), ITS(Ile(GAT)+Ala(TGC)), and ITS (Ile(GAT)+Pseudo). All of the identified tRNA(Ala(TGC)) molecules consisted of 73 bases, and all of the tRNA(Ile(GAT)) molecules consisted of 74 bases. We also detected striking variability in the size of the ITS region among the various examined isolates. Highest variability was detected within the ITS-2. The importance of this study is that this is the first comparison of the 16S-23S rDNA ITS sequence similarities and tRNA genes from sphingomonads. Collectively the data obtained in this study revealed the heterogeneity and extent of variability within the ITS region compared to the 16S rRNA gene within closely related isolates. Sequence and length polymorphisms within the ITS region along with the ITS types (tRNA-containing or lacking and the type of tRNA) and ITS-2 size and sequence similarities allowed us to overcome the limitation we previously encountered in resolving closely related isolates based on the 16S rRNA gene sequence. 17. Teaching International Public Relations: An Update Report among Educators Science.gov (United States) Mak, Angela Ka Ying 2017-01-01 Involvement in international and multicultural career-related practices is ever on the rise in a global economic and political society, especially in public relations. This article reported an update of examining the attributes of public relations educators and their institutions in teaching of international public relations (IPR) through an… 18. Transcriptome sequencing of Crucihimalaya himalaica (Brassicaceae) reveals how Arabidopsis close relative adapt to the Qinghai-Tibet Plateau. Science.gov (United States) Qiao, Qin; Wang, Qia; Han, Xi; Guan, Yanlong; Sun, Hang; Zhong, Yang; Huang, Jinling; Zhang, Ticao 2016-02-24 The extreme environment of the Qinghai-Tibet Plateau (QTP) provides an ideal natural laboratory for studies on adaptive evolution. Few genome/transcriptome based studies have been conducted on how plants adapt to the environments of QTP compared to numerous studies on vertebrates. Crucihimalaya himalaica is a close relative of Arabidopsis with typical QTP distribution, and is hoped to be a new model system to study speciation and ecological adaptation in extreme environment. In this study, we de novo generated a transcriptome sequence of C. himalaica, with a total of 49,438 unigenes. Compared to five relatives, 10,487 orthogroups were shared by all six species, and 4,286 orthogroups contain putative single copy gene. Further analysis identified 487 extremely significantly positively selected genes (PSGs) in C. himalaica transcriptome. Theses PSGs were enriched in functions related to specific adaptation traits, such as response to radiation, DNA repair, nitrogen metabolism, and stabilization of membrane. These functions are responsible for the adaptation of C. himalaica to the high radiation, soil depletion and low temperature environments on QTP. Our findings indicate that C. himalaica has evolved complex strategies for adapting to the extreme environments on QTP and provide novel insights into genetic mechanisms of highland adaptation in plants. 19. 26 CFR 1.6045-4 - Information reporting on real estate transactions with dates of closing on or after January 1, 1991. Science.gov (United States) 2010-04-01 ... 26 Internal Revenue 13 2010-04-01 2010-04-01 false Information reporting on real estate... Information Returns § 1.6045-4 Information reporting on real estate transactions with dates of closing on or... (d) of this section, a real estate reporting person (“reporting person”) must make an information... 20. High-pressure Raman study of two ferroelectric crystals closely related to PbTiO3 Science.gov (United States) Burns, Gerald; Sanjurjo, J. A.; López-Cruz, E. 1984-12-01 We report high-pressure Raman measurements of the zone-center phonons in two ferroelectric crystals that closely resemble the ABO3 perovskite crystal PbTiO3. These crystals are (Pb0.22Ba0.78)TiO3, i.e., Ba replacing Pb on the A site, and Pb(Ti0.81Sn0.19)O3, i.e., Sn replacing Ti on the B site. In both cases, at room temperature, we follow the modes and determine Pc, the transition pressure from the ferroelectric tetragonal phase to the cubic phase, to be 4.3 and 9.0 GPa, respectively. By observing the coalescence to the same frequency of the appropriate high-energy A1(TO)+E(TO) pairs of phonons, we determine the second-order character of the phase transitions at Pc. The tendency towards a second-order phase transition seems to be the rule at Pc as long as one makes the measurements at a temperature well below Tc; this is in agreement with theory. Thus, these systems exhibit tricritical points in the (P,T) phase diagram. The soft-E(TO)-phonon frequency (ω0) and damping constant (γ) can be measured to pressures reasonably close to Pc while the mode remains underdamped. These results are discussed in terms of a frequency-independent damping constant for the behavior of ω0 and γ near Pc. In the (Pb,Ba)TiO3 crystal, the hydrostatic pressure increases the intensity of the soft A1(TO) mode making it observable. This seems to happen in general in the perovskites. In the Pb(Ti,Sn)O3 crystal we observe the coupling of the soft E(TO) mode with an extra mode at 59 cm-1; this also has been studied as a function of temperature. 1. Mass spectrometry of planetary exospheres at high relative velocity: direct comparison of open- and closed source measurements Science.gov (United States) Meyer, Stefan; Tulej, Marek; Wurz, Peter 2016-04-01 The exploration of habitable worlds around the gas giants in the Solar System is of major interest in upcoming planetary missions. Exactly this theme is addressed by the Jupiter Icy Moons Explorer (JUICE) mission of ESA, which will characterise Ganymede, Europa and Callisto as planetary objects and potential habitats [1], [2]. We developed a prototype of the Neutral gas and Ion Mass spectrometer (NIM) of the Particle Environment Package (PEP) for the JUICE mission intended for composition measurements of neutral gas and thermal plasma. NIM/PEP will be used to measure the chemical composition of the exospheres of the icy Jovian moons. Besides direct ion measurement, the NIM instrument is able to measure the inflowing neutral gas in two different modes: in neutral mode the gas enters directly the ion source (open source) and in thermal mode, the gas gets thermally accommodated to wall temperature by several collisions inside an equilibrium sphere before entering the ion source (closed source). We performed measurements with the prototype NIM using a neutral gas beam of 1 up to 5 km/s velocity in the neutral and thermal mode. The current trajectory of JUICE foresees a flyby velocity of 4 km/s at Europa, other flybys are in the range of 1 up to 7 km/s and velocity in Ganymede orbits is around 2 km/s. Different species are used for gas beam, such as noble gases Ne, Ar, Kr as well as molecules like H2, Methane, Ethane, Propane and more complex ones. We will present the results of these measurements with respect to fragmentation and density enhancements in the closed source mode. Furthermore, we will give a direct comparison between open and closed source mode measurements. References: [1] ESA, "JUICE assessment study report (Yellow Book)", ESA/SRE(2011)18, 2012. [2] O. Grasset, M.K. Dougherty, A. Coustenis, E.J. Bunce, C. Erd, D. Titov, M. Blanc, A. Coates, P. Drossart, L.N. Fletcher, H. Hussmann, R. Jaumann, N. Krupp, J.-P. Lebreton, O. Prieto-Ballesteros, P. Tortora, F 2. 29 CFR 776.17 - Employment in a “closely related process or occupation directly essential to” production of goods. Science.gov (United States) 2010-07-01 ... § 776.17 Employment in a “closely related process or occupation directly essential to” production of... process or occupation directly essential to the production thereof, in any State.” 77 Prior to the Fair... criteria for determining whether a process or occupation is “closely related” to production cannot... 3. Characterization of a novel Lactobacillus species closely related to Lactobacillus johnsonii using a combination of molecular and comparative genomics methods Directory of Open Access Journals (Sweden) Pérez-Martínez Gaspar 2010-09-01 Full Text Available Abstract Background Comparative genomic hybridization (CGH constitutes a powerful tool for identification and characterization of bacterial strains. In this study we have applied this technique for the characterization of a number of Lactobacillus strains isolated from the intestinal content of rats fed with a diet supplemented with sorbitol. Results Phylogenetic analysis based on 16S rRNA gene, recA, pheS, pyrG and tuf sequences identified five bacterial strains isolated from the intestinal content of rats as belonging to the recently described Lactobacillus taiwanensis species. DNA-DNA hybridization experiments confirmed that these five strains are distinct but closely related to Lactobacillus johnsonii and Lactobacillus gasseri. A whole genome DNA microarray designed for the probiotic L. johnsonii strain NCC533 was used for CGH analysis of L. johnsonii ATCC 33200T, L. johnsonii BL261, L. gasseri ATCC 33323T and L. taiwanensis BL263. In these experiments, the fluorescence ratio distributions obtained with L. taiwanensis and L. gasseri showed characteristic inter-species profiles. The percentage of conserved L. johnsonii NCC533 genes was about 83% in the L. johnsonii strains comparisons and decreased to 51% and 47% for L. taiwanensis and L. gasseri, respectively. These results confirmed the separate status of L. taiwanensis from L. johnsonii at the level of species, and also that L. taiwanensis is closer to L. johnsonii than L. gasseri is to L. johnsonii. Conclusion Conventional taxonomic analyses and microarray-based CGH analysis have been used for the identification and characterization of the newly species L. taiwanensis. The microarray-based CGH technology has been shown as a remarkable tool for the identification and fine discrimination between phylogenetically close species, and additionally provided insight into the adaptation of the strain L. taiwanensis BL263 to its ecological niche. 4. Vibrio metoecus sp. nov., a close relative of Vibrio cholerae isolated from coastal brackish ponds and clinical specimens. Science.gov (United States) Kirchberger, Paul C; Turnsek, Maryann; Hunt, Dana E; Haley, Bradd J; Colwell, Rita R; Polz, Martin F; Tarr, Cheryl L; Boucher, Yan 2014-09-01 A Gram-staining-negative, curved-rod-shaped bacterium with close resemblance to Vibrio cholerae, the aetiological agent of cholera, was isolated over the course of several years from coastal brackish water (17 strains) and from clinical cases (two strains) in the United States. 16S rRNA gene identity with V. cholerae exceeded 98 % yet an average nucleotide identity based on genome data of around 86 % and multi locus sequence analysis of six housekeeping genes (mdh, adk, gyrB, recA, pgi and rpoB) clearly delineated these isolates as a distinct genotypic cluster within the V. cholerae-V. mimicus clade. Most standard identification techniques do not differentiate this cluster of isolates from V. cholerae. Only amplification of the ompW gene using V. cholerae-specific primers and a negative Voges-Proskauer test showed a difference between the two clusters. Additionally, all isolated strains differed phenotypically from V. cholerae in their ability to utilize N-acetyl-d-galactosamine and d-glucuronic acid as sole carbon sources. Furthermore, they were generally unable to infect the slime mould Dictyostelium discoideum, a widespread ability in V. cholerae. Based on these clear phenotypic differences that are not necessarily apparent in standard tests as well as average nucleotide identity and phylogeny of protein-coding genes, we propose the existence of a novel species, Vibrio metoecus sp. nov. with the type strain OP3H(T) ( = LMG 27764(T) = CIP 110643(T)). Due to its close resemblance to V. cholerae and the increasing number of strains isolated over the past several years, we suggest that V. metoecus sp. nov. is a relatively common species of the genus Vibrio, isolates of which have been identified as atypical isolates of V. cholerae in the past. Its isolation from clinical samples also indicates that strains of this species, like V. cholerae, are opportunistic pathogens. © 2014 IUMS. 5. Differences in Glycoprotein Complex Receptor Binding Site Accessibility Prompt Poor Cross-Reactivity of Neutralizing Antibodies between Closely Related Arenaviruses. Science.gov (United States) Brouillette, Rachel B; Phillips, Elisabeth K; Ayithan, Natarajan; Maury, Wendy 2017-04-01 The glycoprotein complex (GPC) of arenaviruses, composed of stable signal peptide, GP1, and GP2, is the only antigen correlated with antibody-mediated neutralization. However, despite strong cross-reactivity of convalescent antisera between related arenavirus species, weak or no cross-neutralization occurs. Two closely related clade B viruses, Machupo virus (MACV) and Junín virus (JUNV), have nearly identical overall GPC architecture and share a host receptor, transferrin receptor 1 (TfR1). Given structural and functional similarities of the GP1 receptor binding site (RBS) of these viruses and the recent demonstration that the RBS is an important target for neutralizing antibodies, it is not clear how these viruses avoid cross-neutralization. To address this, MACV/JUNV chimeric GPCs were assessed for interaction with a group of α-JUNV GPC monoclonal antibodies (MAbs) and mouse antisera against JUNV or MACV GPC. All six MAbs targeted GP1, with those that neutralized JUNV GPC-pseudovirions competing with each other for RBS binding. However, these MAbs were unable to bind to a chimeric GPC composed of JUNV GP1 containing a small disulfide bonded loop (loop 10) unique to MACV GPC, suggesting that this loop may block MAbs interaction with the GP1 RBS. Consistent with this loop causing interference, mouse anti-JUNV GPC antisera that solely neutralized pseudovirions bearing autologous GP1 provided enhanced neutralization of MACV GPC when this loop was removed. Our studies provide evidence that loop 10, which is unique to MACV GP1, is an important impediment to binding of neutralizing antibodies and contributes to the poor cross-neutralization of α-JUNV antisera against MACV.IMPORTANCE Multiple New World arenaviruses can cause severe disease in humans, and some geographic overlap exists among these viruses. A vaccine that protects against a broad range of New World arenaviruses is desirable for purposes of simplicity, cost, and broad protection against multiple National 6. Summary report on close-coupled subsurface barrier technology: Initial field trials to full-scale demonstration Energy Technology Data Exchange (ETDEWEB) Heiser, J.H. [Brookhaven National Lab., Upton, NY (United States). Environmental and Waste Technology Center; Dwyer, B. [Sandia National Lab., Albuquerque, NM (United States) 1997-09-01 The primary objective of this project was to develop and demonstrate the installation and measure the performance of a close-coupled barrier for the containment of subsurface waste or contaminant migration. A close-coupled barrier is produced by first installing a conventional, low-cost, cement-grout containment barrier followed by a thin lining of a polymer grout. The resultant barrier is a cement-polymer composite that has economic benefits derived from the cement and performance benefits from the durable and resistant polymer layer. The technology has matured from a regulatory investigation of the issues concerning the use of polymers to laboratory compatibility and performance measurements of various polymer systems to a pilot-scale, single column injection at Sandia to full-scale demonstration. The feasibility of the close-coupled barrier concept was proven in a full-scale cold demonstration at Hanford, Washington and then moved to the final stage with a full-scale demonstration at an actual remediation site at Brookhaven National Laboratory (BNL). At the Hanford demonstration the composite barrier was emplaced around and beneath a 20,000 liter tank. The secondary cement layer was constructed using conventional jet grouting techniques. Drilling was completed at a 45{degree} angle to the ground, forming a cone-shaped barrier. The primary barrier was placed by panel jet-grouting with a dual-wall drill stem using a two part polymer grout. The polymer chosen was a high molecular weight acrylic. At the BNL demonstration a V-trough barrier was installed using a conventional cement grout for the secondary layer and an acrylic-gel polymer for the primary layer. Construction techniques were identical to the Hanford installation. This report summarizes the technology development from pilot- to full-scale demonstrations and presents some of the performance and quality achievements attained. 7. Genetic variability and relationship between MT-1 elephant grass and closely related cultivars assessed by SRAP markers Indian Academy of Sciences (India) Xin-Ming Xie; Feng Zhou; Xiang-Qian Zhang; Ju-Ming Zhang 2009-12-01 Genetic variability and relationships among elephant grass cultivars were estimated by the SRAP (sequence-related amplified polymorphism) assay. A total of 60 individuals collected from five cultivars in China were analysed. Sixty-two selected primer combinations generated 1395 bands, with an average of 22.5 per primer combination. The average value of percentage of polymorphic bands (PPB) was 72.8% at species level. The PPB was from 15.2% to 75%, with an average of 39.6% at cultivar level.H_{POP}$, within-cultivar Shannon’s index was 1.738 at cultivar level; at species level, the Shannon’s index$(H_{SP})$was 3.880. An assessment of diversity between cultivars$[(H_{SP} −H_{POP})/H_{SP}]indicated that most of the diversity (55.2%) was detected among cultivars, and only 44.8% was within cultivars in total genetic variation. According to UPGMA dendrogram, the five cultivars were clustered into three main groups. One group included MT-1 and Mott with a bootstrap support of 100%, another consisted of Huanan and N51 with a bootstrap support of 81%, and last one was only Guimu-1. The results indicate that the MT-1 and Mott have a closest genetic relationship; Huanan and N51 possess a relatively close relationship, and Guimu-1 is the most distinct from the other four cultivars. 8. Molecular evidence that the spiny mouse (Acomys) is more closely related to gerbils (Gerbillinae) than to true mice (Murinae). Science.gov (United States) Chevret, P; Denys, C; Jaeger, J J; Michaux, J; Catzeflis, F M 1993-04-15 Spiny mice of the genus Acomys traditionally have been classified as members of the Murinae, a subfamily of rodents that also includes rats and mice with which spiny mice share a complex set of morphological characters, including a unique molar pattern. The origin and evolution of this molar pattern, documented by many fossils from Southern Asia, support the hypothesis of the monophyly of Acomys and all other Murinae. This view has been challenged by immunological studies that have suggested that Acomys is as distantly related to mice (Mus) as are other subfamilies (e.g., hamsters: Cricetinae) of the muroid rodents. We present molecular evidence derived from DNA.DNA hybridization data that indicate that the spiny mouse Acomys and two African genera of Murinae, Uranomys and Lophuromys, constitute a monophyletic clade, a view that was recently suggested on the basis of dental characters. However, our DNA.DNA hybridization data also indicate that the spiny mice (Acomys) are more closely related to gerbils (Gerbillinae) than to the true mice and rats (Murinae) with which they have been classified. Because Acomys and the brush-furred mice Uranomys and Lophuromys share no derived morphological characters with the Gerbillinae, their murine morphology must have evolved by convergence, including the molar pattern previously considered to support the monophyly of the Murinae. 9. DNA sequence conservation between the Bacillus anthracis pXO2 plasmid and genomic sequence from closely related bacteria Directory of Open Access Journals (Sweden) Sabin Robert 2002-12-01 Full Text Available Abstract Background Complete sequencing and annotation of the 96.2 kb Bacillus anthracis plasmid, pXO2, predicted 85 open reading frames (ORFs. Bacillus cereus and Bacillus thuringiensis isolates that ranged in genomic similarity to B. anthracis, as determined by amplified fragment length polymorphism (AFLP analysis, were examined by PCR for the presence of sequences similar to 47 pXO2 ORFs. Results The two most distantly related isolates examined, B. thuringiensis 33679 and B. thuringiensis AWO6, produced the greatest number of ORF sequences similar to pXO2; 10 detected in 33679 and 16 in AWO6. No more than two of the pXO2 ORFs were detected in any one of the remaining isolates. Dot-blot DNA hybridizations between pXO2 ORF fragments and total genomic DNA from AWO6 were consistent with the PCR assay results for this isolate and also revealed nine additional ORFs shared between these two bacteria. Sequences similar to the B. anthracis cap genes or their regulator, acpA, were not detected among any of the examined isolates. Conclusions The presence of pXO2 sequences in the other Bacillus isolates did not correlate with genomic relatedness established by AFLP analysis. The presence of pXO2 ORF sequences in other Bacillus species suggests the possibility that certain pXO2 plasmid gene functions may also be present in other closely related bacteria. 10. Identification and characterization of two closely related unclassifiable endogenous retroviruses in pythons (Python molurus and Python curtus). Science.gov (United States) Huder, Jon B; Böni, Jürg; Hatt, Jean-Michel; Soldati, Guido; Lutz, Hans; Schüpbach, Jörg 2002-08-01 Boid inclusion body disease (BIBD) is a fatal disorder of boid snakes that is suspected to be caused by a retrovirus. In order to identify this agent, leukocyte cultures (established from Python molurus specimens with symptoms of BIBD or kept together with such diseased animals) were assessed for reverse transcriptase (RT) activity. Virus from cultures exhibiting high RT activity was banded on sucrose density gradients, and the RT peak fraction was subjected to highly efficient procedures for the identification of unknown particle-associated retroviral RNA. A 7-kb full retroviral sequence was identified, cloned, and sequenced. This virus contained intact open reading frames (ORFs) for gag, pro, pol, and env, as well as another ORF of unknown function within pol. Phylogenetic analysis showed that the virus is distantly related to viruses from both the B and D types and the mammalian C type but cannot be classified. It is present as a highly expressed endogenous retrovirus in all P. molurus individuals; a closely related, but much less expressed virus was found in all tested Python curtus individuals. All other boid snakes tested, including Python regius, Python reticulatus, Boa constrictor, Eunectes notaeus, and Morelia spilota, were virus negative, independent of whether they had BIBD or not. Virus isolated from P. molurus could not be transmitted to the peripheral blood mononuclear cells of B. constrictor or P. regius. Thus, there is no indication that this novel virus, which we propose to name python endogenous retrovirus (PyERV), is causally linked with BIBD. 11. Identifying the Best-Fitting Factor Structure of the Experience of Close Relations - Revised in a Scandinavian Example. Directory of Open Access Journals (Sweden) Barbara Hoff Esbjørn Full Text Available The aim of this study was to enhance the understanding of cultural and sample differences in the assessment of attachment by examining the factor structure of the Experiences in Close Relationships-Revised (ECR-R. The ECR-R is a self-report measure of adult romantic attachment dimensions. The present study used a Danish sample with the purpose of addressing limitations in previous studies, such as the lack of diversity in cultural background, restricted sample characteristics, and poorly fitting structure models. Participants consisted of 253 parents of children between the ages of 7 and 12 years, 53% being mothers. The parents completed the paper version of the questionnaire. Confirmatory Factor Analyses were carried out to determine whether theoretically and empirically established models including one and two factors would also provide adequate fits in a Danish sample. A previous study using the original ECR suggested that Scandinavian samples may best be described using a five-factor solution. Our results indicated that the one- and two-factor models of the ECR-R did not fit the data well. Exploratory Factor Analysis revealed a five-factor model. Our study provides evidence that further investigation is needed to establish which model may provide the best model fit in the Scandinavian countries. 12. Absence of XMRV and closely related viruses in primary prostate cancer tissues used to derive the XMRV-infected cell line 22Rv1. Directory of Open Access Journals (Sweden) Jaydip Das Gupta Full Text Available The 22Rv1 cell line is widely used for prostate cancer research and other studies throughout the world. These cells were established from a human prostate tumor, CWR22, that was serially passaged in nude mice and selected for androgen independence. The 22Rv1 cells are known to produce high titers of xenotropic murine leukemia virus-related virus (XMRV. Recent studies suggested that XMRV was inadvertently created in the 1990's when two murine leukemia virus (MLV genomes (pre-XMRV1 and pre-XMRV-2 recombined during passaging of the CWR22 tumor in mice. The conclusion that XMRV originated from mice and not the patient was based partly on the failure to detect XMRV in early CWR22 xenografts. While that deduction is certainly justified, we examined the possibility that a closely related virus could have been present in primary tumor tissue. Here we report that we have located the original prostate tumor tissue excised from patient CWR22 and have assayed the corresponding DNA by PCR and the tissue sections by fluorescence in situ hybridization for the presence of XMRV or a similar virus. The primary tumor tissues lacked mouse DNA as determined by PCR for intracisternal A type particle DNA, thus avoiding one of the limitations of studying xenografts. We show that neither XMRV nor a closely related virus was present in primary prostate tissue of patient CWR22. Our findings confirm and reinforce the conclusion that XMRV is a recombinant laboratory-generated mouse virus that is highly adapted for human prostate cancer cells. 13. Single substitutions to closely related amino acids contribute to the functional diversification of an insect-inducible, positively selected plant cystatin. Science.gov (United States) Rasoolizadeh, Asieh; Goulet, Marie-Claire; Sainsbury, Frank; Cloutier, Conrad; Michaud, Dominique 2016-04-01 A causal link has been reported between positively selected amino acids in plant cystatins and the inhibitory range of these proteins against insect digestive cysteine (Cys) proteases. Here we assessed the impact of single substitutions to closely related amino acids on the contribution of positive selection to cystatin diversification. Cystatin sequence alignments, while confirming hypervariability, indicated a preference for related amino acids at positively selected sites. For example, the non-polar residues leucine (Leu), isoleucine (Ile) and valine (Val) were shown to predominate at positively selected site 2 in the N-terminal region, unlike selected sites 6 and 10, where polar residues are preferred. The model cystatin SlCYS8 and single variants with Leu, Ile or Val at position 2 were compared with regard to their ability to bind digestive proteases of the coleopteran pest Leptinotarsa decemlineata and to induce compensatory responses in this insect. A functional proteomics procedure to capture target Cys proteases in midgut extracts allowed confirmation of distinct binding profiles for the cystatin variants. A shotgun proteomics procedure to monitor whole Cys protease complements revealed protease family specific compensatory responses in the insect, dependent on the variant ingested. Our data confirm the contribution of closely related amino acids to the functional diversity of positively selected plant cystatins in a broader structure/function context imposing physicochemical constraints to primary structure alterations. They also underline the complexity of protease/inhibitor interactions in plant-insect systems, and the challenges still to be met in order to harness the full potential of ectopically expressed protease inhibitors in crop protection. 14. TEST REPORT OF MOBILE SOURCE EMISSIONS CONTROL DEVICES DONALDSON COMPANY INC.SERIES 6000 DISEL OXIDATION CATALYST MUFFLER AND SPIRACLE CLOSED CRANKCASE FILTRATION SYSTEM Science.gov (United States) This report is on testing of a Donaldson Corp. catalytic muffler and closed crankcase filtration system for diesel trucks. It verified the emissions for these systems using low sufur and ultra low sulfur fuel. 15. Molecular detection of novel Anaplasmataceae closely related to Anaplasma platys and Ehrlichia canis in the dromedary camel (Camelus dromedarius). Science.gov (United States) Bastos, Armanda D S; Mohammed, Osama B; Bennett, Nigel C; Petevinos, Charalambos; Alagaili, Abdulaziz N 2015-09-30 Serological surveys have confirmed Anaplasma marginale and Anaplasma phagocytophilum infections in dromedary camels, but molecular surveys and genetic characterisation of camel-associated Anaplasma species are lacking. In this study, we detected tick-borne Anaplasmataceae in 30 of 100 (30%) healthy dromedary camels screened using a combined 16S rRNA-groEL PCR-sequencing approach. Nucleotide sequencing confirmed Anaplasmataceae genome presence in 28 of the 33 16S rRNA PCR-positive samples, with two additional positive samples, for which 16S rRNA sequence data were ambiguous, being identified by groEL gene characterisation. Phylogenetic analyses of a 1289 nt segment of the 16S rRNA gene confirmed the presence of a unique Ehrlichia lineage and a discrete Anaplasma lineage, comprising three variants, occurring at an overall prevalence of 4% and 26%, respectively. Genetic characterisation of an aligned 559 nt groEL gene region revealed the camel-associated Anaplasma and Ehrlichia lineages to be novel and most closely related to Anaplasma platys and Ehrlichia canis. Based on the confirmed monophyly, minimum pairwise genetic distances between each novel lineage and its closest sister taxon, and the inability to isolate the bacteria, we propose that Candidatus status be assigned to each. This first genetic characterisation of Anaplasmataceae from naturally infected, asymptomatic dromedary camels in Saudi Arabia confirms the presence of two novel lineages that are phylogenetically linked to two pathogenic canid species of increasing zoonotic concern. 16. The Use of Differential EXAFS Analysis for the determination of Small Structural Differences between two closely-related Ruthenium Complexes Science.gov (United States) Gianolio, D.; Borfecchia, E.; Garino, C.; Ruiu, T.; Lamberti, C.; Salassa, L. 2013-04-01 X-ray Absorption Spectroscopy (XAS) is a sensitive and powerful technique in revealing the structure of a material, providing as well high accuracy on interatomic distances. Nevertheless, when dealing with systems that differ only by small structural features, a standard data analysis might be unable of discriminating between such differences. A differential approach was proposed by Bressler, Chergui, and co-workers [2003, Phys. Rev. Lett. 90, 047403][2006, J. Phys. Chem B, 110, 14035][2009 Angew. Chem., Int. Ed. 48 2711] to solve this problem and differentiate between excited and unexcited state structures during pump-and-probe transient XAS experiments. In this contribution, we apply the differential data analysis procedure to the study of two closely-related molecular complexes, namely cis-[Ru(bpy)2(py)2]2+ and cis-[Ru(bpy)2(py)(H2O)]2+, characterized under static conditions. It is herein demonstrated that the method, based on a direct fit of differential curves, is able to reveal the small differences present between the two structures which, conversely, could not be resolved by standard EXAFS fitting of full spectra. 17. ATGC: a database of orthologous genes from closely related prokaryotic genomes and a research platform for microevolution of prokaryotes Energy Technology Data Exchange (ETDEWEB) Novichkov, Pavel S.; Ratnere, Igor; Wolf, Yuri I.; Koonin, Eugene V.; Dubchak, Inna 2009-07-23 The database of Alignable Tight Genomic Clusters (ATGCs) consists of closely related genomes of archaea and bacteria, and is a resource for research into prokaryotic microevolution. Construction of a data set with appropriate characteristics is a major hurdle for this type of studies. With the current rate of genome sequencing, it is difficult to follow the progress of the field and to determine which of the available genome sets meet the requirements of a given research project, in particular, with respect to the minimum and maximum levels of similarity between the included genomes. Additionally, extraction of specific content, such as genomic alignments or families of orthologs, from a selected set of genomes is a complicated and time-consuming process. The database addresses these problems by providing an intuitive and efficient web interface to browse precomputed ATGCs, select appropriate ones and access ATGC-derived data such as multiple alignments of orthologous proteins, matrices of pairwise intergenomic distances based on genome-wide analysis of synonymous and nonsynonymous substitution rates and others. The ATGC database will be regularly updated following new releases of the NCBI RefSeq. The database is hosted by the Genomics Division at Lawrence Berkeley National laboratory and is publicly available at http://atgc.lbl.gov. 18. Differences in c-Jun N-terminal kinase recognition and phosphorylation of closely related stathmin-family members. Science.gov (United States) Yip, Yan Y; Yeap, Yvonne Y C; Bogoyevitch, Marie A; Ng, Dominic C H 2014-03-28 The stathmin (STMN) family of tubulin-binding phosphoproteins are critical regulators of interphase microtubule dynamics and organization in a broad range of cellular processes. c-Jun N-terminal kinase (JNK) signalling to STMN family proteins has been implicated specifically in neuronal maturation, degeneration and cell stress responses more broadly. Previously, we characterized mechanisms underlying JNK phosphorylation of STMN at proline-flanked serine residues (Ser25 and Ser38) that are conserved across STMN-like proteins. In this study, we demonstrated using in vitro kinase assays and alanine replacement of serine residues that JNK phosphorylated the STMN-like domain (SLD) of SCG10 on Ser73, consistent with our previous finding that STMN Ser38 was the primary JNK target site. In addition, we confirmed that a JNK binding motif ((41)KKKDLSL(47)) that facilitates JNK targeting of STMN is conserved in SCG10. In contrast, SCLIP was phosphorylated by JNK primarily on Ser60 which corresponds to Ser25 on STMN. Moreover, although the JNK-binding motif identified in STMN and SCG10 was not conserved in SCLIP, JNK phosphorylation of SCLIP was inhibited by a substrate competitive peptide (TI-JIP) highlighting kinase-substrate interaction as required for JNK targeting. Thus, STMN and SCG10 are similarly targeted by JNK but there are clear differences in JNK recognition and phosphorylation of the closely related family member, SCLIP. 19. Genetic entities and mating system in hermaphroditic Fucus spiralis and its close dioecious relative F. vesiculosus (Fucaceae, Phaeophyceae). Science.gov (United States) Engel, C R; Daguin, C; Serrão, E A 2005-06-01 To date, molecular markers have not settled the question of the specific status of the closely related, but phylogenetically unresolved, brown seaweeds, hermaphroditic Fucus spiralis and dioecious Fucus vesiculosus, nor their propensity for natural hybridization. To test the degree of species integrity and to assess effect of the mating system on the population genetic structure, 288 individuals coming from parapatric (discontinuous) and sympatric (contiguous) spatial configurations at two sites were genotyped with five microsatellite loci. Using a Bayesian admixture analysis, our results show that F. spiralis and F. vesiculosus comprise clearly distinct genetic entities (clusters) generally characterized by cosexual and unisexual individuals, respectively. Genetic diversity within each entity suggests that F. spiralis reproduces primarily through selfing while F. vesiculosus is characterized by an endogamous breeding regime. Nevertheless, aberrant sexual phenotypes were observed in each cluster, no diagnostic alleles were revealed and 10% of study individuals were intermediate between the two genetic entities. This pattern can be explained by recent divergence of two taxa with retention of ancestral polymorphism or asymmetrical, introgressive hybridization. However, given (i) coincident monomorphism at three loci in spiralis clusters and (ii) that significantly more intermediates were observed in sympatric stations than in parapatric stations, we argue that interspecific gene flow has occurred after divergence of the two taxa. Finally, we show that whether recently separated or recently introgressive, the divergent breeding systems probably contribute to species integrity in these two taxa. 20. Wing pattern morphology of three closely related Melitaea (Lepidoptera, Nymphalidae species reveals highly inaccurate external morphology-based species identification Directory of Open Access Journals (Sweden) Jure Jugovic 2014-06-01 Full Text Available Wing morphology of the three closely related species of Melitaea – M. athalia (Rottemburg, 1775, M. aurelia (Nickerl, 1850 and M. britomartis Assmann, 1847 – co-occurring in the Balkans (SE Europe was investigated in detail through visual inspection, morphometric analysis and multivariate statistical analysis. Results are compared to recent phylogenetic studies, searching for concordant patterns and discrepancies between the two approaches. The morphology of the genitalic structures is also compared with the results of the other two approaches. The main conclusions are as follows: (1 small albeit significant differences in wing morphology exist among the three species and (2 while the structure of male genitalia and phylogenetic position of the three species are concordant, they are (3 in discordance with the wing morphology. The present study represents another example where identification based on external morphology would lead to highly unreliable determinations, hence identification based on phylogenetic studies and/or genitalia is strongly recommended not only for the three studied species but also more broadly within the genus. Furthermore, we show that some of the characters generally used in the identification of these three Melitaea species should be avoided in future. 1. Identification of structurally closely related monosaccharide and disaccharide isomers by PMP labeling in conjunction with IM-MS/MS. Science.gov (United States) Yang, Hongmei; Shi, Lei; Zhuang, Xiaoyu; Su, Rui; Wan, Debin; Song, Fengrui; Li, Jinying; Liu, Shuying 2016-06-16 It remains particularly difficult for gaining unambiguous information on anomer, linkage, and position isomers of oligosaccharides using conventional mass spectrometry (MS) methods. In our laboratory, an ion mobility (IM) shift strategy was employed to improve confidence in the identification of structurally closely related disaccharide and monosaccharide isomers using IMMS. Higher separation between structural isomers was achieved using 1-phenyl-3-methyl-5-pyrazolone (PMP) derivatization in comparison with phenylhydrazine (PHN) derivatization. Furthermore, the combination of pre-IM fragmentation of PMP derivatives provided sufficient resolution to separate the isomers not resolved in the IMMS. To chart the structural variation observed in IMMS, the collision cross sections (CCSs) for the corresponding ions were measured. We analyzed nine disaccharide and three monosaccharide isomers that differ in composition, linkages, or configuration. Our data show that coexisting carbohydrate isomers can be identified by the PMP labeling technique in conjunction with ion-mobility separation and tandem mass spectrometry. The practical application of this rapid and effective method that requires only small amounts of sample is demonstrated by the successful analysis of water-soluble ginseng extract. This demonstrated the potential of this method to measure a variety of heterogeneous sample mixtures, which may have an important impact on the field of glycomics. 2. Candida parapsilosis sensu stricto and the closely related species Candida orthopsilosis and Candida metapsilosis in vulvovaginal candidiasis. Science.gov (United States) Zhu, Yuxia; Shan, Yingying; Fan, Shangrong; Li, Jianling; Liu, Xiaoping 2015-02-01 This study aimed to determine the clinical characteristics and in vitro susceptibilities of Candida parapsilosis sensu stricto, Candida orthopsilosis and Candida metapsilosis isolates from patients with vulvovaginal candidiasis (VVC). We analysed 63 vaginal C. parapsilosis specimens. After the molecular analyses, the isolates were characterised as C. parapsilosis sensu stricto (77.8%), C. orthopsilosis (7.9%) and C. metapsilosis (14.3%). The signs and symptoms of VVC caused by C. parapsilosis sensu lato, including itching, erythema and abnormal discharge, were milder than those caused by C. albicans. None of the C. parapsilosis sensu lato isolates were resistant to fluconazole, miconazole or itraconazole. The resistance rates of C. albicans to fluconazole, itraconazole, miconazole and clotrimazole were 2.3, 1.5, 3.1 and 0.8%, respectively. Both C. parapsilosis sensu lato and C. albicans were susceptible to nystatin. The mycological eradication rate at follow-up days 7-14 and 30-35 were 77.8% (49/63) and 76.2% (48/63), respectively, when treated with various antifungal agents and regimens. We conclude that C. parapsilosis sensu stricto and the closely related species C. orthopsilosis and C. metapsilosis were present in the vaginal samples of VVC patients. The symptoms and signs of VVC caused by C. parapsilosis are milder than those caused by C. albicans. The antifungal susceptibility and therapeutic efficacy in patients colonised by C. parapsilosis sensu lato were similar to those observed in C. albicans-colonised patients. 3. Genome scanning for interspecific differentiation between two closely related oak species [Quercus robur L. and Q. petraea (Matt.) Liebl.]. Science.gov (United States) Scotti-Saintagne, Caroline; Mariette, Stéphanie; Porth, Ilga; Goicoechea, Pablo G; Barreneche, Teresa; Bodénès, Catherine; Burg, Kornel; Kremer, Antoine 2004-11-01 Interspecific differentiation values (G(ST)) between two closely related oak species (Quercus petraea and Q. robur) were compiled across different studies with the aim to explore the distribution of differentiation at the genome level. The study was based on a total set of 389 markers (isozymes, AFLPs, SCARs, microsatellites, and SNPs) for which allelic frequencies were estimated in pairs of populations sampled throughout the sympatric distribution of the two species. The overall distribution of G(ST) values followed an L-shaped curve with most markers exhibiting low species differentiation (G(ST) 10% levels. Twelve percent of the loci exhibited significant G(ST) deviations to neutral expectations, suggesting that selection contributed to species divergence. Coding regions expressed higher differentiation than noncoding regions. Among the 389 markers, 158 could be mapped on the 12 linkage groups of the existing Q. robur genetic map. Outlier loci with large G(ST) values were distributed over 9 linkage groups. One cluster of three outlier loci was found within 0.51 cM; but significant autocorrelation of G(ST) was observed at distances <2 cM. The size and distribution of genomic regions involved in species divergence are discussed in reference to hitchhiking effects and disruptive selection. 4. A new isolation with migration model along complete genomes infers very different divergence processes among closely related great ape species. Directory of Open Access Journals (Sweden) Thomas Mailund Full Text Available We present a hidden Markov model (HMM for inferring gradual isolation between two populations during speciation, modelled as a time interval with restricted gene flow. The HMM describes the history of adjacent nucleotides in two genomic sequences, such that the nucleotides can be separated by recombination, can migrate between populations, or can coalesce at variable time points, all dependent on the parameters of the model, which are the effective population sizes, splitting times, recombination rate, and migration rate. We show by extensive simulations that the HMM can accurately infer all parameters except the recombination rate, which is biased downwards. Inference is robust to variation in the mutation rate and the recombination rate over the sequence and also robust to unknown phase of genomes unless they are very closely related. We provide a test for whether divergence is gradual or instantaneous, and we apply the model to three key divergence processes in great apes: (a the bonobo and common chimpanzee, (b the eastern and western gorilla, and (c the Sumatran and Bornean orang-utan. We find that the bonobo and chimpanzee appear to have undergone a clear split, whereas the divergence processes of the gorilla and orang-utan species occurred over several hundred thousands years with gene flow stopping quite recently. We also apply the model to the Homo/Pan speciation event and find that the most likely scenario involves an extended period of gene flow during speciation. 5. Frequent cytoplasmic exchanges between oak species that are not closely related: Quercus suber and Q. ilex in Morocco. Science.gov (United States) Belahbib, N; Pemonge, M H; Ouassou, A; Sbay, H; Kremer, A; Petit, R J 2001-08-01 Chloroplast (cp) and mitochondrial (mt) DNA variation were studied in 97 populations of cork oak (Quercus suber) in Morocco; in 31 of these populations, holm oak (Quercus ilex), a clearly distinct species, also occurred and was compared with Q. suber. Three cpDNA and one mtDNA primer pairs were used in the survey, each in combination with one restriction enzyme. Six haplotypes belonging to two very divergent lineages were detected; one lineage predominates in each species, and is probably ancestral, as inferred from comparisons with other oak species. In the mixed-species populations, cytoplasmic genomes were frequently shared across species, as indicated by an introgression ratio of 0.63. This index is a new measure of the propensity of species to share locally genetic markers, varying from zero (complete differentiation) to one (no differentiation). By contrast, more closely related deciduous oak species (Q. robur, Q. petraea and Q. pubescens) have introgression ratios varying from 0.82 to 0.97. The introgression events appear to have been more frequent in the direction Q. ilex (female) x Q. suber (male), a finding which seems attributable to the flowering phenology of these two species. This asymmetry may have favoured immigration of Q. suber beyond its main range, in regions already colonized by Q. ilex. There, rare hybridization and further introgression through long distance pollen flow have established populations that are morphologically indistinguishable from Q. suber but that have cytoplasmic genomes originating from the local Q. ilex populations. 6. Hybridization between alien species Rumex obtusifolius and closely related native vulnerable species R. longifolius in a mountain tourist destination Science.gov (United States) Takahashi, Koichi; Hanyu, Masaaki 2015-01-01 Alien species expand their distribution by transportation network development. Hybridization between alien species Rumex obtusifolius and closely related native vulnerable species R. longifolius was examined in a mountain tourist destination in central Japan. The three taxa were morphologically identified in the field. Stem height and leaf area were greater in R. longifolius than R. obtusifolius; hybrids were intermediate between the two Rumex species. R. longifolius and the hybrids grew mainly in wet land and the river tributary; R. obtusifolius grew mainly at the roadside and in meadows. Hybrid germination rates of pollen and seeds were much lower than for the two Rumex species. Clustering analysis showed the three taxa each formed a cluster. Most hybrids were F1 generation; the possibility was low of introgression into the two Rumex species by backcross. This study clarified that (1) hybridization occurred between R. obtusifolius and R. longifolius because they occurred together in a small area, but grew in different water habitat conditions, and (2) hybridization was mostly F1 generation because hybrid pollen and seed fertility was low. However, we need caution about introgression into R. longifolius by R. obtusifolius in this area because of the slight possibility of F2 generation and backcrosses. PMID:26354180 7. Hybridization between alien species Rumex obtusifolius and closely related native vulnerable species R. longifolius in a mountain tourist destination. Science.gov (United States) Takahashi, Koichi; Hanyu, Masaaki 2015-09-10 Alien species expand their distribution by transportation network development. Hybridization between alien species Rumex obtusifolius and closely related native vulnerable species R. longifolius was examined in a mountain tourist destination in central Japan. The three taxa were morphologically identified in the field. Stem height and leaf area were greater in R. longifolius than R. obtusifolius; hybrids were intermediate between the two Rumex species. R. longifolius and the hybrids grew mainly in wet land and the river tributary; R. obtusifolius grew mainly at the roadside and in meadows. Hybrid germination rates of pollen and seeds were much lower than for the two Rumex species. Clustering analysis showed the three taxa each formed a cluster. Most hybrids were F1 generation; the possibility was low of introgression into the two Rumex species by backcross. This study clarified that (1) hybridization occurred between R. obtusifolius and R. longifolius because they occurred together in a small area, but grew in different water habitat conditions, and (2) hybridization was mostly F1 generation because hybrid pollen and seed fertility was low. However, we need caution about introgression into R. longifolius by R. obtusifolius in this area because of the slight possibility of F2 generation and backcrosses. 8. The Dynamics of Genetic Interactions between Vibrio metoecus and Vibrio cholerae, Two Close Relatives Co-Occurring in the Environment. Science.gov (United States) Orata, Fabini D; Kirchberger, Paul C; Méheust, Raphaël; Barlow, E Jed; Tarr, Cheryl L; Boucher, Yan 2015-10-09 Vibrio metoecus is the closest relative of Vibrio cholerae, the causative agent of the potent diarrheal disease cholera. Although the pathogenic potential of this new species is yet to be studied in depth, it has been co-isolated with V. cholerae in coastal waters and found in clinical specimens in the United States. We used these two organisms to investigate the genetic interaction between closely related species in their natural environment. The genomes of 20 V. cholerae and 4 V. metoecus strains isolated from a brackish coastal pond on the US east coast, as well as 4 clinical V. metoecus strains were sequenced and compared with reference strains. Whole genome comparison shows 86-87% average nucleotide identity (ANI) in their core genes between the two species. On the other hand, the chromosomal integron, which occupies approximately 3% of their genomes, shows higher conservation in ANI between species than any other region of their genomes. The ANI of 93-94% observed in this region is not significantly greater within than between species, meaning that it does not follow species boundaries. Vibrio metoecus does not encode toxigenic V. cholerae major virulence factors, the cholera toxin and toxin-coregulated pilus. However, some of the pathogenicity islands found in pandemic V. cholerae were either present in the common ancestor it shares with V. metoecus, or acquired by clinical and environmental V. metoecus in partial fragments. The virulence factors of V. cholerae are therefore both more ancient and more widespread than previously believed. There is high interspecies recombination in the core genome, which has been detected in 24% of the single-copy core genes, including genes involved in pathogenicity. Vibrio metoecus was six times more often the recipient of DNA from V. cholerae as it was the donor, indicating a strong bias in the direction of gene transfer in the environment. © The Author(s) 2015. Published by Oxford University Press on behalf of the 9. Light response, oxidative stress management and nucleic acid stability in closely related Linderniaceae species differing in desiccation tolerance. Science.gov (United States) Dinakar, Challabathula; Bartels, Dorothea 2012-08-01 In the present study, three closely related Linderniaceae species which differ in their sensitivity to desiccation are compared in response to light and oxidative stress defence. Lindernia brevidens, a desiccation-tolerant plant, displayed intense purple pigmentation in leaves under long-day conditions in contrast to Craterostigma plantagineum (desiccation tolerant) and Lindernia subracemosa (desiccation sensitive). The intense pigmentation in leaves does not affect the desiccation tolerance behaviour but seems to be related to oxidative stress protection. Green leaves of short-day and purple leaves of long-day plants provided suitable material for comparing basic photosynthetic parameters. An increase in non-photochemical quenching in purple leaves appears to prevent photoinhibition. Treatment with methyl viologen decreased the photochemical activities in both long-day and short-day plants but long-day plants which accumulate anthocyanins maintained a higher non-photochemical quenching than short-day plants. No differences were seen in the expression of desiccation-induced proteins and proteins involved in carbohydrate metabolism in short-day and long-day grown plants, whereas differences were observed in the expression of transcripts encoding chloroplast-localised stress proteins and transcripts encoding antioxidant enzymes. While the expression of genes encoding antioxidant enzymes were either constitutive or up-regulated during desiccation in C. plantagineum, the expression was down-regulated in L. subracemosa. RNA expression analysis indicated degradation of mRNA during desiccation in L. subracemosa but not in desiccation tolerant species. These results indicate that a better oxidative stress management and mRNA stability are correlated with desiccation tolerance. 10. Relations and Utilities Operation monthly report, September, 1956 Energy Technology Data Exchange (ETDEWEB) Johnson, D.M. 1956-10-24 This document contains the September 1956 management and operations statistics of the Hanford Atomic Products Operation (HAPO) for their Relations and Utilities Operations. This is a monthly report. (BN) 11. 2013 Service Academy Gender Relations Focus Group; Overview Report Science.gov (United States) 2013-11-30 reporting unwanted sexual contact because they may be afraid people will think they’re homosexual when they’re not. There’s more social pressure...if you treat people like children they’ll act like children . If you treat people like adults, they’ll act like adults.” (Male) Sexting...close relationship. It’s just almost like a sponsor parent . A sponsor parent basically. I would definitely go to coach if I had any problems or 12. The Closed End Fund in the Vietnam Stock Market: An Examination of Market relation, Foreign Speculation, and Investor Sentiment OpenAIRE Nguyen, Thanh Tung, 2007-01-01 The Vietnam stock market is a young and small stock market, but it has attracted much attention from the financial public. The Vietnam stock market is also one of the most volatile markets with 2 “bubbles” and 2 recessions within 1 year. Closed end fund is considered as a measure of the sentiment of individual investors (De Long, Shleifer, Summers, and Waldmann (1990)). Closed end fund is one of the shares that we can measure its fundamentals through the Net Asset Value (NAV). The closed end ... 13. Neuropathological review of 138 cases genetically tested for X-linked hydrocephalus: evidence for closely related clinical entities of unknown molecular bases. Science.gov (United States) Adle-Biassette, Homa; Saugier-Veber, Pascale; Fallet-Bianco, Catherine; Delezoide, Anne-Lise; Razavi, Férecheté; Drouot, Nathalie; Bazin, Anne; Beaufrère, Anne-Marie; Bessières, Bettina; Blesson, Sophie; Bucourt, Martine; Carles, Dominique; Devisme, Louise; Dijoud, Frédérique; Fabre, Blandine; Fernandez, Carla; Gaillard, Dominique; Gonzales, Marie; Jossic, Frédérique; Joubert, Madeleine; Laurent, Nicole; Leroy, Brigitte; Loeuillet, Laurence; Loget, Philippe; Marcorelles, Pascale; Martinovic, Jelena; Perez, Marie-José; Satge, Daniel; Sinico, Martine; Tosi, Mario; Benichou, Jacques; Gressens, Pierre; Frebourg, Thierry; Laquerrière, Annie 2013-09-01 L1 syndrome results from mutations in the L1CAM gene located at Xq28. It encompasses a wide spectrum of diseases, X-linked hydrocephalus being the most severe phenotype detected in utero, and whose pathophysiology is incompletely understood. The aim of this study was to report detailed neuropathological data from patients with mutations, to delineate the neuropathological criteria required for L1CAM gene screening in foetuses by characterizing the sensitivity, specificity and positive predictive value of the cardinal signs, and to discuss the main differential diagnoses in non-mutated foetuses in order to delineate closely related conditions without L1CAM mutations. Neuropathological data from 138 cases referred to our genetic laboratory for screening of the L1CAM gene were retrospectively reviewed. Fifty-seven cases had deleterious L1CAM mutations. Of these, 100 % had hydrocephalus, 88 % adducted thumbs, 98 % pyramidal tract agenesis/hypoplasia, 90 % stenosis of the aqueduct of Sylvius and 68 % agenesis/hypoplasia of the corpus callosum. Two foetuses had L1CAM mutations of unknown significance. Seventy-nine cases had no L1CAM mutations; these were subdivided into four groups: (1) hydrocephalus sometimes associated with corpus callosum agenesis (44 %); (2) atresia/forking of the aqueduct of Sylvius/rhombencephalosynapsis spectrum (27 %); (3) syndromic hydrocephalus (9 %), and (4) phenocopies with no mutations in the L1CAM gene (20 %) and in whom family history strongly suggested an autosomal recessive mode of transmission. These data underline the existence of closely related clinical entities whose molecular bases are currently unknown. The identification of the causative genes would greatly improve our knowledge of the defective pathways involved in these cerebral malformations. 14. A study on some welfare-related parameters of hDAF transgenic pigs when compared with their conventional close relatives. Science.gov (United States) Martelli, G; Sardi, L; Stancampiano, L; Govoni, N; Zannoni, A; Nannoni, E; Forni, M; Bacci, M L 2014-05-01 Pigs are increasingly used in medical research as transgenic laboratory animals; however, little knowledge is presently available concerning their welfare assessment. The aim of the present study was to investigate some welfare-related parameters of transgenic pigs intended for xenotrasplantation (human decay-accelerating factor (hDAF)) when compared with their conventional (i.e. not transgenic) close relatives (full sibs and half sibs). A total of 14 Large White female transgenic pigs and 10 female non-transgenic (conventional) pigs from four litters were used. All pigs were from the same conventional boar, donor of the semen treated for sperm-mediated gene transfer. During the experiment, BW ranged from 50 to about 80 kg and pigs were weighed at the beginning and at the end of the experiment. Animals were subjected to a set of behavioural tests: a human approach test (HAT), a novel object test (NOT) and an open-door test (ODT). Food preferences were tested through the offer of different foods (banana, apple, carrot, cracker and lemon). During a 4-day period, pigs were diurnally videotaped to study the prevalence of the different behaviours and social interactions (aggressive and non-aggressive interactions). At the end of the trial, cortisol level had been assessed on bristles. No significant differences (P>0.05) were observed between hDAF transgenic and conventional pigs with respect to growth traits, reactivity towards unexpected situations (HAT, NOT, ODT), food preferences, main behavioural traits, social interactions and hair cortisol. 15. Perceived job demands relate to self-reported health complaints NARCIS (Netherlands) Roelen, C.A.M.; Schreuder, K.J.; Koopmans, P.C.; Groothoff, J.W. 2008-01-01 Background Illness and illness behaviour are important problems in the Dutch workforce. Illness has been associated with job demands, with high demands relating to poorer health. It has not been reported whether subjective health complaints relate to job demands. Aims To investigate whether perceive 16. The changes in various hydroxyproline fractions in aortic tissue of rabbits are closely related to the progression of atherosclerosis Directory of Open Access Journals (Sweden) Alhomida AS 2010-03-01 Full Text Available Abstract Background The most important function of collagen and elastin is to induce several mechanical parameters which are known to play a dominant role in governing mechanical properties of the blood vessels. The aortic tissue of rabbit is one of the important sources of collagen and elastin. The effects of high fat diet (HFD on the hydroxyproline (Hyp fractions in serum and aortic tissues of rabbits and collagen content in the aortic tissues of rabbits have not been documented before. The present study was undertaken to investigate the changes in Hyp fractions in serum and aortic tissues of rabbits and collagen content in the aortic tissues of rabbits during the progression of atherosclerosis. The atherosclerotic model used in this study was the New Zealand white rabbit (male; 12 weeks old. Twenty five rabbits were individually caged, and divided into control group (NOR; n = 10 and HFD group (CHO; n = 15. The control group was fed (100 g/day of normal (NOR diet for a period of 15 weeks. The HFD group was fed normal diet supplemented with 1.0% cholesterol plus 1.0% olive oil (100 g/day for the same period of time. Results We found that the TC, LDLC, and TG (mg/dl were significantly (p Conclusions These results suggest that percentage decrease in various Hyp fractions in aortic tissue of HFD rabbits are closely related to percentage decrease of collagen content in aortic tissues of HFD rabbits. These results also suggest that it may be possible to use the changes in various Hyp fractions in aortic tissues of rabbits as an important risk factor during the progression of atherosclerosis. 17. Choose Your Weaponry: Selective Storage of a Single Toxic Compound, Latrunculin A, by Closely Related Nudibranch Molluscs. Directory of Open Access Journals (Sweden) Karen L Cheney Full Text Available Natural products play an invaluable role as a starting point in the drug discovery process, and plants and animals use many interesting biologically active natural products as a chemical defense mechanism against predators. Among marine organisms, many nudibranch gastropods are known to derive defensive metabolites from the sponges they eat. Here we investigated the putative sequestration of the toxic compound latrunculin A--a 16-membered macrolide that prevents actin polymerization within cellular processes--which has been identified from sponge sources, by five closely related nudibranch molluscs of the genus Chromodoris. Only latrunculin A was present in the rim of the mantle of these species, where storage reservoirs containing secondary metabolites are located, whilst a variety of secondary metabolites were found in their viscera. The species studied thus selectively accumulate latrunculin A in the part of the mantle that is more exposed to potential predators. This study also demonstrates that latrunculin-containing sponges are not their sole food source. Latrunculin A was found to be several times more potent than other compounds present in these species of nudibranchs when tested by in vitro and in vivo toxicity assays. Anti-feedant assays also indicated that latrunculin A was unpalatable to rock pool shrimps, in a dose-dependent manner. These findings led us to propose that this group of nudibranchs has evolved means both to protect themselves from the toxicity of latrunculin A, and to accumulate this compound in the mantle rim for defensive purposes. The precise mechanism by which the nudibranchs sequester such a potent compound from sponges without disrupting their own key physiological processes is unclear, but this work paves the way for future studies in this direction. Finally, the possible occurrence of both visual and chemosensory Müllerian mimicry in the studied species is discussed. 18. Counteraction of tetherin antiviral activity by two closely related SIVs differing by the presence of a Vpu gene. Directory of Open Access Journals (Sweden) Kristina Nikovics Full Text Available In different primate lentiviruses, three proteins (Vpu, Env and Nef have been shown to have anti-tetherin activities. SIVden is a primate lentivirus harbored by a Cercopithecus denti (C. denti whose genome code for a Vpu gene. We have compared the activity of HIV-1 Vpu and of SIVden Vpu on tetherin proteins from humans, from C. denti and from Cercopithecus neglectus (C. neglectus, a monkey species that is naturally infected by SIVdeb, a virus closely related to SIVden but which does not encode a Vpu protein. Here, we demonstrate that SIVden Vpu, is active against C. denti tetherin, but not against human tetherin. Interestingly, C. neglectus tetherin was more sensitive to SIVden Vpu than to HIV-1 Vpu. We also identify residues in the tetherin transmembrane domains that are responsible for the species-specific Vpu effect. Simultaneous mutation (P40L and T45I of human tetherin conferred sensitivity to SIVden Vpu, while abolishing its sensitivity to HIV-1 Vpu. We next analyzed the anti-tetherin activity of the Nef proteins from HIV-1, SIVden and SIVdeb. All three Nef proteins were unable to rescue virus release in the presence of human or C. denti tetherin. Conversely, SIVdeb Nef enhanced virus release in the presence of C. neglectus tetherin, suggesting that SIVdeb relies on Nef in its natural host. Finally, while HIV-1 Vpu not only removed human tetherin from the cell surface but also directed it for degradation, SIVden Vpu only induced the redistribution of both C. denti and C. neglectus tetherins, resulting in a predominantly perinuclear localization. 19. Anthracnose disease of centipedegrass turf caused by Colletotrichum eremochloae, a new fungal species closely related to Colletotrichum sublineola. Science.gov (United States) Crouch, Jo Anne; Tomaso-Peterson, Maria 2012-01-01 Colletotrichum is a cosmopolitan, anamorphic fungal genus responsible for anthracnose disease in hundreds of plant species worldwide, including members of the Poaceae. Anthracnose disease of the widely planted, non-native, warm-season lawn grass, Eremochloae ophiuroides (centipedegrass), is commonly encountered in the southern United States, but the causal agent has never been identified. We use DNA sequence data from modern cultures and archival fungarium specimens in this study to determine the identity of the fungus responsible for centipedegrass anthracnose disease and provide experimental confirmation of pathogenicity. C. eremochloae sp. nov., a pathogen of centipedegrass, is proposed based on phylogenetic evidence from four sequence markers (Apn2, Apn2/ Mat1, Sod2, ITS). C. eremochloae isolates from centipedegrass shared common morphology and phenotype with C. sublineola, a destructive pathogen of cultivated sorghum and Johnsongrass weeds (Sorghum halepense, S. vulgaris). Molecular phylogenetic analysis identified C. eremochloae and C. sublineola as closely related sister taxa, but genealogical concordance supported their distinction as unique phylogenetic species. Fixed nucleotide differences between C. eremochloae and C. sublineola were observed from collections of these fungi spanning 105 y, including the 1904 lectotype specimen of C. sublineola. C. eremochloae was identified from a fungarium specimen of centipedegrass intercepted at a USA port from a 1923 Chinese shipment; the multilocus sequence from this specimen was identical to modern samples of the fungus. Thus, it appears that the fungus might have migrated to the USA around the same time that centipedegrass first was introduced to the USA in 1916 from China, where the grass is indigenous. The new species C. eremochloae is described and illustrated, along with a description and discussion of C. sublineola based on the lectotype and newly designated epitype. 20. Identification of chloroplast genome loci suitable for high-resolution phylogeographic studies of Colocasia esculenta (L.) Schott (Araceae) and closely related taxa. Science.gov (United States) Ahmed, Ibrar; Matthews, Peter J; Biggs, Patrick J; Naeem, Muhammad; McLenachan, Patricia A; Lockhart, Peter J 2013-09-01 Recently, we reported the chloroplast genome-wide association of oligonucleotide repeats, indels and nucleotide substitutions in aroid chloroplast genomes. We hypothesized that the distribution of oligonucleotide repeat sequences in a single representative genome can be used to identify mutational hotspots and loci suitable for population genetic, phylogenetic and phylogeographic studies. Using information on the location of oligonucleotide repeats in the chloroplast genome of taro (Colocasia esculenta), we designed 30 primer pairs to amplify and sequence polymorphic loci. The primers have been tested in a range of intra-specific to intergeneric comparisons, including ten taro samples (Colocasia esculenta) from diverse geographical locations, four other Colocasia species (C. affinis, C. fallax, C. formosana, C. gigantea) and three other aroid genera (represented by Remusatia vivipara, Alocasia brisbanensis and Amorphophallus konjac). Multiple sequence alignments for the intra-specific comparison revealed nucleotide substitutions (point mutations) at all 30 loci and microsatellite polymorphisms at 14 loci. The primer pairs reported here reveal levels of genetic variation suitable for high-resolution phylogeographic and evolutionary studies of taro and other closely related aroids. Our results confirm that information on repeat distribution can be used to identify loci suitable for such studies, and we expect that this approach can be used in other plant groups. 1. Standardized subsets of the HGDP-CEPH Human Genome Diversity Cell Line Panel, accounting for atypical and duplicated samples and pairs of close relatives. Science.gov (United States) Rosenberg, Noah A 2006-11-01 The HGDP-CEPH Human Genome Diversity Cell Line Panel is a widely-used resource for studies of human genetic variation. Here, pairs of close relatives that have been included in the panel are identified. Together with information on atypical and duplicated samples, the inferred relative pairs suggest standardized subsets of the panel for use in future population-genetic studies. 2. Asymmetric female preferences for courtship pheromones in two closely-related newt species, the smooth newt (Lissotriton vulgaris) and the Carpathian newt (L. montandoni) (Salamandridae). Science.gov (United States) Osikowski, Artur 2012-06-01 The smooth (Lissotriton vulgaris) and Carpathian (L. montandoni) newts are sister species. These are separated by a moderate genetic distance, but exhibit striking morphological differences, especially in male epigamic traits. In the areas where they co-occur, they readily mate with each other and produce viable hybrids. However, a high level of pre-zygotic isolation with an unknown behavioral basis has been reported. The complex courtship of newts consists of at least three types of modality: chemical, visual, and tactile. The relative significance of these in mate choice is unclear, but it is commonly accepted that pheromones are an important communication channel. The goal of this study was to determine whether the females of L. vulgaris and L. montandoni exhibit preferences for conspecific extracts from the pheromone-producing abdominal (dorsal) glands. Females of both species spent more time in proximity to the source of the abdominal gland extracts of their own species when a liver extract was presented as an alternative. In a second trial, females were simultaneously confronted with conspecific and heterospecific abdominal gland extracts. Asymmetric preferences were found. Lissotriton vulgaris females were not selective, whereas L. montandoni females preferred the conspecific abdominal gland extract. This finding is consistent with the results of earlier experiments on mate choice in these species. The results strongly indicate that pheromones play a crucial role in courtship and species recognition in this pair of closely related, hybridizing species. 3. The genomes of closely related Pantoea ananatis maize seed endophytes having different effects on the host plant differ in secretion system genes and mobile genetic elements. Science.gov (United States) Sheibani-Tezerji, Raheleh; Naveed, Muhammad; Jehl, Marc-André; Sessitsch, Angela; Rattei, Thomas; Mitter, Birgit 2015-01-01 The seed as a habitat for microorganisms is as yet under-explored and has quite distinct characteristics as compared to other vegetative plant tissues. In this study, we investigated three closely related P. ananatis strains (named S6, S7, and S8), which were isolated from maize seeds of healthy plants. Plant inoculation experiments revealed that each of these strains exhibited a different phenotype ranging from weak pathogenic (S7), commensal (S8), to a beneficial, growth-promoting effect (S6) in maize. We performed a comparative genomics analysis in order to find genetic determinants responsible for the differences observed. Recent studies provided exciting insight into the genetic drivers of niche adaption and functional diversification of the genus Pantoea. However, we report here for the first time on the analysis of P. ananatis strains colonizing the same ecological niche but showing distinct interaction strategies with the host plant. Our comparative analysis revealed that genomes of these three strains are highly similar. However, genomic differences in genes encoding protein secretion systems and putative effectors, and transposase/integrases/phage related genes could be observed. 4. The genomes of closely related Pantoea ananatis maize seed endophytes having different effects on the host plant differ in secretion system genes and mobile genetic elements Directory of Open Access Journals (Sweden) Raheleh eSheibani-Tezerji 2015-05-01 Full Text Available The seed as a habitat for microorganisms is as yet under-explored and has quite distinct characteristics as compared to other vegetative plant tissues. In this study, we investigated three closely related P. ananatis strains (named S6, S7 and S8, which were isolated from maize seeds of healthy plants. Plant inoculation experiments revealed that each of these strains exhibited a different phenotype ranging from weak pathogenic (S7, commensal (S8, to a beneficial, growth-promoting effect (S6 in maize. We performed a comparative genomics analysis in order to find genetic determinants responsible for the differences observed. Recent studies provided exciting insight into the genetic drivers of niche adaption and functional diversification of the genus Pantoea. However, we report here for the first time on the analysis of P. ananatis strains colonizing the same ecological niche but showing distinct interaction strategies with the host plant. Our comparative analysis revealed that genomes of these three strains are highly similar. However, genomic differences in genes encoding protein secretion systems and putative effectors, and transposase/integrases/phage related genes could be observed. 5. Relation of completeness of reporting of health research to journals’ endorsement of reporting guidelines: systematic review Science.gov (United States) Stevens, Adrienne; Shamseer, Larissa; Weinstein, Erica; Yazdi, Fatemeh; Turner, Lucy; Thielman, Justin; Altman, Douglas G; Hirst, Allison; Hoey, John; Palepu, Anita; Schulz, Kenneth F 2014-01-01 Objective To assess whether the completeness of reporting of health research is related to journals’ endorsement of reporting guidelines. Design Systematic review. Data sources Reporting guidelines from a published systematic review and the EQUATOR Network (October 2011). Studies assessing the completeness of reporting by using an included reporting guideline (termed “evaluations”) (1990 to October 2011; addendum searches in January 2012) from searches of either Medline, Embase, and the Cochrane Methodology Register or Scopus, depending on reporting guideline name. Study selection English language reporting guidelines that provided explicit guidance for reporting, described the guidance development process, and indicated use of a consensus development process were included. The CONSORT statement was excluded, as evaluations of adherence to CONSORT had previously been reviewed. English or French language evaluations of included reporting guidelines were eligible if they assessed the completeness of reporting of studies as a primary intent and those included studies enabled the comparisons of interest (that is, after versus before journal endorsement and/or endorsing versus non-endorsing journals). Data extraction Potentially eligible evaluations of included guidelines were screened initially by title and abstract and then as full text reports. If eligibility was unclear, authors of evaluations were contacted; journals’ websites were consulted for endorsement information where needed. The completeness of reporting of reporting guidelines was analyzed in relation to endorsement by item and, where consistent with the authors’ analysis, a mean summed score. Results 101 reporting guidelines were included. Of 15 249 records retrieved from the search for evaluations, 26 evaluations that assessed completeness of reporting in relation to endorsement for nine reporting guidelines were identified. Of those, 13 evaluations assessing seven reporting guidelines (BMJ 6. A bridge between a lonely soul and the surrounding world: A study on existential consequences of being closely related to a person with aphasia. Science.gov (United States) Nyström, Maria 2011-01-01 This study illuminates existential consequences of being closely related to a person suffering from aphasia. Seventeen close relatives were interviewed and their narratives were interpreted with inspiration from Ricoeur, Levinas, Husserl, Winnicot, and Maurice Merleau-Ponty. The emerging interpretations resulted in four themes that illuminate a life characterized by lost freedom, staying, a new form of relationship, and growing strong together with others. An overarching theme suggests that a life together with an aphasic person means being used as a bridge between the aphasic person and the surrounding world. Moreover, it illuminates that a close relative to a person with aphasia is a person who does not leave, despite a heavy burden of lonely responsibility. It is concluded that community services need to fulfill their responsibility of providing support to informal caregivers as suggested by the Swedish lawmakers. 7. A bridge between a lonely soul and the surrounding world: A study on existential consequences of being closely related to a person with aphasia Science.gov (United States) Nyström, Maria 2011-01-01 This study illuminates existential consequences of being closely related to a person suffering from aphasia. Seventeen close relatives were interviewed and their narratives were interpreted with inspiration from Ricoeur, Levinas, Husserl, Winnicot, and Maurice Merleau-Ponty. The emerging interpretations resulted in four themes that illuminate a life characterized by lost freedom, staying, a new form of relationship, and growing strong together with others. An overarching theme suggests that a life together with an aphasic person means being used as a bridge between the aphasic person and the surrounding world. Moreover, it illuminates that a close relative to a person with aphasia is a person who does not leave, despite a heavy burden of lonely responsibility. It is concluded that community services need to fulfill their responsibility of providing support to informal caregivers as suggested by the Swedish lawmakers. PMID:22114621 8. A bridge between a lonely soul and the surrounding world: A study on existential consequences of being closely related to a person with aphasia Directory of Open Access Journals (Sweden) Maria Nyström 2011-11-01 Full Text Available This study illuminates existential consequences of being closely related to a person suffering from aphasia. Seventeen close relatives were interviewed and their narratives were interpreted with inspiration from Ricoeur, Levinas, Husserl, Winnicot, and Maurice Merleau-Ponty. The emerging interpretations resulted in four themes that illuminate a life characterized by lost freedom, staying, a new form of relationship, and growing strong together with others. An overarching theme suggests that a life together with an aphasic person means being used as a bridge between the aphasic person and the surrounding world. Moreover, it illuminates that a close relative to a person with aphasia is a person who does not leave, despite a heavy burden of lonely responsibility. It is concluded that community services need to fulfill their responsibility of providing support to informal caregivers as suggested by the Swedish lawmakers. 9. The Relative Effects upon High School Students of Inductive and Programmed Instruction in the Close Reading of Poetry. Science.gov (United States) Weiss, James David To examine the effects of inductive and programmed instruction in the close reading of poetry, four control classes of urban 11th graders receiving inductive instruction in poetry were compared with four equivalent experimental classes using programmed textbooks. Both groups were given free response tests on two poems: one poem, included in… 10. Not equal in the face of habitat change: closely related fishes differ in their ability to use predation-related information in degraded coral. Science.gov (United States) Ferrari, Maud C O; McCormick, Mark I; Allan, Bridie J M; Chivers, Douglas P 2017-04-12 Coral reefs are biodiversity hotpots that are under significant threat due to the degradation and death of hard corals. When obligate coral-dwelling species die, the remaining species must either move or adjust to the altered conditions. Our goal was to investigate the effect of coral degradation on the ability of coral reef fishes to assess their risk of predation using alarm cues from injured conspecifics. Here, we tested the ability of six closely related species of juvenile damselfish (Pomacentridae) to respond to risk cues in both live coral or dead-degraded coral environments. Of those six species, two are exclusively associated with live coral habitats, two are found mostly on dead-degraded coral rubble, while the last two are found in both habitat types. We found that the two live coral associates failed to respond appropriately to the cues in water from degraded habitats. In contrast, the cue response of the two rubble associates was unaffected in the same degraded habitat. Interestingly, we observed a mixed response from the species found in both habitat types, with one species displaying an appropriate cue response while the other did not. Our second experiment suggested that the lack of responses stemmed from deactivation of the alarm cues, rather than the inability of the species to smell. Habitat preference (live coral versus dead coral associates) and phylogeny are good candidates for future work aimed at predicting which species are affected by coral degradation. Our results point towards a surprising level of variation in the ability of congeneric species to fare in altered habitats and hence underscores the difficulty of predicting community change in degraded habitats. © 2017 The Authors. 11. When the presence of creative coworkers is related to creativity: role of supervisor close monitoring, developmental feedback, and creative personality. Science.gov (United States) Zhou, Jing 2003-06-01 Study 1 was conducted to examine the contribution of the joint condition of supervisor close monitoring and the presence of creative coworkers to employees' creativity. In addition to replicating Study 1's results, Study 2 examined (a) the joint condition of supervisor developmental feedback and presence of creative coworkers and (b) whether creative personality moderated the contributions of the 2 joint conditions. Converging results from the 2 field studies demonstrated that when creative coworkers were present, the less supervisors engaged in close monitoring, the more employees exhibited creativity. Study 2 also found that the contribution of this joint condition was stronger for employees with less creative personalities and that when creative coworkers were present, the more supervisors provided developmental feedback, the more employees exhibited creativity. 12. BAF Complex Is Closely Related to and Interacts with NF1/CTF and RNA Polymerase Ⅱ in Gene Transcriptional Activation Institute of Scientific and Technical Information of China (English) Li-Hui ZHAO; Xue-Qing BA; Xiao-Guang WANG; Xiao-Juan ZHU; Li WANG; Xian-Lu ZENG 2005-01-01 Brg- or hBrm-associated factor (BAF) complexes, a chromatin-remodeling complex family of mammalian cells, facilitate transcriptional activity by remodeling nucleosome structure. Brg 1 is the core subunit of Brg-associated factor complexes. In the present study, we investigated the spatial relationship between Brg1 and nuclear factor 1 (NF1/CTF) and RNA polymerase Ⅱ (RNAP Ⅱ) upon gene transcriptional activation in vivo by employing immuno-gold labeling. The data showed that Brg1 was closely co-localized with NF1/CTF and RNAP Ⅱ in HeLa cells. Moreover, the co-immunoprecipitation assay further revealed that Brg1 can be isolated together with NF1/CTF and RNAP Ⅱ in the ConA-stimulated, but not the resting,T lymphocyte. The combined results suggested that BAF complexes can interact with NF1/CTF and RNAP Ⅱ, and this interaction is closely dependent on the activation of gene transcription. 13. Related giant viruses in distant locations and different habitats: Acanthamoeba polyphaga moumouvirus represents a third lineage of the Mimiviridae that is close to the megavirus lineage. Science.gov (United States) Yoosuf, Niyaz; Yutin, Natalya; Colson, Philippe; Shabalina, Svetlana A; Pagnier, Isabelle; Robert, Catherine; Azza, Said; Klose, Thomas; Wong, Jimson; Rossmann, Michael G; La Scola, Bernard; Raoult, Didier; Koonin, Eugene V 2012-01-01 The 1,021,348 base pair genome sequence of the Acanthamoeba polyphaga moumouvirus, a new member of the Mimiviridae family infecting Acanthamoeba polyphaga, is reported. The moumouvirus represents a third lineage beside mimivirus and megavirus. Thereby, it is a new member of the recently proposed Megavirales order. This giant virus was isolated from a cooling tower water in southeastern France but is most closely related to Megavirus chiliensis, which was isolated from ocean water off the coast of Chile. The moumouvirus is predicted to encode 930 proteins, of which 879 have detectable homologs. Among these predicted proteins, for 702 the closest homolog was detected in Megavirus chiliensis, with the median amino acid sequence identity of 62%. The evolutionary affinity of moumouvirus and megavirus was further supported by phylogenetic tree analysis of conserved genes. The moumouvirus and megavirus genomes share near perfect orthologous gene collinearity in the central part of the genome, with the variations concentrated in the terminal regions. In addition, genomic comparisons of the Mimiviridae reveal substantial gene loss in the moumouvirus lineage. The majority of the remaining moumouvirus proteins are most similar to homologs from other Mimiviridae members, and for 27 genes the closest homolog was found in bacteria. Phylogenetic analysis of these genes supported gene acquisition from diverse bacteria after the separation of the moumouvirus and megavirus lineages. Comparative genome analysis of the three lineages of the Mimiviridae revealed significant mobility of Group I self-splicing introns, with the highest intron content observed in the moumouvirus genome. 14. Mimetic Muscles in a Despotic Macaque (Macaca mulatta) Differ from Those in a Closely Related Tolerant Macaque (M. nigra). Science.gov (United States) Burrows, Anne M; Waller, Bridget M; Micheletta, Jérôme 2016-10-01 Facial displays (or expressions) are a primary means of visual communication among conspecifics in many mammalian orders. Macaques are an ideal model among primates for investigating the co-evolution of facial musculature, facial displays, and social group size/behavior under the umbrella of "ecomorphology". While all macaque species share some social behaviors, dietary, and ecological parameters, they display a range of social dominance styles from despotic to tolerant. A previous study found a larger repertoire of facial displays in tolerant macaque species relative to despotic species. The present study was designed to further explore this finding by comparing the gross morphological features of mimetic muscles between the Sulawesi macaque (Macaca nigra), a tolerant species, and the rhesus macaque (M. mulatta), a despotic species. Five adult M. nigra heads were dissected and mimetic musculature was compared to those from M. mulatta. Results showed that there was general similarity in muscle presence/absence between the species as well as muscle form except for musculature around the external ear. M. mulatta had more musculature around the external ear than M. nigra. In addition, M. nigra lacked a zygomaticus minor while M. mulatta is reported to have one. These morphological differences match behavioral observations documenting a limited range of ear movements used by M. nigra during facial displays. Future studies focusing on a wider phylogenetic range of macaques with varying dominance styles may further elucidate the roles of phylogeny, ecology, and social variables in the evolution of mimetic muscles within Macaca Anat Rec, 299:1317-1324, 2016. © 2016 Wiley Periodicals, Inc. 15. Phytophthora megakarya and P. palmivora, closely related causal agents of cacao black pod rot, underwent increases in genome sizes and gene numbers by different mechanisms Science.gov (United States) Phytophthora megakarya (Pmeg) and P. palmivora (Ppal) are closely related species causing black pod rot of cacao. While Ppal is a cosmopolitan plant pathogen, cacao is the only known host of importance for Pmeg. Pmeg is more virulent on cacao than Ppal. Therefore, we have sequenced both the Pmeg and... 16. A Holistic Approach to Taxonomic Evaluation of Two Closely Related Endangered Freshwater Mussel Species, the Oyster Mussel (Epioblasma capsaeformis) and Tan Riffleshell (Epioblasma florentina walkeri) (Bivalvia: Unionidae) OpenAIRE Jones, Jess Walter 2004-01-01 A Holistic Approach to Taxonomic Evaluation of Two Closely Related Endangered Freshwater Mussel Species, the Oyster Mussel (Epioblasma capsaeformis) and Tan Riffleshell (Epioblasma florentina walkeri) (Bivalvia: Unionidae) by Jess W. Jones Richard J. Neves, Chairperson Fisheries and Wildlife Sciences (ABSTRACT) Primers for 10 polymorphic DNA microsatellite loci were developed and characterized for the endangered oyster mussel Epioblasma capsaeformis from the Clinch River, TN. Microsatellite... 17. Aspergillus waksmanii sp. nov. and Aspergillus marvanovae sp. nov., two closely related species in section Fumigati DEFF Research Database (Denmark) Hubka, Vit; Peterson, Stephen W.; Frisvad, Jens Christian 2013-01-01 Two new and phylogenetically closely related species in Aspergillus section Fumigati are described and illustrated. Homothallic Aspergillus waksmanii sp. nov. was isolated from New Jersey soil (USA) and is represented by the ex-type isolate NRRL 179T (=CCF 4266T=Thom 4138.HS2T=IBT 31900T). Asperg... 18. Relative humidity effects on water vapour fluxes measured with closed-path eddy-covariance systems with short sampling lines DEFF Research Database (Denmark) Fratini, Gerardo; Ibrom, Andreas; Arriga, Nicola 2012-01-01 and correction method proposed here is deemed applicable to closed-path systems featuring a broad range of sampling lines, and indeed applicable also to passive gases as a special case. The methods described in this paper are incorporated, as processing options, in the free and open-source eddy......, a composite of two existing approaches, for correcting eddy-covariance fluxes. By means of a comparison with parallel open-path measurements, we show that the mixed method leads to an improved estimation of latent heat fluxes, with respect to the method described by Ibrom et al. (2007). The quantification......-covariance software packages ECO2S and EddyPro.... 19. A minimally invasive technique for closing an iatrogenic subclavian artery cannulation using the Angio-Seal closure device: two case reports Directory of Open Access Journals (Sweden) Szkup Peter L 2012-03-01 Full Text Available Abstract Introduction In the two cases described here, the subclavian artery was inadvertently cannulated during unsuccessful access to the internal jugular vein. The puncture was successfully closed using a closure device based on a collagen plug (Angio-Seal, St Jude Medical, St Paul, MN, USA. This technique is relatively simple and inexpensive. It can provide clinicians, such as intensive care physicians and anesthesiologists, with a safe and straightforward alternative to major surgery and can be a life-saving procedure. Case presentation In the first case, an anesthetist attempted ultrasound-guided access to the right internal jugular vein during the preoperative preparation of a 66-year-old Caucasian man. A 7-French (Fr triple-lumen catheter was inadvertently placed into his arterial system. In the second case, an emergency physician inadvertently placed a 7-Fr catheter into the subclavian artery of a 77-year-old Caucasian woman whilst attempting access to her right internal jugular vein. Both arterial punctures were successfully closed by means of a percutaneous closure device (Angio-Seal. No complications were observed. Conclusions Inadvertent subclavian arterial puncture can be successfully managed with no adverse clinical sequelae by using a percutaneous vascular closure device. This minimally invasive technique may be an option for patients with non-compressible arterial punctures. This report demonstrates two practical points that may help clinicians in decision-making during daily practice. First, it provides a practical solution to a well-known vascular complication. Second, it emphasizes a role for proper vascular ultrasound training for the non-radiologist. 20. Bisphosphonate related osteonecrosis of the jaws: report of two cases Energy Technology Data Exchange (ETDEWEB) Han, Jin Woo [College of Dentistry, Gangneung Wonju National University, Gangneung (Korea, Republic of) 2011-09-15 Bisphosphonates are compounds used to treat osteoporosis and malignant bone metastasis. Despite the benefits related to the use of these medications, osteonecrosis of the jaws is a significant complication in a subset of patients receiving these drugs. This complication occurs either spontaneously or after a simple dento-alveolar surgery. Recently there were two patients who showed the features of bisphosphonate related osteonecrosis of the jaws (BRONJ) in Gangneung Wonju National University Dental Hospital. The patients revealed the clinical and radiological features of classical osteomyelitis. This report presents two cases of BRONJ which were examined by plain radiography and computed tomography. 1. [Boxing-related cranial injury in children: a case report]. Science.gov (United States) Timsit, S; Rougeau, T; Grevent, D; Chéron, G 2012-11-01 No pediatric recommendations exist in France on the exercise of boxing by children and adolescents despite the risk of traumatic injury, sometimes serious. We report the case of a 15-year-old boy who participated in amateur boxing and had a subdural hematoma. Brain injuries and concussions are frequent and multiple. Severity is not always correlated with the intensity of the blows. There are age-related features. Several international medical organizations oppose boxing for children and adolescents. 2. Post-Closure Report for Closed Resource Conservation and Recovery Act Corrective Action Units, Nevada National Security Site, Nevada for fiscal year 2013 (October 2012 - September 2013) Energy Technology Data Exchange (ETDEWEB) None, 2014-01-31 This report serves as the combined annual report for post-closure activities for the following closed Corrective Action Units (CAUs): CAU 90, Area 2 Bitcutter Containment; CAU 91, Area 3 U-3fi Injection Well; CAU 92, Area 6 Decon Pond Facility; CAU 110, Area 3 WMD U-3ax/bl Crater; CAU 111, Area 5 WMD Retired Mixed Waste Pits; and, CAU 112, Area 23 Hazardous Waste Trenches. 3. Mass spectrometry of planetary exospheres at high relative velocity: direct comparison of open- and closed-source measurements Science.gov (United States) Meyer, Stefan; Tulej, Marek; Wurz, Peter 2017-01-01 The exploration of habitable environments on or inside icy moons around the gas giants in the solar system is of major interest in upcoming planetary missions. Exactly this theme is addressed by the JUpiter ICy moons Explorer (JUICE) mission of ESA, which will characterise Ganymede, Europa and Callisto as planetary objects and potential habitats. We developed a prototype of the Neutral Gas and Ion Mass spectrometer (NIM) of the Particle Environment Package (PEP) for the JUICE mission intended for composition measurements of neutral gas and thermal plasma. NIM/PEP will be used to measure the chemical composition of the exospheres of the icy Jovian moons. Besides direct ion measurement, the NIM instrument is able to measure the inflowing neutral gas in two different modes: in neutral mode, where the gas enters directly the ion source (open source), and in thermal mode, where the gas gets thermally accommodated to the wall temperature by several collisions inside an equilibrium sphere, called antechamber, before entering the ion source (closed source). We performed measurements with the prototype NIM using a neutral gas beam of 1 up to 4.5 km s-1 velocity in the neutral and thermal mode. The current trajectory of JUICE foresees a flyby velocity of 4 km s-1 at Europa; other flybys are in the range of 1 up to 7 km s-1 and orbital velocity in Ganymede orbits is around 2 km s-1. Different species are used for the gas beam, such as noble gases Ne, Ar, Kr as well as molecules like H2, methane, ethane, propane and more complex ones. The NIM prototype was successfully tested under realistic JUICE mission conditions. In addition, we find that the antechamber (closed source) behaves as expected with predictable density enhancement over the specified mass range and within the JUICE mission phase velocities. Furthermore, with the open source and the closed source we measure almost the same composition for noble gases, as well as for molecules, indicating no additional 4. Critical experiments supporting close proximity water storage of power reactor fuel. Technical progress report, October 1, 1977-December 31, 1977 Energy Technology Data Exchange (ETDEWEB) Baldwin, M.N.; Hoovler, G.S. 1978-03-01 Experiments are being conducted on critical configurations of clusters of fuel rods, mocking up LWR-type fuel elements in close proximity water storage. Spacings between fuel clusters and the intervening material are being varied to provide a variety of benchmark loadings. (DLC) 5. Report on the Development of a Close Range Photogrammetry (CRP) Educational Technician Program (Museum and Archive Use). Science.gov (United States) Kobelin, Joel A close range photogrammetry (CRP) technician training program was developed at Miami-Dade Community College and used to teach the technology to 16 students. Although the results of the study show that it is possible to teach CRP in a two-year program, the technology is too new in the United States to support a sustaining educational program. The… 6. The enigmatic monotypic crab plover Dromas ardeola is closely related to pratincoles and coursers (Aves, Charadriiformes, Glareolidae Directory of Open Access Journals (Sweden) Sergio L. Pereira 2010-01-01 Full Text Available The phylogenetic placement of the monotypic crab plover Dromas ardeola (Aves, Charadriiformes remains controversial. Phylogenetic analysis of anatomical and behavioral traits using phenetic and cladistic methods of tree inference have resulted in conflicting tree topologies, suggesting a close association of Dromas to members of different suborders and lineages within Charadriiformes. Here, we revisited the issue by applying Bayesian and parsimony methods of tree inference to 2,012 anatomical and 5,183 molecular characters to a set of 22 shorebird genera (including Turnix. Our results suggest that Bayesian analysis of anatomical characters does not resolve the phylogenetic relationship of shorebirds with strong statistical support. In contrast, Bayesian and parsimony tree inference from molecular data provided much stronger support for the phylogenetic relationships within shorebirds, and support a sister relationship of Dromas to Glareolidae (pratincoles and coursers, in agreement with previously published DNA-DNA hybridization studies. 7. a new record of acanthodactylus cantoris (sauria: lacertidae) and its comparison with closely related a.blanfordi in southeastern iran Institute of Scientific and Technical Information of China (English) 2012-01-01 a new record ofacanthodactylus cantoris from sistan and baluchistan in southeastern iran is presented in this paper,and this lizard is found occurring in the coastal area of the persian gulf from govater to chabahar.this species is mainly sympatric with a.blanfordi,and their habits and habitats support their close relationship within the cantoris group.in total,29 specimens ofa.cantoris (n =12) and a.blanfordi (n =17) were compared morphologically using statistical methods.the occurrence of a.cantoris in iran has been questioned for a long time by different herpetologists,and the distribution,ecology and taxonomy of this newly recorded species were investigated and provided in this paper.an updated identification key for the species of acanthodactylus in iran is given. 8. Closeness and distance in the nurse-patient relation. The relevance of Edith Stein's concept of empathy. Science.gov (United States) Määttä, Sylvia M 2006-01-01 This paper emanates from the concept of empathy as understood by the German philosopher Edith Stein. It begins by highlighting different interpretations of empathy. According to the German philosopher Martin Buber, empathy cannot be achieved as an act of will. In contrast, the psychologist Carl Rogers believes that empathy is identical with dialogue and is the outcome of a cognitive act of active listening. The empathy concept of Edith Stein, philosopher and follower of Edmund Husserl's phenomenology, goes beyond these conflicting views and offers a more complex interpretation, with relevance for both healthcare and nursing education. When studying Stein's three-level model of empathy, a field of tension between perspectives of closeness and distance becomes apparent. The paper concludes by suggesting Stein's model of empathy as a strategy to overcome the tension and meet the demands of empathy. 9. DENOSUMAB-RELATED OSTEONECROSIS OF THE JAWS: A CASE REPORT Directory of Open Access Journals (Sweden) Milena Petkova 2017-03-01 Full Text Available Bisphosphonates are potent and effective drugs frequently used to prevent the skeletal complications associated with postmenopausal osteoporosis in women, to manage patients with multiple myeloma, hypercalcemia, and metastasis of cancer to the bone. The search for new medications with the same therapeutic effectiveness as the bisphosphonates but fewer side effects has resulted in the discovery of Denosumab, a human monoclonal antibody against the receptor activator for nuclear factor kappa B ligand (RANKL, therefore inhibiting osteoclast differentiation and function. Denosumab is a class of drugs that are entirely different from the traditional antiresorptive drugs, the bisphosphonates. Denosumab has several advantages, including better tolerability, ease of subcutaneous injection, a shorter half-life, and a reduced incidence of nephrotoxicity. Patients receiving bisphosphonates are at risk to develop a severe devastating complication - osteonecrosis of the jaws (ONJ - which is challenging to treat. Since 2010 there have been reports of ONJ in patients taking denosumab. In the 2014 position paper of the American Association of Oral and Maxillofacial Surgeons, the nomenclature “bisphosphonate-related osteonecrosis of the jaw” was changed to “medication related osteonecrosis of the jaw” (MRONJ. The change is justified to accommodate the growing number of osteonecrosis cases involving the maxilla and mandible associated with other antiresorptive (denosumab and antiangiogenic therapies. Here we report a development of denosumab-related osteonecrosis of the jaw (DRONJ - a new type of bony necrosis- in patient with bone metastases of breast cancer on Denosumab therapy. The patient has no previous history of taking bisphosphonates. 10. Close-coupled Catalytic Two-Stage Liquefaction (CTSL{trademark}) process bench studies. Final report, [October 1, 1988--July 31, 1993 Energy Technology Data Exchange (ETDEWEB) Comolli, A.G.; Johanson, E.S.; Karolkiewicz, W.F.; Lee, L.K.; Popper, G.A.; Stalzer, R.H.; Smith, T.O. 1993-06-01 This is the final report of a four year and ten month contract starting on October 1, 1988 to July 31, 1993 with the US Department of Energy to study and improve Close-Coupled Catalytic Two-Stage Direct Liquefaction of coal by producing high yields of distillate with improved quality at lower capital and production costs in comparison to existing technologies. Laboratory, Bench and PDU scale studies on sub-bituminous and bituminous coals are summarized and referenced in this volume. Details are presented in the three topical reports of this contract; CTSL Process Bench Studies and PDU Scale-Up with Sub-Bituminous Coal-DE-88818-TOP-1, CTSL Process Bench Studies with Bituminous Coal-DE-88818-TOP-2, and CTSL Process Laboratory Scale Studies, Modelling and Technical Assessment-DE-88818-TOP-3. Results are summarized on experiments and studies covering several process configurations, cleaned coals, solid separation methods, additives and catalysts both dispersed and supported. Laboratory microautoclave scale experiments, economic analysis and modelling studies are also included along with the PDU-Scale-Up of the CTSL processing of sub-bituminous Black Thunder Mine Wyoming coal. During this DOE/HRI effort, high distillate yields were maintained at higher throughput rates while quality was markedly improved using on-line hydrotreating and cleaned coals. Solid separations options of filtration and delayed coking were evaluated on a Bench-Scale with filtration successfully scaled to a PDU demonstration. Directions for future direct coal liquefaction related work are outlined herein based on the results from this and previous programs. 11. [Closing diastemas]. Science.gov (United States) Vieira, L C; Pereira, J C; Coradazzi, J L; Francischone, C E 1990-01-01 The authors describe a clinical case of closing upper central incisives diastema, reconstructiva of a conoid upper lateral and the rechaping of an upper canine to a lateral incisive. The material used was composite resin. 12. Desferrioxamine-related ocular toxicity: A case report Directory of Open Access Journals (Sweden) Sumu Simon 2012-01-01 Full Text Available A 29-year-old lady receiving repeated blood transfusions for β thalassemia since childhood, presented with rapidly deteriorating symptoms of night blindness and peripheral visual field loss. She was recently commenced on high-dose intravenous desferrioxamine for reducing the systemic iron overload. Clinical and investigative findings were consistent with desferrioxamine-related pigmentary retinopathy and optic neuropathy. Recovery was partial following cessation of desferrioxamine. This report highlights the ocular side-effects of desferrioxamine mesylate and the need to be vigilant in patients on high doses of desferrioxamine. 13. Siderophore-mediated iron acquisition in the entomopathogenic bacterium Pseudomonas entomophila L48 and its close relative Pseudomonas putida KT2440. Science.gov (United States) Matthijs, Sandra; Laus, Georges; Meyer, Jean-Marie; Abbaspour-Tehrani, Kourosch; Schäfer, Mathias; Budzikiewicz, Herbert; Cornelis, Pierre 2009-12-01 Pseudomonas entomophila L48 is a recently identified entomopathogenic bacterium which, upon ingestion, kills Drosophila melanogaster, and is closely related to P. putida. The complete genome of this species has been sequenced and therefore a genomic, genetic and structural analysis of the siderophore-mediated iron acquisition was undertaken. P. entomophila produces two siderophores, a structurally new and unique pyoverdine and the secondary siderophore pseudomonine, already described in P. fluorescens species. Structural analysis of the pyoverdine produced by the closely related P. putida KT2440 showed that this strain produces an already characterised pyoverdine, but different from P. entomophila, and no evidence was found for the production of a second siderophore. Growth stimulation assays with heterologous pyoverdines demonstrated that P. entomophila is able to utilize a large variety of structurally distinct pyoverdines produced by other Pseudomonas species. In contrast, P. putida KT2440 is able to utilize only its own pyoverdine and the pyoverdine produced by P. syringae LMG 1247. Our data suggest that although closely related, P. entomophila is a more efficient competitor for iron than P. putida. 14. Varying importance of cuticular hydrocarbons and iridoids in the species-specific mate recognition pheromones of three closely related Leptopilina species Directory of Open Access Journals (Sweden) Ingmar eWeiss 2015-03-01 Full Text Available Finding a suitable mate for reproduction is one of the most important tasks for almost all animals. In insects this task is often facilitated by pheromone-mediated communication. While insect pheromones in general show enormous chemical diversity, closely related species often use structurally similar compounds in their pheromones. Despite this similarity, pheromones of congeneric species living in sympatry need to be species specific.We investigated the pheromone-mediated mate recognition by males of three closely related species of Leptopilina, a genus of parasitoid wasps that utilize the larvae of Drosophila as hosts. The study species, L. heterotoma, L. boulardi, and L. victoriae, occur sympatrically and have a similar ecology and life history. We have found that mate recognition is species specific in all three species. This species specificity is achieved by a differing importance of cuticular hydrocarbons (CHCs and iridoids in the female mate recognition pheromones. In L. heterotoma the iridoids are of major importance while CHCs play a negligible role. In L. boulardi, however, the CHCs are as important as the iridoids, while in L. victoriae, the CHCs alone elicit a full behavioral response of males.Our results provide novel insights into pheromone evolution in insects by showing that selection on two completely different classes of chemical compounds may generate conditions where compounds from both classes contribute to a varying degree to the chemical communication of closely related species and that this variation also generates the species specificity of the signals. 15. Characterization of leaf cuticular waxes and cutin monomers of Camelina sativa and closely-related Camelina species Science.gov (United States) Camelina sativa is an old world crop newly introduced to the semi-arid regions of the Southwestern US. Recently, Camelina gained attention as a biofuel feedstock crop due to its relatively high oil content, polyunsaturated fatty acids, very short growing season with fairly good adaption to marginal ... 16. The Relationship between Instructor Misbehaviors and Student Antisocial Behavioral Alteration Techniques: The Roles of Instructor Attractiveness, Humor, and Relational Closeness Science.gov (United States) Claus, Christopher J.; Booth-Butterfield, Melanie; Chory, Rebecca M. 2012-01-01 Using rhetorical/relational goal theory as a guiding frame, we examined relationships between instructor misbehaviors (i.e., indolence, incompetence, and offensiveness) and the likelihood of students communicating antisocial behavioral alteration techniques (BATs). More specifically, the study focused on whether students' perceptions of instructor… 17. The Relationship between Instructor Misbehaviors and Student Antisocial Behavioral Alteration Techniques: The Roles of Instructor Attractiveness, Humor, and Relational Closeness Science.gov (United States) Claus, Christopher J.; Booth-Butterfield, Melanie; Chory, Rebecca M. 2012-01-01 Using rhetorical/relational goal theory as a guiding frame, we examined relationships between instructor misbehaviors (i.e., indolence, incompetence, and offensiveness) and the likelihood of students communicating antisocial behavioral alteration techniques (BATs). More specifically, the study focused on whether students' perceptions of instructor… 18. Production of mycotoxins by Aspergillus lentulus and other medically important and closely related species in section Fumigati DEFF Research Database (Denmark) Larsen, Thomas Ostenfeld; Smedsgaard, Jørn; Nielsen, Kristian Fog; 2007-01-01 The production of mycotoxins and other secondary metabolites have been studied by LC-DAD-MS from six species in Aspergillus section Fumigati. This includes the three new species Aspergillus lentulus, A. novofumigatus and A. fumigatiaffinis as well as A. fumigatus, Neosartoria fisheri and N....... pseudofisheri. A major finding was detection of gliotoxin from N. pseudofisheri, a species not previously reported to produce this mycotoxin. Gliotoxin was also detected from A. fumigatus together with fumagillin, fumigaclavine C, fumitremorgin C, fumiquinazolines, trypacidin, methyl- sulochrin, TR-2... 19. The proxy problem: Child report versus parent report in health-related quality of life research NARCIS (Netherlands) Theunissen, N.C.M.; Vogels, T.G.C.; Koopman, H.M.; Verrips, G.H.W.; Zwinderman, K.A.H.; Verloove-Vanhorick, S.P.; Wit, J.M. 1998-01-01 This study evaluates the agreement between child and parent reports on children's health-related quality of life (HRQoL) in a representative sample of 1,105 Dutch children (age 8-11 years old). Both children and their parents completed a 56 item questionnaire (TACQOL). The questionnaire contains sev 20. Relation between hydraulic properties and plant coverage of the closed-landfill soils in Piacenza (Po Valley, Italy) Science.gov (United States) Cassinari, C.; Manfredi, P.; Giupponi, L.; Trevisan, M.; Piccini, C. 2015-02-01 In this paper the results of a study of soil hydraulic properties and plant coverage of a landfill located in Piacenza (Po Valley, Italy) are presented, together with the attempt to put the hydraulic properties in relation with plant coverage. The measured soil water retention curve was first compared with the output of some pedotransfer functions taken from the literature and then with the output of the same pedotransfer functions applied to a reference soil. The landfill plant coverage was also studied. The relation between soil hydraulic properties and plant coverage showed that the landfill soils have a low water content available for plants and this fact, together with their lack of depth and compacted structure, justifies the presence of a nitrophilous, disturbed-soil vegetation type, dominated by ephemeral annual species (therophytes). 1. TRADE EFFECTS: REGULATORY, ACCOUNTING PRACTICES AND REPORTING OF INFORMATION RELATED Directory of Open Access Journals (Sweden) ARISTIŢA ROTILĂ 2014-05-01 Full Text Available It is known that within trade relations providers often credit customers for the value of goods or services which are the subject of conducted commercial transactions, this aspect being materialized in the issuance and acceptance of a trade effect. From the time of acceptance until maturity / settlement, trade effects should be reflected separately in the accounts and, to the extent that were not settled until the end of exercise, their value must be presented in the financial statements. Based on analysis of the Romanian accounting regulations, also taking into consideration the opinions expressed in specific literature concerning accounting reflection of trade effects, in this article we try to point out some aspects which, in our opinion, require clarification. We also want to point out some contradictions / inconsistencies regarding the reporting of information on the trade effects, specifically between the text of accounting regulations concerning the definition of accounting structures „cash and bank accounts” and “short term investments” and their contents when presented as positions in the balance sheet structure. In relation to the issues raised we try to prove the effects on the indicators concerning financial position and to make some suggestions that would have effects on Romanian accounting regulations, namely the improvement of financial reporting performed by the economic operators. 2. 34 CFR 611.47 - What are a scholarship recipient's reporting responsibilities upon the close of the LEA's... Science.gov (United States) 2010-07-01 ... 34 Education 3 2010-07-01 2010-07-01 false What are a scholarship recipient's reporting... EDUCATION TEACHER QUALITY ENHANCEMENT GRANTS PROGRAM Scholarships § 611.47 What are a scholarship recipient...'s academic year, a scholarship recipient whose LEA reports under § 611.46(a) that he or she... 3. Male attractiveness is influenced by UV wavelengths in a newt species but not in its close relative. Directory of Open Access Journals (Sweden) Jean Secondi Full Text Available BACKGROUND: Functional communication in the UV range has been reported in Invertebrates and all major groups of Vertebrates but Amphibians. Although perception in this wavelength range has been shown in a few species, UV signalling has not been demonstrated in this group. One reason may be that in lentic freshwater habitats, litter decomposition generates dissolved organic carbon that absorbs UV radiation and thus hinders its use for visual signalling. We tested the effect of male UV characteristics on female sexual preference in two newt species that experience contrasting levels of UV water transmission when breeding. METHODOLOGY/PRINCIPAL FINDINGS: We analysed water spectral characteristics of a sample of breeding ponds in both species. We quantified male ventral coloration and measured male attractiveness under two lighting conditions (UV present, UV absent using a no-choice female preference design. UV transmission was higher in Lissotriton vulgaris breeding sites. Male UV patterns also differed between experimental males of the two species. We observed a first common peak around 333 nm, higher in L. vulgaris, and a second peak around 397 nm, more frequent and higher in L. helveticus. Male attractiveness was significantly reduced in L. vulgaris when UV was not available but not in L. helveticus. Male attractiveness depended on the hue of the first UV peak in L. vulgaris. CONCLUSION/SIGNIFICANCE: Our study is the first report of functional UV-based communication in Amphibians. Interestingly, male spectral characteristics and female preferences were consistent with the differences in habitat observed between the two species as L. helveticus often breeds in ponds containing more UV blocking compounds. We discuss the three hypotheses proposed so far for UV signalling in animals (enhanced signal detectability, private communication channel, indicator of individual quality. 4. "Impulsivity": relations between self-report and behavior. Science.gov (United States) Sharma, Leigh; Kohl, Krista; Morgan, Theresa A; Clark, Lee Anna 2013-03-01 The trait of "impulsivity" is difficult to place within a personality framework due to the many potential pathways to impulsive behavior and the lack of consensus regarding the structure of the trait(s). This lack of consensus also hinders systematic investigation into relations between "impulsivity" and its behavioral manifestations. Undergraduates (Sample 1 N = 507) completed a battery of self-report measures, all purporting to assess trait "impulsivity"; a subset (n = 408) and Sample 2 (N = 388) also completed a retrospective questionnaire about specific behaviors they may have engaged in over the past year, and another subset of Sample 1 agreed to complete (n = 208) and actually completed (n = 152) a 2-week prospective measure of impulsive behaviors. Finally, a subset of Sample 1 (n = 321) and Sample 2 completed an omnibus self-report inventory in a follow-up study. Structural equation modeling confirmed a 3-factor structure of what we call impulsigenic traits-traits that are manifested in impulsive behavior. This finding is consistent with previous research and supports the growing consensus that "impulsivity" is a colloquial label attached to a group of distinct traits that have phenotypically similar behavioral manifestations. Each of these impulsigenic traits relates differentially to impulsive behavior and to broad temperamental dimensions. The results also show clear 2-factor structures of both daily and less frequent (yearly/semiyearly) impulsive behaviors. Finally, a unique method of data collection permitted an investigation of relations between the impulsigenic and other personality traits and observed behaviors, demonstrating the predictive utility of personality traits to discrete, in situ behaviors. 5. An analysis of psychotropic drug sales. Increasing sales of selective serotonin reuptake inhibitors anre closely related to number of products DEFF Research Database (Denmark) Nielsen, Margrethe; Gøtzsche, Peter C. 2011-01-01 by changes in sales of the benzodiazepines and SSRIs. We found a decline in the sales of benzodiazepines after a peak in 1986, likely due to the recognition that they cause dependence. From a low level in 1992, we found that the sales of SSRIs increased almost linearly by a factor of 18, up to 44 DDD per......BACKGROUND: Prescribing of selective serotonin reuptake inhibitors (SSRIs) has increased dramatically. OBJECTIVE: To compare the sales of benzodiazepines and SSRIs within the primary care sector in Denmark and relate changes in usage to number of indications and products on the market. METHODS: We... 6. Discovery of a novel insect neuropeptide signaling system closely related to the insect adipokinetic hormone and corazonin hormonal systems DEFF Research Database (Denmark) Hansen, Karina Kiilerich; Stafflinger, Elisabeth; Schneider, Martina 2010-01-01 that are structurally related to the AKHs but represent a different neuropeptide signaling system. We have previously cloned an orphan GPCR from the malaria mosquito Anopheles gambiae that was structurally intermediate between the A. gambiae AKH and corazonin GPCRs. Using functional expression of the receptor in cells...... receptors, this is a prominent example of receptor/ligand co-evolution, probably originating from receptor and ligand gene duplications followed by mutations and evolutionary selection, thereby yielding three independent hormonal systems. The ACP signaling system occurs in the mosquitoes A. gambiae, Aedes... 7. Replications of Two Closely Related Groups of Jumbo Phages Show Different Level of Dependence on Host-encoded RNA Polymerase Science.gov (United States) Matsui, Takeru; Yoshikawa, Genki; Mihara, Tomoko; Chatchawankanphanich, Orawan; Kawasaki, Takeru; Nakano, Miyako; Fujie, Makoto; Ogata, Hiroyuki; Yamada, Takashi 2017-01-01 Ralstonia solanacearum phages ΦRP12 and ΦRP31 are jumbo phages isolated in Thailand. Here we show that they exhibit similar virion morphology, genome organization and host range. Genome comparisons as well as phylogenetic and proteomic tree analyses support that they belong to the group of ΦKZ-related phages, with their closest relatives being R. solanacearum phages ΦRSL2 and ΦRSF1. Compared with ΦRSL2 and ΦRSF1, ΦRP12 and ΦRP31 possess larger genomes (ca. 280 kbp, 25% larger). The replication of ΦRP12 and ΦRP31 was not affected by rifampicin treatment (20 μg/ml), suggesting that phage-encoded RNAPs function to start and complete the infection cycle of these phages without the need of host-encoded RNAPs. In contrast, ΦRSL2 and ΦRSF1, encoding the same set of RNAPs, did not produce progeny phages in the presence of rifampicin (5 μg/ml). This observation opens the possibility that some ΦRP12/ΦRP31 factors that are absent in ΦRSL2 and ΦRSF1 are involved in their host-independent transcription. PMID:28659872 8. New insights into the phylogeny and worldwide dispersion of two closely related nematode species, Bursaphelenchus xylophilus and Bursaphelenchus mucronatus. Directory of Open Access Journals (Sweden) Filipe Pereira Full Text Available The pinewood nematode, Bursaphelenchus xylophilus, is one of the greatest threats to coniferous forests worldwide, causing severe ecological damage and economic loss. The biology of B. xylophilus is similar to that of its closest relative, B. mucronatus, as both species share food resources and insect vectors, and have very similar morphological characteristics, although little pathogenicity to conifers has been associated with B. mucronatus. Using both nuclear and mitochondrial DNA markers, we show that B. xylophilus and B. mucronatus form distinct phylogenetic groups with contrasting phylogeographic patterns. B. xylophilus presents lower levels of intraspecific diversity than B. mucronatus, as expected for a species that evolved relatively recently through geographical or reproductive isolation. Genetic diversity was particularly low in recently colonised areas, such as in southwestern Europe. By contrast, B. mucronatus displays high levels of genetic diversity and two well-differentiated clades in both mitochondrial and nuclear DNA phylogenies. The lack of correlation between genetic and geographic distances in B. mucronatus suggests intense gene flow among distant regions, a phenomenon that may have remained unnoticed due to the reduced pathogenicity of the species. Overall, our findings suggest that B. xylophilus and B. mucronatus have different demographic histories despite their morphological resemblance and ecological overlap. These results suggest that Bursaphelenchus species are a valuable model for understanding the dispersion of invasive species and the risks posed to native biodiversity and ecosystems. 9. Genes coding for intermediate filament proteins closely related to the hagfish "thread keratins (TK)" alpha and gamma also exist in lamprey, teleosts and amphibians. Science.gov (United States) Schaffeld, Michael; Schultess, Jan 2006-05-15 The "thread keratins (TK)" alpha and gamma so far have been considered highly specialized intermediate filament (IF) proteins restricted to hagfish. From lamprey, we now have sequenced five novel IF proteins closely related to TKalpha and TKgamma, respectively. Moreover, we have detected corresponding sequences in EST and genomic databases of teleosts and amphibians. The structure of the TKalpha genes and the positions of their deduced amino acid sequences in a phylogenetic tree clearly support their classification as type II keratins. The genes encoding TKgamma show a structure typical for type III IF proteins, whereas their positions in phylogenetic trees favor a close relationship to the type I keratins. Considering that most keratin-like sequences detected in the lancelet also exhibit a gene structure typical for type III IF proteins, it seems likely that the keratin gene(s) originated from an ancient type III IF protein gene. According to EST analyses, the expression of the thread keratins in teleost fish and amphibians may be particularly restricted to larval stages, which, in conjunction with the observed absence of TKalpha and TKgamma genes in any of the available Amniota databases, indicates a thread keratin function closely related to larval development in an aquatic environment. 10. Antibody potency relates to the ability to recognize the closed, pre-fusion form of HIV Env Science.gov (United States) Guttman, Miklos; Cupo, Albert; Julien, Jean-Philippe; Sanders, Rogier W.; Wilson, Ian A.; Moore, John P.; Lee, Kelly K. 2015-02-01 HIV’s envelope glycoprotein (Env) is the sole target for neutralizing antibodies. The structures of many broadly neutralizing antibodies (bNAbs) in complex with truncated Env subunits or components have been reported. However, their interaction with the intact Env trimer, and the structural determinants that underlie neutralization resistance in this more native context are less well understood. Here we use hydrogen/deuterium exchange to examine the interactions between a panel of bNAbs and native-like Env trimers (SOSIP.664 trimers). Highly potent bNAbs cause only localized effects at their binding interface, while the binding of less potent antibodies is associated with elaborate changes throughout the trimer. In conjunction with binding kinetics, our results suggest that poorly neutralizing antibodies can only bind when the trimer transiently samples an open state. We propose that the kinetics of such opening motions varies among isolates, with Env from neutralization-sensitive viruses opening more frequently than Env from resistant viruses. 11. Production of mycotoxins by Aspergillus lentulus and other medically important and closely related species in section Fumigati. Science.gov (United States) Larsen, Thomas O; Smedsgaard, Jørn; Nielsen, Kristian F; Hansen, Michael A E; Samson, Robert A; Frisvad, Jens C 2007-05-01 The production of mycotoxins and other secondary metabolites have been studied by LC-DAD-MS from six species in Aspergillus section Fumigati. This includes the three new species Aspergillus lentulus, A. novofumigatus and A. fumigatiaffinis as well as A. fumigatus, Neosartoria fisheri and N. pseudofisheri. A major finding was detection of gliotoxin from N. pseudofisheri, a species not previously reported to produce this mycotoxin. Gliotoxin was also detected from A. fumigatus together with fumagillin, fumigaclavine C, fumitremorgin C, fumiquinazolines, trypacidin, methyl-sulochrin, TR-2, verruculogen, helvolic acid and pyripyropenes. Major compounds from A. lentulus were cyclopiazonic acid, terrein, neosartorin, auranthine and pyripyropenes A, E and O. Thus in the present study A. fumigatus and A. lentulus did not produce any of the same metabolites except for pyripyropenes. The fact that A. lentulus apparently does not produce gliotoxin supports the idea that other compounds than gliotoxin might play an important role in the effective invasiveness of A. lentulus. An overall comparison of secondary metabolite production by strains of the six species was achieved by analysis of fungal extracts by direct injection mass spectrometry and cluster analysis. Separate groupings were seen for all the six species even though only one isolate was included in this study for the two species A. novofumigatus and A. fumigatiaffinis. 12. Inhibition of RNA silencing by the coat protein of Pelargonium flower break virus: distinctions from closely related suppressors. Science.gov (United States) Martínez-Turiño, Sandra; Hernández, Carmen 2009-02-01 Viral-derived double-stranded RNAs (dsRNAs) activate RNA silencing, generating small interfering RNAs (siRNAs) which are incorporated into an RNA-induced silencing complex (RISC) that promotes homology-dependent degradation of cognate RNAs. To counteract this, plant viruses express RNA silencing suppressors. Here, we show that the coat protein (CP) of Pelargonium flower break virus (PFBV), a member of the genus Carmovirus, is able to efficiently inhibit RNA silencing. Interestingly, PFBV CP blocked both sense RNA- and dsRNA-triggered RNA silencing and did not preclude generation of siRNAs, which is in contrast with the abilities that have been reported for other carmoviral CPs. We have also found that PFBV CP can bind siRNAs and that this ability correlates with silencing suppression activity and enhancement of potato virus X pathogenicity. Collectively, the results indicate that PFBV CP inhibits RNA silencing by sequestering siRNAs and preventing their incorporation into a RISC, thus behaving similarly to unrelated viral suppressors but dissimilarly to orthologous ones. 13. Molecular and biological analysis of eight genetic islands that distinguish Neisseria meningitidis from the closely related pathogen Neisseria gonorrhoeae. Science.gov (United States) Klee, S R; Nassif, X; Kusecek, B; Merker, P; Beretti, J L; Achtman, M; Tinsley, C R 2000-04-01 The pathogenic species Neisseria meningitidis and Neisseria gonorrhoeae cause dramatically different diseases despite strong relatedness at the genetic and biochemical levels. N. meningitidis can cross the blood-brain barrier to cause meningitis and has a propensity for toxic septicemia unlike N. gonorrhoeae. We previously used subtractive hybridization to identify DNA sequences which might encode functions specific to bacteremia and invasion of the meninges because they are specific to N. meningitidis and absent from N. gonorrhoeae. In this report we show that these sequences mark eight genetic islands that range in size from 1.8 to 40 kb and whose chromosomal location is constant. Five of these genetic islands were conserved within a representative set of strains and/or carried genes with homologies to known virulence factors in other species. These were deleted, and the mutants were tested for correlates of virulence in vitro and in vivo. This strategy identified one island, region 8, which is needed to induce bacteremia in an infant rat model of meningococcal infection. Region 8 encodes a putative siderophore receptor and a disulfide oxidoreductase. None of the deleted mutants was modified in its resistance to the bactericidal effect of serum. Neither were the mutant strains altered in their ability to interact with endothelial cells, suggesting that such interactions are not encoded by large genetic islands in N. meningitidis. 14. Closing the quality gap: revisiting the state of the science (vol. 5: public reporting as a quality improvement strategy). Science.gov (United States) Totten, Annette M; Wagner, Jesse; Tiwari, Arpita; O'Haire, Christen; Griffin, Jessica; Walker, Miranda 2012-07-01 The goal of this review was to evaluate the effectiveness of public reporting of health care quality information as a quality improvement strategy. We sought to determine if public reporting results in improvements in health care delivery and patient outcomes. We also considered whether public reporting affects the behavior of patients or of health care providers. Finally we assessed whether the characteristics of the public reports and the context affect the impact of public reports. Articles available between 1980 and 2011 were identified through searches of the following bibliographical databases: MEDLINE®, Embase, EconLit, PsychINFO, Business Source Premier, CINAHL, PAIS, Cochrane Database of Systematic Reviews, EPOC Register of Studies, DARE, NHS EED, HEED, NYAM Grey Literature Report database, and other sources (experts, reference lists, and gray literature). We screened citations based on inclusion and exclusion criteria developed based on our definition of public reporting. We initially did not exclude any studies based on study design. Of the 11,809 citations identified through title and abstract triage, we screened and reviewed 1,632 articles. A total of 97 quantitative and 101 qualitative studies were included, abstracted, entered into tables, and evaluated. The heterogeneity of outcomes as well as methods prohibited formal quantitative synthesis. Systematic reviews were used to identify studies, but their conclusions were not incorporated into this review. For most of the outcomes, the strength of the evidence available to assess the impact of public reporting was moderate. This was due in part to the methodological challenges researchers face in designing and conducting research on the impact of population-level interventions. Public reporting is associated with improvement in health care performance measures such as those included in Nursing Home Compare. Almost all identified studies found no evidence or only weak evidence that public reporting 15. Digestive proteolysis organization in two closely related Tenebrionid beetles: red flour beetle (Tribolium castaneum) and confused flour beetle (Tribolium confusum). Science.gov (United States) Vinokurov, K S; Elpidina, E N; Zhuzhikov, D P; Oppert, B; Kodrik, D; Sehnal, F 2009-04-01 The spectra of Tribolium castaneum and T. confusum larval digestive peptidases were characterized with respect to the spatial organization of protein digestion in the midgut. The pH of midgut contents in both species increased from 5.6-6.0 in the anterior to 7.0-7.5 in the posterior midgut. However, the pH optimum of the total proteolytic activity of the gut extract from either insect was pH 4.1. Approximately 80% of the total proteolytic activity was in the anterior and 20% in the posterior midgut of either insect when evaluated in buffers simulating the pH and reducing conditions characteristic for each midgut section. The general peptidase activity of gut extracts from either insect in pH 5.6 buffer was mostly due to cysteine peptidases. In the weakly alkaline conditions of the posterior midgut, the serine peptidase contribution was 31 and 41% in T. castaneum and T. confusum, respectively. A postelectrophoretic peptidase activity assay with gelatin also revealed the important contribution of cysteine peptidases in protein digestion in both Tribolium species. The use of a postelectrophoretic activity assay with p-nitroanilide substrates and specific inhibitors revealed a set of cysteine and serine endopeptidases, 8 and 10 for T. castaneum, and 7 and 9 for T. confusum, respectively. Serine peptidases included trypsin-, chymotrypsin-, and elastase-like enzymes, the latter being for the first time reported in Tenebrionid insects. These data support a complex system of protein digestion in the Tribolium midgut with the fundamental role of cysteine peptidases. 16. Tube Thoracostomy-Related Necrotizing Fasciitis: A Case Report Directory of Open Access Journals (Sweden) Shun-Pin Hsu 2006-12-01 Full Text Available Spontaneous pneumothorax is a serious complication of pulmonary tuberculosis that requires immediate treatment. Necrotizing fasciitis is a serious, rapidly progressive infection of the subcutaneous tissue and fascia, most related to trauma or surgery. Here, we report a case of pulmonary tuberculosis with spontaneous pneumothorax. A standard procedure of tube thoracostomy was performed for lung re-expansion. Two days after the tube was removed, necrotizing fasciitis developed from the puncture site. Computed tomography of the chest showed focal thickness with gas formation and loss of the fat plane over the chest wall, which is compatible with the diagnosis of necrotizing fasciitis. Aggressive treatment was given, including emergency fasciectomy and adequate systemic antibiotic and antituberculous treatment. The necrotizing fasciitis was successfully treated. The patient was discharged and sent home with maintenance antituberculous therapy. 17. Psychopathology Related to Energy Drinks: A Psychosis Case Report Directory of Open Access Journals (Sweden) Daniel Hernandez-Huerta 2017-01-01 Full Text Available Energy drinks (ED are nonalcoholic beverages that have caffeine as their most common active substance. The rapid expansion of ED consumption has created concern in the scientific community as well as in the public opinion. We report a psychotic episode probably triggered by ED abuse in a young adult without previous psychotic disorders. We have reviewed the literature regarding the relationship between caffeine, energy drinks, and psychopathology. Few articles have been published about mental health effects of energy drinks and caffeine abuse. Nevertheless, this relationship has been suggested, specifically with anxiety disorders, manic episodes, suicide attempts, psychotic decompensation, and substance use disorder. ED consumption could represent a global public health problem because of the potential severe adverse effects in mental and physical health. To our knowledge, this article is probably the first case of psychosis related to ED abuse in an individual without previous psychotic disorders. 18. Psychopathology Related to Energy Drinks: A Psychosis Case Report Science.gov (United States) Martin-Larregola, Maria; Gomez-Arnau, Jorge; Correas-Lauffer, Javier 2017-01-01 Energy drinks (ED) are nonalcoholic beverages that have caffeine as their most common active substance. The rapid expansion of ED consumption has created concern in the scientific community as well as in the public opinion. We report a psychotic episode probably triggered by ED abuse in a young adult without previous psychotic disorders. We have reviewed the literature regarding the relationship between caffeine, energy drinks, and psychopathology. Few articles have been published about mental health effects of energy drinks and caffeine abuse. Nevertheless, this relationship has been suggested, specifically with anxiety disorders, manic episodes, suicide attempts, psychotic decompensation, and substance use disorder. ED consumption could represent a global public health problem because of the potential severe adverse effects in mental and physical health. To our knowledge, this article is probably the first case of psychosis related to ED abuse in an individual without previous psychotic disorders. PMID:28116203 19. Recent speciation in three closely related sympatric specialists: inferences using multi-locus sequence, post-mating isolation and endosymbiont data. Directory of Open Access Journals (Sweden) Huai-Jun Xue Full Text Available Shifting between unrelated host plants is relatively rare for phytophagous insects, and distinct host specificity may play crucial roles in reproductive isolation. However, the isolation status and the relationship between parental divergence and post-mating isolation among closely related sympatric specialists are still poorly understood. Here, multi-locus sequence were used to estimate the relationship among three host plant-specific closely related flea beetles, Altica cirsicola, A. fragariae and A. viridicyanea (abbreviated as AC, AF and AV respectively. The tree topologies were inconsistent using different gene or different combinations of gene fragments. The relationship of AF+(AC+AV was supported, however, by both gene tree and species tree based on concatenated data. Post-mating reproductive data on the results of crossing these three species are best interpreted in the light of a well established phylogeny. Nuclear-induced but not Wolbachia-induced unidirectional cytoplasmic incompatibility, which was detected in AC-AF and AF-AV but not in AC-AV, may also suggest more close genetic affinity between AC and AV. Prevalence of Wolbachia in these three beetles, and the endosymbiont in most individuals of AV and AC sharing a same wsp haplotype may give another evidence of AF+(AC+AV. Our study also suggested that these three flea beetles diverged in a relative short time (0.94 My, which may be the result of shifting between unrelated host plants and distinct host specificity. Incomplete post-mating isolation while almost complete lineage sorting indicated that effective pre-mating isolation among these three species should have evolved. 20. Four tropical, closely related fern species belonging to the genus Adiantum L. are genetically distinct as revealed by ISSR fingerprinting. Science.gov (United States) Korpelainen, Helena; de Britto, John; Doublet, Jérémy; Pravin, Sahaya 2005-11-01 The level and pattern of genetic variation was analyzed in four species of the fern genus Adiantum L., A. hispidulum Sw., A. incisum Forrsk., A. raddianum C.Presl, and A. zollingeri Mett. ex Kuhn, originating from South India, using the ISSR fingerprinting method. The populations of Adiantum possessed a considerable level of genetic variation, the diversity indices ranging from 0.284 to 0.464. Only 12% of the ISSR markers found were restricted to one species only, and 54% were detected in all four species. The analysis of molecular variance revealed that 71.1% of variation was present within populations. The proportion of variation detected among species was only 18.5% while the proportion of variation among populations within species equalled 10.4%. Despite the low level of intrageneric differentiation, the discriminant analysis and clustering of genetic distances indicated that the four Adiantum species are genetically distinct. The F(ST) values calculated for the species were low, varying from 0.089 to 0.179. No linkage disequilibrium was detected between the loci. Such low level of differentiation among populations and the presence of linkage equilibrium reflect that the life history of Adiantum ferns apparently involves common or relatively common sexuality, effective wind-dispersal of spores and outcrossing. 1. Magnetic resonance imaging of blood brain/nerve barrier dysfunction and leukocyte infiltration: closely related or discordant? Directory of Open Access Journals (Sweden) Gesa eWeise 2012-12-01 Full Text Available Unlike other organs the nervous system is secluded from the rest of the organism by the blood brain (BBB or blood nerve barrier (BNB preventing passive influx of fluids from the circulation. Similarly, leukocyte entry to the nervous system is tightly controlled. Breakdown of these barriers and cellular inflammation are hallmarks of inflammatory as well as ischemic neurological diseases and thus represent potential therapeutic targets. The spatiotemporal relationship between BBB/BNB disruption and leukocyte infiltration has been a matter of debate. We here review contrast-enhanced magnetic resonance imaging (MRI as a non-invasive tool to depict barrier dysfunction and its relation to macrophage infiltration in the central and peripheral nervous system under pathological conditions. Novel experimental contrast agents like Gadofluorine M (Gf allow more sensitive assessment of BBB dysfunction than conventional Gadolinium (Gd-DTPA-enhanced MRI. In addition, Gf facilitates visualization of functional and transient alterations of the BBB remote from lesions. Cellular contrast agents such as superparamagnetic iron oxide particles (SPIO and perfluorocarbons (PFC enable assessment of leukocyte (mainly macrophage infiltration by MR technology. Combined use of these MR contrast agents disclosed that leukocytes can enter the nervous system independent from a disturbance of the BBB, and vice versa, a dysfunctional BBB/BNB by itself is not sufficient to attract inflammatory cells from the circulation. We will illustrate these basic imaging findings in animal models of multiple sclerosis (MS, cerebral ischemia and traumatic nerve injury and review corresponding findings in patients. 2. Morphological, phylogenetic, and ecological diversity of the new model species Setaria viridis (Poaceae: Paniceae) and its close relatives. Science.gov (United States) Layton, Daniel J; Kellogg, Elizabeth A 2014-03-01 Species limits of the emerging model organism Setaria viridis (tribe Paniceae, subtribe Cenchrinae) are not well defined. It is thought to be related to S. adhaerens, S. faberi, S. verticillata, and S. verticilliformis and in North America occurs with the morphologically similar S. pumila. An integrated approach was taken to evaluate its variation and relationships with the other taxa. Statistical morphology, flow cytometry, molecular phylogenetics, and growth experiments were employed to examine the group's physical variation, polyploidy, evolutionary relationships, and drought ecology, respectively. SETARIA VIRIDIS contributed one genome to the tetraploids S. faberi, S. verticillata, and S. verticilliformis; the other genome of the latter two was contributed by S. adhaerens. Setaria pumila is unrelated. Morphologically, S. viridis is most similar to S. faberi, but all tested accessions of S. viridis were diploid, whereas those of S. faberi were all tetraploid. Principal component analysis of 70 morphological characters consistently separated S. viridis from S. faberi, largely by spikelet characters. The diagnostic morphological characters are not affected by watering. Setaria faberi is far more sensitive to drought, in terms of mortality and morphological stunting, than S. viridis or S. pumila. SETARIA VIRIDIS is a diploid species and has contributed to several polyploid derivatives. The most morphologically similar of the polyploids is S. faberi, which differs in spikelet features, phylogenetics, genome size, and ecological response to drought. Researchers using field-collected S. viridis as a model organism will benefit from the clear delimitation provided in this study. 3. Selaginella moellendorffii has a reduced and highly conserved expansin superfamily with genes more closely related to angiosperms than to bryophytes. Science.gov (United States) Carey, Robert E; Hepler, Nathan K; Cosgrove, Daniel J 2013-01-03 Expansins are plant cell wall loosening proteins encoded by a large superfamily of genes, consisting of four families named EXPA, EXPB, EXLA, and EXLB. The evolution of the expansin superfamily is well understood in angiosperms, thanks to synteny-based evolutionary studies of the gene superfamily in Arabidopsis, rice, and Populus. Analysis of the expansin superfamily in the moss Physcomitrella patens revealed a superfamily without EXLA or EXLB genes that has evolved considerably and independently of angiosperm expansins. The sequencing of the Selaginella moellendorffii genome has allowed us to extend these analyses into an early diverging vascular plant. The expansin superfamily in Selaginella moellendorffii has now been assembled from genomic scaffolds. A smaller (and less diverse) superfamily is revealed, consistent with studies of other gene families in Selaginella. Selaginella has an expansin superfamily, which, like Physcomitrella, lacks EXLA or EXLB genes, but does contain two EXPA genes that are related to a particular Arabidopsis-rice clade involved in root hair development. From sequence-based phylogenetic analysis, most Selaginella expansins lie outside the Arabidopsis-rice clades, leading us to estimate the minimum number of expansins present in the last common ancestor of Selaginella and angiosperms at 2 EXPA genes and 1 EXPB gene. These results confirm Selaginella as an important intermediary between bryophytes and angiosperms. 4. Similar local, but different systemic, metabolomics responses of closely related pine subspecies to folivory by caterpillars of the processionary moth Energy Technology Data Exchange (ETDEWEB) Rivas-Ubach, A. [Environmental Molecular Sciences Laboratory, Pacific Northwest National Laboratory, Richland WA USA; CSIC, Global Ecology Unit CREAF-CEAB-CSIC-UAB, Cerdanyola del Vallès, Catalonia Spain; Cerdanyola del Vallès, CREAF, Catalonia Spain; Sardans, J. [CSIC, Global Ecology Unit CREAF-CEAB-CSIC-UAB, Cerdanyola del Vallès, Catalonia Spain; Cerdanyola del Vallès, CREAF, Catalonia Spain; Hódar, J. A. [Grupo de Ecología Terrestre, Departamento de Biología Animal y Ecología, Facultad de Ciencias, Universidad de Granada, Granada Spain; Garcia-Porta, J. [Institute of Evolutionary Biology, CSIC-Universitat Pompeu Fabra, Barcelona Spain; Guenther, A. [Department of Earth System Science, University of California, Irvine CA USA; Global Change Research Centre, Academy of Sciences of the Czech Republic, Brno Czech Republic; Oravec, M. [Global Change Research Centre, Academy of Sciences of the Czech Republic, Brno Czech Republic; Urban, O. [Global Change Research Centre, Academy of Sciences of the Czech Republic, Brno Czech Republic; Peñuelas, J. [CSIC, Global Ecology Unit CREAF-CEAB-CSIC-UAB, Cerdanyola del Vallès, Catalonia Spain; Cerdanyola del Vallès, CREAF, Catalonia Spain; Leiss, K. 2016-05-16 Plants respond locally and systemically to herbivore attack. Most of the research conducted on plant-herbivore relationships at elemental and molecular levels have focused on nutrients or/and certain molecular compounds or specific families of defensive metabolites showing that herbivores tend to select plant individuals or species with higher nutrient concentrations and to avoid those with higher levels of phenolics and terpenes. Unfortunately, the defensive role of phenolics in conifers is still unclear. We performed stoichiometric and metabolomics, local and systemic, analyses in two subspecies of Pinus sylvestris under the herbivorous attack by the caterpillars of the pine processionary moth, an important pest in the Mediterranean Basin. Herbivorous attack was not associated with any of the elements analyzed. Both pine subspecies responded locally to folivory mainly by increasing the concentrations of various terpenes and phenolics. Systemic responses differed between subspecies and most of the metabolites presented intermediate concentrations between those of the affected parts and unattacked trees. Contrary as usually thought, foliar nutrient concentrations did not show to be a main factor of an alleged plant selection by adult female processionary moths for oviposition. Local increases in phenolics were more associated with antioxidant function for protection against oxidative damage produced by folivory. On the other hand, terpenes were directly related to defense against herbivores. Herbivory attack produced a general systemic shift in pines, including both primary and secondary metabolisms, that was, however, less intense and chemically different from the local responses. Subspecies responded similarly locally but differently to folivory at systemic level. 5. Magnetic resonance imaging of blood brain/nerve barrier dysfunction and leukocyte infiltration: closely related or discordant? Science.gov (United States) Weise, Gesa; Stoll, Guido 2012-01-01 Unlike other organs the nervous system is secluded from the rest of the organism by the blood brain barrier (BBB) or blood nerve barrier (BNB) preventing passive influx of fluids from the circulation. Similarly, leukocyte entry to the nervous system is tightly controlled. Breakdown of these barriers and cellular inflammation are hallmarks of inflammatory as well as ischemic neurological diseases and thus represent potential therapeutic targets. The spatiotemporal relationship between BBB/BNB disruption and leukocyte infiltration has been a matter of debate. We here review contrast-enhanced magnetic resonance imaging (MRI) as a non-invasive tool to depict barrier dysfunction and its relation to macrophage infiltration in the central and peripheral nervous system under pathological conditions. Novel experimental contrast agents like Gadofluorine M (Gf) allow more sensitive assessment of BBB dysfunction than conventional Gadolinium (Gd)-DTPA enhanced MRI. In addition, Gf facilitates visualization of functional and transient alterations of the BBB remote from lesions. Cellular contrast agents such as superparamagnetic iron oxide particles (SPIO) and perfluorocarbons enable assessment of leukocyte (mainly macrophage) infiltration by MR technology. Combined use of these MR contrast agents disclosed that leukocytes can enter the nervous system independent from a disturbance of the BBB, and vice versa, a dysfunctional BBB/BNB by itself is not sufficient to attract inflammatory cells from the circulation. We will illustrate these basic imaging findings in animal models of multiple sclerosis, cerebral ischemia, and traumatic nerve injury and review corresponding findings in patients. 6. Allergic reaction related to ramipril use: a case report Directory of Open Access Journals (Sweden) Alencar Renata C 2010-01-01 Full Text Available Abstract Background Angiotensin-converting enzyme (ACE inhibitors are widely prescribed for patients with diabetes as a nephroprotector drug or to treat hypertension. Generally they are safe for clinical practice, but the relationship between these drugs and angioedema is known. The exact mechanism for ACE inhibitors-induced angioedema is not clear and it is still a matter of discussion. Case Report We reported a case of a 23-year-old black female with an 11 year history of type 1 diabetes, regularly monitored in the department of diabetes, in use of 0,98 UI/kg/day of human insulin, which presented an allergic reaction 24 h after ramipril use. The drug had been prescribed to treat diabetic nephropathy. There was no previous history of drug induced or alimentary allergy. The patient was instructed to discontinue the use of ramipril and oral antihistaminic drug and topical corticosteroid were prescribed. Skin biopsies were performed and confirmed the clinical hypothesis of pharmacodermy. The evaluation of ACE polymorphism identified DD genotype. Six months after the withdrawal of ramipril the patient was prescribed the angiotensin-II receptor blocker (ARB losartan as nephroprotector. She remained well without adverse reactions. Conclusions ACE inhibitors-induced angioedema is uncommon and the clinical presentation is variable with lips, tongue, oropharinge, and larynge as the most common locations. The presence of angioedema during treatment requires the immediate cessation of treatment due to the risk of possible severe complications. The case reported presented moderate symptoms, with the development of early onset edema in uncommon regions. ACE DD genotype had been associated with angioedema-ACE inhibitors induced. In patients who have experienced ACE inhibitor-related angioedema, ARB should be used cautiously used. However in the case of our patient, the prescription of losartan as nefroprotector did not result in any recurrent adverse effect. 7. Field and experimental evidence of a new caiman trypanosome species closely phylogenetically related to fish trypanosomes and transmitted by leeches Directory of Open Access Journals (Sweden) Bruno R. Fermino 2015-12-01 Full Text Available Trypanosoma terena and Trypanosoma ralphi are known species of the South American crocodilians Caiman crocodilus, Caiman yacare and Melanosuchus niger and are phylogenetically related to the tsetse-transmitted Trypanosoma grayi of the African Crocodylus niloticus. These trypanosomes form the Crocodilian clade of the terrestrial clade of the genus Trypanosoma. A PCR-survey for trypanosomes in caiman blood samples and in leeches taken from caimans revealed unknown trypanosome diversity and frequent mixed infections. Phylogenies based on SSU (small subunit of rRNA and gGAPDH (glycosomal Glyceraldehyde Phosphate Dehydrogenase gene sequences revealed a new trypanosome species clustering with T. terena and T. ralphi in the crocodilian clade and an additional new species nesting in the distant Aquatic clade of trypanosomes, which is herein named Trypanosoma clandestinus n. sp. This new species was found in Caiman yacare, Caiman crocodilus and M. niger from the Pantanal and Amazonian biomes in Brazil. Large numbers of dividing epimastigotes and unique thin and long trypomastigotes were found in the guts of leeches (Haementeria sp. removed from the mouths of caimans. The trypanosomes recovered from the leeches had sequences identical to those of T. clandestinus of caiman blood samples. Experimental infestation of young caimans (Caiman yacare with infected leeches resulted in long-lasting T. clandestinus infections that permitted us to delineate its life cycle. In contrast to T. terena, T. ralphi and T. grayi, which are detectable by hemoculturing, microscopy and standard PCR of caiman blood, T. clandestinus passes undetected by these methods due to very low parasitemia and could be detected solely by the more sensitive nested PCR method. T. clandestinus n. sp. is the first crocodilian trypanosome known to be transmitted by leeches and positioned in the aquatic clade closest to fish trypanosomes. Our data show that caimans can host trypanosomes 8. Applying DNA Barcodes to Identify Closely Related Species of Ferns: A Case Study of the Chinese Adiantum (Pteridaceae). Science.gov (United States) Wang, Fan-Hong; Lu, Jin-Mei; Wen, Jun; Ebihara, Atsushi; Li, De-Zhu 2016-01-01 DNA barcoding is a fast-developing technique to identify species by using short and standard DNA sequences. Universal selection of DNA barcodes in ferns remains unresolved. In this study, five plastid regions (rbcL, matK, trnH-psbA, trnL-F and rps4-trnS) and eight nuclear regions (ITS, pgiC, gapC, LEAFY, ITS2, IBR3_2, DET1, and SQD1_1) were screened and evaluated in the fern genus Adiantum from China and neighboring areas. Due to low primer universality (matK) and/or the existence of multiple copies (ITS), the commonly used barcodes matK and ITS were not appropriate for Adiantum. The PCR amplification rate was extremely low in all nuclear genes except for IBR3_2. rbcL had the highest PCR amplification rate (94.33%) and sequencing success rate (90.78%), while trnH-psbA had the highest species identification rate (75%). With the consideration of discriminatory power, cost-efficiency and effort, the two-barcode combination of rbcL+ trnH-psbA seems to be the best choice for barcoding Adiantum, and perhaps basal polypod ferns in general. The nuclear IBR3_2 showed 100% PCR amplification success rate in Adiantum, however, it seemed that only diploid species could acquire clean sequences without cloning. With cloning, IBR3_2 can successfully distinguish cryptic species and hybrid species from their related species. Because hybridization and allopolyploidy are common in ferns, we argue for including a selected group of nuclear loci as barcodes, especially via the next-generation sequencing, as it is much more efficient to obtain single-copy nuclear loci without the cloning procedure. 9. Field and experimental evidence of a new caiman trypanosome species closely phylogenetically related to fish trypanosomes and transmitted by leeches Science.gov (United States) Fermino, Bruno R.; Paiva, Fernando; Soares, Priscilla; Tavares, Luiz Eduardo R.; Viola, Laerte B.; Ferreira, Robson C.; Botero-Arias, Robinson; de-Paula, Cátia D.; Campaner, Marta; Takata, Carmen S.A.; Teixeira, Marta M.G.; Camargo, Erney P. 2015-01-01 Trypanosoma terena and Trypanosoma ralphi are known species of the South American crocodilians Caiman crocodilus, Caiman yacare and Melanosuchus niger and are phylogenetically related to the tsetse-transmitted Trypanosoma grayi of the African Crocodylus niloticus. These trypanosomes form the Crocodilian clade of the terrestrial clade of the genus Trypanosoma. A PCR-survey for trypanosomes in caiman blood samples and in leeches taken from caimans revealed unknown trypanosome diversity and frequent mixed infections. Phylogenies based on SSU (small subunit) of rRNA and gGAPDH (glycosomal Glyceraldehyde Phosphate Dehydrogenase) gene sequences revealed a new trypanosome species clustering with T. terena and T. ralphi in the crocodilian clade and an additional new species nesting in the distant Aquatic clade of trypanosomes, which is herein named Trypanosoma clandestinus n. sp. This new species was found in Caiman yacare, Caiman crocodilus and M. niger from the Pantanal and Amazonian biomes in Brazil. Large numbers of dividing epimastigotes and unique thin and long trypomastigotes were found in the guts of leeches (Haementeria sp.) removed from the mouths of caimans. The trypanosomes recovered from the leeches had sequences identical to those of T. clandestinus of caiman blood samples. Experimental infestation of young caimans (Caiman yacare) with infected leeches resulted in long-lasting T. clandestinus infections that permitted us to delineate its life cycle. In contrast to T. terena, T. ralphi and T. grayi, which are detectable by hemoculturing, microscopy and standard PCR of caiman blood, T. clandestinus passes undetected by these methods due to very low parasitemia and could be detected solely by the more sensitive nested PCR method. T. clandestinus n. sp. is the first crocodilian trypanosome known to be transmitted by leeches and positioned in the aquatic clade closest to fish trypanosomes. Our data show that caimans can host trypanosomes of the aquatic or 10. Bacillus tequilensis sp. nov., isolated from a 2000-year-old Mexican shaft-tomb, is closely related to Bacillus subtilis. Science.gov (United States) Gatson, Joshua W; Benz, Bruce F; Chandrasekaran, Chitra; Satomi, Masataka; Venkateswaran, Kasthuri; Hart, Mark E 2006-07-01 A Gram-positive, spore-forming bacillus was isolated from a sample taken from an approximately 2000-year-old shaft-tomb located in the Mexican state of Jalisco, near the city of Tequila. Tentative identification using conventional biochemical analysis consistently identified the isolate as Bacillus subtilis. DNA isolated from the tomb isolate, strain 10b(T), and closely related species was used to amplify a Bacillus-specific portion of the highly conserved 16S rRNA gene and an internal region of the superoxide dismutase gene (sodA(int)). Trees derived from maximum-likelihood methods applied to the sodA(int) sequences yielded non-zero branch lengths between strain 10b(T) and its closest relative, whereas a comparison of a Bacillus-specific 546 bp amplicon of the 16S rRNA gene demonstrated 99 % similarity with B. subtilis. Although the 16S rRNA gene sequences of strain 10b(T) and B. subtilis were 99 % similar, PFGE of NotI-digested DNA of strain 10b(T) revealed a restriction profile that was considerably different from those of B. subtilis and other closely related species. Whereas qualitative differences in whole-cell fatty acids were not observed, significant quantitative differences were found to exist between strain 10b(T) and each of the other closely related Bacillus species examined. In addition, DNA-DNA hybridization studies demonstrated that strain 10b(T) had a relatedness value of less than 70 % with B. subtilis and other closely related species. Evidence from the sodA(int) sequences, whole-cell fatty acid profiles and PFGE analysis, together with results from DNA-DNA hybridization studies, justify the classification of strain 10b(T) as representing a distinct species, for which the name Bacillus tequilensis sp. nov. is proposed. The type strain is 10b(T) (=ATCC BAA-819(T)=NCTC 13306(T)). 11. Standardized reporting for rapid relative effectiveness assessments of pharmaceuticals. Science.gov (United States) Kleijnen, Sarah; Pasternack, Iris; Van de Casteele, Marc; Rossi, Bernardette; Cangini, Agnese; Di Bidino, Rossella; Jelenc, Marjetka; Abrishami, Payam; Autti-Rämö, Ilona; Seyfried, Hans; Wildbacher, Ingrid; Goettsch, Wim G 2014-11-01 Many European countries perform rapid assessments of the relative effectiveness (RE) of pharmaceuticals as part of the reimbursement decision making process. Increased sharing of information on RE across countries may save costs and reduce duplication of work. The objective of this article is to describe the development of a tool for rapid assessment of RE of new pharmaceuticals that enter the market, the HTA Core Model® for Rapid Relative Effectiveness Assessment (REA) of Pharmaceuticals. Eighteen member organisations of the European Network of Health Technology Assessment (EUnetHTA) participated in the development of the model. Different versions of the model were developed and piloted in this collaboration and adjusted accordingly based on feedback on the content and feasibility of the model. The final model deviates from the traditional HTA Core Model® used for assessing other types of technologies. This is due to the limited scope (strong focus on RE), the timing of the assessment (just after market authorisation), and strict timelines (e.g. 90 days) required for performing the assessment. The number of domains and assessment elements was limited and it was decided that the primary information sources should preferably be a submission file provided by the marketing authorisation holder and the European Public Assessment Report. The HTA Core Model® for Rapid REA (version 3.0) was developed to produce standardised transparent RE information of pharmaceuticals. Further piloting can provide input for possible improvements, such as further refining the assessment elements and new methodological guidance on relevant areas. 12. Differences in the mannose oligomer specificities of the closely related lectins from Galanthus nivalis and Zea mays strongly determine their eventual anti-HIV activity Directory of Open Access Journals (Sweden) Fouquaert Elke 2011-02-01 Full Text Available Abstract Background In a recent report, the carbohydrate-binding specificities of the plant lectins Galanthus nivalis (GNA and the closely related lectin from Zea mays (GNAmaize were determined by glycan array analysis and indicated that GNAmaize recognizes complex-type N-glycans whereas GNA has specificity towards high-mannose-type glycans. Both lectins are tetrameric proteins sharing 64% sequence similarity. Results GNAmaize appeared to be ~20- to 100-fold less inhibitory than GNA against HIV infection, syncytia formation between persistently HIV-1-infected HuT-78 cells and uninfected CD4+ T-lymphocyte SupT1 cells, HIV-1 capture by DC-SIGN and subsequent transmission of DC-SIGN-captured virions to uninfected CD4+ T-lymphocyte cells. In contrast to GNA, which preferentially selects for virus strains with deleted high-mannose-type glycans on gp120, prolonged exposure of HIV-1 to dose-escalating concentrations of GNAmaize selected for mutant virus strains in which one complex-type glycan of gp120 was deleted. Surface Plasmon Resonance (SPR analysis revealed that GNA and GNAmaize interact with HIV IIIB gp120 with affinity constants (KD of 0.33 nM and 34 nM, respectively. Whereas immobilized GNA specifically binds mannose oligomers, GNAmaize selectively binds complex-type GlcNAcβ1,2Man oligomers. Also, epitope mapping experiments revealed that GNA and the mannose-specific mAb 2G12 can independently bind from GNAmaize to gp120, whereas GNAmaize cannot efficiently bind to gp120 that contained prebound PHA-E (GlcNAcβ1,2man specific or SNA (NeuAcα2,6X specific. Conclusion The markedly reduced anti-HIV activity of GNAmaize compared to GNA can be explained by the profound shift in glycan recognition and the disappearance of carbohydrate-binding sites in GNAmaize that have high affinity for mannose oligomers. These findings underscore the need for mannose oligomer recognition of therapeutics to be endowed with anti-HIV activity and that mannose, but 13. Comparative analysis of emm type pattern of Group A Streptococcus throat and skin isolates from India and their association with closely related SIC, a streptococcal virulence factor Directory of Open Access Journals (Sweden) Ganguly Nirmal K 2008-09-01 Full Text Available Abstract Background Group A streptococcus (GAS causes a wide variety of life threatening diseases in humans and the incidence of such infections is high in developing countries like India. Although distribution of emm types of GAS in India has been described, there is a lack of data describing either the comparative distribution of emm types in throat versus skin isolates, or the distribution of certain virulence factors amongst these isolates. Therefore in the present study we have monitored the emm type pattern of Group A streptococcus throat and skin isolates from India. Additionally, the association of these isolates with closely related sic (crs, a multifunctional compliment binding virulence factor, was also explored. Results Of the 94 (46 throat and 48 skin isolates analyzed, 37 emm types were identified. The most frequently observed emm types were emm49 (8.5% and emm112 (7.5% followed by 6.5% each of emm1-2, emm75, emm77, and emm81. Out of 37 emm types, 27 have been previously reported and rest were isolated for the first time in the Indian Community. The predominant emm types of throat (emm49 and emm75 samples were different from those of skin (emm44, emm81 and emm112 samples. After screening all the 94 isolates, the crs gene was found in six emm1-2 (crs1-2 isolates, which was confirmed by DNA sequencing and expression analysis. Despite the polymorphic nature of crs, no intravariation was observed within crs1-2. However, insertions and deletions of highly variable sizes were noticed in comparison to CRS isolated from other emm types (emm1.0, emm57. CRS1-2 showed maximum homology with CRS57, but the genomic location of crs1-2 was found to be the same as that of sic1.0. Further, among crs positive isolates, speA was only present in skin samples thus suggesting possible role of speA in tissue tropism. Conclusion Despite the diversity in emm type pattern of throat and skin isolates, no significant association between emm type and source of 14. A minimally invasive technique for closing an iatrogenic subclavian artery cannulation using the Angio-Seal closure device: two case reports OpenAIRE 2012-01-01 Abstract Introduction In the two cases described here, the subclavian artery was inadvertently cannulated during unsuccessful access to the internal jugular vein. The puncture was successfully closed using a closure device based on a collagen plug (Angio-Seal, St Jude Medical, St Paul, MN, USA). This technique is relatively simple and inexpensive. It can provide clinicians, such as intensive care physicians and anesthesiologists, with a safe and straightforward alternative to major surgery an... 15. Potential utility of cinacalcet as a treatment for CDC73-related primary hyperparathyroidism: a case report. Science.gov (United States) Sato, Takeshi; Muroya, Koji; Hanakawa, Junko; Yamashita, Sumimasa; Nozawa, Kumiko; Masudo, Katsuhiko; Yamakawa, Tadashi; Asakura, Yumi; Hasegawa, Tomonobu; Adachi, Masanori 2016-07-01 We report a Japanese pedigree with familial primary hyperparathyroidism due to a CDC73 mutation. To our knowledge, this is the first report of cinacalcet as a treatment for CDC73-related primary hyperparathyroidism. The proband had severe psychomotor retardation and received laryngotracheal separation surgery. At 19 yr of age, he developed acute pancreatitis. Hypercalcemia (12.2-13.8 mg/dL), elevated levels of intact PTH (86-160 pg/mL), and a tumor detected upon neck ultrasonography led to the diagnosis of primary hyperparathyroidism. Family history and biochemical examinations revealed that three family members (the proband's mother, elder brother, and maternal grandfather) had primary hyperparathyroidism. We identified a novel heterozygous mutation, c.240delT, p.Glu81Lysfs*28, in the CDC73 gene in three affected family members, excluding the proband's elder brother who refused genetic testing. Parathyroidectomy for the proband was considered as high-risk, because the tumor was located close to the tracheostomy orifice. After receiving approval from the institutional review board and obtaining the consent, we initiated cinacalcet treatment. At 22 yr of age, treatment with 100 mg of cinacalcet maintained serum calcium levels below 11.0 mg/dL with no apparent side effects. Our report presents the potential efficacy of cinacalcet as a treatment for CDC73-related primary hyperparathyroidism, in particularly inoperative cases. 16. Conserved PCR primer set designing for closely-related species to complete mitochondrial genome sequencing using a sliding window-based PSO algorithm. Science.gov (United States) Yang, Cheng-Hong; Chang, Hsueh-Wei; Ho, Chang-Hsuan; Chou, Yii-Cheng; Chuang, Li-Yeh 2011-03-18 Complete mitochondrial (mt) genome sequencing is becoming increasingly common for phylogenetic reconstruction and as a model for genome evolution. For long template sequencing, i.e., like the entire mtDNA, it is essential to design primers for Polymerase Chain Reaction (PCR) amplicons which are partly overlapping each other. The presented chromosome walking strategy provides the overlapping design to solve the problem for unreliable sequencing data at the 5' end and provides the effective sequencing. However, current algorithms and tools are mostly focused on the primer design for a local region in the genomic sequence. Accordingly, it is still challenging to provide the primer sets for the entire mtDNA. The purpose of this study is to develop an integrated primer design algorithm for entire mt genome in general, and for the common primer sets for closely-related species in particular. We introduce ClustalW to generate the multiple sequence alignment needed to find the conserved sequences in closely-related species. These conserved sequences are suitable for designing the common primers for the entire mtDNA. Using a heuristic algorithm particle swarm optimization (PSO), all the designed primers were computationally validated to fit the common primer design constraints, such as the melting temperature, primer length and GC content, PCR product length, secondary structure, specificity, and terminal limitation. The overlap requirement for PCR amplicons in the entire mtDNA is satisfied by defining the overlapping region with the sliding window technology. Finally, primer sets were designed within the overlapping region. The primer sets for the entire mtDNA sequences were successfully demonstrated in the example of two closely-related fish species. The pseudo code for the primer design algorithm is provided. In conclusion, it can be said that our proposed sliding window-based PSO algorithm provides the necessary primer sets for the entire mt genome amplification and 17. Conserved PCR primer set designing for closely-related species to complete mitochondrial genome sequencing using a sliding window-based PSO algorithm. Directory of Open Access Journals (Sweden) Cheng-Hong Yang Full Text Available BACKGROUND: Complete mitochondrial (mt genome sequencing is becoming increasingly common for phylogenetic reconstruction and as a model for genome evolution. For long template sequencing, i.e., like the entire mtDNA, it is essential to design primers for Polymerase Chain Reaction (PCR amplicons which are partly overlapping each other. The presented chromosome walking strategy provides the overlapping design to solve the problem for unreliable sequencing data at the 5' end and provides the effective sequencing. However, current algorithms and tools are mostly focused on the primer design for a local region in the genomic sequence. Accordingly, it is still challenging to provide the primer sets for the entire mtDNA. METHODOLOGY/PRINCIPAL FINDINGS: The purpose of this study is to develop an integrated primer design algorithm for entire mt genome in general, and for the common primer sets for closely-related species in particular. We introduce ClustalW to generate the multiple sequence alignment needed to find the conserved sequences in closely-related species. These conserved sequences are suitable for designing the common primers for the entire mtDNA. Using a heuristic algorithm particle swarm optimization (PSO, all the designed primers were computationally validated to fit the common primer design constraints, such as the melting temperature, primer length and GC content, PCR product length, secondary structure, specificity, and terminal limitation. The overlap requirement for PCR amplicons in the entire mtDNA is satisfied by defining the overlapping region with the sliding window technology. Finally, primer sets were designed within the overlapping region. The primer sets for the entire mtDNA sequences were successfully demonstrated in the example of two closely-related fish species. The pseudo code for the primer design algorithm is provided. CONCLUSIONS/SIGNIFICANCE: In conclusion, it can be said that our proposed sliding window-based PSO 18. Recommendations on selecting the closing relations for calculating friction pressure drop in the loops of nuclear power stations equipped with VVER reactors Science.gov (United States) Alipchenkov, V. M.; Belikov, V. V.; Davydov, A. V.; Emel'yanov, D. A.; Mosunova, N. A. 2013-05-01 Closing relations describing friction pressure drop during the motion of two-phase flows that are widely applied in thermal-hydraulic codes and in calculations of the parameters characterizing the flow of water coolant in the loops of reactor installations used at nuclear power stations and in other thermal power systems are reviewed. A new formula developed by the authors of this paper is proposed. The above-mentioned relations are implemented in the HYDRA-IBRAE thermal-hydraulic computation code developed at the Nuclear Safety Institute of the Russian Academy of Sciences. A series of verification calculations is carried out for a wide range of pressures, flowrates, and heat fluxes typical for transient and emergency operating conditions of nuclear power stations equipped with VVER reactors. Advantages and shortcomings of different closing relations are revealed, and recommendations for using them in carrying out thermal-hydraulic calculations of coolant flow in the loops of VVER-based nuclear power stations are given. 19. Temperature as an ecological factor in the distribution of two closely related freshwater Triclads: an experimental study. [Polycelis tenuis, polycelis nigra Energy Technology Data Exchange (ETDEWEB) Lascombe, C.; Pattee, E.; Bornard, C. 1975-01-01 The influence of temperature on the ecophysiology of two closely related limnophilic Triclads, Polycelis tenuis and P. nigra, in the Lyons region was investigated. Both species have the same physiological rate in the middle zone of the temperature range, but P. tenuis prevails at both ends of the range. It tolerates higher temperatures and its reproduction rate is greater in the cold. Also, because of the existence of physiological races, it seems adapted to a greater diversity of situations. It appears as a real eurytherm. These different points contribute to the explanation of the habitat of both species in the region. 20. Enhanced depth imaging is less suited than indocyanine green angiography for close monitoring of primary stromal choroiditis: a pilot report. Science.gov (United States) Balci, Ozlem; Gasc, Amel; Jeannin, Bruno; Herbort, Carl P 2016-08-02 The purpose of this study is to investigate the performance, utility, and precision of enhanced depth imaging optical coherence tomography (EDI-OCT) versus indocyanine green angiography (ICGA) in tracking any fluctuation in the activity of stromal choroiditis in response to therapeutic interventions during long-term follow-up. Patients with a diagnosis of Vogt-Koyanagi-Harada (VKH) disease or birdshot retinochoroiditis (BRC), with untreated initial disease, and having had long-term follow-up, including both ICGA and EDI-OCT, were recruited at the Centre for Ophthalmic Specialised care, Lausanne, Switzerland. Angiography signs were quantified according to established dual fluorescein angiography (FA) and ICGA scoring systems for uveitis. Changes in ICGA score and EDI choroidal thickness, in response to therapeutic intervention, were assessed. In the four eyes analysed (2 BRC and 2 VKH), mean EDI-OCT choroidal thickness decreased from 672 ± 101 µm at presentation to 358.5 ± 44.5 µm in a mean of 26.5 months, i.e. the time taken to stabilize the disease. Mean ICGA scores decreased from 28 ± 4.2 at presentation to 5 ± 7 at stabilization. Only ICGA was sufficiently sensitive and reactive having the ability to detect disease recurrences and efficacy or the absence of effect of successive treatment changes, detected in seven instances during follow-up, not recorded by EDI-OCT. This pilot study showed that ICGA was a more sensitive methodology, which promptly identifies evolving subclinical and occult choroidal disease, and flag occult recurrence and/or therapeutic responses that were otherwise missed by EDI-OCT. Although choroidal thickness was proportional to treatment course, demonstrating a linear decrease, these changes were too sluggish to be relied upon for close follow-up and timely adjustment of therapy. 1. Work-Related Upper Limb Disorders: A Case Report Directory of Open Access Journals (Sweden) Zlatka Borisova Stoyneva 2015-03-01 Full Text Available In this study the complex interrelationship between physical factors, job stress, lifestyle and genetic factors on symptoms of work-related musculoskeletal disorders of the upper limbs is demonstrated by a case report and discussion of the literature. A 58 year old woman with long lasting complaints of the upper limbs with increasing intensity and duration, generalisation, combined with skin thickness, Raynaud’s phenomenon, joint disorders, arterial and pulmonary hypertension, metabolic lipid dysfunctions is presented. Occupational history proves continuous duration of service at a job with occupational physical static load with numerous repetitive monotonous systematic motions of fingers and hands as a weaver of Persian rugs followed by work at an automated loom and variable labour activities. Though the complaints dated since the time she was a manual weaver, the manifestations of generalized joint degenerative changes, system sclerosis with Raynaud’s phenomenon with similar upper extremities signs and symptoms discount upper limbs musculoskeletal disorder as caused only or mainly by occupational risk factors. The main principles and criteria for occupational diagnosis of musculoskeletal upper limb disorders and legislative requirements for their reglamentation are discussed. 2. [Scleroderma related to specific immunotherapy. A report of a case]. Science.gov (United States) Morfín Maciel, Blanca María; Castillo Morfín, Blanca María 2009-01-01 It has been described two main phenotypes of helper T cells. On activation, the immune system develops the most effective Th response. Whereas Th1 cells promote cell-mediate immunity against intracellular pathogens and an over expression could favor autoimmune diseases; Th2 cells develop humoral immunity against extracellular pathogens promoting allergic response. Normally, the two profiles coexist in the same individual with different grades of expression. Recently, it has been described a new subset: Th17, which is related to tissue injury in autoimmune diseases. Then, allergic and autoimmune diseases result from an unbalanced response of the immune system. Allergen-specific immunotherapy is the only curative treatment of a specific allergy, which leads to a life-long tolerance against allergens. There are no controlled studies about the effectiveness or risks associated with allergen-specific immunotherapy in patients with autoimmune disorders. On the other hand, scleroderma is an autoimmune chronic systemic disorder of unknown etiology characterized by excess collagen deposition in the skin and viscera, along with vascular injury. We report a girl with allergic asthma and with a second degree family history of systemic sclerosis who developed localized scleroderma during allergen specific immunotherapy. Because allergy vaccination alter the balance between effector and regulatory T-cell populations, which regulate immune tolerance, a positive family history of autoimmunity in first or second degree, could be a contraindication for allergen-specific immunotherapy. 3. Desmin-related myopathy: Report of a rare case Directory of Open Access Journals (Sweden) Sridhar E 2005-01-01 Full Text Available The Protein Surplus Myopathies (PSM are characterized by accumulation of protein aggregates, identifiable ultrastructurally, resulting due to mutations of the encoding genes. Desmin-related myopathies (DRM are a form of PSM characterized by mutations of the desmin gene resulting in the formation of protein aggregates comprising mutant protein desmin and disturbance of the regular desmin intermediate network in the muscle fibers. We describe a rare case of DRM in a 23-year-old man who presented with complaints of difficulty in climbing stairs and running since the age of 5 years. EMG studies revealed a myopathic pattern. Muscle biopsy showed the features of muscular dystrophy with bluish rimmed vacuoles and sarcoplasmic inclusions, which were immunoreactive to desmin. Ultrastructural examination showed sarcoplasmic bodies and granulofilamentous inclusions. Although rare, the possibility of DRM/desminopathy should be considered in the presence of bluish rimmed vacuoles on light microscopy and characteristic ultrastructural inclusions. To the best of our knowledge this is the first case of DRM/desminopathy reported from India. 4. Genomics of sponge-associated Streptomyces spp. closely related to Streptomyces albus J1074: insights into marine adaptation and secondary metabolite biosynthesis potential. Directory of Open Access Journals (Sweden) Elena Ian Full Text Available A total of 74 actinomycete isolates were cultivated from two marine sponges, Geodia barretti and Phakellia ventilabrum collected at the same spot at the bottom of the Trondheim fjord (Norway. Phylogenetic analyses of sponge-associated actinomycetes based on the 16S rRNA gene sequences demonstrated the presence of species belonging to the genera Streptomyces, Nocardiopsis, Rhodococcus, Pseudonocardia and Micromonospora. Most isolates required sea water for growth, suggesting them being adapted to the marine environment. Phylogenetic analysis of Streptomyces spp. revealed two isolates that originated from different sponges and had 99.7% identity in their 16S rRNA gene sequences, indicating that they represent very closely related strains. Sequencing, annotation, and analyses of the genomes of these Streptomyces isolates demonstrated that they are sister organisms closely related to terrestrial Streptomyces albus J1074. Unlike S. albus J1074, the two sponge streptomycetes grew and differentiated faster on the medium containing sea water. Comparative genomics revealed several genes presumably responsible for partial marine adaptation of these isolates. Genome mining targeted to secondary metabolite biosynthesis gene clusters identified several of those, which were not present in S. albus J1074, and likely to have been retained from a common ancestor, or acquired from other actinomycetes. Certain genes and gene clusters were shown to be differentially acquired or lost, supporting the hypothesis of divergent evolution of the two Streptomyces species in different sponge hosts. 5. Use of two novel approaches to discriminate between closely related host microRNAs that are manipulated by Toxoplasma gondii during infection. Science.gov (United States) Zeiner, Gusti M; Boothroyd, John C 2010-06-01 MicroRNAs (miRNAs) are a class of small, endogenously encoded regulatory RNAs that function to post-transcriptionally regulate gene expression in a wide variety of eukaryotes. Within organisms, some mature miRNAs, such as paralogous miRNAs, have nearly identical nucleotide sequences, which makes them virtually indistinguishable from one another by conventional hybridization-based approaches. Here we describe two inexpensive, sensitive methods for rapidly discriminating between paralogous miRNAs or other closely related miRNAs and for quantifying their abundance. The first approach is a sequential ribonuclease-protection and primer-extension assay; the second approach is a primer-extension assay that employs short oligonucleotide probes to exacerbate the instability of mismatched probe:miRNA hybrids. Both approaches are rapid and can be easily performed in their entirety using common laboratory equipment. As a proof of concept, we have used these methods to determine the exact identities of the human miR-17 family members that are increased by infection with the intracellular parasite Toxoplasma gondii. These methods can be used to rapidly and inexpensively discriminate between any closely related miRNAs in any organism. 6. Molecular investigation and phylogeny of Anaplasma spp. in Mediterranean ruminants reveal the presence of neutrophil-tropic strains closely related to A. platys. Science.gov (United States) Zobba, Rosanna; Anfossi, Antonio G; Pinna Parpaglia, Maria Luisa; Dore, Gian Mario; Chessa, Bernardo; Spezzigu, Antonio; Rocca, Stefano; Visco, Stefano; Pittau, Marco; Alberti, Alberto 2014-01-01 Few data are available on the prevalence and molecular typing of species belonging to the genus Anaplasma in Mediterranean ruminants. In this study, PCR analysis and sequencing of both 16S rRNA and groEL genes were combined to investigate the presence, prevalence, and molecular traits of Anaplasma spp. in ruminants sampled on the Island of Sardinia, chosen as a subtropical representative area. The results demonstrate a high prevalence of Anaplasma spp. in ruminants, with animals infected by at least four of six Anaplasma species (Anaplasma marginale, A. bovis, A. ovis, and A. phagocytophilum). Moreover, ruminants host a number of neutrophil-tropic strains genetically closely related to the canine pathogen A. platys. The high Anaplasma spp. prevalence and the identification of as-yet-unclassified neutrophil-tropic strains raise concerns about the specificity of serological tests routinely used in ruminants and provide additional background for reconstructing the evolutionary history of species genetically related to A. phagocytophilum. 7. Karyotyping of female and male Hediste japonica (Polychaeta, Annelida) in comparison with those of two closely related species, H. diadroma and H. atoka. Science.gov (United States) Tosuji, Hiroaki; Miyamoto, Junko; Hayata, Yuki; Sato, Masanori 2004-02-01 Karyotypes of females and males of the brackish-water polychaete Hediste japonica sensu stricto, collected from the Ariake Sea, Japan, were examined by using regenerating tails. We used the Giemsa staining method and a computer-assisted image-analyzing system for the identification of each chromosome pair. The somatic chromosome number was 2n=28. The presence of an XX-XY (male heterogametic) sex chromosome system was determined from well-spread metaphase plates of somatic cells. The type of sex chromosomes related with phenotype exactly. The metacentric Y chromosome was much larger than the submetacentric X chromosome. All autosomes were metacentric. The karyotype of this species was compared with those of the other two closely related species (H. diadroma and H. atoka). The karyotypes of all the three species were similar to one another. 8. Occlusal factors are not related to self-reported bruxism NARCIS (Netherlands) Manfredini, D.; Visscher, C.M.; Guarda-Nardini, L.; Lobbezoo, F. 2012-01-01 AIMS: To estimate the contribution of various occlusal features of the natural dentition that may identify self-reported bruxers compared to nonbruxers. METHODS: Two age- and sex-matched groups of self-reported bruxers (n = 67) and self-reported nonbruxers (n = 75) took part in the study. For each 9. Novel low abundance and transient RNAs in yeast revealed by tiling microarrays and ultra high-throughput sequencing are not conserved across closely related yeast species. Directory of Open Access Journals (Sweden) Albert Lee 2008-12-01 Full Text Available A complete description of the transcriptome of an organism is crucial for a comprehensive understanding of how it functions and how its transcriptional networks are controlled, and may provide insights into the organism's evolution. Despite the status of Saccharomyces cerevisiae as arguably the most well-studied model eukaryote, we still do not have a full catalog or understanding of all its genes. In order to interrogate the transcriptome of S. cerevisiae for low abundance or rapidly turned over transcripts, we deleted elements of the RNA degradation machinery with the goal of preferentially increasing the relative abundance of such transcripts. We then used high-resolution tiling microarrays and ultra high-throughput sequencing (UHTS to identify, map, and validate unannotated transcripts that are more abundant in the RNA degradation mutants relative to wild-type cells. We identified 365 currently unannotated transcripts, the majority presumably representing low abundance or short-lived RNAs, of which 185 are previously unknown and unique to this study. It is likely that many of these are cryptic unstable transcripts (CUTs, which are rapidly degraded and whose function(s within the cell are still unclear, while others may be novel functional transcripts. Of the 185 transcripts we identified as novel to our study, greater than 80 percent come from regions of the genome that have lower conservation scores amongst closely related yeast species than 85 percent of the verified ORFs in S. cerevisiae. Such regions of the genome have typically been less well-studied, and by definition transcripts from these regions will distinguish S. cerevisiae from these closely related species. 10. Rare Head and Neck Benign Mesenchymoma in Close Proximity to Submandibular Gland in a Pediatric Patient: Case Report and Review of the Literature Directory of Open Access Journals (Sweden) Priyanka Jain 2015-01-01 Full Text Available Pediatric head and neck masses are commonly congenital in origin or of infectious etiology. We present a rare case of benign mesenchymoma in close proximity to the submandibular gland in an otherwise asymptomatic child. Computerized tomography (CT scan of the head and neck area revealed a benign lesion, which was later determined to be a benign mesenchymoma on histopathology. The child did well after surgery without any reported recurrence. We discuss the salient features of a benign mesenchymoma in a child and also discuss relevant imaging and management. 11. Genome-wide Identification and Expression Analysis of Calcium-dependent Protein Kinase and Its Closely Related Kinase Genes in Capsicum annuum Directory of Open Access Journals (Sweden) hanyang ecai 2015-09-01 Full Text Available As Ca2+ sensors and effectors, calcium-dependent protein kinases (CDPKs play important roles in regulating the downstream components of calcium signaling, which are ubiquitously involved in plant growth, development, and response to environmental cues. However, no CDPKs have been characterized in Capsicum annuum thus far. Herein, a comprehensive analysis of genes encoding pepper CDPKs and CDPK-related protein kinases (CRKs was performed, and 31 CDPK genes and five closely related kinase genes were identified, which were phylogenetically divided into four distinct subfamilies and unevenly distributed across nine chromosomes. Conserved sequence and exon-intron structures were found to be shared by pepper CDPKs within the same subfamily, and the expansion of the CaCPK family in pepper was found to be due to segmental duplication events. Five CDPKs in the Capsicum annuum variety CM334 were found to be mutated in the Chiltepin variety, and one CDPK present in CM334 was lost in Chiltepin. The majority of CDPK and CRK genes were expressed in different pepper tissues and developmental stages, and 10, 12, and eight CDPK genes were transcriptionally modified by salt, heat, and Ralstonia solanacearum stresses, respectively. Furthermore, these genes were found to respond specifically to one stress as well as respond synergistically to two stresses or three stresses, suggesting that these CDPK genes might be involved in the specific or synergistic response of pepper to salt, heat, and R. solanacearum. Our results lay the foundation for future functional characterization of pepper CDPK and its closely related gene families. 12. Hybridization and massive mtDNA unidirectional introgression between the closely related Neotropical toads Rhinella marina and R. schneideri inferred from mtDNA and nuclear markers Directory of Open Access Journals (Sweden) Schneider Horacio 2011-09-01 Full Text Available Abstract Background The classical perspective that interspecific hybridization in animals is rare has been changing due to a growing list of empirical examples showing the occurrence of gene flow between closely related species. Using sequence data from cyt b mitochondrial gene and three intron nuclear genes (RPL9, c-myc, and RPL3 we investigated patterns of nucleotide polymorphism and divergence between two closely related toad species R. marina and R. schneideri. By comparing levels of differentiation at nuclear and mtDNA levels we were able to describe patterns of introgression and infer the history of hybridization between these species. Results All nuclear loci are essentially concordant in revealing two well differentiated groups of haplotypes, corresponding to the morphologically-defined species R. marina and R. schneideri. Mitochondrial DNA analysis also revealed two well-differentiated groups of haplotypes but, in stark contrast with the nuclear genealogies, all R. schneideri sequences are clustered with sequences of R. marina from the right Amazon bank (RAB, while R. marina sequences from the left Amazon bank (LAB are monophyletic. An Isolation-with-Migration (IM analysis using nuclear data showed that R. marina and R. schneideri diverged at ≈ 1.69 Myr (early Pleistocene, while R. marina populations from LAB and RAB diverged at ≈ 0.33 Myr (middle Pleistocene. This time of divergence is not consistent with the split between LAB and RAB populations obtained with mtDNA data (≈ 1.59 Myr, which is notably similar to the estimate obtained with nuclear genes between R. marina and R. schneideri. Coalescent simulations of mtDNA phylogeny under the speciation history inferred from nuclear genes rejected the hypothesis of incomplete lineage sorting to explain the conflicting signal between mtDNA and nuclear-based phylogenies. Conclusions The cytonuclear discordance seems to reflect the occurrence of interspecific hybridization between these 13. Two atomic constraints unambiguously position the S4 segment relative to S1 and S2 segments in the closed state of Shaker K channel. Science.gov (United States) Campos, Fabiana V; Chanda, Baron; Roux, Benoît; Bezanilla, Francisco 2007-05-01 It is now well established that the voltage-sensing S4 segment in voltage-dependent ion channels undergoes a conformational change in response to varying membrane potential. However, the magnitude of the movement of S4 relative to the membrane and the rest of the protein remains controversial. Here, by using histidine scanning mutagenesis in the Shaker K channel, we identified mutants I241H (S1 segment) and I287H (S2 segment) that generate inward currents at hyperpolarized potentials, suggesting that these residues are part of a hydrophobic plug that separates the water-accessible crevices. Additional experiments with substituted cysteine residues showed that, at hyperpolarized potentials, both I241C and I287C can spontaneously form disulphide and metal bridges with R362C, the position of the first charge-carrying residue in S4. These results constrain unambiguously the closed-state positions of the S4 segment with respect to the S1 and S2 segments, which are known to undergo little or no movement during gating. To satisfy these constraints, the S4 segment must undergo an axial rotation of approximately 180 degrees and a transmembrane (vertical) movement of approximately 6.5 A at the level of R362 in going from the open to the closed state of the channel, moving the gating charge across a focused electric field. 14. Bacterial Species-Specific Activity of a Fluoroquinolone against Two Closely Related Pasteurellaceae with Similar MICs: Differential In Vitro Inoculum Effects and In Vivo Efficacies. Directory of Open Access Journals (Sweden) Guillaume Lhermie Full Text Available We investigated the antimicrobial activity of a fluoroquinolone against two genetically close bacterial species belonging to the Pasteurellaceae family. Time-kill experiments were used to measure the in vitro activity of marbofloxacin against two strains of Mannheimia haemolytica and Pasteurella multocida with similar MICs. We observed that marbofloxacin was equally potent against 105 CFU/mL inocula M. haemolytica and P. multocida. However, an inoculum effect was observed with P. multocida, meaning that marbofloxacin activity was decreased against a 108 CFU/mL inoculum, whereas no inoculum effect was observed with M. haemolytica. Marbofloxacin activity was also tested in a lung infection model with immunocompromised mice intratracheally infected with 109 CFU of each bacteria. At the same dose, the clinical and bacteriological outcomes were much better for mice infected with M. haemolytica than for those infected with P. multocida. Moreover, bacteriological eradication was obtained with a lower marbofloxacin dose for mice infected with M. haemolytica. Our results suggest that the differential in vivo marbofloxacin efficacy observed with the two bacterial species of similar MIC could be explained by a differential inoculum effect. Consequently, MICs determined on 105 CFU inocula were not predictive of the differences in antibiotic efficacies against high bacterial inocula of closely related bacterial strains. These results could stimulate further investigations on bacterial species-specific antibiotic doses in a clinical setting. 15. Bacterial Species-Specific Activity of a Fluoroquinolone against Two Closely Related Pasteurellaceae with Similar MICs: Differential In Vitro Inoculum Effects and In Vivo Efficacies Science.gov (United States) Lhermie, Guillaume; El Garch, Farid; Toutain, Pierre-Louis; Ferran, Aude A.; Bousquet-Mélou, Alain 2015-01-01 We investigated the antimicrobial activity of a fluoroquinolone against two genetically close bacterial species belonging to the Pasteurellaceae family. Time-kill experiments were used to measure the in vitro activity of marbofloxacin against two strains of Mannheimia haemolytica and Pasteurella multocida with similar MICs. We observed that marbofloxacin was equally potent against 105 CFU/mL inocula M. haemolytica and P. multocida. However, an inoculum effect was observed with P. multocida, meaning that marbofloxacin activity was decreased against a 108 CFU/mL inoculum, whereas no inoculum effect was observed with M. haemolytica. Marbofloxacin activity was also tested in a lung infection model with immunocompromised mice intratracheally infected with 109 CFU of each bacteria. At the same dose, the clinical and bacteriological outcomes were much better for mice infected with M. haemolytica than for those infected with P. multocida. Moreover, bacteriological eradication was obtained with a lower marbofloxacin dose for mice infected with M. haemolytica. Our results suggest that the differential in vivo marbofloxacin efficacy observed with the two bacterial species of similar MIC could be explained by a differential inoculum effect. Consequently, MICs determined on 105 CFU inocula were not predictive of the differences in antibiotic efficacies against high bacterial inocula of closely related bacterial strains. These results could stimulate further investigations on bacterial species-specific antibiotic doses in a clinical setting. PMID:26506096 16. 18 CFR 12.10 - Reporting safety-related incidents. Science.gov (United States) 2010-04-01 ... at the project, the applicant or licensee must report that drowning or other accident to the Regional... the Regional Engineer any condition affecting the safety of a project or projects works, as defined in...)(1), the applicant or licensee must submit to the Regional Engineer a written report on the condition... 17. Pacemaker Related Infective Endocarditis from Staphylococcus Lugdunensis: A Case Report Directory of Open Access Journals (Sweden) Michael Ward 2013-01-01 Full Text Available Staphylococcus lugdunensis is a common skin flora not typically associated with infection. There are, however, several cases reported in the literature of Staphylococcus lugdunensis as a causative bacterium of various infections. This paper reports an additional case of pacemaker associated endocarditis with Staphylococcus lugdunensis as the causative bacterium. 18. Discrimination of Bacillus anthracis from closely related microorganisms by analysis of 16S and 23S rRNA with oligonucleotide microchips Science.gov (United States) Bavykin, Sergei G.; Mirzabekov, Andrei D. 2007-10-30 The present invention is directed to a novel method of discriminating a highly infectious bacterium Bacillus anthracis from a group of closely related microorganisms. Sequence variations in the 16S and 23S rRNA of the B. cereus subgroup including B. anthracis are utilized to construct an array that can detect these sequence variations through selective hybridizations. The identification and analysis of these sequence variations enables positive discrimination of isolates of the B. cereus group that includes B. anthracis. Discrimination of single base differences in rRNA was achieved with a microchip during analysis of B. cereus group isolates from both single and in mixed probes, as well as identification of polymorphic sites. Successful use of a microchip to determine the appropriate subgroup classification using eight reference microorganisms from the B. cereus group as a study set, was demonstrated. 19. Autism Symptoms Related to Tyrosinemia Type III: A Case Report Directory of Open Access Journals (Sweden) Ayşegül Yolga Tahiroğlu 2008-08-01 Full Text Available The published literature on tyrosinemia type III consists of only a few case reports. In this report, we present a patient with tyrosinemia type III, autism, and mental retardation. This patient’s speech improved and his autistic symptoms lessened on a tyrosine-restricted diet, although his mental retardation remained unchanged. This is the first published report of a patient with tyrosinemia type III and autism. This observation is significant due to the paucity of published information about tyrosinemia type III. Turk Jem 2008; 12: 55-6 20. Secondary metabolite profiles and antifungal drug susceptibility of Aspergillus fumigatus and closely related species, Aspergillus lentulus, Aspergillus udagawae, and Aspergillus viridinutans. Science.gov (United States) Tamiya, Hiroyuki; Ochiai, Eri; Kikuchi, Kazuyo; Yahiro, Maki; Toyotome, Takahito; Watanabe, Akira; Yaguchi, Takashi; Kamei, Katsuhiko 2015-05-01 The incidence of Aspergillus infection has been increasing in the past few years. Also, new Aspergillus fumigatus-related species, namely Aspergillus lentulus, Aspergillus udagawae, and Aspergillus viridinutans, were shown to infect humans. These fungi exhibit marked morphological similarities to A. fumigatus, albeit with different clinical courses and antifungal drug susceptibilities. The present study used liquid chromatography/time-of-flight mass spectrometry to identify the secondary metabolites secreted as virulence factors by these Aspergillus species and compared their antifungal susceptibility. The metabolite profiles varied widely among A. fumigatus, A. lentulus, A. udagawae, and A. viridinutans, producing 27, 13, 8, and 11 substances, respectively. Among the mycotoxins, fumifungin, fumiquinazoline A/B and D, fumitremorgin B, gliotoxin, sphingofungins, pseurotins, and verruculogen were only found in A. fumigatus, whereas auranthine was only found in A. lentulus. The amount of gliotoxin, one of the most abundant mycotoxins in A. fumigatus, was negligible in these related species. In addition, they had decreased susceptibility to antifungal agents such as itraconazole and voriconazole, even though metabolites that were shared in the isolates showing higher minimum inhibitory concentrations than epidemiological cutoff values were not detected. These strikingly different secondary metabolite profiles may lead to the development of more discriminative identification protocols for such closely related Aspergillus species as well as improved treatment outcomes. 1. Study of variations as desired-relative (DELTA), rather than absolute, differences: falsification of the purpose of achieving source-representative and closely comparable lab-results CERN Document Server Datta, B P 2014-01-01 Recently (arXiv:1101.0973), it has been pointed out by us that the possible variation in any source (S) specific elemental isotopic (viz. 2H/1H) abundance ratio SR can more accurately be assessed by its absolute estimate Sr [viz. as (Sr - DR), with D as a standard-source] than by either corresponding measured-relative (S/W-DELTA) estimate ([Sr/Wr] - 1) or DELTA-scale-converted-relative (S/D-DELTA) estimate ([Sr/DR] - 1). Here, we present the fundamentals behind scale-conversion, thereby enabling to understand why at all Sr should be the source- and/ or variation-characterizing key, i.e. why different lab-specific results should be more closely comparable as absolute estimates (SrLab1, SrLab2) than as desired-relative (S/D-DELTALab1, S/D-DELTALab2) estimates. Further, the study clarifies that: (i) the DELTA-scale-conversion (S/W-DELTA into S/D-DELTA, even with the aid of calibrated auxiliary-reference-standard(s) Ai(s)) cannot make the estimates (as S/D-DELTA, and thus Sr) free of the measurement-reference W; ... 2. Can mixed-species groups reduce individual parasite load? A field test with two closely related poeciliid fishes (Poecilia reticulata and Poecilia picta. Directory of Open Access Journals (Sweden) Felipe Dargent Full Text Available Predation and parasitism are two of the most important sources of mortality in nature. By forming groups, individuals can gain protection against predators but may increase their risk of being infected with contagious parasites. Animals might resolve this conflict by forming mixed-species groups thereby reducing the costs associated with parasites through a relative decrease in available hosts. We tested this hypothesis in a system with two closely related poeciliid fishes (Poecilia reticulata and Poecilia picta and their host-specific monogenean ectoparasites (Gyrodactylus spp. in Trinidad. Fish from three different rivers were sampled from single and mixed-species groups, measured and scanned for Gyrodactylus. The presence and abundance of Gyrodactylus were lower when fish of both species were part of mixed-species groups relative to single-species groups. This is consistent with the hypothesis that mixed-species groups provide a level of protection against contagious parasites. We discuss the importance of potentially confounding factors such as salinity and individual fish size. 3. Can mixed-species groups reduce individual parasite load? A field test with two closely related poeciliid fishes (Poecilia reticulata and Poecilia picta). Science.gov (United States) Dargent, Felipe; Torres-Dowdall, Julián; Scott, Marilyn E; Ramnarine, Indar; Fussmann, Gregor F 2013-01-01 Predation and parasitism are two of the most important sources of mortality in nature. By forming groups, individuals can gain protection against predators but may increase their risk of being infected with contagious parasites. Animals might resolve this conflict by forming mixed-species groups thereby reducing the costs associated with parasites through a relative decrease in available hosts. We tested this hypothesis in a system with two closely related poeciliid fishes (Poecilia reticulata and Poecilia picta) and their host-specific monogenean ectoparasites (Gyrodactylus spp.) in Trinidad. Fish from three different rivers were sampled from single and mixed-species groups, measured and scanned for Gyrodactylus. The presence and abundance of Gyrodactylus were lower when fish of both species were part of mixed-species groups relative to single-species groups. This is consistent with the hypothesis that mixed-species groups provide a level of protection against contagious parasites. We discuss the importance of potentially confounding factors such as salinity and individual fish size. 4. Industrial Change and Black Men's Relative Earnings: Final Report. Science.gov (United States) Vroman, Wayne This study examines the relative earnings of black men from a time series perspective covering 1930 to 1990. Regression analyses were fitted to annual data to isolate factors responsible for changes in relative earnings. National and regional data on population growth and employment growth by industry were analyzed to determine the degree of… 5. Relation of Spatial Skills to Calculus Proficiency: A Brief Report Science.gov (United States) Cromley, Jennifer G.; Booth, Julie L.; Wills, Theodore W.; Chang, Briana L.; Tran, Nhi; Madeja, Michael; Shipley, Thomas F.; Zahner, William 2017-01-01 Spatial skills have been shown in various longitudinal studies to be related to multiple science, technology, engineering, and math (STEM) achievement and retention. The specific nature of this relation has been probed in only a few domains, and has rarely been investigated for calculus, a critical topic in preparing students for and in STEM… 6. Relation of Spatial Skills to Calculus Proficiency: A Brief Report Science.gov (United States) Cromley, Jennifer G.; Booth, Julie L.; Wills, Theodore W.; Chang, Briana L.; Tran, Nhi; Madeja, Michael; Shipley, Thomas F.; Zahner, William 2017-01-01 Spatial skills have been shown in various longitudinal studies to be related to multiple science, technology, engineering, and math (STEM) achievement and retention. The specific nature of this relation has been probed in only a few domains, and has rarely been investigated for calculus, a critical topic in preparing students for and in STEM… 7. CULTURAL AND SOCIOLOGICAL FACTORS RELATING TO LEARNING DEVELOPMENT. FINAL REPORT. Science.gov (United States) MACCOBY, MICHAEL; MODIANO, NANCY THE PRIMARY PURPOSE OF THIS STUDY WAS TO COMPARE CULTURAL AND CHARACTER VARIABLES AND RELATE THEM TO THE COGNITIVE DEVELOPMENT OF MEXICAN PEASANT CHILDREN. THE CULTURAL VARIABLES STUDIED INCLUDE ECONOMIC LEVELS, MORAL AND AFFECTIVE JUDGMENTS, AND THE RELATIONSHIPS BETWEEN PARENTS AND CHILDREN. MODES OF ASSIMILATION, SOCIAL RELATIONS, FIXATIONS,… 8. Closed orbit response to quadrupole strength variation Energy Technology Data Exchange (ETDEWEB) Wolski, Andrzej; Zimmermann, Frank 2004-01-20 We derive two formulae relating the variation in closed orbit in a storage ring to variations in quadrupole strength, neglecting nonlinear and dispersive effects. These formulae correct results previously reported [1,2,3]. We compare the results of the formulae applied to the ATF with simulations using MAD, and consider their application to beam-based alignment. 9. Live music therapy in waiting area of intensive care units: a novel concept for betterment of close relatives of ICU patients Directory of Open Access Journals (Sweden) Sundar Sumathy 2016-03-01 Full Text Available Family members of ICU patients experience high levels of stress and anxiety. We explored a novel concept of live music therapy for relatives of ICU patients. Weekly 1-hour sessions of live music therapy consisting of devotional songs and prayers were performed in waiting area of ICU in a tertiary care hospital. Responses of 100 first degree relatives of ICU patients were documented using an 8-item questionnaire. 69% of the subjects rated live music therapy sessions as and ldquo;excellent and rdquo;; 50% of the subjects reported that they felt and ldquo;excellent and rdquo; after a single session. Such sessions were reported as a felt need by 77% of the subjects; 92% of the subjects reported that there were high chances that they would recommend such sessions in the hospital in future. In our study, we found our concept to be feasible, acceptable and highly appreciated as well as encouraged by first degree relatives of ICU patients. [Int J Res Med Sci 2016; 4(3.000: 947-949 10. Correlation between serum hepatitis B virus core-related antigen and intrahepatic covalently closed circular DNA in chronic hepatitis B patients. Science.gov (United States) Suzuki, Fumitaka; Miyakoshi, Hideo; Kobayashi, Mariko; Kumada, Hiromitsu 2009-01-01 Nucleos(t)ide analogues are utilized for the treatment of chronic HBV infection, and HBe seroconversion and HBV DNA levels are commonly used as markers of viral status and as primary treatment endpoints. Recently, a new assay was prepared for the detection of serum HBV core-related antigen (HBcrAg), consisting of HBcAg, HBeAg, and p22cr, which is a precore protein from amino acid -28 to at least amino acid 150, by coding the precore/core region. In this study, we examined the correlation between serum HBcrAg concentration and viral status by the analysis of serum HBeAg, HBsAg, peripheral HBV DNA, and intrahepatic covalently closed circular DNA (cccDNA) in 57 chronic hepatitis B patients. Intrahepatic cccDNA was detected in all 57 patients, 42 patients were HBcrAg-positive, and serum HBcrAg concentration level was closely correlated with cccDNA. Additionally, positive HBcrAg concentration level results were observed in 6 out of 13 HBsAg seroclearance patients and 20 out of 31 HBV DNA-negative patients. Moreover, the correlation between HBcrAg and cccDNA in these 31 HBV DNA-negative patients was statistically significant (r = 0.482, P = 0.006). These data suggest that serum HBcrAg concentration is well correlated with intrahepatic cccDNA level, and that the measurement of serum HBcrAg may be clinically useful for monitoring intrahepatic HBV viral status, especially in patients under treatment with nucleos(t)ide analogues. 11. Pain Report and Pain-Related Evoked Potentials Operantly Conditioned NARCIS (Netherlands) Lousberg, Richel; Vuurman, Eric; Lamers, Theo; Breukelen, van Gerard; Jongen, Ellen; Rijnen, Heidi; Maessen, Christa; Hermens, Hermie 2005-01-01 Objective: The purpose of the present study was to answer the ques- tion whether pain report can be increased and decreased by operant conditioning. We predicted that the conditioned pain effects would remain significant after correction for social desirability and fantasy proneness. Furthermore, we 12. Pain Report and Pain-Related Evoked Potentials Operantly Conditioned NARCIS (Netherlands) Lousberg, Richel; Vuurman, Eric; Lamers, Theo; van Breukelen, Gerard; Jongen, Ellen; Rijnen, Heidi; Maessen, Christa; Hermens, Hermanus J. Objective: The purpose of the present study was to answer the ques- tion whether pain report can be increased and decreased by operant conditioning. We predicted that the conditioned pain effects would remain significant after correction for social desirability and fantasy proneness. Furthermore, we 13. Transfusion-related acute lung injury：A case report Institute of Scientific and Technical Information of China (English) Emmanouil Petrou; Vasiliki Karali; Vasiliki Vartela 2015-01-01 Transfusion-related acute lung injury is the most common cause of serious morbidity and mortality associated with the transfusion of plasma-containing blood components. The syndrome can be confused with other causes of acute respiratory failure. Herein, we describe a 71-year-old man who was transfused with fresh frozen plasma due to prolonged INR, and died of what was considered as transfusion-related acute lung injury, despite treatment. 14. Clinical reports for peritoneal dialysis-related peritonitis Institute of Scientific and Technical Information of China (English) 任海滨 2014-01-01 Objective To investigate causes and risk factors of peritoneal dialysis-related peritonitis,explore the pathogenic bacteria and drug sensitivity.Methods CAPD patients suffered peritoneal dialysis-related peritonitis were recruited in the First Affiliated Hospital of Nanjing Medical University in 2012.Gender,age and possible risk factors were analyzed by unvaried and multivariate logistic regression analysis.The causes,pathogenic bacteria, 15. A case report of suicidal behavior related to subclinical hyperthyroidism OpenAIRE 2014-01-01 Abnormalities in thyroid function are associated with many psychiatric symptoms. We present a report of a 15-year-old girl who was admitted to the psychiatry inpatient unit with symptoms of suicidal behavior, irritability, and impulsivity. One year previously, she had become more short-tempered, and had started to cut her wrists impulsively. Laboratory tests revealed subclinical hyperthyroidism. She was treated with anxiolytic and antithyroid drugs, and her suicidal ideation and irritability ... 16. Obesity-Related Adipokines Predict Patient-Reported Shoulder Pain Directory of Open Access Journals (Sweden) Rajiv Gandhi 2013-12-01 Full Text Available Background/Aims: Increasingly, an inflammatory modulating effect of adipokines within synovial joints is being recognized. To date, there has been no work examining a potential association between the presence of adipokines in the shoulder and patient-reported outcomes. This study undertakes an investigation assessing these potential links. Methods: 50 osteoarthritis patients scheduled for shoulder surgery completed a pre-surgery questionnaire capturing demographic information including validated, patient-reported function (Disabilities of the Arm, Shoulder, and Hand questionnaire and pain (Short Form McGill Pain Questionnaire measures. Synovial fluid (SF samples were analyzed for leptin, adiponectin, and resistin levels using Milliplex MAP assays. Linear regression modeling was used to assess the association between adipokine levels and patient-reported outcomes, adjusted for age, sex, BMI, and disease severity. Results: 54% of the cohort was female (n = 27. The mean age (SD of the sample was 62.9 (9.9 years and the mean BMI (SD was 28.1 (5.4 kg/m2. From regression analyses, greater SF leptin and adiponectin levels, but not regarding resistin, were found to be associated with greater pain (p Conclusions: The identified association between shoulder-derived SF leptin and adiponectin and shoulder pain is likely explained by the pro-inflammatory characteristics of the adipokines and represents potentially important therapeutic targets. 17. Post-Closure Report for Closed Resource Conservation and Recovery Act Corrective Action Units, Nevada National Security Site, Nevada, for Fiscal Year 2014 Energy Technology Data Exchange (ETDEWEB) Silvas, Alissa J. [NSTec 2015-01-14 This report serves as the combined annual report for post-closure activities for the following closed Corrective Action Units (CAUs): • CAU 90, Area 2 Bitcutter Containment • CAU 91, Area 3 U-3fi Injection Well • CAU 92, Area 6 Decon Pond Facility • CAU 110, Area 3 WMD U-3ax/bl Crater • CAU 111, Area 5 WMD Retired Mixed Waste Pits • CAU 112, Area 23 Hazardous Waste Trenches This report covers fiscal year 2014 (October 2013–September 2014). The post-closure requirements for these sites are described in Resource Conservation and Recovery Act Permit Number NEV HW0101 and summarized in each CAU-specific section in Section 1.0 of this report. The results of the inspections, a summary of maintenance activities, and an evaluation of monitoring data are presented in this report. Site inspections are conducted semiannually at CAUs 90 and 91 and quarterly at CAUs 92, 110, 111, and 112. Additional inspections are conducted at CAU 92 if precipitation occurs in excess of 0.50 inches (in.) in a 24-hour period and at CAU 111 if precipitation occurs in excess of 1.0 in. in a 24-hour period. Inspections include an evaluation of the condition of the units, including covers, fences, signs, gates, and locks. In addition to visual inspections, soil moisture monitoring, vegetation evaluations, and subsidence surveys are conducted at CAU 110. At CAU 111, soil moisture monitoring, vegetation evaluations, subsidence surveys, direct radiation monitoring, air monitoring, radon flux monitoring, and groundwater monitoring are conducted. The results of the vegetation surveys and an analysis of the soil moisture monitoring data at CAU 110 are presented in this report. Results of additional monitoring at CAU 111 are documented annually in the Nevada National Security Site Waste Management Monitoring Report Area 3 and Area 5 Radioactive Waste Management Sites and in the Nevada National Security Site Data Report: Groundwater Monitoring Program Area 5 Radioactive Waste Management Site 18. The IAB Iron-Meteorite Complex: A Group, Five Subgroups, Numerous Grouplets, Closely Related, Mainly Formed by Crystal Segregation in Rapidly Cooling Melts Science.gov (United States) Wasson, J. T.; Kallemeyn, G. W. 2002-01-01 We present new data or iron meteorites that are members of group IAB or are closely related to this large group, and we have also reevaluated some of our earlier data for these irons. In the past it was not possible to distinguish IAB and IIICD irons on the basis of their positions on element-Ni diagrams. We now find that plotting, the new and revised data yields six sets of compact fields on element-Au diagrams, each set corresponding to a compositional group. The largest set includes the majority (approximately equal to 70) of irons previously designated IA: We christened this set the IAB main group. The remaining five sets we designate subgroups within the IAB complex. Three of these subgroups have Au contents similar to the main group, and form parallel trends in most element-Ni diagrams. The groups originally designated IIIC and IIID are two of these subgroups: they are now well resolved from each other and from the main group. The other low-Au subgroup has Ni contents just above the main group. Two other IAB subgroups have appreciably higher Au contents than the main group and show weaker compositional links to it. We have named these five subgroups on the basis of their Au and Ni contents. The three subgroups having Au contents similar to the main group are the low-Au (L) subgroups the two others the high-Au (H) subgroups. The Ni contents are designated high (H), medium (M), or low (L). Thus the old group IIID is now the sLH subgroup. the old group IIIC is the sLM subgroup. In addition, eight irons assigned to two grouplets plot between sLL and sLM on most element-Au diagrams. A large number (27) of related irons plot outside these compact fields but nonetheless appear to be sufficiently related to also be included in the IAB complex. 19. Extensive inter- and intraspecific venom variation in closely related parasites targeting the same host: the case of Leptopilina parasitoids of Drosophila. Science.gov (United States) Colinet, Dominique; Deleury, Emeline; Anselme, Caroline; Cazes, Dominique; Poulain, Julie; Azema-Dossat, Carole; Belghazi, Maya; Gatti, Jean-Luc; Poirié, Marylène 2013-07-01 The arms race between immune suppressive parasites that produce virulence factors and hosts that evolve resistance to these factors is suggested to be a key driver for the diversification of both partners. However, little is known regarding the diversity of virulence factors in closely related parasites or the mechanisms underlying the variation of virulence. One of the best-described model to address this issue is the interaction between Leptopilina parasitic wasps and their Drosophila hosts, in which variation of virulence is well documented. Thanks to a combined transcriptomic and proteomic approach, we have identified the main secreted proteins in the venom of Leptopilina heterotoma (Gotheron strain, 66 proteins) and of two well-characterized strains of Leptopilina boulardi, ISm and ISy (65 and 49 proteins, respectively). Results revealed significant quantitative differences in venom components between the L. boulardi strains, in agreement with their different virulence properties. Strikingly, the two related Leptopilina species did not share any abundant venom protein. The main identified proteins in L. boulardi were RhoGAPs and serpins while an aspartylglucosaminidase (AGA) was found abundant in L. heterotoma. The extensive quantitative variation observed between these species may be related with their use of different virulence strategies and/or to differences in their host range (specialist versus generalist). Altogether, our data suggests that parasitoid venom can quickly evolve, mainly through rapid changes in regulation of gene expression. It also evidences venom evolutionary processes largely described in other venomous animals i.e. the convergent recruitment of venom proteins between phylogenetically unrelated organisms, and the role of duplications in the emergence of multigenic families of virulence factors. 20. Work-related musculoskeletal disorders : back to work report NARCIS (Netherlands) Pinder, A.; Yeomans, L.; Heuvel, S. van den; Blatter, B.; Verjans, M.; Muylaert, K.; Broeck, V.de; Buffet, M.A.; Nevala, N. 2007-01-01 Work-related musculoskeletal disorders (MSDs) are impairments of bodily structures, such as muscles, joints, tendons, ligaments, nerves or the localised blood circulation system. MSDs can interfere with activities at work, and can cause an increase in sickness absence, and chronic occupational 1. 2016 Service Academy Gender Relations Survey: Overview Report Science.gov (United States) 2017-02-01 were constructed based on 2017 2016 Service Academy Gender Relations Survey 239 | OPA feedback from Academy focus groups and frequencies and...stop sexual harassment and sexual assault. They provided feedback on the actions of Academy senior leadership, officers, and non-commissioned...harassment after having been previously spoken to. Response categories were collapsed so that large extent represents the combination of moderate extent 2. Is anti-doping analysis so far from clinical, legal or forensic targets?: The added value of close relationships between related disciplines. Science.gov (United States) Segura, Jordi 2009-11-01 There are many areas of common interest between anti-doping laboratories and those working in the clinical, legal and forensic fields. In addition to methodological similarities, there are aspects of the findings in sport drug testing that overlap with other fields in such a way that sport drug testing and clinical, legal or forensic work may benefit from mutual interaction. Three recent examples are presented from the author's experience. Case report 1 concerns the clinical relevance of hCG findings in sport drug testing as potential indicators of the presence of a (testicular) tumour in athletes. Case report 2 refers to difficulties that accredited laboratories can encounter due to differences between national legal systems and the administrative regulation systems of sport authorities. The example involves a network of blood collection for further autologous transfusion. Case report 3 relates to additional forensic-type investigations needed to interpret a situation where intoxication of a whole delegation was responsible for apparent doping cases. Clinical, legal and forensic fields must recognize the added value that some results and developments coming from anti-doping laboratories may have. At the same time anti-doping analysts should be aware of new issues, methodologies and problems appearing in related fields. 3. A case report of suicidal behavior related to subclinical hyperthyroidism. Science.gov (United States) Joo, Soo-Hyun; Jeong, Jong-Hyun; Hong, Seung-Chul 2014-01-01 Abnormalities in thyroid function are associated with many psychiatric symptoms. We present a report of a 15-year-old girl who was admitted to the psychiatry inpatient unit with symptoms of suicidal behavior, irritability, and impulsivity. One year previously, she had become more short-tempered, and had started to cut her wrists impulsively. Laboratory tests revealed subclinical hyperthyroidism. She was treated with anxiolytic and antithyroid drugs, and her suicidal ideation and irritability resolved. This case demonstrates that subclinical hyperthyroidism can be associated with suicidal behavior as well as overt hyperthyroidism. Early intervention is required to prevent suicidal behavior in patients with subclinical hyperthyroidism. 4. Energy-related inventions program invention 637. Final technical report Energy Technology Data Exchange (ETDEWEB) NONE 1997-07-31 The final technical report for the Pegasus plow, a stalk and root embedding apparatus, describes progress from the development stage to the product support stage. The US Department of Agriculture - Agriculture Research Service (ARS) is now in the second year of a three year study comparing the Pegasus to conventional tillage. So far, no downside has been with the Pegasus and the following benefits have been documented: (1) Energy savings of 65.0 kilowatt hours per hectare over conventional tillage. This is when the Pegasus plow is used to bury whole stalks, and represents a 70% savings over conventional tillage (92.5 kilowatt hours per hectare). (2) Four to seven fewer passes of tillage, depending on the particular situation. This represents a substantial time savings to farmers. (3) So far, no differences in cotton yields. Recent cotton boll counts in one study indicate a higher yield potential with the Pegasus. (4) No disease problems. (5) Significantly higher levels of organic matter in the soil. A hypothesis of the study is that whole stalk burial may reduce plant disease problems. This hypothesis has not yet been proven. (6) Significantly higher levels of nitrate nitrogen. Total nitrogen and ammonia nitrogen trended higher but were not significantly different. This shows that whole stalk burial does not adversely affect the nitrogen cycle in the soil and may actually improve it. The marketing support stage of the project is also described in the report. 5. TRADE EFFECTS: REGULATORY, ACCOUNTING PRACTICES AND REPORTING OF INFORMATION RELATED OpenAIRE ARISTIŢA ROTILĂ 2014-01-01 It is known that within trade relations providers often credit customers for the value of goods or services which are the subject of conducted commercial transactions, this aspect being materialized in the issuance and acceptance of a trade effect. From the time of acceptance until maturity / settlement, trade effects should be reflected separately in the accounts and, to the extent that were not settled until the end of exercise, their value must be presented in the financial ... 6. 2015 Service Academy Gender Relations Focus Groups: Overview Report Science.gov (United States) 2015-11-30 gender focus groups, similar procedures were used, selecting an equal number of junior and senior men and women to achieve sessions of approximately 10...Male) Service Academy Gender Relations Focus Groups 2015 68 | DMDC Some cadets indicated that the Corps in general understands the importance of...aspect of gender equality almost brought into CASHA. So it’s not just like about sexual harassment, sexual assault, and don’t do this, don’t do that 7. Unusual exercise-related stress fractures. Two case reports Energy Technology Data Exchange (ETDEWEB) Fink-Bennett, D.M.; Benson, M.T. 1984-08-01 We describe two unusual exercise-related stress fractures, one in the sacroiliac joint of a long distance runner, the other in the body of the scapulae of an above-knee amputee. Each were detected on a 2-hour delay bone scan. To our knowledge, neither have been described scintigraphically. The bilateral scapular fracture is an unreported entity, and the fractured SI joint is a very uncommon site for an overuse injury. 8. Brain spontaneous fluctuations in sensorimotor regions were directly related to eyes open and eyes closed: evidences from a machine learning approach Directory of Open Access Journals (Sweden) Bishan eLiang 2014-08-01 Full Text Available Previous studies have demonstrated that the difference between resting-state brain activations depends on whether the subject was eyes open (EO or eyes closed (EC. However, whether the spontaneous fluctuations are directly related to these two different resting states are still largely unclear. In the present study, we acquired resting-state functional magnetic resonance imaging data from 24 healthy subjects (11 males, 20.17 ± 2.74 years under the EO and EC states. The amplitude of the spontaneous brain activity in low-frequency band was subsequently investigated by using the metric of fractional amplitude of low frequency fluctuation (fALFF for each subject under each state. A support vector machine (SVM analysis was then applied to evaluate whether the category of resting states could be determined from the brain spontaneous fluctuations. We demonstrated that these two resting states could be decoded from the identified pattern of brain spontaneous fluctuations, predominantly based on fALFF in the sensorimotor module. Specifically, we observed prominent relationships between increased fALFF for EC and decreased fALFF for EO in sensorimotor regions. Overall, the present results indicate that a SVM performs well in the discrimination between the brain spontaneous fluctuations of distinct resting states and provide new insight into the neural substrate of the resting states during EC and EO. 9. Towards harmonised procedures in wildlife epidemiological investigations: a serosurvey of infection with Mycobacterium bovis and closely related agents in wild boar (Sus scrofa) in Switzerland. Science.gov (United States) Beerli, Olivia; Blatter, Sohvi; Boadella, Mariana; Schöning, Janne; Schmitt, Sarah; Ryser-Degiorgis, Marie-Pierre 2015-01-01 Bovine tuberculosis (bTB) is a (re-)emerging disease in European countries, including Switzerland. This study assesses the seroprevalence of infection with Mycobacterium bovis and closely related agents in wild boar (Sus scrofa) in Switzerland, because wild boar are potential maintenance hosts of these pathogens. The study employs harmonised laboratory methods to facilitate comparison with the situation in other countries. Eighteen out of 743 blood samples tested seropositive (2.4%, CI: 1.5-3.9%) by ELISA, and the results for 61 animals previously assessed using culture and PCR indicated that this serological test was not 100% specific for M. bovis, cross-reacting with M. microti. Nevertheless, serology appears to be an appropriate test methodology in the harmonisation of wild boar testing throughout Europe. In accordance with previous findings, the low seroprevalence found in wild boar suggests wildlife is an unlikely source of the M. bovis infections recently detected in cattle in Switzerland. This finding contrasts with the epidemiological situation pertaining in southern Spain. 10. Heterogeneity in ess transcriptional organization and variable contribution of the Ess/Type VII protein secretion system to virulence across closely related Staphylocccus aureus strains. Science.gov (United States) Kneuper, Holger; Cao, Zhen Ping; Twomey, Kate B; Zoltner, Martin; Jäger, Franziska; Cargill, James S; Chalmers, James; van der Kooi-Pol, Magdalena M; van Dijl, Jan Maarten; Ryan, Robert P; Hunter, William N; Palmer, Tracy 2014-09-01 The Type VII protein secretion system, found in Gram-positive bacteria, secretes small proteins, containing a conserved W-x-G amino acid sequence motif, to the growth medium. Staphylococcus aureus has a conserved Type VII secretion system, termed Ess, which is dispensable for laboratory growth but required for virulence. In this study we show that there are unexpected differences in the organization of the ess gene cluster between closely related strains of S. aureus. We further show that in laboratory growth medium different strains of S. aureus secrete the EsxA and EsxC substrate proteins at different growth points, and that the Ess system in strain Newman is inactive under these conditions. Systematic deletion analysis in S. aureus RN6390 is consistent with the EsaA, EsaB, EssA, EssB, EssC and EsxA proteins comprising core components of the secretion machinery in this strain. Finally we demonstrate that the Ess secretion machinery of two S. aureus strains, RN6390 and COL, is important for nasal colonization and virulence in the murine lung pneumonia model. Surprisingly, however, the secretion system plays no role in the virulence of strain SA113 under the same conditions. 11. Molecular analyses of a potentially novel Anaplasma species closely related to Anaplasma phagocytophilum detected in sika deer (Cervus nippon yesoensis) in Japan. Science.gov (United States) Ybañez, Adrian P; Matsumoto, Kotaro; Kishimoto, Toshio; Inokuma, Hisashi 2012-05-25 An Anaplasma species closely related to Anaplasma phagocytophilum detected in sika deer in Hokkaido, Japan was molecularly analyzed using 16S rRNA, citrate synthase (gltA), and heat-shock operon (groEL) gene sequences. Genome walking was performed to determine its complete gltA and groEL sequences (1233 bp and 1650 bp, respectively). Percent identities to the closest A. phagocytophilum sequences from the US and European strains were 98.6-98.8%, 76.5%, and 80.3-80.8% for 16S rRNA, gltA, and groEL genes, respectively. For deduced amino acid sequences, percent identities to the closest A. phagocytophilum sequences were 66.7% and 97.6% for gltA and groEL genes, respectively. Phylogenetic analyses revealed divergence from any known A. phagocytophilum strain. The lower identities and the divergent phylogenetic position of the Anaplasma sp. detected from sika deer in Japan with established A. phagocytophilum strains provide evidence of its potential novelty. Copyright © 2011 Elsevier B.V. All rights reserved. 12. A novel PCR-RFLP assay for molecular characterization of Echinococcus granulosus sensu lato and closely related species in developing countries. Science.gov (United States) Chaâbane-Banaoues, Raja; Oudni-M'rad, Myriam; M'rad, Selim; Amani, Hizem; Mezhoud, Habib; Babba, Hamouda 2016-10-01 Cystic echinococcosis, due to Echinococcus granulosus sensu lato (s. l.), currently affects three million people, especially in low-income countries and results in high livestock production loss. DNA-based methods demonstrated genetic variability of E. granulosus s. l., and five species were recognized to belong to the complex, including E. granulosus sensu stricto (s.s) (genotypes G1-G3), Echinococcus equinus (genotype G4), Echinococcus ortleppi (genotype G5), Echinococcus canadensis (genotypes G6-G10), and the lion strain Echinococcus felidis. The characterization of Echinococcus species responsible for human and animal echinococcosis is crucial to adapt the preventive measures against this parasitic disease. The sequencing approach is the gold standard for genotyping assays. Unfortunately, developing countries do not often have access to these techniques. Based on in silico RFLP tools, we described an accurate PCR-RFLP method for Echinococcus spp. characterization. The double digestion with the HaeIII and HinfI restriction enzymes of the PCR product from nad1 gene (1071 bp) led to a clear discrimination between E. granulosus s. l. and most closely related species (Echinococcus shiquicus and Echinococcus multilocularis).Molecular procedures and phylogenetic analysis confirmed the efficiency and the reproducibility of this simple and fast PCR-RFLP method. This technique is proved useful for fresh/unfixed and FF-PET tissues and enables large-scale molecular epidemiological screening in developing countries. 13. Description of larvae of two closely related species Cassida palaestina Reiche, 1858 and Cassida rubiginosa Müller, 1776 (Coleoptera: Chrysomelidae: Cassidinae). Science.gov (United States) Swiętojańska, Jolanta; Moradian, Hossein; Borowiec, Lech; Ostovan, Hadi 2013-11-29 Larvae of two closely related species Cassida palaestina Reiche, 1858 and Cassida rubiginosa Müller, 1776 are described in detail including SEM microstructures. First instars are extremely similar with no clear diagnostic characters, larvae of Cassida palaestina are slightly more contrastingly coloured than larvae of C. rubiginosa, the latter having darker scoli, basal part of supra-anal processes and legs. Last instars differ in very subtle but constant characters: lateral scoli of C. palaestina are slightly shorter than those of C. rubiginosa, in C. palaestina tops of the lateral branches are armed apically with an elongate cauliflower-shaped sensillum while in C. rubiginosa tops of the lateral branches are more often armed with a pointed seta than with an elongate cauliflower-shaped sensillum, and cauliflower-shaped sensilla on tergites are less elongate in C. palaestina than in C. rubiginosa. These differences accompanied by distinguishing characters of adults and their distribution range indicate that both taxa are probably vicariant species with partial parapatric occurrence. Centaurea behen is a new host plant for C. palaestina. 14. Gray mold populations in german strawberry fields are resistant to multiple fungicides and dominated by a novel clade closely related to Botrytis cinerea. Science.gov (United States) Leroch, Michaela; Plesken, Cecilia; Weber, Roland W S; Kauff, Frank; Scalliet, Gabriel; Hahn, Matthias 2013-01-01 The gray mold fungus Botrytis cinerea is a major threat to fruit and vegetable production. Strawberry fields usually receive several fungicide treatments against Botrytis per season. Gray mold isolates from several German strawberry-growing regions were analyzed to determine their sensitivity against botryticides. Fungicide resistance was commonly observed, with many isolates possessing resistance to multiple (up to six) fungicides. A stronger variant of the previously described multidrug resistance (MDR) phenotype MDR1, called MDR1h, was found to be widely distributed, conferring increased partial resistance to two important botryticides, cyprodinil and fludioxonil. A 3-bp deletion mutation in a transcription factor-encoding gene, mrr1, was found to be correlated with MDR1h. All MDR1h isolates and the majority of isolates with resistance to multiple fungicides were found to be genetically distinct. Multiple-gene sequencing confirmed that they belong to a novel clade, called Botrytis group S, which is closely related to B. cinerea and the host-specific species B. fabae. Isolates of Botrytis group S genotypes were found to be widespread in all German strawberry-growing regions but almost absent from vineyards. Our data indicate a clear subdivision of gray mold populations, which are differentially distributed according to their host preference and adaptation to chemical treatments. 15. Identification of Enterobacter sakazakii from closely related species: The use of Artificial Neural Networks in the analysis of biochemical and 16S rDNA data Directory of Open Access Journals (Sweden) Waddington Michael 2006-03-01 Full Text Available Abstract Background Enterobacter sakazakii is an emergent pathogen associated with ingestion of infant formula and accurate identification is important in both industrial and clinical settings. Bacterial species can be difficult to accurately characterise from complex biochemical datasets and computer algorithms can potentially simplify the process. Results Artificial Neural Networks were applied to biochemical and 16S rDNA data derived from 282 strains of Enterobacteriaceae, including 189 E. sakazakii isolates, in order to identify key characteristics which could improve the identification of E. sakazakii. The models developed resulted in a predictive performance for blind (validation data of 99.3 % correct discrimination between E. sakazakii and closely related species for both phenotypic and genotypic data. Three main regions of the partial rDNA sequence were found to be key in discriminating the species. Comparison between E. sakazakii and other strains also constitutively positive for expression of the enzyme α-glucosidase resulted in a predictive performance of 98.7 % for 16S rDNA sequence data and 100% for phenotypic data. Conclusion The computationally based methods developed here show a remarkable ability in reducing data dimensionality and complexity, in order to eliminate noise from the system in order to facilitate the speed and reliability of a potential strain identification system. Furthermore, the approaches described are also able to provide valuable information regarding the population structure and distribution of individual species thus providing the foundations for novel assays and diagnostic tests for rapid identification of pathogens. 16. A phylogenetic lineage of closely related trypanosomes (Trypanosomatidae, Kinetoplastida) of anurans and sand flies (Psychodidae, Diptera) sharing the same ecotopes in brazilian amazonia. Science.gov (United States) Ferreira, Robson C; De Souza, Adelson A; Freitas, Rui A; Campaner, Marta; Takata, Carmem S A; Barrett, Toby V; Shaw, Jeffrey J; Teixeira, Marta M G 2008-01-01 Analysis of the phylogenetic relationships among trypanosomes from vertebrates and invertebrates disclosed a new lineage of trypanosomes circulating among anurans and sand flies that share the same ecotopes in Brazilian Amazonia. This assemblage of closely related trypanosomes was determined by comparing whole SSU rDNA sequences of anuran trypanosomes from the Brazilian biomes of Amazonia, the Pantanal, and the Atlantic Forest and from Europe, North America, and Africa, and from trypanosomes of sand flies from Amazonia. Phylogenetic trees based on maximum likelihood and parsimony corroborated the positioning of all new anuran trypanosomes in the aquatic clade but did not support the monophyly of anuran trypanosomes. However, all analyses always supported four major clades (An01-04) of anuran trypanosomes. Clade An04 is composed of trypanosomes from exotic anurans. Isolates in clades An01 and An02 were from Brazilian frogs and toads captured in the three biomes studied, Amazonia, the Pantanal and the Atlantic Forest. Clade An01 contains mostly isolates from Hylidae whereas clade An02 comprises mostly isolates from Bufonidae; and clade An03 contains trypanosomes from sand flies and anurans of Bufonidae, Leptodactylidae, and Leiuperidae exclusively from Amazonia. To our knowledge, this is the first study describing morphological and growth features, and molecular phylogenetic affiliation of trypanosomes from anurans and phlebotomines, incriminating these flies as invertebrate hosts and probably also as important vectors of Amazonian terrestrial anuran trypanosomes. 17. Recurrent prurigo nodularis related to infected tonsils: a case report Directory of Open Access Journals (Sweden) Katotomichelakis Michael 2008-07-01 Full Text Available Abstract Introduction Prurigo nodularis is an unusual disorder of unknown aetiology, which is notoriously resistant to therapy, and is characterized by extremely pruritic nodules with well-defined clinical symptoms and histopathological findings. Case presentation We report the case of a patient presenting with pruritic papules and nodules on his legs, arms and trunk over the past 4 years, recurring after episodes of acute tonsillitis. Although oral and topical corticosteroids, oral antibiotics and emollients were used in his therapy, only tonsillectomy finally proved the definitive treatment. Conclusion We discuss the aetiopathogenesis, diagnosis and treatment of prurigo nodularis associated with chronic tonsillitis, and we further review the literature on this rare condition. 18. A case report of suicidal behavior related to subclinical hyperthyroidism Directory of Open Access Journals (Sweden) Joo SH 2014-04-01 Full Text Available Soo-Hyun Joo, Jong-Hyun Jeong, Seung-Chul HongDepartment of Psychiatry, St Vincent's Hospital, College of Medicine, The Catholic University of Korea, Suwon, KoreaAbstract: Abnormalities in thyroid function are associated with many psychiatric symptoms. We present a report of a 15-year-old girl who was admitted to the psychiatry inpatient unit with symptoms of suicidal behavior, irritability, and impulsivity. One year previously, she had become more short-tempered, and had started to cut her wrists impulsively. Laboratory tests revealed subclinical hyperthyroidism. She was treated with anxiolytic and antithyroid drugs, and her suicidal ideation and irritability resolved. This case demonstrates that subclinical hyperthyroidism can be associated with suicidal behavior as well as overt hyperthyroidism. Early intervention is required to prevent suicidal behavior in patients with subclinical hyperthyroidism.Keywords: suicidal behavior, subclinical hyperthyroidism, anxiolytics 19. Multiplicity of Galactic Cepheids from long-baseline interferometry~III. Sub-percent limits on the relative brightness of a close companion of\\delta$~Cephei CERN Document Server Gallenne, A; Kervella, P; Monnier, J D; Schaefer, G H; Roettenbacher, R M; Gieren, W; Pietrzynski, G; McAlister, H; Brummelaar, T ten; Sturmann, J; Sturmann, L; Turner, N; Anderson, R I 2016-01-01 We report new CHARA/MIRC interferometric observations of the Cepheid archetype$\\delta$Cep, which aimed at detecting the newly discovered spectroscopic companion. We reached a maximum dynamic range$\\Delta H $= 6.4, 5.8, and 5.2 mag, respectively within the relative distance to the Cepheid$r 9.15, 8.31$and 7.77 mag, respectively for$r < 25$mas,$25 < r < 50$mas and$50 < r < 100$mas. We also found that to be consistent with the predicted orbital period, the companion has to be located at a projected separation$< 24\$ mas with a spectral type later than a F0V star.
20. Work-related posttraumatic upper limb disorder. A case report.
Science.gov (United States)
Capodaglio, P; Nigrelli, M P; Malaguti, S; Panigazzi, M; Pierobon, A
1999-01-01
In this paper we describe a patient with mor-sensory loss in the right forearm and hand, which persisted more than 2 years after work-related crush trauma of the left hand. Radiographic and electromyographic investigations, somatosensory evoked potentials, CT scans of the encephalus as well as the Minnesota Multiphasic Personality Inventory and the Roarschach test have been performed. On the basis of these investigations, we think this represents a case of conversion disorder with somatic features. Included is a brief overview of other psychological illness with physical findings involving the upper limb.
1. Speciation history of three closely related pines Pinus mugo (T.), P. uliginosa (N.) and P. sylvestris (L.).
Science.gov (United States)
Wachowiak, Witold; Palmé, Anna E; Savolainen, Outi
2011-04-01
Nucleotide polymorphisms at genomic regions including 17 nuclear loci, two chloroplast and one mitochondrial DNA fragments were used to study the speciation history of three pine species: dwarf mountain pine (Pinus mugo), peat-bog pine (P. uliginosa) and Scots pine (P. sylvestris). We set out to investigate three specific speciation scenarios: (I) P. uliginosa is a homoploid hybrid between the other two, (II) the species have evolved without gene flow after divergence and (III) there has been substantial gene flow between the species since their divergence. Overall, the genetic data suggest that P. mugo and P. uliginosa share the same gene pool (average net divergence of 0.0001) and that the phenotypic differences (e.g. growth form) are most likely due to very limited areas of the genome. P. mugo and P. uliginosa are more diverged from P. sylvestris than from each other (average net divergence of 0.0027 and 0.0026, respectively). The nucleotide patterns can best be explained by the divergence with migration speciation scenario, although the hybrid speciation scenario with small genomic contribution from P. sylvestris cannot be completely ruled out. We suggest that the large amount of shared polymorphisms between the pine taxa and the lack of monophyly at all loci studied between P. sylvestris and P. mugo-P. uliginosa can largely be explained by relatively recent speciation history and large effective population sizes but also by interspecific gene flow. These closely related pine taxa form an excellent system for searching for loci involved in adaptive variation as they are differentiated in phenotype and ecology but have very similar genetic background.
2. Genetic relationships and variation in reproductive strategies in four closely related bromeliads adapted to neotropical ‘inselbergs’: Alcantarea glaziouana, A. regina, A. geniculata and A. imperialis (Bromeliaceae)
Science.gov (United States)
Barbará, Thelma; Martinelli, Gustavo; Palma-Silva, Clarisse; Fay, Michael F.; Mayo, Simon; Lexer, Christian
2009-01-01
Background and Aims Bromeliads (Bromeliaceae) adapted to rock outcrops or ‘inselbergs’ in neotropical rain forests have been identified as suitable plant models for studying population divergence and speciation during continental plant radiations. Little is known about genetic relationships and variation in reproductive strategies within and among inselberg-adapted species, yet knowledge of these parameters is important for understanding divergence processes and for conservation planning. Methods Nuclear microsatellites were used to assess the role of clonal reproduction, estimate genetic diversity and explore genetic relationships and variation in reproductive strategies for a total of 15 populations of four closely related Alcantarea inselberg species in south-eastern Brazil: A. glaziouana, A. regina, A. geniculata and A. imperialis. Key Results Clonal propagation is frequent in coastal populations of A. glaziouana and A. regina, but absent in the high-altitude species A. geniculata and A. imperialis. Considerable variation in clonal diversity, gene diversity (He), allelic richness, and Wright's inbreeding coefficient (FIS) exists within and between species of Alcantarea. A Bayesian analysis of coastal inselberg species indicated pronounced genetic structure. A neighbor-joining analysis grouped populations of each species together with moderate bootstrap support, except for the high altitude species A. imperialis. Conclusions The coastal inselberg species A. glaziouana and A. regina tend to propagate asexually via vegetative clonal growth, and both reproductive strategies and breeding systems vary greatly between populations and species of Alcantarea. The microsatellite data indicate a history of hybridization and reticulation involving the high-altitude species A. geniculata and A. imperialis in areas of co-occurrence. The results highlight the need to understand similarities and differences in reproductive strategies both within and between related species
3. Species-level determination of closely related araucarian resins using FTIR spectroscopy and its implications for the provenance of New Zealand amber
Directory of Open Access Journals (Sweden)
Leyla J. Seyfullah
2015-07-01
Full Text Available Some higher plants, both angiosperms and gymnosperms, can produce resins and some of these resins can polymerize and fossilize to form ambers. Various physical and chemical techniques have been used to identify and profile different plant resins and have then been applied to fossilized resins (ambers, to try to detect their parent plant affinities and understand the process of polymerization, with varying levels of success. Here we focus on resins produced from today’s most resinous conifer family, the Araucariaceae, which are thought to be the parent plants of some of the Southern Hemisphere’s fossil resin deposits. Fourier transform infrared (FTIR spectra of the resins of closely related Araucariaceae species were examined to test whether they could be distinguished at genus and species level and whether the results could then be used to infer the parent plant of a New Zealand amber. The resin FTIR spectra are distinguishable from each other, and the three Araucaria species sampled produced similar FTIR spectra, to which Wollemia resin is most similar. Interspecific variability of the FTIR spectra is greatest in the three Agathis species tested. The New Zealand amber sample is similar in key shared features with the resin samples, but it does differ from the extant resin samples in key distinguishing features, nonetheless it is most similar to the resin of Agathis australis in this dataset. However on comparison with previously published FTIR spectra of similar aged amber and older (Eocene resinites both found in coals from New Zealand and fresh Agathis australis resin, our amber has some features that imply a relatively immature resin, which was not expected from an amber of the Miocene age.
4. Identification of distinct quantitative trait loci associated with defence against the closely related aphids Acyrthosiphon pisum and A. kondoi in Medicago truncatula
KAUST Repository
Guo, Su-Min
2012-03-21
Aphids are a major family of plant insect pests. Medicago truncatula and Acyrthosiphon pisum (pea aphid, PA) are model species with a suite of resources available to help dissect the mechanism underlying plant-aphid interactions. A previous study focused on monogenic and relatively strong resistance in M. truncatula to PA and other aphid species. In this study a moderate resistance to PA was characterized in detail in the M. truncatula line A17 and compared with the highly susceptible line A20 and the more resistant line Jester. The results show that PA resistance in A17 involves both antibiosis and tolerance, and that resistance is phloem based. Quantitative trait locus (QTL) analysis using a recombinant inbred line (RIL) population (n=114) from a cross between A17 and A20 revealed that one locus, which co-segregated with AIN (Acyrthosiphon-induced necrosis) on chromosome 3, is responsible for the reduction of aphid biomass (indicator of antibiosis) for both PA and bluegreen aphid (BGA, A. kondoi), albeit to a lesser degree for PA than BGA. Interestingly, two independent loci on chromosomes 5 and 3 were identified for the plant biomass reduction (indicator of plant tolerance) by PA and BGA, respectively, demonstrating that the plant\\'s tolerance response to these two closely related aphid species is distinct. Together with previously identified major resistant (R) genes, the QTLs identified in this study are powerful tools to understand fully the spectrum of plant defence against sap-sucking insects and provide opportunities for breeders to generate effective and sustainable strategies for aphid control. 2012 The Author.
5. Single cell genomics of uncultured, health-associated Tannerella BU063 (Oral Taxon 286 and comparison to the closely related pathogen Tannerella forsythia.
Directory of Open Access Journals (Sweden)
Clifford J Beall
Full Text Available The uncultivated bacterium Tannerella BU063 (oral taxon 286 is the closest relative to the periodontal pathogen Tannerella forsythia, but is not disease-associated itself. Using a single cell genomics approach, we isolated 12 individual BU063 cells by flow cytometry, and we amplified and sequenced their genomes. Comparative analyses of the assembled genomic scaffolds and their gene contents allowed us to study the diversity of this taxon within the oral community of a single human donor that provided the sample. Eight different BU063 genotypes were represented, all about 5% divergent at the nucleotide level. There were 2 pairs of cells and one group of three that were more highly identical, and may represent clonal populations. We did pooled assemblies on the nearly identical genomes to increase the assembled genomic coverage. The presence of a set of 66 "core" housekeeping genes showed that two of the single cell assemblies and the assembly derived from the three putatively identical cells were essentially complete. As expected, the genome of BU063 is more similar to Tannerella forsythia than any other known genome, although there are significant differences, including a 44% difference in gene content, changes in metabolic pathways, loss of synteny, and an 8-9% difference in GC content. Several identified virulence genes of T. forsythia are not found in BU063 including karilysin, prtH, and bspA. The absence of these genes may explain the lack of periodontal pathogenesis by this species and provides a new foundation to further understand the genome evolution and mechanisms of bacterial-host interaction in closely related oral microbes with different pathogenicity potential.
6. Single cell genomics of uncultured, health-associated Tannerella BU063 (Oral Taxon 286) and comparison to the closely related pathogen Tannerella forsythia.
Science.gov (United States)
Beall, Clifford J; Campbell, Alisha G; Dayeh, Daniel M; Griffen, Ann L; Podar, Mircea; Leys, Eugene J
2014-01-01
The uncultivated bacterium Tannerella BU063 (oral taxon 286) is the closest relative to the periodontal pathogen Tannerella forsythia, but is not disease-associated itself. Using a single cell genomics approach, we isolated 12 individual BU063 cells by flow cytometry, and we amplified and sequenced their genomes. Comparative analyses of the assembled genomic scaffolds and their gene contents allowed us to study the diversity of this taxon within the oral community of a single human donor that provided the sample. Eight different BU063 genotypes were represented, all about 5% divergent at the nucleotide level. There were 2 pairs of cells and one group of three that were more highly identical, and may represent clonal populations. We did pooled assemblies on the nearly identical genomes to increase the assembled genomic coverage. The presence of a set of 66 "core" housekeeping genes showed that two of the single cell assemblies and the assembly derived from the three putatively identical cells were essentially complete. As expected, the genome of BU063 is more similar to Tannerella forsythia than any other known genome, although there are significant differences, including a 44% difference in gene content, changes in metabolic pathways, loss of synteny, and an 8-9% difference in GC content. Several identified virulence genes of T. forsythia are not found in BU063 including karilysin, prtH, and bspA. The absence of these genes may explain the lack of periodontal pathogenesis by this species and provides a new foundation to further understand the genome evolution and mechanisms of bacterial-host interaction in closely related oral microbes with different pathogenicity potential.
7. 2015 QuickCompass of Sexual Assult-Related Responders: Statistical Methodology Report
Science.gov (United States)
2016-02-01
AND RESPONSE-RELATED RESPONDERS: STATISTICAL METHODOLOGY REPORT Defense Research , Surveys, and Statistics Center Defense Manpower Data Center...2015 QuickCompass of Sexual Assault Prevention and Response- Related Responders Statistical Methodology Report Additional copies of this report...Defense Research , Surveys, and Statistics Center (RSSC) 4800 Mark Center Drive, Suite 04E25-01, Alexandria, VA 22350-4000 ii Acknowledgments
8. Geophysical variables and behavior: XXIII. Relations between UFO reports within the Uinta Basin and local seismicity.
Science.gov (United States)
Persinger, M A; Derr, J S
1985-02-01
A strong temporal correlation was found between the numbers of reports of UFOs (unidentified flying objects) and nearby seismic activity within the Uinta Basin for the year 1967. The numbers of UFO reports per month during this classic UFO flap were correlated 0.80 with the sum of the earthquake magnitudes per month for events within 150 km of the report area. Numbers of UFO reports were not correlated significantly with earthquake activity at distances greater than 150 km but less than 250 km away. The strongest correlation occurred between UFO reports and nearby seismic activity within the same month but not for previous or consequent months. Close scrutiny of daily shifts in epicenters and reports of UFOs indicate that they occurred when the locus of successive epicenters shifted across the area. These analyses were interpreted as support for the existence of strain fields whose movements generate natural phenomena that are reported as UFOs.
9. Investigations on detonation shock dynamics and related topics. Final report
Energy Technology Data Exchange (ETDEWEB)
Stewart, D.S. [Univ. of Illinois, Urbana, IL (United States). Dept. of Theoretical and Applied Mechanics
1993-11-01
This document is a final report that summarizes the research findings and research activities supported by the subcontract DOE-LANL-9-XG8-3931P-1 between the University of Illinois (D. S. Stewart Principal Investigator) and the University of California (Los Alamos National Laboratory, M-Division). The main focus of the work has been on investigations of Detonation Shock Dynamics. A second emphasis has been on modeling compaction of energetic materials and deflagration to detonation in those materials. The work has led to a number of extensions of the theory of Detonation Shock Dynamics (DSD) and its application as an engineering design method for high explosive systems. The work also enhanced the hydrocode capabilities of researchers in M-Division by modifications to CAVEAT, an existing Los Alamos hydrocode. Linear stability studies of detonation flows were carried out for the purpose of code verification. This work also broadened the existing theory for detonation. The work in this contract has led to the development of one-phase models for dynamic compaction of porous energetic materials and laid the groundwork for subsequent studies. Some work that modeled the discrete heterogeneous behavior of propellant beds was also performed. The contract supported the efforts of D. S. Stewart and a Postdoctoral student H. I. Lee at the University of Illinois.
10. Diaphragmatic rupture caused by inappropriate closed drainage of thoracic cavity:a case report%胸腔闭式引流不当致膈肌破裂1例
Institute of Scientific and Technical Information of China (English)
汪洋; 张进祥; 杨冲; 陈立波
2013-01-01
Drainage of thoracic cavity is a routine treatment for traumatic pleural effusion or pneurnothorax, whereas improper operation may cause serious consequences, A case of 47-year-old man with traffic injury is reported herein. The patient had abdominal pain, chest distress, and trouble breathing when admitted to our hospital. After admission, the patient's blood pressure decreased, heart rate increased and blood was draw upon from the chest tubes. Chest examination indicated wet rales in both sides and decreased breath sounds in the left side. Abdominal examination reversed peritonitis symptoms. Abdominal X-ray indicated there were free gas under left hernidia-phragm and moderate amount of left pleural effusion. The abdominal computed tomography (CT) scan showed pleural drainage tube in the abdominal cavity which was closely related to spleen. We made diagnosis as following: ①multiple injuries caused by traffic injury;②diaphragmatic injury;③splenic rupture.
11. 33 CFR 150.825 - Reporting a diving-related casualty.
Science.gov (United States)
2010-07-01
... 33 Navigation and Navigable Waters 2 2010-07-01 2010-07-01 false Reporting a diving-related casualty. 150.825 Section 150.825 Navigation and Navigable Waters COAST GUARD, DEPARTMENT OF HOMELAND... Reporting a diving-related casualty. Deaths and injuries related to diving within the safety zone of...
12. EDITORIAL: Close contact Close contact
Science.gov (United States)
Demming, Anna
2010-07-01
The development of scanning probe techniques, such as scanning tunnelling microscopy [1], has often been touted as the catalyst for the surge in activity and progress in nanoscale science and technology. Images of nanoscale structural detail have served as an invaluable investigative resource and continue to fascinate with the fantastical reality of an intricate nether world existing all around us, but hidden from view of the naked eye by a disparity in scale. As is so often the case, the invention of the scanning tunnelling microscope heralded far more than just a useful new apparatus, it demonstrated the scope for exploiting the subtleties of electronic contact. The shrinking of electronic devices has been a driving force for research into molecular electronics, in which an understanding of the nature of electronic contact at junctions is crucial. In response, the number of experimental techniques in molecular electronics has increased rapidly in recent years. Scanning tunnelling microscopes have been used to study electron transfer through molecular films on a conducting substrate, and the need to monitor the contact force of scanning tunnelling electrodes led to the use of atomic force microscopy probes coated in a conducting layer as studied by Cui and colleagues in Arizona [2]. In this issue a collaboration of researchers at Delft University and Leiden University in the Netherlands report a new device architecture for the independent mechanical and electrostatic tuning of nanoscale charge transport, which will enable thorough studies of molecular transport in the future [3]. Scanning probes can also be used to pattern surfaces, such as through spatially-localized Suzuki and Heck reactions in chemical scanning probe lithography. Mechanistic aspects of spatially confined Suzuki and Heck chemistry are also reported in this issue by researchers in Oxford [4]. All these developments in molecular electronics fabrication and characterization provide alternative
13. Mitragynine 'Kratom' related fatality: a case report with postmortem concentrations.
Science.gov (United States)
McIntyre, Iain M; Trochta, Amber; Stolberg, Susan; Campman, Steven C
2015-03-01
A 24-year-old man whose medical history was significant for alcohol abuse and depression was found unresponsive in bed. He had several prior suicide attempts with 'pills' and had also been hospitalized for an accidental overdose on a previous occasion. Autopsy findings were unremarkable apart from pulmonary edema and congestion, and urinary retention. Postmortem peripheral blood initially screened positive for mitragynine 'Kratom' (by routine alkaline drug screen by gas chromatography-mass spectrometry, GC-MS), which was subsequently confirmed by a specific GC-MS selective ion mode analysis following solid-phase extraction. Concentrations were determined in the peripheral blood (0.23 mg/L), central blood (0.19 mg/L), liver (0.43 mg/kg), vitreous (<0.05 mg/L), urine (0.37 mg/L) and was not detected in the gastric. Therapeutic concentrations of venlafaxine, diphenhydramine and mirtazapine were also detected together with a negligible ethanol of 0.02% (w/v). The results are discussed in relation to previous cases of toxicity, and the lack of potential for mitragynine postmortem redistribution.
14. The Castleman's Disease and Related Disorders--A Case Report.
Science.gov (United States)
Khan, M K; Talukder, R H; Kamruzzaman, M
2016-01-01
Castleman's disease is a rare primary disease of the lymph nodes. Little is known about the management of the disease. Surgical treatment gives a very good result. What other modalities of treatment could be done is not yet established. The role of surgery gives good result and follow up evaluation is satisfactory. We found a solitary intra-abdominal mass of lymphoid hyperplasia with a histological diagnosis of Castlemans disease identified in the pathological data base. Unicentric disease was defined as it was a solitary mass. Clinical, Radiological and Laboratory data were analysed to evaluate treatment response. The patient also has related disorders as Acanthosis nigricans, Myoneuronal disorder as-MG and bronchiolitis. The patient diagnosed as angiofollicular hyperplasia (Castleman's disease). After evaluation patient under went surgical treatment, partial excision of tumor mass due to morbid adhesion with inferior vena cava. The patient becomes symptom free and lump disappears within 60 days of treatment. There was no recurrence of the disease after further evaluation. The author recommends that in Unicentric variant of Castlemans disease surgical resection of the tumor is curative. The unicentric tumour may be hyaline-vascular or hyaline-vascular/ plasma cell type. Partial resection, Radiotherapy or observation alone may avoid excessive aggressive therapy.
15. Fine definition of the pedigree haplotypes of closely related rice cultivars by means of genome-wide discovery of single-nucleotide polymorphisms
Directory of Open Access Journals (Sweden)
Shibaya Taeko
2010-04-01
Full Text Available Abstract Background To create useful gene combinations in crop breeding, it is necessary to clarify the dynamics of the genome composition created by breeding practices. A large quantity of single-nucleotide polymorphism (SNP data is required to permit discrimination of chromosome segments among modern cultivars, which are genetically related. Here, we used a high-throughput sequencer to conduct whole-genome sequencing of an elite Japanese rice cultivar, Koshihikari, which is closely related to Nipponbare, whose genome sequencing has been completed. Then we designed a high-throughput typing array based on the SNP information by comparison of the two sequences. Finally, we applied this array to analyze historical representative rice cultivars to understand the dynamics of their genome composition. Results The total 5.89-Gb sequence for Koshihikari, equivalent to 15.7× the entire rice genome, was mapped using the Pseudomolecules 4.0 database for Nipponbare. The resultant Koshihikari genome sequence corresponded to 80.1% of the Nipponbare sequence and led to the identification of 67 051 SNPs. A high-throughput typing array consisting of 1917 SNP sites distributed throughout the genome was designed to genotype 151 representative Japanese cultivars that have been grown during the past 150 years. We could identify the ancestral origin of the pedigree haplotypes in 60.9% of the Koshihikari genome and 18 consensus haplotype blocks which are inherited from traditional landraces to current improved varieties. Moreover, it was predicted that modern breeding practices have generally decreased genetic diversity Conclusions Detection of genome-wide SNPs by both high-throughput sequencer and typing array made it possible to evaluate genomic composition of genetically related rice varieties. With the aid of their pedigree information, we clarified the dynamics of chromosome recombination during the historical rice breeding process. We also found several
16. No evidence of contemporary interploidy gene flow between the closely related European woodland violets Viola reichenbachiana and V. riviniana (sect. Viola, Violaceae).
Science.gov (United States)
Migdałek, G; Nowak, J; Saługa, M; Cieślak, E; Szczepaniak, M; Ronikier, M; Marcussen, T; Słomka, A; Kuta, E
2017-07-01
Viola reichenbachiana (2n = 4x = 20) and V. riviniana (2n = 8x = 40) are closely related species widely distributed in Europe, often sharing the same habitat throughout their overlapping ranges. It has been suggested in numerous studies that their high intraspecific morphological variability and plasticity might have been further increased by interspecific hybridisation in contact zones, given the sympatry of the species and the incomplete sterility of their hybrid. The aims of this study were to: (i) confirm that V. reichenbachiana and V. riviniana have one 4x genome in common, and (ii) determine the impact of hybridisation and introgression on genetic variation of these two species in selected European populations. For our study, we used 31 Viola populations from four European countries, which were analysed using AFLP and sequencing of a variable plastid intergenic spacer, trnH-psbA. Our analysis revealed that V. reichenbachiana exhibited larger haplotype diversity, having three species-specific haplotypes versus one in V. riviniana. The relationships among haplotypes suggest transfer of common haplotypes into V. riviniana from both V. reichenbachiana and hypothetically the other, now extinct, parental species. AFLP analysis showed low overall genetic diversity of both species, with V. riviniana showing higher among-population diversity. None of the morphologically designated hybrid populations had additive AFLP polymorphisms that would have indicated recent hybridisation. Also, kinship coefficients between both species did not indicate gene flow. V. riviniana showed significant population subdivision and significant isolation by distance, in contrast to V. reichenbachiana. The results indicate lack of gene flow between species, high influence of selfing on genetic variability, as well as probably only localised introgression toward V. riviniana. © 2017 German Botanical Society and The Royal Botanical Society of the Netherlands.
17. Patient self-assessed shoulder comfort and function and active motion are not closely related to surgically documented rotator cuff tear integrity.
Science.gov (United States)
Hsu, Jason E; Tang, Anna; Matsen, Frederick A
2017-07-06
The rationale for rotator cuff repair surgery is that better integrity of the cuff should be associated with better comfort and function. However, in patients with cuff disease, there is not good evidence that the degree of rotator cuff integrity is closely associated with the shoulder's comfort, function, or active motion. The goal of this study was to explore these relationships in shoulders with surgically documented cuff disease. In 55 shoulders having surgery for cuff-related symptoms, we correlated the preoperative Simple Shoulder Test score with the objectively measured preoperative active shoulder motion and with the integrity of the cuff observed at surgery. The 16 shoulders with tendinosis or partial-thickness tears had an average Simple Shoulder Test score of 3.7 ± 3.3, active abduction of 111° ± 38°, and active flexion of 115° ± 36°. The corresponding values were 3.6 ± 2.8, 94° ± 47°, and 94° ± 52° for the 22 full-thickness supraspinatus tears and 3.9 ± 2.7, 89° ± 39°, and 100° ± 39° for the 17 supraspinatus and infraspinatus tears. In this study, surgically observed cuff integrity was not strongly associated with the shoulder's comfort or function. Whereas surgeons often seek to improve the integrity of the rotator cuff, the management of patients with rotator cuff disorders needs to be informed by a better understanding of the factors other than cuff integrity that influence the comfort and functioning of shoulders with cuff disease. Copyright © 2017 Journal of Shoulder and Elbow Surgery Board of Trustees. Published by Elsevier Inc. All rights reserved.
18. A DNA barcoding method to discriminate between the model plant Brachypodium distachyon and its close relatives B. stacei and B. hybridum (Poaceae).
Science.gov (United States)
López-Alvarez, Diana; López-Herranz, Maria Luisa; Betekhtin, Alexander; Catalán, Pilar
2012-01-01
Brachypodium distachyon s. l. has been widely investigated across the world as a model plant for temperate cereals and biofuel grasses. However, this annual plant shows three cytotypes that have been recently recognized as three independent species, the diploids B. distachyon (2n = 10) and B. stacei (2n = 20) and their derived allotetraploid B. hybridum (2n = 30). We propose a DNA barcoding approach that consists of a rapid, accurate and automatable species identification method using the standard DNA sequences of complementary plastid (trnLF) and nuclear (ITS, GI) loci. The highly homogenous but largely divergent B. distachyon and B. stacei diploids could be easily distinguished (100% identification success) using direct trnLF (2.4%), ITS (5.5%) or GI (3.8%) sequence divergence. By contrast, B. hybridum could only be unambiguously identified through the use of combined trnLF+ITS sequences (90% of identification success) or by cloned GI sequences (96.7%) that showed 5.4% (ITS) and 4% (GI) rate divergence between the two parental sequences found in the allopolyploid. Our data provide an unbiased and effective barcode to differentiate these three closely-related species from one another. This procedure overcomes the taxonomic uncertainty generated from methods based on morphology or flow cytometry identifications that have resulted in some misclassifications of the model plant and its allies. Our study also demonstrates that the allotetraploid B. hybridum has resulted from bi-directional crosses of B. distachyon and B. stacei plants acting either as maternal or paternal parents.
19. 关注电磁学相关物理效应的教学%Paying Close Attention to Teaching of the Physical Effects Related to Electromagnetics
Institute of Scientific and Technical Information of China (English)
李长胜; 冯丽爽
2015-01-01
We propose to pay close attention to teaching of the physical effects related to electromagnetics in the courses of Theory of Electromagnetic Field and Electromagnetic Field&Wave,and analyze necessity and feasibility of the proposed teaching content. Teaching of electromagnetic effects is of great help to students to let them under-stand basic concepts and theorems of electromagnetic field and wave,to improve their innovation abilities,and to stimulate their interests of study and scientific research. Such factors as different students'majors,dependence on teaching content,and significance in theory and application,play great roles in the selection of electromagnetic effects to teach.%本文提出在“电磁场理论”和“电磁场与电磁波”课程教学中关注电磁学相关物理效应，并分析其必要性和可行性。关注电磁学效应的教学，将有助于学生对电磁场与电磁波相关基本概念和定理的理解，有利于提高学生的创新研究能力，有助于激发学生的学习兴趣和科研热情。在本课程教学过程中，可根据不同专业的需要和教学内容的相关性等，适当选讲具有一定理论和实际意义的电磁学效应。
20. Three novel rice genes closely related to the Arabidopsis IRX9, IRX9L, and IRX14 genes and their roles in xylan biosynthesis
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Dawn eChiniquy
2013-04-01
Full Text Available Xylan is the second most abundant polysaccharide on Earth, and represents a major component of both dicot wood and the cell walls of grasses. Much knowledge has been gained from studies of xylan biosynthesis in the model plant, Arabidopsis. In particular, the irregular xylem (irx mutants, named for their collapsed xylem cells, have been essential in gaining a greater understanding of the genes involved in xylan biosynthesis. In contrast, xylan biosynthesis in grass cell walls is poorly understood. We identified three rice genes Os07g49370 (OsIRX9, Os01g48440 (OsIRX9L, and Os06g47340 (OsIRX14, from glycosyltransferase family 43 as putative orthologs to the putative β-1,4-xylan backbone elongating Arabidopsis IRX9, IRX9L, and IRX14 genes, respectively. We demonstrate that the overexpression of the closely related rice genes, in full or partly complement the two well-characterized Arabidopsis irregular xylem (irx mutants: irx9 and irx14. Complementation was assessed by measuring dwarfed phenotypes, irregular xylem cells in stem cross sections, xylose content of stems, xylosyltransferase activity of stems, and stem strength. The expression of OsIRX9 in the irx9 mutant resulted in xylosyltransferase activity of stems that was over double that of wild type plants, and the stem strength of this line increased to 124% above that of wild type. Taken together, our results suggest that OsIRX9/OsIRX9L, and OsIRX14, have similar functions to the Arabidopsis IRX9 and IRX14 genes, respectively. Furthermore, our expression data indicate that OsIRX9 and OsIRX9L may function in building the xylan backbone in the secondary and primary cell walls, respectively. Our results provide insight into xylan biosynthesis in rice and how expression of a xylan synthesis gene may be modified to increase stem strength.
1. Head Transcriptomes of Two Closely Related Species of Fruit Flies of the Anastrepha fraterculus Group Reveals Divergent Genes in Species with Extensive Gene Flow
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Victor Borges Rezende
2016-10-01
Full Text Available Several fruit flies species of the Anastrepha fraterculus group are of great economic importance for the damage they cause to a variety of fleshy fruits. Some species in this group have diverged recently, with evidence of introgression, showing similar morphological attributes that render their identification difficult, reinforcing the relevance of identifying new molecular markers that may differentiate species. We investigated genes expressed in head tissues from two closely related species: A. obliqua and A. fraterculus, aiming to identify fixed single nucleotide polymorphisms (SNPs and highly differentiated transcripts, which, considering that these species still experience some level of gene flow, could indicate potential candidate genes involved in their differentiation process. We generated multiple libraries from head tissues of these two species, at different reproductive stages, for both sexes. Our analyses indicate that the de novo transcriptome assemblies are fairly complete. We also produced a hybrid assembly to map each species’ reads, and identified 67,470 SNPs in A. fraterculus, 39,252 in A. obliqua, and 6386 that were common to both species. We identified 164 highly differentiated unigenes that had a mean interspecific index (D¯ of at least 0.94. We selected unigenes that had Ka/Ks higher than 0.5, or had at least three or more highly differentiated SNPs as potential candidate genes for species differentiation. Among these candidates, we identified proteases, regulators of redox homeostasis, and an odorant-binding protein (Obp99c, among other genes. The head transcriptomes described here enabled the identification of thousands of genes hitherto unavailable for these species, and generated a set of candidate genes that are potentially important to genetically identify species and understand the speciation process in the presence of gene flow of A. obliqua and A. fraterculus.
2. A DNA barcoding method to discriminate between the model plant Brachypodium distachyon and its close relatives B. stacei and B. hybridum (Poaceae.
Directory of Open Access Journals (Sweden)
Diana López-Alvarez
Full Text Available BACKGROUND: Brachypodium distachyon s. l. has been widely investigated across the world as a model plant for temperate cereals and biofuel grasses. However, this annual plant shows three cytotypes that have been recently recognized as three independent species, the diploids B. distachyon (2n = 10 and B. stacei (2n = 20 and their derived allotetraploid B. hybridum (2n = 30. METHODOLOGY/PRINCIPAL FINDINGS: We propose a DNA barcoding approach that consists of a rapid, accurate and automatable species identification method using the standard DNA sequences of complementary plastid (trnLF and nuclear (ITS, GI loci. The highly homogenous but largely divergent B. distachyon and B. stacei diploids could be easily distinguished (100% identification success using direct trnLF (2.4%, ITS (5.5% or GI (3.8% sequence divergence. By contrast, B. hybridum could only be unambiguously identified through the use of combined trnLF+ITS sequences (90% of identification success or by cloned GI sequences (96.7% that showed 5.4% (ITS and 4% (GI rate divergence between the two parental sequences found in the allopolyploid. CONCLUSION/SIGNIFICANCE: Our data provide an unbiased and effective barcode to differentiate these three closely-related species from one another. This procedure overcomes the taxonomic uncertainty generated from methods based on morphology or flow cytometry identifications that have resulted in some misclassifications of the model plant and its allies. Our study also demonstrates that the allotetraploid B. hybridum has resulted from bi-directional crosses of B. distachyon and B. stacei plants acting either as maternal or paternal parents.
3. Advantageous Direct Quantification of Viable Closely Related Probiotics in Petit-Suisse Cheeses under In Vitro Gastrointestinal Conditions by Propidium Monoazide - qPCR
Science.gov (United States)
Villarreal, Martha Lissete Morales; Padilha, Marina; Vieira, Antonio Diogo Silva; Franco, Bernadette Dora Gombossy de Melo; Martinez, Rafael Chacon Ruiz; Saad, Susana Marta Isay
2013-01-01
Species-specific Quantitative Real Time PCR (qPCR) alone and combined with the use of propidium monoazide (PMA) were used along with the plate count method to evaluate the survival of the probiotic strains Lactobacillus acidophilus La-5 and Bifidobacterium animalis subsp. lactis Bb-12, and the bacteriocinogenic and potentially probiotic strain Lactobacillus sakei subsp. sakei 2a in synbiotic (F1) and probiotic (F2) petit-suisse cheeses exposed throughout shelf-life to in vitro simulated gastrointestinal tract conditions. The three strains studied showed a reduction in their viability after the 6 h assay. Bb-12 displayed the highest survival capacity, above 72.6 and 74.6% of the initial populations, respectively, by plate count and PMA-qPCR, maintaining population levels in the range or above 6 log CFU/g. The prebiotic mix of inulin and FOS did not offer any additional protection for the strains against the simulated gastrointestinal environment. The microorganisms' populations were comparable among the three methods at the initial time of the assay, confirming the presence of mainly viable and culturable cells. However, with the intensification of the stress induced throughout the various stages of the in vitro test, the differences among the methods increased. The qPCR was not a reliable enumeration method for the quantification of intact bacterial populations, mixed with large numbers of injured and dead bacteria, as confirmed by the scanning electron microscopy results. Furthermore, bacteria plate counts were much lower (P<0.05) than with the PMA-qPCR method, suggesting the accumulation of stressed or dead microorganisms unable to form colonies. The use of PMA overcame the qPCR inability to differentiate between dead and alive cells. The combination of PMA and species-specific qPCR in this study allowed a quick and unequivocal way of enumeration of viable closely related species incorporated into probiotic and synbiotic petit-suisse cheeses and under stress
4. Advantageous direct quantification of viable closely related probiotics in petit-suisse cheeses under in vitro gastrointestinal conditions by Propidium Monoazide--qPCR.
Directory of Open Access Journals (Sweden)
Martha Lissete Morales Villarreal
Full Text Available Species-specific Quantitative Real Time PCR (qPCR alone and combined with the use of propidium monoazide (PMA were used along with the plate count method to evaluate the survival of the probiotic strains Lactobacillus acidophilus La-5 and Bifidobacterium animalis subsp. lactis Bb-12, and the bacteriocinogenic and potentially probiotic strain Lactobacillus sakei subsp. sakei 2a in synbiotic (F1 and probiotic (F2 petit-suisse cheeses exposed throughout shelf-life to in vitro simulated gastrointestinal tract conditions. The three strains studied showed a reduction in their viability after the 6 h assay. Bb-12 displayed the highest survival capacity, above 72.6 and 74.6% of the initial populations, respectively, by plate count and PMA-qPCR, maintaining population levels in the range or above 6 log CFU/g. The prebiotic mix of inulin and FOS did not offer any additional protection for the strains against the simulated gastrointestinal environment. The microorganisms' populations were comparable among the three methods at the initial time of the assay, confirming the presence of mainly viable and culturable cells. However, with the intensification of the stress induced throughout the various stages of the in vitro test, the differences among the methods increased. The qPCR was not a reliable enumeration method for the quantification of intact bacterial populations, mixed with large numbers of injured and dead bacteria, as confirmed by the scanning electron microscopy results. Furthermore, bacteria plate counts were much lower (P<0.05 than with the PMA-qPCR method, suggesting the accumulation of stressed or dead microorganisms unable to form colonies. The use of PMA overcame the qPCR inability to differentiate between dead and alive cells. The combination of PMA and species-specific qPCR in this study allowed a quick and unequivocal way of enumeration of viable closely related species incorporated into probiotic and synbiotic petit-suisse cheeses and
5. Airflow limitation or static hyperinflation: which is more closely related to dyspnea with activities of daily living in patients with COPD?
Directory of Open Access Journals (Sweden)
Nishimura Takashi
2011-10-01
Full Text Available Abstract Background Dyspnea while performing the activities of daily living has been suggested to be a better measurement than peak dyspnea during exercise. Furthermore, the inspiratory capacity (IC has been shown to be more closely related to exercise tolerance and dyspnea than the FEV1, because dynamic hyperinflation is the main cause of shortness of breath in patients with COPD. However, breathlessness during exercise is measured in most studies to evaluate this relationship. Purpose To evaluate the correlation between breathlessness during daily activities and airflow limitation or static hyperinflation in COPD. Methods We examined 167 consecutive outpatients with stable COPD. The Baseline Dyspnea Index (BDI was used to evaluate dyspnea with activities of daily living. The relationship between the BDI score and the clinical measurements of pulmonary function was then investigated. Results The Spearman rank correlation coefficients (Rs between the BDI score and the FEV1(L, FEV1(%pred and FEV1/FVC were 0.60, 0.56 and 0.56, respectively. On the other hand, the BDI score also correlated with the IC, IC/predicted total lung capacity (TLC and IC/TLC (Rs = 0.45, 0.46 and 0.47, respectively. Although all of the relationships studied were strongly correlated, the correlation coefficients were better between dyspnea and airflow limitation than between dyspnea and static hyperinflation. In stepwise multiple regression analyses, the BDI score was most significantly explained by the FEV1 (R2 = 26.2% and the diffusion capacity for carbon monoxide (R2 = 14.4% (Cumulative R2 = 40.6%. Static hyperinflation was not a significant factor for clinical dyspnea on the stepwise multiple regression analysis. Conclusion Both static hyperinflation and airflow limitation contributed greatly to dyspnea in COPD patients.
6. Prognostic Patterns in Self-Report, Relative Report, and Professional Evaluation Measures for Hospitalized and Day-Care Patients
Science.gov (United States)
Sappington, A. A.; Michaux, Mary H.
1975-01-01
This study attempted to determine differences between patients who relapse and those who do not in both hospital and day-care settings. Subjects were 142 adult psychiatric patients. Three groups of measures were used: one based on professional evaluation, one based on self-report, and one based on relative report. (Author)
7. Visceral fat dominant distribution in male type 2 diabetic patients is closely related to hepatic insulin resistance, irrespective of body type
Directory of Open Access Journals (Sweden)
Miyazaki Yoshinori
2009-08-01
Full Text Available Abstract Background All previous studies that investigated the association between abdominal fat distribution and insulin resistance evaluated subcutaneous and visceral fat area and/or volume, but these values were not related to the body type of each subject. In the present study we have examined the association between abdominal fat distribution and peripheral (muscle/hepatic sensitivity to insulin using the visceral to abdominal subcutaneous fat area ratio (VF/SF ratio in male patients with type 2 diabetes mellitus. This ratio defines the predominancy of visceral or subcutaneous abdominal adiposity, independent of the body type of each individual. Methods Thirty-six type 2 diabetic male patients underwent a euglycemic insulin clamp (insulin infusion rate = 40 mU/m2·min with 3-3H-glucose to measure insulin-mediated total body (primarily reflects muscle glucose disposal (TGD and suppression of endogenous (primarily reflects liver glucose production (EGP in response to a physiologic increase in plasma insulin concentration. Abdominal subcutaneous (SF and intraabdominal visceral fat (VF areas were quantitated with magnetic resonance imaging (MRI at the level of L4–5. Results TGD and TGD divided by steady state plasma insulin concentration during the insulin clamp (TGD/SSPI correlated inversely with body mass index (BMI, total fat mass (FM measured by 3H2O, SF and VF areas, while VF/SF ratio displayed no significant relationship with TGD or TGD/SSPI. In contrast, EGP and the product of EGP and SSPI during the insulin clamp (an index hepatic insulin resistance correlated positively with VF/SF ratio, but not with BMI, FM, VF or SF. Conclusion We conclude that, independent of the individual's body type, visceral fat dominant accumulation as opposed to subcutaneous fat accumulation is associated with hepatic insulin resistance, whereas peripheral (muscle insulin resistance is more closely related to general obesity (i.e. higher BMI and total FM
8. Metabolic and evolutionary insights into the closely-related species Streptomyces coelicolor and Streptomyces lividans deduced from high-resolution comparative genomic hybridization
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Harrison Marcus
2010-12-01
Full Text Available Abstract Background Whilst being closely related to the model actinomycete Streptomyces coelicolor A3(2, S. lividans 66 differs from it in several significant and phenotypically observable ways, including antibiotic production. Previous comparative gene hybridization studies investigating such differences have used low-density (one probe per gene PCR-based spotted arrays. Here we use new experimentally optimised 104,000 × 60-mer probe arrays to characterize in detail the genomic differences between wild-type S. lividans 66, a derivative industrial strain, TK24, and S. coelicolor M145. Results The high coverage and specificity (detection of three nucleotide differences of the new microarrays used has highlighted the macroscopic genomic differences between two S. lividans strains and S. coelicolor. In a series of case studies we have validated the microarray and have identified subtle changes in genomic structure which occur in the Asp-activating adenylation domains of CDA non-ribosomal peptide synthetase genes which provides evidence of gene shuffling between these domains. We also identify single nucleotide sequence inter-species differences which exist in the actinorhodin biosynthetic gene cluster. As the glyoxylate bypass is non-functional in both S. lividans strains due to the absence of the gene encoding isocitrate lyase it is likely that the ethylmalonyl-CoA pathway functions as the alternative mechanism for the assimilation of C2 compounds. Conclusions This study provides evidence for widespread genetic recombination, rather than it being focussed at 'hotspots', suggesting that the previously proposed 'archipelago model' of genomic differences between S. coelicolor and S. lividans is unduly simplistic. The two S. lividans strains investigated differ considerably in genetic complement, with TK24 lacking 175 more genes than its wild-type parent when compared to S. coelicolor. Additionally, we confirm the presence of bldB in S. lividans and
9. Multiplicity of Galactic Cepheids from long-baseline interferometry - III. Sub-percent limits on the relative brightness of a close companion of δ Cephei
Science.gov (United States)
Gallenne, A.; Mérand, A.; Kervella, P.; Monnier, J. D.; Schaefer, G. H.; Roettenbacher, R. M.; Gieren, W.; Pietrzyński, G.; McAlister, H.; ten Brummelaar, T.; Sturmann, J.; Sturmann, L.; Turner, N.; Anderson, R. I.
2016-09-01
We report new CHARA/Michigan InfraRed Combiner interferometric observations of the Cepheid archetype δ Cep, which aimed at detecting the newly discovered spectroscopic companion. We reached a maximum dynamic range ΔH = 6.4, 5.8 and 5.2 mag, respectively, within the relative distance to the Cepheid r 9.15, 8.31 and 7.77 mag, respectively, for r < 25 mas, 25 < r < 50 mas and 50 < r < 100 mas. We also found that to be consistent with the predicted orbital period (Anderson et al.), the companion has to be located at a projected separation <24 mas with a spectral type later than an F0V star.
10. Temporomandibular Joint, Closed
Science.gov (United States)
... Gallery > Oral Health > The Temporomandibular Joint, Closed The Temporomandibular Joint, Closed Main Content Title: The Temporomandibular Joint, Closed Description: The temporomandibular joint connects the lower ...
11. Evolutionary insights from bat trypanosomes: morphological, developmental and phylogenetic evidence of a new species, Trypanosoma (Schizotrypanum) erneyi sp. nov., in African bats closely related to Trypanosoma (Schizotrypanum) cruzi and allied species.
Science.gov (United States)
Lima, Luciana; Silva, Flávia Maia da; Neves, Luis; Attias, Márcia; Takata, Carmen S A; Campaner, Marta; de Souza, Wanderley; Hamilton, Patrick B; Teixeira, Marta M G
2012-11-01
Parasites of the genus Trypanosoma are common in bats and those of the subgenus Schizotrypanum are restricted to bats throughout the world, with the exception of Trypanosoma (Schizotrypanum) cruzi that also infects other mammals and is restricted to the American Continent. We have characterized trypanosome isolates from Molossidae bats captured in Mozambique, Africa. Morphology and behaviour in culture, supported by phylogenetic inferences using SSU (small subunit) rRNA, gGAPDH (glycosomal glyceraldehyde 3-phosphate dehydrogenase) and Cyt b (cytochrome b) genes, allowed to classify the isolates as a new Schizotrypanum species named Trypanosoma (Schizotrypanum) erneyi sp. nov. This is the first report of a Schizotrypanum species from African bats cultured, characterized morphologically and biologically, and positioned in phylogenetic trees. The unprecedented finding of a new species of the subgenus Schizotrypanum from Africa that is closest related to the America-restricted Trypanosoma (Schizotrypanum) cruzi marinkellei and T. cruzi provides new insights into the origin and evolutionary history of T. cruzi and closely related bat trypanosomes. Altogether, data from our study support the hypothesis of an ancestor trypanosome parasite of bats evolving to infect other mammals, even humans, and adapted to transmission by triatomine bugs in the evolutionary history of T. cruzi in the New World.
12. HTF: A b-ZIP transcription factor that is closely related to the human XBP/TREB5 and is activated by hepatocellular carcinoma in rats.
Science.gov (United States)
Kishimoto, T; Kokura, K; Kumagai, Y; Wakamatsu, T; Makino, Y; Tamura, T
1996-06-25
We screened for rat hepatocellular carcinoma (HCC)-related genes by a novel cDNA subtraction method and obtained one gene. This gene was transcribed as 2.0- and 2.5-kb mRNAs, and its transcription was specifically enhanced in HCC. These cDNAs had the same open reading frame, but the 2.5 kb transcript had an extra 495 bases of 5'-UTR at the 5'-terminus. The deduced aa sequence revealed a basic-leucine zipper (b-ZIP) and proline/glutamine-rich structures, both of which are characteristic motifs for transcription factors. We designated the translation product of this gene HTF (Hepatocarcinogenesis-related Transcription Factor). Electrophoretic mobility shift assay demonstrated the DNA-binding ability of the recombinant HTF. It is most interesting that HTF had a considerable homology with human XBP/TREB5, which has been reported to be a binding factor for the X-box of the MHC class II gene and for the 21-bp enhancer of the HTLV-1 LTR. Genomic Southern analysis suggested that the 2.0- and 2.5-kb mRNAs are transcribed by a dual promoter of a single gene. Our results may suggest that HTF is a b-ZIP-type transcription factor involved in rat hepatocellular carcinoma.
13. Evaluation of technical feasibility of closed-cycle non-equilibrium MHD power generation with direct coal firing. Final report, Task 1
Energy Technology Data Exchange (ETDEWEB)
1981-11-01
Program accomplishments in a continuing effort to demonstrate the feasibility of direct coal fired, closed cycle, magnetohydrodynamic power generation are detailed. These accomplishments relate to all system aspects of a CCMHD power generation system including coal combustion, heat transfer to the MHD working fluid, MHD power generation, heat and cesium seed recovery and overall systems analysis. Direct coal firing of the combined cycle has been under laboratory development in the form of a high slag rejection, regeneratively air cooled cyclone coal combustor concept, originated within this program. A hot bottom ceramic regenerative heat exchanger system was assembled and test fired with coal for the purposes of evaluating the catalytic effect of alumina on NO/sub x/ emission reduction and operability of the refractory dome support system. Design, procurement, fabrication and partial installation of a heat and seed recovery flow apparatus was accomplished and was based on a stream tube model of the full scale system using full scale temperatures, tube sizes, rates of temperature change and tube geometry. Systems analysis capability was substantially upgraded by the incorporation of a revised systems code, with emphasis on ease of operator interaction as well as separability of component subroutines. The updated code was used in the development of a new plant configuration, the Feedwater Cooled (FCB) Brayton Cycle, which is superior to the CCMHD/Steam cycle both in performance and cost. (WHK)
14. Bead-probe complex capture a couple of SINE and LINE family from genomes of two closely related species of East Asian cyprinid directly using magnetic separation
Science.gov (United States)
Tong, Chaobo; Guo, Baocheng; He, Shunping
2009-01-01
Background Short and long interspersed elements (SINEs and LINEs, respectively), two types of retroposons, are active in shaping the architecture of genomes and powerful tools for studies of phylogeny and population biology. Here we developed special protocol to apply biotin-streptavidin bead system into isolation of interspersed repeated sequences rapidly and efficiently, in which SINEs and LINEs were captured directly from digested genomic DNA by hybridization to bead-probe complex in solution instead of traditional strategy including genomic library construction and screening. Results A new couple of SINEs and LINEs that shared an almost identical 3'tail was isolated and characterized in silver carp and bighead carp of two closely related species. These SINEs (34 members), designated HAmo SINE family, were little divergent in sequence and flanked by obvious TSD indicated that HAmo SINE was very young family. The copy numbers of this family was estimated to 2 × 105 and 1.7 × 105 per haploid genome by Real-Time qPCR, respectively. The LINEs, identified as the homologs of LINE2 in other fishes, had a conserved primary sequence and secondary structures of the 3'tail region that was almost identical to that of HAmo SINE. These evidences suggest that HAmo SINEs are active and amplified recently utilizing the enzymatic machinery for retroposition of HAmoL2 through the recognition of higher-order structures of the conserved 42-tail region. We analyzed the possible structures of HAmo SINE that lead to successful amplification in genome and then deduced that HAmo SINE, SmaI SINE and FokI SINE that were similar in sequence each other, were probably generated independently and created by LINE family within the same lineage of a LINE phylogeny in the genomes of different hosts. Conclusion The presented results show the advantage of the novel method for retroposons isolation and a pair of young SINE family and its partner LINE family in two carp fishes, which strengthened
15. Bead-probe complex capture a couple of SINE and LINE family from genomes of two closely related species of East Asian cyprinid directly using magnetic separation
Directory of Open Access Journals (Sweden)
Guo Baocheng
2009-02-01
Full Text Available Abstract Background Short and long interspersed elements (SINEs and LINEs, respectively, two types of retroposons, are active in shaping the architecture of genomes and powerful tools for studies of phylogeny and population biology. Here we developed special protocol to apply biotin-streptavidin bead system into isolation of interspersed repeated sequences rapidly and efficiently, in which SINEs and LINEs were captured directly from digested genomic DNA by hybridization to bead-probe complex in solution instead of traditional strategy including genomic library construction and screening. Results A new couple of SINEs and LINEs that shared an almost identical 3'tail was isolated and characterized in silver carp and bighead carp of two closely related species. These SINEs (34 members, designated HAmo SINE family, were little divergent in sequence and flanked by obvious TSD indicated that HAmo SINE was very young family. The copy numbers of this family was estimated to 2 × 105 and 1.7 × 105 per haploid genome by Real-Time qPCR, respectively. The LINEs, identified as the homologs of LINE2 in other fishes, had a conserved primary sequence and secondary structures of the 3'tail region that was almost identical to that of HAmo SINE. These evidences suggest that HAmo SINEs are active and amplified recently utilizing the enzymatic machinery for retroposition of HAmoL2 through the recognition of higher-order structures of the conserved 42-tail region. We analyzed the possible structures of HAmo SINE that lead to successful amplification in genome and then deduced that HAmo SINE, SmaI SINE and FokI SINE that were similar in sequence each other, were probably generated independently and created by LINE family within the same lineage of a LINE phylogeny in the genomes of different hosts. Conclusion The presented results show the advantage of the novel method for retroposons isolation and a pair of young SINE family and its partner LINE family in two carp
16. 13 CFR 120.1060 - Confidentiality of Reports, Risk Ratings and related Confidential Information.
Science.gov (United States)
2010-01-01
... order prior to disclosure. For purposes of this regulation, “Information Provider” means any contractor... abides by them. Any disclosure of the Report, Risk Rating, or Confidential Information other than as... Confidentiality of Reports, Risk Ratings and related Confidential Information. (a) In general. Reports and other...
17. The Relation of Recent Tampon Use, Douching, Coitus, and Vaginal Medications for Reported Cervical Cytology Results
Science.gov (United States)
1993-01-01
or cervical intraepithelial neoplasia (CIN) on the pathology report. Assumptions Tampon use is drying to the vaginal epithelium and has been...SUBTITLE 5, FUNDING NUMBERS The Relation of Recent Tamplon Use, Douching, Coitus, and Vaginal Medications for Reported Cervical Cytology Results. 6. AUTHOR...11¾ .. ?j’ U..- THE RELATION OF RECENT TAMPON USE, DOUCHING, COITUS, AND VAGINAL MEDICATIONS TO REPORTED CERVICAL CYTOLOGY RESULTS By MARYANN
18. Appendiceal immunoglobulin G4-related disease mimicking appendiceal tumor or appendicitis: A case report
Energy Technology Data Exchange (ETDEWEB)
Kim, Hyun Soo; Kang, Won Kyung; Chung, Dong Jin [Yeouido St. Mary' s Hospital, The Catholic University of Korea, Seoul (Korea, Republic of)
2016-02-15
Immunoglobulin G4 (IgG4)-related disease is an autoimmune disease that forms tumorous lesions. Several cases involving various organs are reported, however, IgG4-related disease involving appendix has not been reported yet. In this report, we presented a case of IgG4-related disease of appendix, which raised a suspicion of appendiceal tumor or usual appendicitis and, therefore, led to unnecessary surgical resection. IgG4-related disease should be considered in the differential diagnosis for a mass-like swelling of the appendix, in order to avoid unnecessary surgery.
19. On the relation between the fundamental equation of thermodynamics and the energy balance equation in the context of closed and open systems
NARCIS (Netherlands)
Knuiman, J.T.; Barneveld, P.A.
2012-01-01
In this paper, we elaborate on the connection between the fundamental equation of thermodynamics, which is essentially the combination of the First and Second Laws of thermodynamics, and the energy balance equation in the context of closed and open systems. We point out some misinterpretations in
20. On the relation between the fundamental equation of thermodynamics and the energy balance equation in the context of closed and open systems
NARCIS (Netherlands)
Knuiman, J.T.; Barneveld, P.A.
2012-01-01
In this paper, we elaborate on the connection between the fundamental equation of thermodynamics, which is essentially the combination of the First and Second Laws of thermodynamics, and the energy balance equation in the context of closed and open systems. We point out some misinterpretations in at | {"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": 0.5314831137657166, "perplexity": 10929.273471296983}, "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-2018-09/segments/1518891816068.93/warc/CC-MAIN-20180224231522-20180225011522-00448.warc.gz"} |
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## math456 2 years ago How do I do this? Delete Cancel Submit
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1. math456
• 2 years ago
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$\int\limits_{0}^{9}f(x)dx=37; \int\limits_{0}^{9}g(x)dx=16$
2. math456
• 2 years ago
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Find: $\int\limits_{0}^{9}[2f(x)+3g(x)]dx$
3. phi
• 2 years ago
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the integral is "linear" in other words, for a constant "a" $\int\limits_{0}^{9} a f(x)dx = a\int\limits_{0}^{9} f(x)dx$
4. math456
• 2 years ago
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so in this case $2\int\limits_{0}^{9} x.dx$??
5. phi
• 2 years ago
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and you can separate integrals (assuming they have the same limits $\int\limits_{0}^{9} f(x) + g(x) dx= \int\limits_{0}^{9} f(x)dx + \int\limits_{0}^{9} g(x)dx$
6. phi
• 2 years ago
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not x , f(x) so separate the problem into $2\int\limits_{0}^{9} f(x)dx + 3\int\limits_{0}^{9} g(x)dx$
7. math456
• 2 years ago
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yea right! so $37x(9,0)+16x(9,0)$
8. phi
• 2 years ago
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I don't know about the x(9,0) part just replace the integral with the number they say it is equal to $2\cancel{(\int\limits_{0}^{9} f(x)dx)}37 + 3\int\limits_{0}^{9} g(x)dx$ and do the same for the other, it is 16
9. phi
• 2 years ago
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I am trying to show you sub in 37 for the result of the first integral
10. math456
• 2 years ago
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ohh alright, i got it!
11. math456
• 2 years ago
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so its 2(37) + 3(16) = 122
12. math456
• 2 years ago
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thanks @phi :)
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Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy. | {"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": 0.9999055862426758, "perplexity": 8576.027184354713}, "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-2015-11/segments/1424936462426.4/warc/CC-MAIN-20150226074102-00302-ip-10-28-5-156.ec2.internal.warc.gz"} |
https://hillsidesc.org/teachers-pages/calculus-chapter-2/differential-calculus-chapters-1-4/ | # Section 2.6
## Homework: p. 144; 1-4, 7,9-19 odd, 25,27,35,37,38,39
Note: I am adding numbers 18 and 26 to this assignment.
### In class, homework discussion topics:
• #17: since the limit was of the form $\lim_{x \to \infty}f(x)$, we used $\sqrt{x^2} \Rightarrow x$. If the limit had been to negative infinity, as in $\lim_{x \to -\infty}f(x)$, we would have said $\sqrt{x^2} \Rightarrow -x$.
Optional: 41,43
# Section 3.1
Videos and Resources
Note: As you work through these problems, try to memorize the differentiation rules.
optional: 57,59
# Section 3.2
Videos and Resources
Note: As you work through these problems, try to memorize the differentiation rules.
Optional: 41,42
# Section 3.4
Videos and Resources
Homework: 1,3,5,9,13,14,15,25,31,33,35,39,47
# Section 3.5
Video lecture and Resources
# Section 3.6
Videos and Resources
Examples of Implicit Differentiation
## Homework:5,9,15,19,23,27,41,43,49,53,55
Optional: 69 (Use a computer algebra system such as Sage Math to solve the system of equations that you develop).
# Section 3.7
Videos and Resources
Videos
# Section 3.9
Feel free to skim/read this section. We’re not going to cover this stuff.
# Section 3.10
Videos and Resources
## Homework: p.257 #1,3,4,5,7,
Optional extra practice: 8,9,17,29
# Section 3.11
## Homework: p.264 #3,5,9,11,15,17,21,25,27,39 (see example 5, p.263)
Linear Approximations Videos and Resources
Differentials Videos and Resources
# Chapter 3 Study Suggestions:
• Be confident on problems like:
• p. 189 #5,25,43,44
• p.195 #3,7,31
• p.213 #3,11,25
• p.222 #36,37
• p.232 #55,56
• p.238 #29
• p.238 #45
• p.257 #7,17
• p.265 #9,10,15-19
# Section 4.3:
## #3,4,5,7,8,11,15,17,31,37,43,51,58
optional extra practice: #6,47
# Section 4.4:
## p.311 #1,2,3,7,9,29,45,47
-Take a crack at #73, but feel free to just review the solution in the solution manual. Mostly, I just want you to see this.
# Section 4.9:
## p. 349 #1,2,3,5,9,13,29
Related Resources:
Newton’s method in python Video | {"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": 8, "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": 0.969000518321991, "perplexity": 12734.643751751499}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-49/segments/1669446711001.28/warc/CC-MAIN-20221205000525-20221205030525-00851.warc.gz"} |
https://www.ias.ac.in/listing/bibliography/pram/Molly_Isaac | • Molly Isaac
Articles written in Pramana – Journal of Physics
• Stability of electrostatic ion cyclotron waves in a multi-ion plasma
We have studied the stability of the electrostatic ion cyclotron wave in a plasma consisting of isotropic hydrogen ions ($H^{+}$) and temperature-anisotropic positively ($O^{+}$) and negatively ($O^{−}$) charged oxygen ions, with the electrons drifting parallel to the magnetic field. Analytical expressions have been derived for the frequency and growth/damping rate of ion cyclotron waves around the first harmonic of both hydrogen and oxygen ion gyrofrequencies. We find that the frequencies and growth/damping rates are dependent on the densities and temperatures of all species of ions. A detailed numerical study, for parameters relevant to comet Halley, shows that the growth rate is dependent on the magnitude of the frequency. The ion cyclotron waves are driven by the electron drift parallel to the magnetic field; the temperature anisotropy of the oxygen ions only slightly enhance the growth rates for small values of temperature anisotropies. A simple explanation, in terms of wave exponentiation times, is offered for the absence of electrostatic ion cyclotron waves in the multi-ion plasma of comet Halley.
• # Pramana – Journal of Physics
Volume 94, 2019
All articles
Continuous Article Publishing mode
• # Editorial Note on Continuous Article Publication
Posted on July 25, 2019 | {"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": 0.9587154984474182, "perplexity": 1639.7757469499966}, "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/1596439735964.82/warc/CC-MAIN-20200805183003-20200805213003-00082.warc.gz"} |
https://www.physicsforums.com/threads/i-need-help-tyvm.227343/ | # I NEED HELP tyvm
1. Apr 8, 2008
### LesVampires
A hypodermic syringe contains a medicine with the density of water (see figure below). The barrel of the syringe has a cross-sectional area of 2.20 10-5 m2. In the absence of a force on the plunger, the pressure everywhere is 1.00 atm. A force of magnitude 1.80 N is exerted on the plunger, making medicine squirt from the needle. Determine the medicine's flow speed through the needle. Assume the pressure in the needle remains equal to 1.00 atm and that the syringe is horizontal.
second question
An 11.3 kg block of metal is suspended from a scale and immersed in water, as in the figure below. The dimensions of the block are 12.0 cm 8.7 cm 8.7 cm. The 12.0 cm dimension is vertical, and the top of the block is 5.00 cm below the surface of the water
i know that P=Po + pgh p=m/v and g i cant figure h out
can u direct me a bit with this ty verymuch
1. The problem statement, all variables and given/known data
2. Relevant equations
3. The attempt at a solution
Last edited: Apr 8, 2008
2. Apr 8, 2008
### ~christina~
http://www.princeton.edu/~asmits/Bicycle_web/Bernoulli.html
height stays same so it cancels
solve for v
3. Apr 8, 2008
### LesVampires
hmm i know that Av= Av and the equations but i keep gettin a wrong answer... A= 2.2x10^-5 m^2
4. Apr 8, 2008
### ~christina~
$$P_1 + 1/2 \rho v^2 + \rho gy_1 = P_2 + 1/2\rho v^2 + \rho g y_2$$
don't forget atmospheric pressure is at the end of the needle solve for v2
P=F/A to find the pressure exerted over the area of the plunger (force exerted on plunger )
After finding the equivalent pressure that is due to the plunger, add that to atm pressure.
show me what you did and I'll tell you what your doing incorrect.
Last edited: Apr 8, 2008
5. Apr 8, 2008
### LesVampires
well the pgys are 0 u have v= 2change in P/pv pv is A right? P=1.01 x10^5 and
6. Apr 8, 2008
### ~christina~
yes pgy is 0 so what is the equation then?
not sure what your saying when you say
and the area is small on the end of the syringe but did they give it to you?
Look at the post above (last post by me) I added stuff.
I have to go but I'll see what you did tommorow (post your work)
A2/A1<<1 -> note
Last edited: Apr 8, 2008
7. Apr 8, 2008
### LesVampires
isnt that whats left of the equation?
8. Apr 8, 2008
### ~christina~
No the A1V1=A2V2 is the continuity equation and that is substituted into the bernoulli equation. And then you can solve for v2 which you want. | {"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": 0.956883430480957, "perplexity": 2724.6822757279315}, "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/1516084886830.8/warc/CC-MAIN-20180117063030-20180117083030-00587.warc.gz"} |
https://link.springer.com/article/10.1007%2Fs11253-013-0726-5 | Ukrainian Mathematical Journal
, Volume 64, Issue 9, pp 1440–1447
# Representations of canonical anticommutation relations with orthogonality condition
• R. Ya. Yakymiv
Article
We study a class of *-representations of the *-algebra $$A_0^{(d) }$$ generated by relations of the form
$$A_0^{(d) }=\mathbb{C}\langle{{a_j},a_j^{*}} |a_j^{*}{a_j}=1-{a_j}a_j^{*},a_i^{*}{a_j}=0,\;i\ne j,\;i\;j=1,\ldots,d\rangle$$
and propose a description of the classes of unitary equivalence of irreducible *-representations of $$A_0^{(d) }$$ such that there exists j = 1, … , d for which $$a_j^{2}\ne 0$$.
## Keywords
Irreducible Representation Orthonormal Basis Orthogonality Condition Polar Decomposition Partial Isometry
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
## References
1. 1.
D. P. Proskurin and K. M. Sukretnyi, “On *-representations of deformations of canonical anticommutation relations,” Ukr. Mat. Zh., 62, No. 2, 203–214 (2010); English translation: Ukr. Math. J., 62, No. 2, 227–240 (2010).
2. 2.
S. Albeverio, D. Proskurin, and L. Turowska, “On *-representations of a deformation of a Wick analogue of the CAR algebra,” Rep. Math. Phys., 56, No. 2, 175–196 (2005).
3. 3.
J. Bunce, “Representations of strongly amenable C*-algebras,” Proc. Amer. Math. Soc., 32, 241–246 (1972).
4. 4.
J. Cuntz, “Simple C*-algebras generated by isometries,” Commun. Math. Phys., 57, 173–185 (1977).
5. 5.
G. J. Murphy, C*-Algebras and Operator Theory, Academic Press, Boston (1990).Google Scholar
6. 6.
G. Nagy, “On the K-theory of the noncommutative circle,” J. Oper. Theory, 31, 303–309 (1994).
7. 7.
G. Nagy and A. Nica, “On the quantum disk and noncommutative circle,” in: P. E. T. Jørgensen and R. Curto (editors), Algebraic Methods in Operator Theory, Birkhäuser, Boston (1994), pp. 276–290.
8. 8.
V. Ostrovskyi and Yu. Samoilenko, Introduction to the Theory of Representations of Finitely Presented Algebras, Gordon and Breach, London (2000).Google Scholar
9. 9.
V. Ostrovskyi, D. Proskurin, and L. Turowska, “Unbounded representations of q-deformation of Cuntz algebra,” Lett. Math. Phys., 85, No. 2–3, 147–162 (2008).
10. 10.
D. Proskurin, “Homogeneous ideals in Wick *-algebras,” Proc. Amer. Math. Soc., 126, No. 11, 3371–3376 (1998).
11. 11.
D. Proskurin, Yu. Savcnuk, and L. Turowska, “On C*-algebras generated by some deformations of CAR relations,” Contemp. Math., 391, 297–312 (2005).
12. 12.
W. Pusz, “Twisted canonical anticommutation relations,” Rep. Math. Phys., 27, 349–360 (1989). | {"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": 0.8933809995651245, "perplexity": 4934.536745084087}, "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/1537267164469.99/warc/CC-MAIN-20180926081614-20180926102014-00451.warc.gz"} |
https://math.stackexchange.com/questions/3167308/how-is-this-population-model-different-from-the-logistic-model | # How is this population model different from the Logistic model?
I have this following population model: $$\frac{dX}{dt} = f(X) = pX(1-\frac{X}{Y})(\frac{X}{Z} -1)$$
and I have to compare it to the following Logistic Growth model: $$\frac{dX}{dt} = f(X) = pX(1-\frac{X}{Y})$$ where p = growth rate and Y is the carrying capacity of the population?
What does the term $$(\frac{X}{Z} -1)$$ do in order to differ it from the standard Logistic model and what kind of populations could I model with this altered version?
For small $$X$$, your model with an $$\frac{X}{Z}-1$$ factor, hereafter the $$Z$$-model, obtained $$\dot{X}\approx -pX$$ so small populations exponentially decay into extinction, whereas in the logistic model they exponentially grow until they're no longer small because $$\dot{X}\approx pX$$.
If $$X$$ were much larger than $$Y$$, on the logistic model $$\dot{X}\approx-\frac{pX^2}{Y}$$ would lead to population decay, which is also true of the $$Z$$ model's approximation $$\dot{X}\approx-\frac{pX^3}{YZ}$$. These asymptotic results are somewhat different though, in that the former implies $$\frac{1}{X}$$ grows approximately linearly, while the latter has this behaviour for $$\frac{1}{X^2}$$ instead, so that the decay is slower. | {"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": 15, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9772027134895325, "perplexity": 439.91479474333295}, "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/1596439738555.33/warc/CC-MAIN-20200809132747-20200809162747-00520.warc.gz"} |
https://freshergate.com/cse/automation-system/discussion/32676 | Home / CSE / Automation System :: Discussion
### Discussion :: Automation System
1. If a sine wave has a frequency of 500 Hz, the period in seconds of the sine wave is:
2. A. 5000 B. 0.003 C. 0.02 D. 0.002. E. None of the above | {"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": 0.9402345418930054, "perplexity": 4061.0929052213737}, "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-2021-49/segments/1637964363400.19/warc/CC-MAIN-20211207140255-20211207170255-00409.warc.gz"} |
http://iris.lmsal.com/itn26/calibration.html | # 6. Calibration of IRIS Observations¶
## 6.1. Wavelength Calibration¶
The wavelength calibration is automatically performed to the best of current knowledge. This is accurate to only a few pixels, and should be manually checked. There are several photospheric spectral lines that can be used for accurate wavelength calibration, most notably the Ni I 279.9474 nm line in the NUV and the O I 135.560 nm line in the FUV.
Note
The IRIS automatic wavelength calibration is based on these lines averaged over the entire slit. The slit may cover regions of significant line-of-sight flows, such as flux emergence in active regions, and thus these photospheric lines may not necessarily be at their nominal rest wavelengths as assumed by the automatic calibration. In such cases, the user is advised, again, to perform manual wavelength calibration by avoiding such regions under the slit coverage.
A detailed discussion of the wavelength calibration steps for IRIS and how to use them on data can be found in IRIS Technical Note 20.
The IRIS data are given in counts or Data Number units (DN). To convert these to a flux in physical units (e.g. erg s-1 sr-1 cm-2 Å-1) one must perform a radiometric calibration. The calibration data is included in the IRIS solarsoft branch, and can be read into an IDL structure with the iris_get_response routine:
IDL> iresp = iris_get_response(time, version='003')
where time is a string with the time of the observations (compatible with anytime), and version is an (optional) calibration version number. By default version='002', which corresponds to the pre-launch values (not time-dependent, therefore time is ignored). Version 003 is very preliminary, but allows for a time-dependent calibration from a combination of throughput trending and cross-calibration with SORCE/SOLSTICE. The output has the following structure:
IDL> help, iresp, /str
DATE_OBS STRING ''
LAMBDA FLOAT Array[3601]
AREA_SG FLOAT Array[3601, 2]
NAME_SG STRING Array[2]
DN2PHOT_SG FLOAT Array[2]
AREA_SJI FLOAT Array[3601, 4]
NAME_SJI STRING Array[4]
DN2PHOT_SJI FLOAT Array[4]
COMMENT STRING ''
VERSION STRING '003'
VERSION_DATE STRING '20150331'
where AREA_SG and AREA_SJI are the effective areas (in cm-2) as a function of wavelength (LAMBDA) respectively for the spectrograph and slit-jaw camera. The DN2PHOT tags give the conversion from DN counts to photons.
Note
With versions other than 003 the DN2PHOT tags are not present.
To convert the spectral units from DN to flux one must do the following:
$\mathrm{Flux}(\mathrm{erg}\: \mathrm{s}^{-1}\: \mathrm{cm}^{-2} \text{Å}^{-1}\: \mathrm{sr}^{-1}) = \mathrm{Flux}(\mathrm{DN}) \frac{E_\lambda \cdot \mathrm{DN2PHOT\_SG}}{A_\mathrm{eff} \cdot \mathrm{Pix}_{xy} \cdot \mathrm{Pix}_{\lambda} \cdot t_\mathrm{exp} \cdot W_\mathrm{slit}},$
where $$E_\lambda \equiv h \cdot c / \lambda$$ is the photon energy (in erg), $$\mathrm{DN2PHOT\_SG}$$ is the number of photons per DN (get from iris_get_response), $$A_\mathrm{eff}$$ is the effective area (in cm-2), $$\mathrm{Pix}_{xy}$$ is the size of the spatial pixels in radians (e.g. multiply the spatial binning factor by $$\pi/(180\cdot 3600 \cdot 6)$$), $$\mathrm{Pix}_{\lambda}$$ is the size of the spectral pixels in Å, $$t_\mathrm{exp}$$ is the exposure time in seconds and $$W_\mathrm{slit}$$ is the slit width in radians ($$W_\mathrm{slit}\equiv \pi/(180\cdot 3600 \cdot 3)$$).
A detailed discussion of the radiometric calibration steps for IRIS and how to use them on data can be found in IRIS Technical Note 24.
Note
The exposure time $$t_\mathrm{exp}$$ can be different for each exposure in the same sequence, when Automatic Exposure Control (AEC) is switched on. This is the default for most active region observations, although different exposures are only used in extreme cases when very bright phenomena can lead to CCD saturation (e.g. a flare). The level 2 FITS headers have only one value for the exposure time (the value without AEC). The sequence-dependent exposure times are available in the auxiliary metadata in the FITS files (see Level 2 chapter), with table index given by EXPTIMEF, EXPTIMEN, and EXPTIME for FUV, NUV, and slit-jaw, respectively.
## 6.3. Background in FUV data¶
FUV spectra with longer exposure times show a faint background most likely caused by a light leak from wavelengths significantly longer than the FUV. This means that the light leak is absorbed at a different CCD depth than the FUV light and thus does not show the same CCD flat-field (which for the FUV is quite prominent and dominated by the CCD annealing pattern). The light leak effectively acts as an extra “dark current” although it appears to have varying intensity levels for different pointings on the Sun. This background has been characterized and is automatically removed by iris_prep, and therefore subtracted in level 1.5 and level 2 data.
## 6.4. Coalignment between channels and SJI/spectra¶
In level 2 data the slit-jaw images from different filters and detectors are automatically co-aligned. This automatic approach is not failsafe, and for precise analysis one should always check if they match. There are two spectral marks on the slit that are called fiducials and block the light from entering. They are used for calibration, and their position should match between slit-jaw images. With smaller fields of view only one of the fiducials is visible.
Note
The position of the slit in different slit-jaw channels is not necessarily the same. Depending on the observing program, different slit-jaw filters may be exposed at different parts of a raster. This is particularly true for two or four step rasters. In such cases the alignment should have in mind the header coordinates from CRPIX and CRVAL.
As in the slit-jaw images, so too the NUV and FUV spectrograms are co-aligned in level 2 data. These too should be checked for the alignment, both between FUV, NUV and slit-jaws. In spectrograms the fiducial marks appear as solid black lines along the wavelength direction, and they should appear in the same exact spatial position for the NUV and FUV channels.
Any misalignment can be corrected for when using option yshift in iris_make_fits_level3. This option can be set to a 3-element array with the shift to be applied in the y direction to the raster files, where yshift=[fuv1, fuv2, nuv] e.g.:
IDL> iris_make_fits_level3, f, [0, 3, 6], yshift=[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": 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": 0.5993934273719788, "perplexity": 2756.509395648792}, "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-2018-26/segments/1529267864191.74/warc/CC-MAIN-20180621153153-20180621173153-00224.warc.gz"} |
https://stats.libretexts.org/Courses/Saint_Mary's_College_Notre_Dame/DSCI_500B_Essential_Probability_Theory_for_Data_Science_(Kuter)/04%3A_Continuous_Random_Variables/4.02%3A_Expected_Value_and_Variance_of_Continuous_Random_Variables | # 4.2: Expected Value and Variance of Continuous Random Variables
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We now consider the expected value and variance for continuous random variables. Note that the interpretation of each is the same as in the discrete setting, but we now have a different method of calculating them in the continuous setting.
### Definition $$\PageIndex{1}$$
If $$X$$ is a continuous random variable with pdf $$f(x)$$, then the expected value (or mean) of $$X$$ is given by
$$\mu = \mu_X = \text{E}[X] = \int\limits^{\infty}_{-\infty}\! x\cdot f(x)\, dx.\notag$$
The formula for the expected value of a continuous random variable is the continuous analog of the expected value of a discrete random variable, where instead of summing over all possible values we integrate (recall Sections 3.4 & 3.5).
For the variance of a continuous random variable, the definition is the same and we can still use the alternative formula given by Theorem 3.5.1, only we now integrate to calculate the value:
$$\text{Var}(X) = \text{E}[X^2] - \mu^2 = \left(\int\limits^{\infty}_{-\infty}\! x^2\cdot f(x)\, dx\right) - \mu^2\notag$$
### Example $$\PageIndex{1}$$
Consider again the context of Example 4.1.1, where we defined the continuous random variable $$X$$ to denote the time a person waits for an elevator to arrive. The pdf of $$X$$ was given by
$$f(x) = \left\{\begin{array}{l l} x, & \text{for}\ 0\leq x\leq 1 \\ 2-x, & \text{for}\ 1< x\leq 2 \\ 0, & \text{otherwise} \end{array}\right.\notag$$
Applying Definition 4.2.1, we compute the expected value of $$X$$:
$$\text{E}[X] = \int\limits^1_0\! x\cdot x\, dx + \int\limits^2_1\! x\cdot (2-x)\, dx = \int\limits^1_0\! x^2\, dx + \int\limits^2_1\! (2x - x^2)\, dx = \frac{1}{3} + \frac{2}{3} = 1.\notag$$
Thus, we expect a person will wait 1 minute for the elevator on average. Figure 1 demonstrates the graphical representation of the expected value as the center of mass of the pdf.
Figure 1: The red arrow represents the center of mass, or the expected value, of $$X$$.
Now we calculate the variance and standard deviation of $$X$$, by first finding the expected value of $$X^2$$.
$$\text{E}[X^2] = \int\limits^1_0\! x^2\cdot x\, dx + \int\limits^2_1\! x^2\cdot (2-x)\, dx = \int\limits^1_0\! x^3\, dx + \int\limits^2_1\! (2x^2 - x^3)\, dx = \frac{1}{4} + \frac{11}{12} = \frac{7}{6}.\notag$$
Thus, we have
\begin{align*}
\text{Var}(X) &= \text{E}[X^2] - \mu^2 = \frac{7}{6} - 1 = \frac{1}{6} \\
\Rightarrow\ \text{SD}(X) &= \sqrt{\text{Var}(X)} = \frac{1}{\sqrt{6}} \approx 0.408
\end{align*}
This page titled 4.2: Expected Value and Variance of Continuous Random Variables is shared under a not declared license and was authored, remixed, and/or curated by Kristin Kuter. | {"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": 0.9988436102867126, "perplexity": 188.68613066350875}, "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/1674764500456.61/warc/CC-MAIN-20230207102930-20230207132930-00650.warc.gz"} |
https://vismor.com/documents/network_analysis/matrix_algorithms/S4.SS10.php | # 4.10 Computational Complexity of Pivoting
Obviously, complete pivoting and partial pivoting differ substantially with regard to the computational effort required to determine the next pivot element. Complete pivoting on a dense, asymmetric matrix is an O(n3) operation requiring
$\frac{2}{3}{n}^{3}+\frac{1}{2}{n}^{2}+\frac{1}{6}n$
floating point comparisons. Partial pivoting on the same matrix is an O(n2) operation requiring
$\frac{{n}^{2}+n}{2}$
floating point comparisons. | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 2, "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": 0.7695059776306152, "perplexity": 1724.6754255711824}, "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-2017-13/segments/1490218188132.48/warc/CC-MAIN-20170322212948-00633-ip-10-233-31-227.ec2.internal.warc.gz"} |
http://www.gradesaver.com/textbooks/math/geometry/elementary-geometry-for-college-students-5th-edition/chapter-3-section-3-1-congruent-triangles-exercises-page-136/29 | ## Elementary Geometry for College Students (5th Edition)
1) Show that $\angle ABC\cong\angle ABD$. 2) Use method SAS for the following pairs: - $\angle ABC\cong\angle ABD$. - $\overline{BC}\cong\overline{BD}$ - $\overline{AB}\cong\overline{AB}$ (by Identity)
We have that $\overline{AB}\bot\overline{BC}$ and $\overline{AB}\bot\overline{BD}$ So $\angle ABC$ and $\angle ABD$ are both right angles, which means $\angle ABC\cong\angle ABD$. Furthermore, it is given that - $\overline{BC}\cong\overline{BD}$ - $\overline{AB}\cong\overline{AB}$ (by Identity) Now we have 2 sides and the included angle of $\triangle ABC$ are congruent with 2 corresponding sides and the included angle of $\triangle ABD$. That means according to method SAS, $\triangle ABC\cong\triangle ABD$. | {"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": 0.6663857102394104, "perplexity": 296.8306536047537}, "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-2017-34/segments/1502886105970.61/warc/CC-MAIN-20170820034343-20170820054343-00226.warc.gz"} |
https://math.ucsd.edu/seminar/backward-propagation-warped-product-structures-under-ricci-flow-and-asymptotically-conical | Printable PDF
##### Department of Mathematics, University of California San Diego
****************************
## Backward propagation of warped-product structures under the Ricci flow and asymptotically conical shrinkers
##### Abstract:
We establish sufficient conditions for a locally-warped product structure to propagate backward in time under the Ricci flow. As an application, we show that if a gradient shrinking soliton is asymptotic to a cone whose cross-section is a locally warped product of Einstein manifolds, the soliton must itself be a warped product over the same manifolds.
### Zoom ID 924 6512 4982
**************************** | {"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": 0.8794842958450317, "perplexity": 646.1136416281522}, "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/1652662510097.3/warc/CC-MAIN-20220516073101-20220516103101-00060.warc.gz"} |
https://cyclostationary.blog/tag/cumulants/ | ## Symmetries of Higher-Order Temporal Probabilistic Parameters in CSP
What are the unique parts of the multidimensional cyclic moments and cyclic cumulants?
In this post, we continue our study of the symmetries of CSP parameters. The second-order parameters–spectral correlation and cyclic correlation–are covered in detail in the companion post, including the symmetries for ‘auto’ and ‘cross’ versions of those parameters.
Here we tackle the generalizations of cyclic correlation: cyclic temporal moments and cumulants. We’ll deal with the generalization of the spectral correlation function, the cyclic polyspectra, in a subsequent post. It is reasonable to me to focus first on the higher-order temporal parameters, because I consider the temporal parameters to be much more useful in practice than the spectral parameters.
This topic is somewhat harder and more abstract than the second-order topic, but perhaps there are bigger payoffs in algorithm development for exploiting symmetries in higher-order parameters than in second-order parameters because the parameters are multidimensional. So it could be worthwhile to sally forth.
## Symmetries of Second-Order Probabilistic Parameters in CSP
Do we need to consider all cycle frequencies, both positive and negative? Do we need to consider all delays and frequencies in our second-order CSP parameters?
As you progress through the various stages of learning CSP (intimidation, frustration, elucidation, puzzlement, and finally smooth operation), the symmetries of the various functions come up over and over again. Exploiting symmetries can result in lower computational costs, quicker debugging, and easier mathematical development.
What exactly do we mean by ‘symmetries of parameters?’ I’m talking primarily about the evenness or oddness of the time-domain functions in the delay $\tau$ and cycle frequency $\alpha$ variables and of the frequency-domain functions in the spectral frequency $f$ and cycle frequency $\alpha$ variables. Or a generalized version of evenness/oddness, such as $f(-x) = g(x)$, where $f(x)$ and $g(x)$ are closely related functions. We have to consider the non-conjugate and conjugate functions separately, and we’ll also consider both the auto and cross versions of the parameters. We’ll look at higher-order cyclic moments and cumulants in a future post.
You can use this post as a resource for mathematical development because I present the symmetry equations. But also each symmetry result is illustrated using estimated parameters via the frequency smoothing method (FSM) of spectral correlation function estimation. The time-domain parameters are obtained from the inverse transforms of the FSM parameters. So you can also use this post as an extension of the second-order verification guide to ensure that your estimator works for a wide variety of input parameters.
## CSP Resources: The Ultimate Guides to Cyclostationary Random Processes by Professor Napolitano
My friend and colleague Antonio Napolitano has just published a new book on cyclostationary signals and cyclostationary signal processing:
Cyclostationary Processes and Time Series: Theory, Applications, and Generalizations, Academic Press/Elsevier, 2020, ISBN: 978-0-08-102708-0. The book is a comprehensive guide to the structure of cyclostationary random processes and signals, and it also provides pointers to the literature on many different applications. The book is mathematical in nature; use it to deepen your understanding of the underlying mathematics that make CSP possible.
You can check out the book on amazon.com using the following link:
Cyclostationary Processes and Time Series
## A Challenge for the Machine Learners
The machine-learning modulation-recognition community consistently claims vastly superior performance to anything that has come before. Let’s test that.
## UPDATE
I’ve decided to post the data set I discuss here to the CSP Blog for all interested parties to use. See the new post on the Data Set. If you do use it, please let me and the CSP Blog readers know how you fared with your experiments in the Comments section of either post. Thanks!
## More on Pure and Impure Sine Waves
Gaussian and binary signals are in some sense at opposite ends of the pure-impure sine-wave spectrum.
Remember when we derived the cumulant as the solution to the pure $n$th-order sine-wave problem? It sounded good at the time, I hope. But here I describe a curious special case where the interpretation of the cumulant as the pure component of a nonlinearly generated sine wave seems to break down.
## Cumulant (4, 2) is a Good Discriminator? Comments on “Energy-Efficient Processor for Blind Signal Classification in Cognitive Radio Networks,” by E. Rebeiz et al.
Let’s talk about another published paper on signal detection involving cyclostationarity and/or cumulants. This one is called “Energy-Efficient Processor for Blind Signal Classification in Cognitive Radio Networks,” (The Literature [R69]), and is authored by UCLA researchers E. Rebeiz and four colleagues.
My focus on this paper is its idea that broad signal-type classes, such as direct-sequence spread-spectrum (DSSS), QAM, and OFDM can be reliably distinguished by the use of a single number: the fourth-order cumulant with two conjugated terms. This kind of cumulant is referred to as the $(4, 2)$ cumulant here at the CSP Blog, and in the paper, because the order is $n=4$ and the number of conjugated terms is $m=2$. | {"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": 0, "wp_latex": 22, "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": 0.6520737409591675, "perplexity": 1220.184420888866}, "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/1631780057329.74/warc/CC-MAIN-20210922041825-20210922071825-00521.warc.gz"} |
https://blog.ukena.de/posts/2021/10/using-env-files-everywhere/ | # Using *.env-files everywhere
Many tools automatically look for a special file called .env, which contains KEY=VALUE pairs, one per line. I am here referring to a file with the same syntax, but with arbitrary names. I use different names to distinguish between configurations for different development stages.
Using environment variables for configuration is pretty much accepted as good practice today for web applications. But it’s always a hassle to deal with them during development, if you are not using a specialised service for them. My current approach is to create separate *.env-file for the development and testing stage: development.env and testing.env. These files use regular bash-syntax for variable declaration:
1 2 3 # development.env DEBUG=True DATABASE_URL=postgresql://postgres:postgres@postgres/devdb
and here is the version for the testing-stage:
1 2 3 # testing.env DEBUG=False DATABASE_URL=postgresql://postgres:postgres@postgres/testdb
The great thing about these files is that many popular tools support them in one way or the other. Either directly as command line arguments, or by using a shell script.
Here are some examples.
## Using .env-files with docker compose
You can specify env-files both as part of your docker-compose.yml file or by passing it on the command line.
# Inside your docker-compose.yml
app:
env_file:
- development.yml
or by passing it on the command line:
\$ docker compose --env-file env/development.env up -d
Note that these two uses are not semantically equivalent. The first makes all environment variables available to the app container, the second makes them only available during the build-process. Passing the --env-file parameter will not magically make those variables available to the container. For each variable you will still need to specify in each container’s environment:-section, which variables are made available.
## Using .env-files with shell-scripts
The most robust way to use .env-files in a shell script seems to be this:
1 2 3 set -o allexport source development.env set +o allexport
## Using .env-files with PyCharm IDE (or any IntelliJ based IDE)
PyCharm does not come with built-in support for using *.env-files for run-configurations, but there is a very popular and robust third-party plugin called EnvFile. It can be installed from Plugins-preference and let’s you specify one or more .env-files as sources for environment variables. If you want to see it in action, there are some screenshot in the official github repo..
## Other uses
• pipenv will automatically load a file named .env if it is found in the project folder. There is no command line argument to override it, but luckily there is an environment variable to tell pipenv to look for a different file-name: PIPENV_DOTENV_LOCATION=development.env pipenv shell will start pipenv-shell with the environment variables from your development.env file.
• Procfile-based application management tools, which have also been adopted by cloud providers like AWS and heroku. The original foreman-repo has a list of ports for other languages.. You can specify different (and multiple) env-files using the --env command line parameter.
• the ´python-dotenv´ library will load environment variables from a .env-file. In most cases I believe this an anti-pattern. After all, the whole idea of environment-variables was to get away from config-files. However, for python scripts that help you manage your environments, this might come in handy. | {"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": 0.2774719297885895, "perplexity": 3060.155517867246}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-49/segments/1637964363420.81/warc/CC-MAIN-20211207232140-20211208022140-00068.warc.gz"} |
https://kuscholarworks.ku.edu/handle/1808/31095?show=full | dc.contributor.author Sirunyan, A. M. dc.contributor.author Sanders, Stephen J. dc.contributor.author CMS Collaboration dc.date.accessioned 2021-01-11T20:06:56Z dc.date.available 2021-01-11T20:06:56Z dc.date.issued 2019-07-03 dc.identifier.citation Sirunyan, A.M., Tumasyan, A., Adam, W. et al. Search for a heavy pseudoscalar boson decaying to a Z and a Higgs boson at 𝑠√=13TeV. Eur. Phys. J. C 79, 564 (2019). https://doi.org/10.1140/epjc/s10052-019-7058-z en_US dc.identifier.uri http://hdl.handle.net/1808/31095 dc.description This work is licensed under a Creative Commons Attribution 4.0 International License. en_US dc.description.abstract A search is presented for a heavy pseudoscalar boson A decaying to a Z boson and a Higgs boson with mass of 125GeV. In the final state considered, the Higgs boson decays to a bottom quark and antiquark, and the Z boson decays either into a pair of electrons, muons, or neutrinos. The analysis is performed using a data sample corresponding to an integrated luminosity of 35.9fb−1 collected in 2016 by the CMS experiment at the LHC from proton–proton collisions at a center-of-mass energy of 13TeV. The data are found to be consistent with the background expectations. Exclusion limits are set in the context of two-Higgs-doublet models in the A boson mass range between 225 and 1000GeV. en_US dc.publisher SpringerOpen en_US dc.rights © CERN for the benefit of the CMS collaboration 2019. en_US dc.rights.uri http://creativecommons.org/licenses/by/4.0/ en_US dc.title Search for a heavy pseudoscalar boson decaying to a Z and a Higgs boson at 𝑠√=13TeV en_US dc.type Article en_US kusw.kuauthor Sanders, Stephen J. kusw.kudepartment Physics and Astronomy en_US dc.identifier.doi 10.1140/epjc/s10052-019-7058-z en_US kusw.oaversion Scholarly/refereed, publisher version en_US kusw.oapolicy This item meets KU Open Access policy criteria. en_US dc.rights.accessrights openAccess en_US
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http://www.ck12.org/probability/Probability-Distribution/lesson/Probability-Distribution-Probability-and-Statistics/r8/ | <meta http-equiv="refresh" content="1; url=/nojavascript/"> Probability Distribution ( Read ) | Probability | CK-12 Foundation
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# Probability Distribution
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Practice Probability Distribution
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Probability Distribution
#### Objective
In this lesson, you will learn about probability distributions and how they describe the probabilities associated with different possible values of a random variable.
#### Concept
Assume you have an unfair coin that is weighted to land on heads 65% of the time. If you flip that coin 3 times and let $T$ represent the number of tails you get, what is the probability distribution for $T$ ?
Look to the end of the lesson for the answer.
#### Watch This
http://youtu.be/s2S1oD3ovps statslectures - Discrete Probability Distributions
#### Guidance
A probability distribution is a list of each value a random variable can attain, along with the probability of attaining each value. In other words, the probability distribution of an event is sort of a map of how each possible outcome relates to the chance it will happen.
For instance, the probability distribution of flipping a coin twice is:
If we define the random variable $X$ to be the number of heads you get when you flip a coin twice, we could create the following probability distribution table for $X$
$X$ $0$ $1$ $2$ $P(X)$ $\frac{1}{8}$ $\frac{3}{4}$ $\frac{1}{8}$
There are various ways of visualizing a probability distribution, and we will review that concept in another lesson. For now, we focus on identifying what a probability distribution is, and how to calculate it for a particular event.
Example A
In Chi’s class, 4 students have one parent, 7 have two parents, and 1 student lives with his uncle. Let $P$ be the number of parents of a randomly selected student from the class. Create a probability distribution for $P$ .
Solution:
Set random variable $P$ to be the number of parents:
$P(P)=\% \ probability \ that \ a \ student \ has \ P \ parents$
Now find the probability of each $P$ , noting that there are 12 students total:
$\text{1 student has 0 parents: } & P(0)=\frac{1}{12} \ or \ 8.3 \overline{3} \% \\\text{4 students have 1 parent: } & P(1)=\frac{4}{12} \ or \ 33.3 \overline{3} \% \\\text{7 students have 2 parents: } & P(2)=\frac{7}{12} \ or \ 58.3 \overline{3} \% \\$
Example B
Roll two fair six-sided dice. Let $D$ equal the sum of the dice. Create a probability distribution for $D$ .
Solution: Make a list of the individual probabilities of each of the 36 possible outcomes:
$& \text{1 possibility with a sum of 2: } && P(D= 2) = \frac{1}{36} = 0.0278\\& \text{2 possibilities with a sum of 3: } && P(D= 3) = \frac{2}{36} = 0.0556\\& \text{3 possibilities with a sum of 4: } && P(D= 4) = \frac{3}{36} = 0.0833\\& \text{4 possibilities with a sum of 5: } && P(D= 5) = \frac{4}{36} = 0.1111\\& \text{5 possibilities with a sum of 6: } && P(D= 6) = \frac{5}{36} = 0.1389\\& \text{6 possibilities with a sum of 7: } && P(D= 7) = \frac{6}{36} = 0.1667\\& \text{5 possibilities with a sum of 8: } && P(D= 8) = \frac{5}{36} = 0.1389\\& \text{4 possibilities with a sum of 9: } && P(D= 9) = \frac{4}{36} = 0.1111\\& \text{3 possibilities with a sum of 10: } && P(D= 10) = \frac{3}{36} = 0.0833\\& \text{2 possibilities with a sum of 11: } && P(D= 11) = \frac{2}{36} = 0.0556\\& \text{1 possibility with a sum of 12: } && P(D= 12) = \frac{1}{36} = 0.0278$
Example C
Janie wants to evaluate the probabilities of pulling various cards from a deck. She sets the discrete random variable $C$ to be the number of diamonds she gets over the course of three trials, if each trial consists of pulling, recording, and replacing one random card from a standard deck. What is the probability distribution of $C$ ?
Solution: To evaluate the probability distribution of $C$ , Janie needs to identify the probability of each of the possible values of $C$ . Note that the chance she will pull a diamond is $\frac{13}{52}$ or $.25$ , meaning that the chance she will not pull a diamond is $1-.25=.75$ :
• For $C=(1)$ , the total probability is: $.14+.14+.14=.42 \ or \ 42 \%$ (see the three possible outcomes resulting in $C=1$ below)
• Diamond, other, other : $.25 \times .75 \times .75=.14$
• Other, Diamond, other : $.75 \times .25 \times .75=.14$
• Other, other, Diamond : $.75 \times .75 \times .25=.14$
• For $C=(2)$ , the total probability is: $.047+.047+.047=.141 \ or \ 14.1 \%$
• Diamond, Diamond, other : $.25 \times .25 \times .75=.047$
• Diamond, other, Diamond : $.25 \times .75 \times .25=.047$
• Other, Diamond, Diamond : $.75 \times .25 \times .25=.047$
• For $C=(3)$ , the probability is : $.25 \times .25 \times .25=.016 \ or \ 1.6 \%$
• Diamond, Diamond, Diamond: $.25 \times .25 \times .25=.016$
##### Concept Problem Revisited
Assume you have an unfair coin that is weighted to land on heads 65% of the time. If you flip that coin 3 times and let $T$ represent the number of tails you get, what is the probability distribution for $T$ ?
If each throw has a 65% chance of heads, then it has a 35% chance of tails:
• For $T=1$ , we could have THH, HTH, or HHT. Each of those has a $.35 \times .65 \times .65=.15$ chance of occurring, so $P(T=1)=.15 \times 3=.45 \ or \ 45 \%$
• For $T=2$ , we could have TTH, THT, or HTH. Each has a $.35 \times .35 \times .65=.08$ chance, so $P(T=2)=.08 \times 3=.24 \ or \ 24 \%$
• For $T=3$ , we could have only TTT, with a chance of $.35 \times .35 \times .35=.043 \ or \ 4.3 \%$
#### Vocabulary
A probability distribution is a list of each value a random variable can attain, along with the probability of attaining each value.
#### Guided Practice
1. Create a probability distribution for number of heads when you flip a coin 3 times.
2. Let $C$ be the number of chocolate chip cookies you get if you randomly pull and replace two cookies from a jar containing 6 chocolate chip, 4 peanut butter, 8 snickerdoodle, and 12 sugar cookies. Create a probability distribution for $C$ .
3. Let $S$ be the score of a single student chosen at random from Mr. Spence’s class. Create a probability distribution for $S$ , given the following:
Number of Students Test 11 87 7 89 13 92 9 94 6 96
Solutions:
1. Write out all the possibilities:
$& \text{TTT has 0 heads.} && \text{TTH has 1 heads.} && \text{THT has 1 heads.}\\& \text{THH has 2 heads.} && \text{HTT has 1 heads.} && \text{HTH has 2 heads.}\\& \text{HHT has 2 heads.} && \text{HHH has 3 heads.}$
$&\text{So we have 1 possibility with 0 heads:} && P(0) = \frac{1}{8} = 0.125\\&\text{3 possibilities with 1 heads:} && P(1) = \frac{3}{8} = 0.375\\&\text{3 possibilities with 2 heads:} && P(2) = \frac{3}{8} = 0.375\\&\text{1 possibility with 3 heads:} && P(3) = \frac{1}{8} = 0.125$
2. There are a total of 30 cookies, the probability of pulling a chocolate chip cookie is $\frac{6}{30}=.20$ , so the probability of not pulling a chocolate chip is $\frac{24}{30}=.80$
• For $C=0$ we have to pull a non-chocolate chip both times: $.8 \times .8=.64 \ or \ 64 \%$
• For $C=1$ we could either pull the chocolate chip cookie first or second, so we get $(.2 \times .8)+(.8 \times .2)=.32 \ or \ 32 \%$
• For $C=2$ we have to pull chocolate chip both times, so we have $.2 \times .2=.04 \ or \ 4 \%$
3. There are a total of 46 students in Mr. Spence’s class, so there are 46 scores. The probability of a random student having score $S$ is the same as that score’s portion of the total number of scores:
• $P(S=87)=\frac{11}{46}$
• $P(S=89)=\frac{7}{46}$
• $P(S=94)=\frac{9}{46}$
• $P(S=96)=\frac{6}{46}$
#### Practice
1. What is a probability distribution?
2. What is a random variable?
3. What is the difference between a discrete and a continuous random variable?
For problems 4-7, refer to the following table:
$S$ 2 3 4 5 6 7 8 9 10 $P(S)$ 0.04 0.12 0.16 0.16 0.12 0.04
4. Assuming the table is a probability distribution for discrete random variable $S$ , which is the sum of two dice rolled once, how many sides does each die have?
5. What is $P(3)$ ?
6. What is $P(6)$ ?
7. What is $P(9)$ ?
8. Roll two seven-sided dice once. Let $S$ be the sum of the two dice. Create a probability distribution for $S$ .
9. Flip a fair coin 3 times, let $H$ be the number of heads. Create a probability distribution for $H$ .
10. Let $S$ be the sum of two standard fair dice. Create a probability distribution for $S$ , if the experiment consists of a single roll of both dice. | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 85, "texerror": 0, "math_score": 0.8978111147880554, "perplexity": 599.9835515691252}, "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-2014-49/segments/1416400378724.10/warc/CC-MAIN-20141119123258-00202-ip-10-235-23-156.ec2.internal.warc.gz"} |
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## samnatha 2 years ago please help find the equations of the tangents to these circles at the points given x^2 + y^2 +2x + 4y - 12 = 0 (3, -1) Delete Cancel Submit
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1. campbell_st
• 2 years ago
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the circle will have a tangent at x = 3 which is in the top half of the circle as the centre is (-1, -2) you need to get the equation of the circle with y as the subject (x + 1)^2 + (y + 2)^2 = 12 - 1 - 4 or (x +1)^2 + (y + 2)^2 = 7 (y + 2)^2 = 7 - (x + 1)^2 $y + 2 = \pm \sqrt{7 - (x + 1)^2}$ so $y = \pm \sqrt{7 - (x + 1)^2} - 2$ so you need to differentiate the which is the upper semicircle $y = \sqrt{7 - (x + 1)^2} - 2$ and then substitute the find the slope of the tangent... once you have the slope... then use the point (3, -1) to find the equations... hope it helps.
2. samnatha
• 2 years ago
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i cam't differentiate as we haven't learnt it yet ?
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https://economictheoryblog.com/2012/06/28/latexlatexs2/?replytocom=255 | # Proof of Unbiasedness of Sample Variance Estimator
Proof of Unbiasness of Sample Variance Estimator
(As I received some remarks about the unnecessary length of this proof, I provide shorter version here)
In different application of statistics or econometrics but also in many other examples it is necessary to estimate the variance of a sample. The estimator of the variance, see equation (1) is normally common knowledge and most people simple apply it without any further concern. The question which arose for me was why do we actually divide by n-1 and not simply by n? In the following lines we are going to see the proof that the sample variance estimator is indeed unbiased.
$s^2$ = variance of the sample
$x_i$ = manifestations of random variable X with $i$ from 1 to n
$\bar x$ = sample average
$\mu$ = mean of the population
$\delta$ = population variance
(1) $s^2=\frac{1}{n-1}\sum\limits_{i=1}^n(x_i-\bar x)^2$
#### First step of the proof
(2) $x_i-\bar x = x_i - \mu + \mu - \bar x$
(3) $x_i-\bar x =( x_i - \mu) + (\mu - \bar x)$
(4) $(x_i-\bar x)^2 = [(x_i - \mu) + (\mu - \bar x)]^2$
(5) $(x_i-\bar x)^2 = (x_i - \mu)(x_i - \mu)+(x_i - \mu)(\mu - \bar x)+(\mu - \bar x)(x_i - \mu)+(\mu - \bar x)(\mu - \bar x)$
(6) $(x_i-\bar x)^2 = (x_i - \mu)^2+2*(x_i - \mu)(\mu - \bar x)+(\mu - \bar x)^2$
(7) $\sum\limits_{i=1}^n(x_i-\bar x)^2 = \sum\limits_{i=1}^n(x_i - \mu)^2+2*\sum\limits_{i=1}^n(x_i - \mu)(\mu - \bar x)+\sum\limits_{i=1}^n(\mu - \bar x)^2$
(8) $\sum\limits_{i=1}^n(x_i-\bar x)^2 = \sum\limits_{i=1}^n(x_i - \mu)^2+2(\mu - \bar x)\sum\limits_{i=1}^n(x_i - \mu)+n(\mu - \bar x)^2$
(9) $\sum\limits_{i=1}^n(x_i-\bar x)^2 = \sum\limits_{i=1}^n(x_i - \mu)^2+n(\mu - \bar x)^2+2(\mu - \bar x)\sum\limits_{i=1}^n(x_i - \mu)$
(10) $\sum\limits_{i=1}^n(x_i-\bar x)^2 = \sum\limits_{i=1}^n(x_i - \mu)^2+n(\mu - \bar x)^2+2(\mu - \bar x)(\sum\limits_{i=1}^n x_i - \sum\limits_{i=1}^n \mu)$
(11) $\sum\limits_{i=1}^n(x_i-\bar x)^2 = \sum\limits_{i=1}^n(x_i - \mu)^2+n(\mu - \bar x)^2+2(\mu - \bar x)(\sum\limits_{i=1}^n x_i - n\mu)$
(12) $\sum\limits_{i=1}^n(x_i-\bar x)^2 = \sum\limits_{i=1}^n(x_i - \mu)^2+n(\mu - \bar x)^2+2(\mu - \bar x)(n\bar x - n\mu)$ as $n\bar x=\sum\limits_{i=1}^n x_i$ which derives from $\bar x=\frac{\sum\limits_{i=1}^n x_i}{n}$
(13) $\sum\limits_{i=1}^n(x_i-\bar x)^2 = \sum\limits_{i=1}^n(x_i - \mu)^2+n(\mu - \bar x)^2+2n(\mu - \bar x)(\bar x - \mu)$
(14) $\sum\limits_{i=1}^n(x_i-\bar x)^2 = \sum\limits_{i=1}^n(x_i - \mu)^2+n(\mu - \bar x)^2+2n(-1)(-\mu + \bar x)(\bar x - \mu)$
(15) $\sum\limits_{i=1}^n (x_i-\bar x)^2 = \sum\limits_{i=1}^n(x_i - \mu)^2+n(\mu - \bar x)^2-2n(\bar x-\mu )(\bar x - \mu)$
(16) $\sum\limits_{i=1}^n(x_i-\bar x)^2 = \sum\limits_{i=1}^n(x_i - \mu)^2+n(\mu - \bar x)^2-2n(\bar x-\mu )^2$
(17) $\sum\limits_{i=1}^n(x_i-\bar x)^2 = \sum\limits_{i=1}^n(x_i - \mu)^2+n(\bar x-\mu)^2-2n(\bar x-\mu )^2$
which can be done as it does not change anything at the result
(18) $\sum\limits_{i=1}^n(x_i-\bar x)^2 = \sum\limits_{i=1}^n(x_i - \mu)^2-n(\bar x-\mu )^2$
#### Second step of the proof
(19)$E(X)=\sum\limits_{i=1}^n x_i f(x_i)$ if x is i.u.d. (identically uniformely distributed) and if $f(x_i)=\frac{1}{n}$ then
(21)$E(X)=\frac{1}{n-1}\sum\limits_{i=1}^n x_i$
(22)$E(S^2)=E(\frac{1}{n -1 }\sum\limits_{i=1}^n(x_i - \mu)^2-n(\bar x-\mu )^2)$
(23)$E(S^2)=\frac{1}{n}[E(\sum\limits_{i=1}^n (x_i - \mu)^2)-n E(\bar x-\mu )^2]$
#### Third step of the proof
(24)$E(X+Y)=\sum\limits_{i=1}^n\sum\limits_{j=1}^n (x_i+y_j)f(x_iy_j)$
(25)$E(X+Y)=\sum\limits_{i=1}^n\sum\limits_{j=1}^n x_if(x_iy_j)+\sum\limits_{i=1}^n\sum\limits_{j=1}^n y_jf(x_iy_j)$
(26)$E(X+Y)=\sum\limits_{i=1}^n x_if(x_i)\sum\limits_{j=1}^n f(y_j)+\sum\limits_{j=1}^n y_jf(y_j)\sum\limits_{i=1}^n f(x_i)$
(27)$E(X+Y)=\sum\limits_{i=1}^n x_if(x_i)+\sum\limits_{j=1}^n y_jf(y_j)\sum\limits_{i=1}^n f(x_i)$ as$\sum\limits_{j=1}^n f(y_j)=1$ and$\sum\limits_{i=1}^n f(x_i)=1$
(28)$E(X+Y)=E(X)+E(Y)$
Applying this on our original function:
(29)$E(g(x_i))=\sum\limits_{i=1}^n g(x_i)f(x_i)$
(30)$E(g(x_i))=\sum\limits_{i=1}^n (x_i - \mu)^2f(x_i)$
(31)$E(g(x_i))=\sum\limits_{i=1}^n (x_i - \mu)^2\frac{1}{n}$ as$f(x_i)=\frac{1}{n}$
(32)$E(g(x_i))=\sum\limits_{i=1}^n \frac{1}{n}(x_i - \mu)^2=\sum\limits_{i=1}^n Var(x_i)$
(33)$E(g(x_i))=\sum\limits_{i=1}^nVar(x_i)$
(34)$E(g(x_i))=nVar(x_i)$
Plugging (34) into (23) gives us:
(35)$E(S^2)=\frac{1}{n-1}[nVar(x_i)-nE(\bar x-\mu )^2]$
Notice also that:
(36)$Var(\bar x)=Var(\frac{\sum\limits_{i=1}^n x_i}{n})=Var(\frac{1}{n}\sum\limits_{i=1}^n x_i)$
and that:
(37)$Var(a+bx_i)$
(38)$\mu_y=a+b\mu_x$
(39)$y_i=a+bx_i$
using (38) and (39) in (37) we get:
(40)$Var(a+bx_i)=\frac{1}{n}\sum\limits_{i=1}^n (y_i-\mu_y)^2$
(41)$Var(a+bx_i)=\frac{1}{n}\sum\limits_{i=1}^n (a+bx_i-(a+b\mu_x)^2$
(42)$Var(a+bx_i)=\frac{1}{n}\sum\limits_{i=1}^n(a+bx_i-a-b\mu_x)^2$
(43)$Var(a+bx_i)=\frac{1}{n}\sum\limits_{i=1}^n(bx_i-b\mu_x)^2$
(44)$Var(a+bx_i)=\frac{1}{n}\sum\limits_{i=1}^n(b(x_i-\mu_x))^2$
(45)$Var(a+bx_i)=\frac{1}{n}\sum\limits_{i=1}^n(b^2(x_i-\mu_x)^2)$
(46)$Var(a+bx_i)=b^2\frac{1}{n}\sum\limits_{i=1}^n(x_i-\mu_x)^2$
(47)$Var(a+bx_i)=b^2Var(x_i)$
(48)$Var(\bar x)=Var(\frac{\sum\limits_{i=1}^n x_i}{n})=Var(\frac{1}{n}\sum\limits_{i=1}^n x_i)$
(49)$Var(\bar x)=Var(\frac{1}{n}\sum\limits_{i=1}^n x_i)$
(50)$Var(\bar x)=\frac{1}{n^2}Var(\sum\limits_{i=1}^n x_i)$
(51)$Var(\bar x)=\frac{1}{n^2}\sum\limits_{i=1}^n Var(x_i)$
(52)$Var(\bar x)=\frac{1}{n^2}\sum\limits_{i=1}^n(\frac{1}{n}\sum\limits_{i=1}^n(x_i-\mu_x)^2)$
just looking at the last part of (51) were we have $Var(x_i)=\sum\limits_{i=1}^n (x_i-\mu_x)^2$ we can apply simple computation rules of variance calulation:
(53)$Var(x_i)=\sum\limits_{i=1}^n(x_i-\mu_x)^2$
(54)$Var(X+Y)=\frac{1}{n}\sum\limits_{i=1}^n((X+Y)-(\mu_x+\mu_y))^2$
now the $x_i$ on the lhs of (53) corresponds to the $(X+Y)$ of the rhs of (54) and $\mu$ of the rhs of (53) corresponds to $\mu_x+\mu_y$ of the rhs of (54). Now what exactly do we mean by that, well
(55)$Var(X+Y)=E[(X+Y)-(\mu_x+\mu_y)]^2$
(56)$Var(X+Y)=E[(X-\mu_x)+(Y-\mu_y)]^2$
(57)$Var(X+Y)=E[(X-\mu_x)^2+(Y-\mu_y)^2+2(X-\mu_x)(Y-\mu_y)]$
(58)$Var(X+Y)=Var(X)+Var(Y)+2(X-\mu_x)(Y-\mu_y)]$
the term $2(X-\mu_x)(Y-\mu_y)$ is the covariance of X and Y and is zero, as X is independent of Y. This leaves us with the variance of X and the variance of Y. From (52) we know that
(59)$Var(\bar x)=\frac{1}{n^2}\sum\limits_{i=1}^n (\frac{1}{n}\sum\limits_{i=1}^n (x_i-\mu_x)^2)$
and playing around with it brings us to the following:
(60)$Var(\bar x)=\frac{1}{n^2}\sum\limits_{i=1}^n Var(X)$
(61)$Var(\bar x)=\frac{1}{n^2}n Var(X)$
(62)$Var(\bar x)=\frac{1}{n}Var(X)$
(63)$Var(\bar x)=\frac{1}{n}\delta^2$
now we have everything to finalize the proof. Return to equation (23)
(64)$E(S^2)=\frac{1}{n-1}[E(\sum\limits_{i=1}^n(x_i - \mu)^2)-nE(\bar x-\mu )^2]$
and we see that we have:
(65)$E(S^2)=\frac{1}{n-1}[E(\sum\limits_{i=1}^n Var(x_i))-n\frac{1}{n}Var(X)]$
(66)$E(S^2)=\frac{1}{n-1}[E(\sum\limits_{i=1}^n \delta^2)-n\frac{1}{n}\delta^2]$
(67)$E(S^2)=\frac{1}{n-1}[n\delta^2-n\frac{1}{n}\delta^2]$
(68)$E(S^2)=\frac{1}{n-1}[n\delta^2-\delta^2]$
so we are able to factorize and we end up with:
(69)$E(S^2)=\frac{1}{n-1}[\delta^2(n-1)]$
which cancels out and it follows that
(70)$E(S^2)=\delta^2$
Sometimes I may have jumped over some steps and it could be that they are not as clear for everyone as they are for me, so in the case it is not possible to follow my reasoning just leave a comment and I will try to describe it better.
As most comments and remarks are not about missing steps, but demand a more compact version of the proof, I felt obliged to provide one here.
## 41 thoughts on “Proof of Unbiasedness of Sample Variance Estimator”
1. Perry Thomas says:
At last someone who does NOT say “It can be easily shown that…”
2. In your step (1) you use n as if it is both a constant (the size of the sample) and also the variable used in the sum (ranging from 1 to N, which is undefined but I guess is the population size). Shouldn’t the variable in the sum be i, and shouldn’t you be summing from i=1 to i=n? This makes it difficult to follow the rest of your argument, as I cannot tell in some steps whether you are referring to the sample or to the population.
1. You are right, I’ve never noticed the mistake. It should clearly be i=1 and not n=1. And you are also right when saying that N is not defined, but as you said it is the sample size. I will add it to the definition of variables.
However, you should still be able to follow the argument, if there any further misunderstandings, please let me know.
3. please how do we show the proving of V( y bar subscript st) = summation W square subscript K x S square x ( 1- f subscript n) / n subscript k …..please I need ur assistant
1. Unfortunately I do not really understand your question. Is your formula taken from the proof outlined above? Do you want to prove that the estimator for the sample variance is unbiased? Or do you want to prove something else and are asking me to help you with that proof? In any case, I need some more information 🙂
4. I am very glad with this proven .how can we calculate for estimate of average size
and whats the formula. including some example thank you
1. I am happy you like it 🙂 But I am sorry that I still do not really understand what you are asking for.
5. please can you enlighten me on how to solve linear equation and linear but not homogenous case 2 in mathematical method
please how can I prove …v(Y bar ) = S square /n(1-f)
and
S subscript = S /root n x square root of N-n /N-1
and
S square = summation (y subscript – Y bar )square / N-1
1. I am getting really confused here 🙂 are you asking for a proof of
$V(\bar{Y}) = \frac{S^{2}}{n(1-f)}$
7. I like it….
an investigator want to know the adequacy of working condition of the employees of a plastic production factory whose total working population is 5000. if the junior staff is 4 times the intermediate staff working population and the senior staff constitute 15% of the working population .if further ,male constitute 75% ,50% and 80% of junior , intermediate and senior staff respectively of the working population .draw a stratified sample sizes in a table ( taking cognizance of the sex and cadres ).
8. please am sorry for the inconvenience ..how can I prove v(Y estimate)
9. Jerry joel says:
Gud day sir, thanks alot for the write-up because it clears some of my confusion but i am stil having problem with 2(x-u_x)+(y-u_y), how it becomes zero. Pls explan to me more.
1. Hello! The expression is zero as X and Y are independent and the covariance of two independent variable is zero. Does this answer you question?
Regards!
10. Jerry joel says:
Pls sir, i need more explanation how 2(x-u_x) + (y-u_y) becomes zero while deriving?
11. Jerry joel says:
Yes!, thanks alot sir.
12. Janio Javier says:
Please I ‘d like an orientation about the proof of the estimate of sample mean variance for cluster design with subsampling (two stages) with probability proportional to the size in the first step and without replacement, and simple random sample in the second step also without replacement. .
Thanks a lot for your help.
1. Thank you for you comment. The proof I provided in this post is very general. However, your question refers to a very specific case to which I do not know the answer. Nevertheless, I saw that Peter Egger and Filip Tarlea recently published an article in Economic Letters called “Multi-way clustering estimation of standard errors in gravity models”, this might be a good place to start.
13. Janio Javier says:
14. Nate says:
Thanks a lot for this proof. All the other ones I found skipped a bunch of steps and I had no idea what was going on. Econometrics is very difficult for me–more so when teachers skip a bunch of steps. This post saved me some serious frustration. Thanks!
What do exactly do you mean by prove the biased estimator of the sample variance? Do you mean the bias that occurs in case you divide by n instead of n-1?
15. sigmaoverrootn says:
it would be better if you break it into several Lemmas
for example, first proving the identities for Linear Combinations of Expected Value, and Variance, and then using the result of the Lemma, in the main proof
you made it more cumbersome that it needed to be
Hi, thanks again for your comments. I really appreciate your in-depth remarks. While it is certainly true that one can re-write the proof differently and less cumbersome, I wonder if the benefit of brining in lemmas outweighs its costs. In my eyes, lemmas would probably hamper the quick comprehension of the proof. This way the proof seems simple. I like things simple. Cheers, ad.
16. abbas says:
pls how do we solve real statistic using excel analysis
Hey Abbas, welcome back! What do you mean by solving real statistics? About excel, I think Excel has a data analysis extension. If I were to use Excel that is probably the place I would start looking. However, use R! It free and a very good statistical software. I could write a tutorial, if you tell me what exactly it is that you need.
1. good day sir.
can u kindly give me the procedure to analyze experimental design using SPSS
Sorry mate. I do not speak SPSS.
17. Eq. (36) contains an error. There the index i is not summed over.
You are right. I fixed it. Much appreciated.
18. I think it should be clarified that over which population is E(S^2) being calculated. Is x_i (for each i=0,…,n) being regarded as a separate random variable? If so, the population would be all permutations of size n from the population on which X is defined. I am confused here. Are N and n separate values?
Hey! Thank you for your comment! Indeed, it was not very clean the way I specified X, n and N. I revised the post and tried to improve the notation. Now, X is a random variables, $x_i$ is one observation of variable X. Overall, we have 1 to n observations. I hope this makes is clearer. | {"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": 89, "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": 0.8671348094940186, "perplexity": 672.7913247423287}, "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-2021-49/segments/1637964362969.51/warc/CC-MAIN-20211204094103-20211204124103-00160.warc.gz"} |
https://en.wikibooks.org/wiki/Calculus/Points,_paths,_surfaces,_and_volumes | Calculus/Points, paths, surfaces, and volumes
This chapter will provide an intuitive interpretation of vector calculus using simple concepts such as multi-points, multi-paths, multi-surfaces, and multi-volumes. Scalar fields will not be simply treated as a function ${\displaystyle f:\mathbb {R} ^{3}\to \mathbb {R} }$ that returns a number given an input point, and vector fields will not be simply treated as a function ${\displaystyle \mathbf {F} :\mathbb {R} ^{3}\to \mathbb {R} ^{3}}$ that returns a vector given an input point.
Basic structures
The basic structures are multi-points, multi-paths, multi-surfaces, and multi-volumes.
Multi-points
A point ${\displaystyle \mathbf {q} _{0}}$ is an arbitrary position. A "multi-point" is a set of point/weight pairs: ${\displaystyle \mathbf {Q} =\{(\mathbf {q} _{1},w_{1}),(\mathbf {q} _{2},w_{2}),...,(\mathbf {q} _{k},w_{k})\}}$ where ${\displaystyle w_{i}}$ is the "weight" that is assigned to point ${\displaystyle \mathbf {q} _{i}}$. Given two point/weight pairs ${\displaystyle (\mathbf {q} ,w_{1})}$ and ${\displaystyle (\mathbf {q} ,w_{2})}$ that cover the same point ${\displaystyle \mathbf {q} }$, the weights add up to get ${\displaystyle (\mathbf {q} ,w_{1}+w_{2})}$ which replaces ${\displaystyle (\mathbf {q} ,w_{1})}$ and ${\displaystyle (\mathbf {q} ,w_{2})}$. Any pair ${\displaystyle (\mathbf {q} ,0)}$ is removed. ${\displaystyle \mathbf {Q} }$ can consist of infinitely many points, and each point may have an infinitesimal weight.
An arbitrary point ${\displaystyle \mathbf {q} _{0}}$ can be described by the scalar field ${\displaystyle \delta _{0}(\mathbf {q} ;\mathbf {q} _{0})=\left\{{\begin{array}{cc}+\infty ^{3}&(\mathbf {q} =\mathbf {q} _{0})\\0&(\mathbf {q} \neq \mathbf {q} _{0})\end{array}}\right.}$. This is the "Dirac delta function" centered on point ${\displaystyle \mathbf {q} _{0}}$. The ${\displaystyle +\infty ^{3}}$ is the inverse of an infinitely small volume that wraps point ${\displaystyle \mathbf {q} _{0}}$. To further explain this, let ${\displaystyle \omega _{0}(\mathbf {q} _{0},v)}$ be a tiny volume with volume ${\displaystyle v}$ that wraps point ${\displaystyle \mathbf {q} _{0}}$. ${\displaystyle \delta _{0}(\mathbf {q} ;\mathbf {q} _{0})}$ can be approximated by ${\displaystyle \Delta _{0}(\mathbf {q} ;\mathbf {q} _{0},v)=\left\{{\begin{array}{cc}1/v&(\mathbf {q} \in \omega _{0}(\mathbf {q} _{0},v))\\0&(\mathbf {q} \notin \omega _{0}(\mathbf {q} _{0},v))\end{array}}\right.}$. A mass of 1 is being crammed into ${\displaystyle \omega _{0}(\mathbf {q} _{0},v)}$ yielding an infinitely high density. Since ${\displaystyle \delta _{0}(\mathbf {q} ;\mathbf {q} _{0})}$ is essentially a density function, it brings with it the units ${\displaystyle [{\text{length}}^{-3}]}$.
Multi-point ${\displaystyle \mathbf {Q} =\{(\mathbf {q} _{1},w_{1}),(\mathbf {q} _{2},w_{2}),...,(\mathbf {q} _{k},w_{k})\}}$ can be described by the scalar field ${\displaystyle \delta _{0}(\mathbf {q} ;\mathbf {Q} )=\sum _{i=1}^{k}w_{i}\delta _{0}(\mathbf {q} ;\mathbf {q} _{i})}$. If ${\displaystyle \mathbf {Q} }$ consists of infinitely many points with each point having infinitesimal weight, then ${\displaystyle \delta _{0}(\mathbf {q} ;\mathbf {Q} )}$ is a density function.
In the image below, the multi-point in the left panel is converted to the scalar field in the center panel by averaging the point weight over each cell. The volume of each cell should be infinitesimal. The multi-point in the right panel corresponds to the same scalar field, and is in a more canonical form where oppositely weighted points have cancelled out.
The multi-point (a collection of weighted points) on the left can be denoted by the scalar field in the middle. On the right is a more canonical multi-point with the same scalar field, where nearby points of opposite sign have cancelled out.
The image below shows how a continuous scalar field ${\displaystyle \rho :\mathbb {R} ^{3}\to \mathbb {R} }$ can be generated as a collection of points. Consider position ${\displaystyle \mathbf {q} _{0}}$ and the infinitesimal volume ${\displaystyle \omega _{0}(\mathbf {q} _{0},v)}$ with volume ${\displaystyle v}$. The total point weight contained by ${\displaystyle \omega _{0}(\mathbf {q} _{0},v)}$ is ${\displaystyle \iiint _{\mathbf {q} \in \omega _{0}(\mathbf {q} _{0},v)}\rho (\mathbf {q} )dV\approx v\cdot \rho (\mathbf {q} _{0})}$. This weight of ${\displaystyle v\cdot \rho (\mathbf {q} _{0})}$ is then split up over an arbitrarily large number of points that are scattered over the volume ${\displaystyle \omega _{0}(\mathbf {q} _{0},v)}$.
A single point of weight 1 can be "smeared out" over the volume that it sits in. The point is divided into an increasing number of points with fractional weights. After an infinite number of steps, there is an infinite number of points that fill the volume and each point has an infinitesimal weight.
In summary, a multi-point is denoted by a scalar field that quantifies the density at each point, and any scalar field that quantifies density at each point is best interpreted as a multi-point.
Multi-paths
A simple path (also called a simple curve) ${\displaystyle C}$ is an oriented continuous curve that extends from a starting point ${\displaystyle C(0)}$ to an ending point ${\displaystyle C(1)}$. Intermediate points are indexed by ${\displaystyle t\in [0,1]}$ and are denoted by ${\displaystyle C(t)}$. A simple path should be continuous (no breaks), and may intersect or retrace itself. A "multi-path" is a set of simple-path/weight pairs: ${\displaystyle \mathbf {C} =\{(C_{1},w_{1}),(C_{2},w_{2}),...,(C_{k},w_{k})\}}$ where ${\displaystyle w_{i}}$ is the weight that is assigned to path ${\displaystyle C_{i}}$. Given two path/weight pairs ${\displaystyle (C,w_{1})}$ and ${\displaystyle (C,w_{2})}$ that cover the same path ${\displaystyle C}$, the weights add up to get ${\displaystyle (C,w_{1}+w_{2})}$ which replaces ${\displaystyle (C,w_{1})}$ and ${\displaystyle (C,w_{2})}$. Any pair ${\displaystyle (C,0)}$ is removed. In addition given two path/weight pairs ${\displaystyle (C_{1},w)}$ and ${\displaystyle (C_{2},w)}$ with the same weight ${\displaystyle w}$ and ${\displaystyle C_{1}(1)=C_{2}(0)}$, then ${\displaystyle C_{1}}$ and ${\displaystyle C_{2}}$ can be linked end-to-end to get the pair ${\displaystyle (C_{1}+C_{2},w)}$ which replaces ${\displaystyle (C_{1},w)}$ and ${\displaystyle (C_{2},w)}$. Assigning a path a negative weight effectively reverses its orientation: if ${\displaystyle -C}$ denotes path ${\displaystyle C}$ with the opposite orientation, then ${\displaystyle (C,-w)}$ is equivalent to ${\displaystyle (-C,w)}$. ${\displaystyle \mathbf {C} }$ can consist of infinitely many paths, and each path may have an infinitesimal weight.
This image depicts the Dirac delta function of a simple path. Unlike the Dirac delta function for a point which is a scalar field, the Dirac delta function for a path is a vector field.
An arbitrary curve ${\displaystyle C}$ can be described by the vector field ${\displaystyle \delta _{1}(\mathbf {q} ;C)=\left\{{\begin{array}{cc}(+\infty ^{2}){\hat {\mathbf {n} }}(\mathbf {q} ;C)&(\mathbf {q} \in C)\\\mathbf {0} &(\mathbf {q} \notin C)\end{array}}\right.}$. This is the "Dirac delta function" for the curve ${\displaystyle C}$. ${\displaystyle {\hat {\mathbf {n} }}(\mathbf {q} ;C)}$ is the unit length tangent vector to path ${\displaystyle C}$ at point ${\displaystyle \mathbf {q} \in C}$. ${\displaystyle {\hat {\mathbf {n} }}(\mathbf {q} ;C)=\mathbf {0} }$ if ${\displaystyle \mathbf {q} \notin C}$. If there are multiple tangent vectors due to ${\displaystyle C}$ intersecting itself, then ${\displaystyle {\hat {\mathbf {n} }}(\mathbf {q} ;C)}$ is the sum of these tangent vectors. The ${\displaystyle +\infty ^{2}}$ is the inverse of the cross-sectional area of an infinitely thin tube that encloses ${\displaystyle C}$. To further explain this, let ${\displaystyle \omega _{1}(C,a)}$ be a thin tube with cross-sectional area ${\displaystyle a}$ that encloses ${\displaystyle C}$. ${\displaystyle \delta _{1}(\mathbf {q} ;C)}$ can be approximated by ${\displaystyle \Delta _{1}(\mathbf {q} ;C,a)=\left\{{\begin{array}{cc}(1/a){\hat {\mathbf {n} }}_{*}(\mathbf {q} ;C,a)&(\mathbf {q} \in \omega _{1}(C,a))\\\mathbf {0} &(\mathbf {q} \notin \omega _{1}(C,a))\end{array}}\right.}$. ${\displaystyle {\hat {\mathbf {n} }}_{*}(\mathbf {q} ;C,a)}$ is the generalization of ${\displaystyle {\hat {\mathbf {n} }}(\mathbf {q} ;C)}$ to the tube ${\displaystyle \omega _{1}(C,a)}$. A path weight of 1 is being crammed into the cross-sectional area of ${\displaystyle \omega _{1}(C,a)}$ yielding an infinitely high path density. Since ${\displaystyle \delta _{1}(\mathbf {q} ;C)}$ is essentially a density over area, it brings with it the units ${\displaystyle [{\text{length}}^{-2}]}$.
The image to the right gives a depiction of the Dirac delta function for a simple curve. The vector field ${\displaystyle \delta _{1}(\mathbf {q} ;C)}$ is ${\displaystyle \mathbf {0} }$ everywhere outside of an infinitely thin tube that encloses the path. Inside the tube, the vectors are parallel to the path, and have a magnitude equal to the inverse of the cross-sectional area. The Dirac delta function is the limit as the tube becomes infinitely thin.
Multi-path ${\displaystyle \mathbf {C} =\{(C_{1},w_{1}),(C_{2},w_{2}),...,(C_{k},w_{k})\}}$ can be described by the vector field ${\displaystyle \delta _{1}(\mathbf {q} ;\mathbf {C} )=\sum _{i=1}^{k}w_{i}\delta _{1}(\mathbf {q} ;C_{i})}$. If ${\displaystyle \mathbf {C} }$ consists of infinitely many paths with each path having infinitesimal weight, then ${\displaystyle \delta _{1}(\mathbf {q} ;\mathbf {C} )}$ is a flow density function.
In the image below, the multi-path in the left panel is converted to the vector field in the center panel by computing the total displacement in each cell and averaging over the volume. The volume of each cell should be infinitesimal. The multi-path in the right panel corresponds to the same vector field, and is in a more canonical form where the individual paths do not cross each other.
The multi-path (a collection of weighted paths) on the left can be denoted by the vector field in the middle (in generating the vector field, each path was approximated to enter each cell through the middle of an edge). On the right is a more canonical multi-path with the same vector field, where nearby path segments with opposite orientations have cancelled out, and the individual paths do not cross each other.
In summary, a multi-path is denoted by a vector field that quantifies the path/flow density at each point, and any vector field that quantifies a flow density at each point (such as current density) is best interpreted as a multi-path. (Flow density is a vector that points in the net direction of a flow, and has a length equal to the flow rate per unit area through a surface that is perpendicular to the net flow.)
Multi-surfaces
A simple surface ${\displaystyle \sigma }$ is an oriented continuous surface. A simple surface may intersect or fold back on itself. A "multi-surface" is a set of simple-surface/weight pairs: ${\displaystyle \mathbf {S} =\{(\sigma _{1},w_{1}),(\sigma _{2},w_{2}),...,(\sigma _{k},w_{k})\}}$ where ${\displaystyle w_{i}}$ is the weight that is assigned to surface ${\displaystyle \sigma _{i}}$. Given two surface/weight pairs ${\displaystyle (\sigma ,w_{1})}$ and ${\displaystyle (\sigma ,w_{2})}$ that cover the same surface ${\displaystyle \sigma }$, the weights add up to get ${\displaystyle (\sigma ,w_{1}+w_{2})}$ which replaces ${\displaystyle (\sigma ,w_{1})}$ and ${\displaystyle (\sigma ,w_{2})}$. Any pair ${\displaystyle (\sigma ,0)}$ is removed. In addition given two surface/weight pairs ${\displaystyle (\sigma _{1},w)}$ and ${\displaystyle (\sigma _{2},w)}$ with the same weight ${\displaystyle w}$, then ${\displaystyle \sigma _{1}}$ and ${\displaystyle \sigma _{2}}$ can be combined to get the pair ${\displaystyle (\sigma _{1}+\sigma _{2},w)}$ which replaces ${\displaystyle (\sigma _{1},w)}$ and ${\displaystyle (\sigma _{2},w)}$. Assigning a surface a negative weight effectively reverses its orientation: if ${\displaystyle -\sigma }$ denotes surface ${\displaystyle \sigma }$ with the opposite orientation, then ${\displaystyle (\sigma ,-w)}$ is equivalent to ${\displaystyle (-\sigma ,w)}$. ${\displaystyle \mathbf {S} }$ can consist of infinitely many surfaces, and each surface may have an infinitesimal weight.
An arbitrary surface ${\displaystyle \sigma }$ can be described by the vector field ${\displaystyle \delta _{2}(\mathbf {q} ;\sigma )=\left\{{\begin{array}{cc}(+\infty ){\hat {\mathbf {n} }}(\mathbf {q} ;\sigma )&(\mathbf {q} \in \sigma )\\\mathbf {0} &(\mathbf {q} \notin \sigma )\end{array}}\right.}$. This is the "Dirac delta function" for the surface ${\displaystyle \sigma }$. ${\displaystyle {\hat {\mathbf {n} }}(\mathbf {q} ;\sigma )}$ is the unit length normal vector to surface ${\displaystyle \sigma }$ at point ${\displaystyle \mathbf {q} \in \sigma }$. ${\displaystyle {\hat {\mathbf {n} }}(\mathbf {q} ;\sigma )=\mathbf {0} }$ if ${\displaystyle \mathbf {q} \notin \sigma }$. If there are multiple normal vectors due to ${\displaystyle \sigma }$ intersecting itself, then ${\displaystyle {\hat {\mathbf {n} }}(\mathbf {q} ;\sigma )}$ is the sum of these normal vectors. The ${\displaystyle +\infty }$ is the inverse of the thickness of an infinitely thin membrane that encloses ${\displaystyle \sigma }$. To further explain this, let ${\displaystyle \omega _{2}(\sigma ,t)}$ be a thin membrane with thickness ${\displaystyle t}$ that encloses ${\displaystyle \sigma }$. ${\displaystyle \delta _{2}(\mathbf {q} ;\sigma )}$ can be approximated by ${\displaystyle \Delta _{2}(\mathbf {q} ;\sigma ,t)=\left\{{\begin{array}{cc}(1/t){\hat {\mathbf {n} }}_{*}(\mathbf {q} ;\sigma ,t)&(\mathbf {q} \in \omega _{2}(\sigma ,t))\\\mathbf {0} &(\mathbf {q} \notin \omega _{2}(\sigma ,t))\end{array}}\right.}$. ${\displaystyle {\hat {\mathbf {n} }}_{*}(\mathbf {q} ;\sigma ,t)}$ is the generalization of ${\displaystyle {\hat {\mathbf {n} }}(\mathbf {q} ;\sigma )}$ to the membrane ${\displaystyle \omega _{2}(\sigma ,t)}$. A surface weight of 1 is being sandwiched into the thickness of ${\displaystyle \omega _{2}(\sigma ,t)}$ yielding an infinitely high surface density. Since ${\displaystyle \delta _{2}(\mathbf {q} ;\sigma )}$ is essentially a density over length, it brings with it the units ${\displaystyle [{\text{length}}^{-1}]}$.
Multi-surface ${\displaystyle \mathbf {S} =\{(\sigma _{1},w_{1}),(\sigma _{2},w_{2}),...,(\sigma _{k},w_{k})\}}$ can be described by the vector field ${\displaystyle \delta _{2}(\mathbf {q} ;\mathbf {S} )=\sum _{i=1}^{k}w_{i}\delta _{2}(\mathbf {q} ;\sigma _{i})}$. If ${\displaystyle \mathbf {S} }$ consists of infinitely many surfaces with each surface having infinitesimal weight, then ${\displaystyle \delta _{2}(\mathbf {q} ;\mathbf {S} )}$ is a rate-of-gain function.
In the image below, the multi-surface in the left panel is converted to the vector field in the center panel by computing the total surface in each cell and averaging over the volume. The volume of each cell should be infinitesimal. The multi-surface in the right panel corresponds to the same vector field, and is in a more canonical form where the individual surfaces do not intersect each other.
The multi-surface (a collection of weighted surfaces) on the left can be denoted by the vector field in the middle (in generating the vector field, each surface was approximated to intersect the edge of each square in the middle). On the right is a more canonical multi-surface with the same vector field, where nearby surface segments with opposite orientations have cancelled out, and the individual surfaces do not intersect.
In summary, a multi-surface is denoted by a vector field that quantifies the rate of gain at each point. To describe the rate-of-gain, imagine that passing through a surface in the preferred direction gives "energy". The rate of gain is a vector that points in the direction that yields the greatest rate of energy increase per unit length, and has a length equal to the maximum rate of energy increase per unit length. Any vector field that quantifies a rate of gain at each point (such as a force field) is best interpreted as a multi-surface.
Multi-volumes
A volume ${\displaystyle \Omega }$ is an arbitrary region of space. A "multi-volume" is a set of volume/weight pairs: ${\displaystyle \mathbf {U} =\{(\Omega _{1},w_{1}),(\Omega _{2},w_{2}),...,(\Omega _{k},w_{k})\}}$ where ${\displaystyle w_{i}}$ is the "weight" that is assigned to volume ${\displaystyle \Omega _{i}}$. Given two volume/weight pairs ${\displaystyle (\Omega ,w_{1})}$ and ${\displaystyle (\Omega ,w_{2})}$ that cover the same volume ${\displaystyle \Omega }$, the weights add up to get ${\displaystyle (\Omega ,w_{1}+w_{2})}$ which replaces ${\displaystyle (\Omega ,w_{1})}$ and ${\displaystyle (\Omega ,w_{2})}$. Any pair ${\displaystyle (\Omega ,0)}$ is removed. In addition given two volume/weight pairs ${\displaystyle (\Omega _{1},w)}$ and ${\displaystyle (\Omega _{2},w)}$ with the same weight ${\displaystyle w}$ and ${\displaystyle \Omega _{1}\cap \Omega _{2}=\emptyset }$, then ${\displaystyle \Omega _{1}}$ and ${\displaystyle \Omega _{2}}$ can be combined to get the pair ${\displaystyle (\Omega _{1}\cup \Omega _{2},w)}$ which replaces ${\displaystyle (\Omega _{1},w)}$ and ${\displaystyle (\Omega _{2},w)}$. ${\displaystyle \mathbf {U} }$ can consist of infinitely many volumes, and each volume may have an infinitesimal weight.
An arbitrary volume ${\displaystyle \Omega }$ can be described by the scalar field ${\displaystyle \delta _{3}(\mathbf {q} ;\Omega )=\left\{{\begin{array}{cc}1&(\mathbf {q} \in \Omega )\\0&(\mathbf {q} \notin \Omega )\end{array}}\right.}$. This is the "Dirac delta function" analog for volumes, and is essentially an indicator function that indicates whether or not a position is contained by ${\displaystyle \Omega }$ or not, 1 being yes and 0 being no. Since ${\displaystyle \delta _{3}(\mathbf {q} ;\Omega )}$ is simply an indicator function, it brings with it no units (it is dimensionless).
Multi-volume ${\displaystyle \mathbf {U} =\{(\Omega _{1},w_{1}),(\Omega _{2},w_{2}),...,(\Omega _{k},w_{k})\}}$ can be described by the scalar field ${\displaystyle \delta _{3}(\mathbf {q} ;\mathbf {U} )=\sum _{i=1}^{k}w_{i}\delta _{3}(\mathbf {q} ;\Omega _{i})}$. If ${\displaystyle \mathbf {U} }$ consists of infinitely many volumes with each volume having infinitesimal weight, then ${\displaystyle \delta _{3}(\mathbf {q} ;\mathbf {U} )}$ is a potential function.
In the image below, the multi-volume in the left panel is converted to the scalar field in the center panel by averaging the volume weight in each cell. The volume of each cell should be infinitesimal. The multi-volume in the right panel corresponds to the same scalar field, and is in a more canonical form where oppositely weighted volumes have cancelled out, and the remaining volume has diffused to fill each cell.
The multi-volume (a collection of weighted volumes) on the left can be denoted by the scalar field in the middle (in generating the scalar field, the beveled corners of each volume where ignored). On the right is a more canonical multi-volume with the same scalar field, where volumes of opposite sign have cancelled out, and the remaining volume is smeared out to fill each cell.
In summary, a multi-volume is denoted by a scalar field that quantifies a potential at each point, and any scalar field that quantifies a potential at each point is best interpreted as a multi-volume.
At infinity
An important requirement is that all multi-points, multi-paths, multi-surfaces, and multi-volumes not extend to infinity. All structures can extend to an arbitrarily large range, as long as this range is not unbounded. Allowing the structures to extend to infinity will cause problems in the later discussions.
Paths that extend to infinity are generally not allowed for most theorems related to vector calculus. Surfaces that extend to infinity are generally not allowed for most theorems related to vector calculus. Volumes that extend to infinity are generally not allowed for most theorems related to vector calculus.
Totals
These sections will describe the total weight of multi-points, the total displacement of multi-paths, the total surface of multi-surfaces, and the total volumes of multi-volumes.
Total point weight
Given a multi-point ${\displaystyle \mathbf {Q} =\{(\mathbf {q} _{1},w_{1}),(\mathbf {q} _{2},w_{2}),...,(\mathbf {q} _{k},w_{k})\}}$, the total point weight is clearly ${\displaystyle \sum _{i=1}^{k}w_{i}}$. Given a scalar field ${\displaystyle \rho }$ that denotes a multi-point, the total weight of ${\displaystyle \rho }$ is ${\displaystyle \iiint _{\mathbf {q} \in \mathbb {R} ^{3}}\rho (\mathbf {q} )dV}$. Given a simple point ${\displaystyle \mathbf {q} _{0}}$, the total weight is 1 so ${\displaystyle \iiint _{\mathbf {q} \in \mathbb {R} ^{3}}\delta _{0}(\mathbf {q} ;\mathbf {q} _{0})dV=1}$.
Total displacement
The displacement between two points is independent of the path that connects them.
Given a simple path ${\displaystyle C}$ that starts at point ${\displaystyle C(0)}$ and ends at point ${\displaystyle C(1)}$, the total displacement generated by ${\displaystyle C}$ is ${\displaystyle \int _{\mathbf {q} \in C}d\mathbf {q} =C(1)-C(0)}$. This displacement is solely dependent on the endpoints as indicated by the top image to the right.
The displacement generated by a closed loop is ${\displaystyle \mathbf {0} }$.
Given a multi-path ${\displaystyle \mathbf {C} =\{(C_{1},w_{1}),(C_{2},w_{2}),...,(C_{k},w_{k})\}}$, the total displacement generated by ${\displaystyle \mathbf {C} }$ is ${\displaystyle \sum _{i=1}^{k}w_{i}\int _{\mathbf {q} \in C_{i}}d\mathbf {q} =\sum _{i=1}^{k}w_{i}(C_{i}(1)-C_{i}(0))}$.
Given a vector field ${\displaystyle \mathbf {J} }$ that denotes a multi-path, the total displacement generated by ${\displaystyle \mathbf {J} }$ is ${\displaystyle \iiint _{\mathbf {q} \in \mathbb {R} ^{3}}\mathbf {J} (\mathbf {q} )dV}$. Since the displacement generated by a simple path ${\displaystyle C}$ is ${\displaystyle \int _{\mathbf {q} \in C}d\mathbf {q} =C(1)-C(0)}$, it is the case that ${\displaystyle \iiint _{\mathbf {q} \in \mathbb {R} ^{3}}\delta _{1}(\mathbf {q} ;C)dV=\int _{\mathbf {q} \in C}d\mathbf {q} =C(1)-C(0)}$.
A path integral can be converted to a volume integral be replacing the displacement differential dq with the shown expression that is proportional to the volume differential dV. As is shown, the path is diffused to fill a thin tube. The integrand of the volume integral at all points outside of this thin tube is 0.
One important observation from ${\displaystyle \int _{\mathbf {q} \in C}d\mathbf {q} =\iiint _{\mathbf {q} \in \mathbb {R} ^{3}}\delta _{1}(\mathbf {q} ;C)dV}$ is that given a path integral over path ${\displaystyle C}$, the differential ${\displaystyle d\mathbf {q} }$ is equal to ${\displaystyle \delta _{1}(\mathbf {q} ;C)dV}$ in a volume integral: ${\displaystyle \int _{\mathbf {q} \in C}f(\mathbf {q} ,d\mathbf {q} )=\iiint _{\mathbf {q} \in \mathbb {R} ^{3}}f(\mathbf {q} ,\delta _{1}(\mathbf {q} ;C)dV)}$ provided that function ${\displaystyle f}$ is linear in the second parameter. In the lower image to the right, the displacement differential ${\displaystyle d\mathbf {q} ={\hat {\mathbf {n} }}\cdot \Delta l}$ is equated to the volume differential ${\displaystyle \left({\frac {\hat {\mathbf {n} }}{\Delta A}}\right)dV=\delta _{1}(\mathbf {q} ;C)dV}$ by diffusing the path over an infintely thin cross-sectional area ${\displaystyle \Delta A}$. The integrand at points outside of the infinitely thin tube is 0: for all points ${\displaystyle \mathbf {q} \notin C}$, ${\displaystyle f(\mathbf {q} ,\delta _{1}(\mathbf {q} ;C)dV)=f(\mathbf {q} ,\mathbf {0} )=0}$.
Total surface vector
A flat surface with area "A", a counter-clockwise boundary denoted by the arrows, and an orientation out of the plane is depicted by this image. Normal vector "n" has a length of 1, is perpendicular to the surface, and is oriented out of the plane as shown. The surface itself can be described by the vector "A n". The length is the area, and the direction is the orientation.
Given an arbitrary oriented surface ${\displaystyle \sigma }$, its "counter-clockwise boundary", denoted by ${\displaystyle \partial \sigma }$, is the boundary of ${\displaystyle \sigma }$ whose orientation is determined in the following manner: Looking at ${\displaystyle \sigma }$ so that the preferred direction through ${\displaystyle \sigma }$ is oriented towards the viewer, the boundary ${\displaystyle \partial \sigma }$ wraps ${\displaystyle \sigma }$ in a counter-clockwise direction.
Given a flat surface as shown in the image to the right, this surface can be quantified by the "surface vector" which is a vector that is perpendicular (normal) to the surface in the preferred orientation, and has a length equal to the area of the surface. In the image to the right, a flat surface has an area of ${\displaystyle A}$ and is oriented to be perpendicular to unit-length normal vector ${\displaystyle {\hat {\mathbf {n} }}}$. The "surface vector" of this surface is ${\displaystyle A\cdot {\hat {\mathbf {n} }}}$.
Given a non-flat surface ${\displaystyle \sigma }$, the total surface vector of ${\displaystyle \sigma }$ is computed by summing the surface vectors of each infinitesimal portion of ${\displaystyle \sigma }$. The total surface vector is ${\displaystyle \mathbf {S} =\iint _{\mathbf {q} \in \sigma }d\mathbf {S} }$.
In a manner similar to how the total displacement of a path is solely a function of the endpoints, the total surface vector of a surface is solely a function of its counter-clockwise boundary. This is not intuitive, and will be explained in greater detail below using two approaches:
Two different surfaces are shown. Both surfaces have identical counter-clockwise boundaries, and because of this, the "total surface vector" for each surface are the same. Similar to how the total displacement along a path is purely a function of its endpoints, the total surface vector of a surface is purely a function of its boundary.
Generalizing from surfaces in 2D space
Below are shown two images related to surface vectors in 2D space. The image to the left shows surface vectors in 2D space. In 2 dimensions, surfaces are called 1D surfaces and are similar to paths. The boundary of a 1D surface consists of 2 points. The surface vector of a 1D surface segment is a 90 degree rotation of the segment and is oriented in the direction of the surface's orientation. The total surface vector of a 1D surface is the sum of all of the surface vectors of the individual components. For each component of the surface, the surface vector is a 90 degree rotation of the displacement that traverses the component, so the total surface vector is a 90 degree rotation of the displacement between the points that form the boundary of the surface. This proves that in two dimensions, the total surface vector depends only on the boundary of the 1D surface.
The image to the right extrudes the 1D surfaces in two dimensional space into 2D "ribbons" in 3 dimensional space. At the top a closed "ribbon" is shown. This "ribbon" is a surface that is always parallel to the vertical dimension, and whose boundary forms two identical loops that are vertically displaced from each other. The boundary loops are also perpendicular to the vertical dimension. The ribbon itself is partitioned into tiny rectangles whose height is equal to that of the ribbon. To the bottom left, a view of the same ribbon from the top down is shown. It can be seen that the length of the each surface vector is proportional to the length of the corresponding rectangular segment, since the heights are all uniform. To the bottom right, by rotating the surface vectors 90 degrees around the vertical dimension, the surface vectors now sum to ${\displaystyle \mathbf {0} }$, so the sum of the unrotated surface vectors is also ${\displaystyle \mathbf {0} }$.
This image depicts how in 2 dimensions, the total surface vector of a 1D surface is a 90 degree rotation of the displacement between the two endpoints (the boundary of a 1D surface), and is therefore purely a function of the endpoints. In the left panel, a 1D surface is a sequence of black line segments, and the surface vectors of each segment are denoted by the dashed red arrows. Each surface vector is a 90 degree rotation of the displacement along the surface. The long grey line is the net displacement between the endpoints of the surface, and the dashed pink arrow is a 90 degree rotation of this net displacement. In the right panel, the pink arrow is shown as the sum of the dashed red arrow vectors, hence the "total surface" is purely a function of the 1D surface's endpoints. This image demonstrates that the total surface vector of a surface that is a closed ribbon is 0. The top image shows a surface that is a closed ribbon where the width of the ribbon is constant, the width is always parallel to the vertical dimension, and the edge is always perpendicular to the vertical dimension. The surface is sub-divided into tiny rectangular portions, the surface vectors of which are shown. The lower-left image shows the same surface from a top down perspective. In the lower-right image, the surface vectors are all rotated 90 degrees counter-clockwise around the vertical dimension and clearly sum to 0.
The fact that the total surface vector of a closed ribbon is ${\displaystyle \mathbf {0} }$ means that if relief is added to a surface without changing its boundaries, the total surface vector is conserved. The two left images below give examples of distorting the interior of a surface by hammering in relief. The vertical surfaces introduced by the relief are ribbons which contribute ${\displaystyle \mathbf {0} }$ to the total surface vector, while the horizontal surfaces are simply displaced vertically be the relief. The rightmost image below shows how the total surface vector is preserved if the "texture" of the surface at infinitesimal scales is converted from "steps" (a union of horizontal and vertical surfaces) to "smooth slopes" and vice versa. The surface formed from the red and green planes is a step, while the surface formed from the blue plane is a slope. These two surfaces can be seen to have equal total surface vectors from the right-angled triangle at the right side of the image.
Adding elevation (depression in this image) or relief to a surface does not change the total surface vector. The red colored horizontal surfaces are clearly conserved, albeit at different elevations. The green colored vertical surfaces sum to 0 at each tier/elevation. Adding elevation (depression in this image) or relief to a surface does not change the total surface vector. The horizontal surfaces are clearly conserved, albeit at different elevations. The green colored vertical surfaces sum to their initial value above the lower red surface, and sum to 0 beneath the lower red surface. In this image there are two surfaces. The first surface is the union of the red and green planes, and the counter-clockwise boundary is shown by the thick black line. The second surface is the blue plane and the counter-clockwise boundary is shown by the dashed blue line. The surface vectors of the red, green, and blue planes are shown. The total surface vector of the first surface is the sum of the surface vectors of the red and green planes, and is equal to the surface vector of the blue plane. This all implies that the total surface vector of a sloped flat surface is unchanged by replacing the surface with its horizontal and vertical components (projections).
Generalizing from displacement vectors
The total displacement along a simple oriented curve can be used to compute the net displacement in a specific direction. Given a simple oriented curve ${\displaystyle C}$ and an oriented straight line with the direction indicated by normal vector ${\displaystyle {\hat {\mathbf {n} }}}$, the total displacement ${\displaystyle \Delta \mathbf {q} }$ along ${\displaystyle C}$ can be used to compute the net displacement in the direction indicated by the line. This displacement is ${\displaystyle {\hat {\mathbf {n} }}\cdot \Delta \mathbf {q} }$, and depends only on the endpoints of the curve.
In a direct analogy, given a simple oriented surface ${\displaystyle \sigma }$ with counter-clockwise boundary ${\displaystyle \partial \sigma }$, and an oriented flat plane whose surface normal is ${\displaystyle {\hat {\mathbf {n} }}}$, a quantity of interest is the total signed area of ${\displaystyle \sigma }$ perpendicularly projected onto the plane. The signed area that is projected by a flat infinitesimal portion of ${\displaystyle \sigma }$ with surface vector ${\displaystyle d\mathbf {S} }$ is ${\displaystyle {\hat {\mathbf {n} }}\cdot d\mathbf {S} }$, and the total signed area is ${\displaystyle \iint _{\mathbf {q} \in \sigma }{\hat {\mathbf {n} }}\cdot d\mathbf {S} ={\hat {\mathbf {n} }}\cdot \iint _{\mathbf {q} \in \sigma }d\mathbf {S} ={\hat {\mathbf {n} }}\cdot \mathbf {S} }$ where ${\displaystyle \mathbf {S} }$ is the total surface vector of ${\displaystyle \sigma }$.
The total signed projected area ${\displaystyle {\hat {\mathbf {n} }}\cdot \mathbf {S} }$ onto the plane is purely a function of the boundary ${\displaystyle \partial \sigma }$, and does not depend on how ${\displaystyle \sigma }$ fills its boundary ${\displaystyle \partial \sigma }$. This is much more obvious and clearer than the claim that the total surface vector ${\displaystyle \mathbf {S} }$ is only a function of ${\displaystyle \partial \sigma }$: the area enclosed by a boundary in 2D space is purely a function of that boundary. Since the projected area is signed, "upside down" surfaces project negative area, and folds and overhangs cancel each other out.
Since ${\displaystyle {\hat {\mathbf {n} }}\cdot \mathbf {S} }$ is purely a function of ${\displaystyle \partial \sigma }$ for all choices of plane orientation ${\displaystyle {\hat {\mathbf {n} }}}$, then the total surface vector ${\displaystyle \mathbf {S} }$ is purely a function of ${\displaystyle \partial \sigma }$.
Given an arbitrary oriented path, the total displacement covered by the perpendicularly projected path onto an oriented straight line does not depend on the placement of the interior points of the path. The displacement only depends on the endpoints. Since this is true no matter the choice of straight line, the total 3D displacement vector generated by an oriented curve is purely a function of its endpoints, and does not change if the interior points are moved. The total signed area of the projection of an oriented surface onto an oriented flat plane depends only on the boundary and not on any of the interior points. The "shadow" does not change if the interior points are moved around. If the surface is deformed so that there is an "overhang" where some projected points fall outside of the projected boundary, such as in the example of the right, these points cancel out with the points on the opposite side (top or bottom) of the overhang. An upside down surface projects negative area, and in the example on the right, all negative projected area is cancelled out with the positive area projected by the upright surface on top of the overhang.
Computing the signed projected area of a flat surface onto a flat plane is equivalent to computing the signed projected length of the surface vector onto the line that is perpendicular to the plane.
Summary
The total surface vector generated by a closed surface is ${\displaystyle \mathbf {0} }$.
Given a multi-surface ${\displaystyle \mathbf {S} =\{(\sigma _{1},w_{1}),(\sigma _{2},w_{2}),...,(\sigma _{k},w_{k})\}}$ the total surface vector generated by ${\displaystyle \mathbf {S} }$ is ${\displaystyle \sum _{i=1}^{k}w_{i}\iint _{\mathbf {q} \in \sigma _{i}}d\mathbf {S} }$.
Given a vector field ${\displaystyle \mathbf {F} }$ that denotes a multi-surface, the total surface vector generated by ${\displaystyle \mathbf {F} }$ is ${\displaystyle \iiint _{\mathbf {q} \in \mathbb {R} ^{3}}\mathbf {F} (\mathbf {q} )dV}$. Since the surface vector generated by simple surface ${\displaystyle \sigma }$ is ${\displaystyle \iint _{\mathbf {q} \in \sigma }d\mathbf {S} }$, it is the case that ${\displaystyle \iiint _{\mathbf {q} \in \mathbb {R} ^{3}}\delta _{2}(\mathbf {q} ;\sigma )dV=\iint _{\mathbf {q} \in \sigma }d\mathbf {S} }$. One important observation is that given a surface integral over ${\displaystyle \sigma }$, the differential ${\displaystyle d\mathbf {S} }$ is equal to ${\displaystyle \delta _{2}(\mathbf {q} ;\sigma )dV}$ in a volume integral: ${\displaystyle \iint _{\mathbf {q} \in \sigma }f(\mathbf {q} ,d\mathbf {S} )=\iiint _{\mathbf {q} \in \mathbb {R} ^{3}}f(\mathbf {q} ,\delta _{2}(\mathbf {q} ;\sigma )dV)}$ provided that function ${\displaystyle f}$ is a linear in the second parameter.
Total volume
Consider a multi-volume ${\displaystyle \mathbf {U} =\{(\Omega _{1},w_{1}),(\Omega _{2},w_{2}),...,(\Omega _{k},w_{k})\}}$, where the volumes of ${\displaystyle \Omega _{1},\Omega _{2},...,\Omega _{k}}$ are respectively ${\displaystyle V_{1},V_{2},...,V_{k}}$, then the total volume of ${\displaystyle \mathbf {U} }$ is ${\displaystyle \sum _{i=1}^{k}w_{i}V_{i}}$. Each volume ${\displaystyle V_{i}}$ can be computed by ${\displaystyle V_{i}=\iiint _{\mathbf {q} \in \Omega _{i}}dV=\iiint _{\mathbf {q} \in \mathbb {R} ^{3}}\delta _{3}(\mathbf {q} ;\Omega _{i})dV}$. The total volume of ${\displaystyle \mathbf {U} }$ is ${\displaystyle V=\sum _{i=1}^{k}w_{i}V_{i}=\sum _{i=1}^{k}w_{i}\iiint _{\mathbf {q} \in \Omega _{i}}dV=\sum _{i=1}^{k}w_{i}\iiint _{\mathbf {q} \in \mathbb {R} ^{3}}\delta _{3}(\mathbf {q} ;\Omega _{i})dV}$ ${\displaystyle =\iiint _{\mathbf {q} \in \mathbb {R} ^{3}}\left(\sum _{i=1}^{k}w_{i}\delta _{3}(\mathbf {q} ;\Omega _{i})\right)dV=\iiint _{\mathbf {q} \in \mathbb {R} ^{3}}\delta _{3}(\mathbf {q} ;\mathbf {U} )dV}$.
If a multi-volume ${\displaystyle \mathbf {U} }$ can be denoted by scalar field ${\displaystyle U}$, then the volume of ${\displaystyle \mathbf {U} }$ is ${\displaystyle \iiint _{\mathbf {q} \in \mathbb {R} ^{3}}U(\mathbf {q} )dV}$.
Given an arbitrary volume ${\displaystyle \Omega }$, a volume integral over ${\displaystyle \Omega }$ can be converted to a volume integral over ${\displaystyle \mathbb {R} ^{3}}$ by replacing the differential ${\displaystyle dV}$ with ${\displaystyle \delta _{3}(\mathbf {q} ;\Omega )dV}$:
${\displaystyle \iiint _{\mathbf {q} \in \Omega }f(\mathbf {q} ,dV)=\iiint _{\mathbf {q} \in \mathbb {R} ^{3}}f(\mathbf {q} ,\delta _{3}(\mathbf {q} ;\Omega )dV)}$ provided that ${\displaystyle f}$ is linear in the second parameter.
Intersections
The union of two multi-points denoted by scalar fields ${\displaystyle \rho _{1}}$ and ${\displaystyle \rho _{2}}$ is simply ${\displaystyle \rho _{1}+\rho _{2}}$, and the same is true for the union of two multi-paths, the union of two multi-surfaces, and the union of two multi-volumes. The union of two structures with different types, such as a multi-point with a multi-path, is forbidden however.
Unions
structure multi-point ${\displaystyle \rho _{2}}$ multi-path ${\displaystyle \mathbf {J} _{2}}$ multi-surface ${\displaystyle \mathbf {F} _{2}}$ multi-volume ${\displaystyle U_{2}}$
multi-point ${\displaystyle \rho _{1}}$ multi-point ${\displaystyle \rho _{1}+\rho _{2}}$ n/a n/a n/a
multi-path ${\displaystyle \mathbf {J} _{1}}$ n/a multi-path ${\displaystyle \mathbf {J} _{1}+\mathbf {J} _{2}}$ n/a n/a
multi-surface ${\displaystyle \mathbf {F} _{1}}$ n/a n/a multi-surface ${\displaystyle \mathbf {F} _{1}+\mathbf {F} _{2}}$ n/a
multi-volume ${\displaystyle U_{1}}$ n/a n/a n/a multi-volume ${\displaystyle U_{1}+U_{2}}$
The intersection on the other hand, is less trivial and can occur between structures of different types.
Point-Volume intersections
When a point ${\displaystyle \mathbf {q} }$ with weight ${\displaystyle w_{1}}$ intersects a volume ${\displaystyle \Omega }$ with weight ${\displaystyle w_{2}}$, then the intersection is point ${\displaystyle \mathbf {q} }$ with weight ${\displaystyle w_{1}w_{2}}$. Given a multi-point and a multi-volume, the intersection is the sum of the pair-wise intersections of each simple point with each simple volume. The image below gives an example of the intersection of a multi-point with a multi-volume.
The left panel depicts both a multi-point and a multi-volume. The right panel depicts the intersection between the multi-point and the multi-volume, which is itself a multi-point. Note that points that intersect a volume with weight -1 have their weights flipped to their negative.
Given a multi-point with scalar field ${\displaystyle \rho }$, and a multi-volume with scalar field ${\displaystyle U}$, then the intersection is a multi-point with scalar field ${\displaystyle \rho U}$.
The total intersection between a multi-point ${\displaystyle \rho }$ and a multi-volume ${\displaystyle U}$ is ${\displaystyle \iiint _{\mathbf {q} \in \mathbb {R} ^{3}}\rho (\mathbf {q} )U(\mathbf {q} )dV}$.
If ${\displaystyle \rho }$ denotes a simple point ${\displaystyle \mathbf {q} _{0}}$, then the total intersection is ${\displaystyle \iiint _{\mathbf {q} \in \mathbb {R} ^{3}}\delta _{0}(\mathbf {q} ;\mathbf {q} _{0})U(\mathbf {q} )dV=U(\mathbf {q} _{0})}$.
If ${\displaystyle U}$ denotes a simple volume ${\displaystyle \Omega }$, then the total intersection is ${\displaystyle \iiint _{\mathbf {q} \in \mathbb {R} ^{3}}\rho (\mathbf {q} )\delta _{3}(\mathbf {q} ;\Omega )dV=\iiint _{\mathbf {q} \in \Omega }\rho (\mathbf {q} )dV}$.
Path-Surface intersections
When a path ${\displaystyle C}$ with weight ${\displaystyle w_{1}}$ intersects a surface ${\displaystyle \sigma }$ with weight ${\displaystyle w_{2}}$ at point ${\displaystyle \mathbf {q} }$, then the intersection is point ${\displaystyle \mathbf {q} }$ with weight ${\displaystyle \pm w_{1}w_{2}}$. The weight is ${\displaystyle +w_{1}w_{2}}$ if ${\displaystyle C}$ passes through ${\displaystyle \sigma }$ in the direction in which ${\displaystyle \sigma }$ is oriented. The weight is ${\displaystyle -w_{1}w_{2}}$ if ${\displaystyle C}$ passes through ${\displaystyle \sigma }$ opposite the direction in which ${\displaystyle \sigma }$ is oriented. Given a multi-path and a multi-surface, the intersection is the sum of the pair-wise intersections of each simple path with each simple surface. The images below give examples of the intersections of a multi-path with a multi-surface.
A 2D image showing the intersection of a multi-path (dark blue dashed curves) with a multi-surface (dark red solid curves). Positive intersection points (red circles) occur when a path intersects a surface in the preferred direction. Negative intersection points (teal circles) occur when a path intersects a surface in the opposite direction. The intersection is effectively a multi-point. A 3D image showing the intersection of a simple path (red curve) with a simple surface (green surface with the counter-clockwise boundary highlighted). The positive intersection points are denoted by red "+" signs, and the negative intersection points are denoted by blue "-" signs. The intersection between a multi-path shown as a blue tube with a multi-surface shown as layers of red sheets. Vector F is the flow density through the blue tube. Vector G is the surface density in the red sheets. The green parallelogram is a 2D projection of the volume of the intersection. The intersection points become more dilute as the angle theta increases, so the intersection point density is the dot product of F and G.
In the image above to the far right, the multi-path is denoted by a vector field which has the value ${\displaystyle \mathbf {F} }$ inside the blue tube, and is ${\displaystyle \mathbf {0} }$ everywhere else. The multi-surface is denoted by a vector field which has the value ${\displaystyle \mathbf {G} }$ among the red sheets, and is ${\displaystyle \mathbf {0} }$ everywhere else. The total path weight in the blue tube is ${\displaystyle |\mathbf {F} |\Delta A}$. The total surface weight in the red sheets is ${\displaystyle |\mathbf {G} |\Delta t}$. The total weight of all the intersection points is ${\displaystyle (|\mathbf {F} |\Delta A)(|\mathbf {G} |\Delta t)=|\mathbf {F} ||\mathbf {G} |\Delta A\Delta t}$. The volume that the intersection points are evenly spread out in is ${\displaystyle \Delta A\Delta t/\cos \theta }$. The intersection point density is ${\displaystyle {\frac {|\mathbf {F} ||\mathbf {G} |\Delta A\Delta t}{\Delta A\Delta t/\cos \theta }}=|\mathbf {F} ||\mathbf {G} |\cos \theta =\mathbf {F} \cdot \mathbf {G} }$.
Given a multi-path with vector field ${\displaystyle \mathbf {J} }$, and a multi-surface with vector field ${\displaystyle \mathbf {F} }$, then the intersection is a multi-point with scalar field ${\displaystyle \mathbf {J} \cdot \mathbf {F} }$.
The total intersection between a multi-path ${\displaystyle \mathbf {J} }$ and a multi-surface ${\displaystyle \mathbf {F} }$ is ${\displaystyle \iiint _{\mathbf {q} \in \mathbb {R} ^{3}}(\mathbf {J} (\mathbf {q} )\cdot \mathbf {F} (\mathbf {q} ))dV}$.
If ${\displaystyle \mathbf {J} }$ is a simple path ${\displaystyle C}$, then the total intersection is ${\displaystyle \iiint _{\mathbf {q} \in \mathbb {R} ^{3}}(\delta _{1}(\mathbf {q} ;C)\cdot \mathbf {F} (\mathbf {q} ))dV=\int _{\mathbf {q} \in C}\mathbf {F} (\mathbf {q} )\cdot d\mathbf {q} }$.
If ${\displaystyle \mathbf {F} }$ is a simple surface ${\displaystyle \sigma }$, then the total intersection is ${\displaystyle \iiint _{\mathbf {q} \in \mathbb {R} ^{3}}(\mathbf {J} (\mathbf {q} )\cdot \delta _{2}(\mathbf {q} ;\sigma ))dV=\iint _{\mathbf {q} \in \sigma }\mathbf {J} (\mathbf {q} )\cdot d\mathbf {S} }$.
Path-Volume intersections
When a path ${\displaystyle C}$ with weight ${\displaystyle w_{1}}$ intersects a volume ${\displaystyle \Omega }$ with weight ${\displaystyle w_{2}}$, then the intersection is path ${\displaystyle C\cap \Omega }$ with weight ${\displaystyle w_{1}w_{2}}$. Given a multi-path and a multi-volume, the intersection is the sum of the pair-wise intersections of each simple path with each simple volume. The image below gives an example of the intersection of a multi-path with a multi-volume.
The left panel depicts both a multi-path and a multi-volume. The right panel depicts the intersection between the multi-path and the multi-volume, which is itself a multi-path. Note that the path's orientation is reversed in the negatively weighted volumes. In addition, the path segment in the weight 2 volume region in the middle has a weight of 2 as indicated by the thicker line.
Given a multi-path with vector field ${\displaystyle \mathbf {J} }$, and a multi-volume with scalar field ${\displaystyle U}$, then the intersection is a multi-path with vector field ${\displaystyle \mathbf {J} U}$.
The total intersection between a multi-path ${\displaystyle \mathbf {J} }$ and a multi-volume ${\displaystyle U}$ is ${\displaystyle \iiint _{\mathbf {q} \in \mathbb {R} ^{3}}\mathbf {J} (\mathbf {q} )U(\mathbf {q} )dV}$.
If ${\displaystyle \mathbf {J} }$ denotes a simple path ${\displaystyle C}$, then the total intersection is ${\displaystyle \iiint _{\mathbf {q} \in \mathbb {R} ^{3}}\delta _{1}(\mathbf {q} ;C)U(\mathbf {q} )dV=\int _{\mathbf {q} \in C}U(\mathbf {q} )d\mathbf {q} }$.
If ${\displaystyle U}$ denotes a simple volume ${\displaystyle \Omega }$, then the total intersection is ${\displaystyle \iiint _{\mathbf {q} \in \mathbb {R} ^{3}}\mathbf {J} (\mathbf {q} )\delta _{3}(\mathbf {q} ;\Omega )dV=\iiint _{\mathbf {q} \in \Omega }\mathbf {J} (\mathbf {q} )dV}$.
Surface-Surface intersections
When a surface ${\displaystyle \sigma _{1}}$ with weight ${\displaystyle w_{1}}$ intersects a surface ${\displaystyle \sigma _{2}}$ with weight ${\displaystyle w_{2}}$, then the intersection is the path ${\displaystyle \sigma _{1}\cap \sigma _{2}}$ with weight ${\displaystyle w_{1}w_{2}}$. The orientation given to path ${\displaystyle \sigma _{1}\cap \sigma _{2}}$ is defined as follows: viewing the intersection where the surface normal vectors of ${\displaystyle \sigma _{1}}$ and ${\displaystyle \sigma _{2}}$ are oriented towards the viewer, the intersection path has ${\displaystyle \sigma _{1}}$ to its right, and ${\displaystyle \sigma _{2}}$ to its left. Put another way, the intersection path is oriented according to the "right-hand rule" where the surface normals of ${\displaystyle \sigma _{1}}$ are the "x" direction, and the surface normals of ${\displaystyle \sigma _{2}}$ are the "y" direction. The images below give examples of the intersections of a multi-surface with a multi-surface.
A 3D image that shows the intersection of 2 surfaces. Surface 1 is blue and the normal vectors are oriented upwards. Surface 2 is red and the normal vectors are oriented to the right. The intersection is the black curve. The orientation of the intersection curve is determined via the right-hand rule with the surface normals of surface 1 as the "x" direction, and the surface normals of surface 2 as the "y" direction. The intersection between two multi-surfaces. The first multi-surface is the layered blue sheets, and the second multi-surface is the layered red sheets. Vector F is the surface density in the blue sheets. Vector G is the surface density in the red sheets. The green parallelogram is a 2D cross-section of the prism that forms the intersection. The intersection paths become more dilute the further angle theta deviates from 90 degrees, so the intersection path density is the cross product of F and G. The intersection paths are also oriented out of the screen in this example.
In the image above to the right, the first multi-surface is denoted by a vector field that has the value ${\displaystyle \mathbf {F} }$ among the blue sheets, and is ${\displaystyle \mathbf {0} }$ everywhere else. The second multi-surface is denoted by a vector field that has the value ${\displaystyle \mathbf {G} }$ among the red sheets, and is ${\displaystyle \mathbf {0} }$ everywhere else. The total surface weight in the blue sheets is ${\displaystyle |\mathbf {F} |\Delta t_{1}}$, and the total surface weight in the red sheets is ${\displaystyle |\mathbf {G} |\Delta t_{2}}$. The total weight of all the intersection paths is ${\displaystyle (|\mathbf {F} |\Delta t_{1})(|\mathbf {G} |\Delta t_{2})=|\mathbf {F} ||\mathbf {G} |\Delta t_{1}\Delta t_{2}}$. The cross-sectional area that the intersection paths are evenly spread out over is ${\displaystyle \Delta t_{1}\Delta t_{2}/\sin \theta }$. The intersection path density is ${\displaystyle {\frac {|\mathbf {F} ||\mathbf {G} |\Delta t_{1}\Delta t_{2}}{\Delta t_{1}\Delta t_{2}/\sin \theta }}=|\mathbf {F} ||\mathbf {G} |\sin \theta =|\mathbf {F} \times \mathbf {G} |}$. Lastly, it should be noted that the intersection paths are oriented out of the screen as per the right-hand rule.
Given a multi-surface with vector field ${\displaystyle \mathbf {F} _{1}}$, and a multi-surface with vector field ${\displaystyle \mathbf {F} _{2}}$, then the intersection is the multi-path with vector field ${\displaystyle \mathbf {F} _{1}\times \mathbf {F} _{2}}$.
The total intersection between multi-surface ${\displaystyle \mathbf {F} _{1}}$ and multi-surface ${\displaystyle \mathbf {F} _{2}}$ is ${\displaystyle \iiint _{\mathbf {q} \in \mathbb {R} ^{3}}(\mathbf {F} _{1}(\mathbf {q} )\times \mathbf {F} _{2}(\mathbf {q} ))dV}$.
If ${\displaystyle \mathbf {F} _{2}}$ denotes a simple surface ${\displaystyle \sigma }$, then the total intersection is ${\displaystyle \iiint _{\mathbf {q} \in \mathbb {R} ^{3}}(\mathbf {F} _{1}(\mathbf {q} )\times \delta _{2}(\mathbf {q} ;\sigma ))dV=\iint _{\mathbf {q} \in \sigma }\mathbf {F} _{1}(\mathbf {q} )\times d\mathbf {S} }$.
Surface-Volume intersections
When a surface ${\displaystyle \sigma }$ with weight ${\displaystyle w_{1}}$ intersects a volume ${\displaystyle \Omega }$ with weight ${\displaystyle w_{2}}$, then the intersection is surface ${\displaystyle \sigma \cap \Omega }$ with weight ${\displaystyle w_{1}w_{2}}$. Given a multi-surface and a multi-volume, the intersection is the sum of the pair-wise intersections of each simple surface with each simple volume. The image below gives an example of the intersection of a multi-surface with a multi-volume.
The left panel depicts both a multi-surface and a multi-volume. The right panel depicts the intersection between the multi-surface and the multi-volume, which is itself a multi-surface. Note that the surface's orientation is reversed in the negatively weighted volume. In addition, the surface segment in the weight 2 volume region in the upper-left has a weight of 2 as indicated by the thicker line.
Given a multi-surface with vector field ${\displaystyle \mathbf {F} }$, and a multi-volume with scalar field ${\displaystyle U}$, then the intersection is a multi-surface with vector field ${\displaystyle \mathbf {F} U}$.
The total intersection between a multi-surface ${\displaystyle \mathbf {F} }$ and a multi-volume ${\displaystyle U}$ is ${\displaystyle \iiint _{\mathbf {q} \in \mathbb {R} ^{3}}\mathbf {F} (\mathbf {q} )U(\mathbf {q} )dV}$.
If ${\displaystyle \mathbf {F} }$ denotes a simple surface ${\displaystyle \sigma }$, then the total intersection is ${\displaystyle \iiint _{\mathbf {q} \in \mathbb {R} ^{3}}\delta _{2}(\mathbf {q} ;\sigma )U(\mathbf {q} )dV=\iint _{\mathbf {q} \in \sigma }U(\mathbf {q} )d\mathbf {S} }$.
If ${\displaystyle U}$ denotes a simple volume ${\displaystyle \Omega }$, then the total intersection is ${\displaystyle \iiint _{\mathbf {q} \in \mathbb {R} ^{3}}\mathbf {F} (\mathbf {q} )\delta _{3}(\mathbf {q} ;\Omega )dV=\iiint _{\mathbf {q} \in \Omega }\mathbf {F} (\mathbf {q} )dV}$.
Volume-Volume intersections
When a volume ${\displaystyle \Omega _{1}}$ with weight ${\displaystyle w_{1}}$ intersects a volume ${\displaystyle \Omega _{2}}$ with weight ${\displaystyle w_{2}}$, then the intersection is the volume ${\displaystyle \Omega _{1}\cap \Omega _{2}}$ with weight ${\displaystyle w_{1}w_{2}}$. Given two multi-volumes, the intersection is the sum of the pair-wise intersections of each simple volume from the first multi-volume with each simple volume from the second multi-volume. The image below gives an example of the intersection between two multi-volumes.
The left two panels each depict a multi-volume, and the rightmost panel depicts the intersection of the two multi-volumes. The weight of the intersection of two simple volumes is the product of the weight of the two volumes.
Given a multi-volume with scalar field ${\displaystyle U_{1}}$, and a multi-volume with scalar field ${\displaystyle U_{2}}$, then the intersection is a multi-volume with scalar field ${\displaystyle U_{1}U_{2}}$.
The total intersection between multi-volume ${\displaystyle U_{1}}$ and multi-volume ${\displaystyle U_{2}}$ is ${\displaystyle \iiint _{\mathbf {q} \in \mathbb {R} ^{3}}U_{1}(\mathbf {q} )U_{2}(\mathbf {q} )dV}$.
If ${\displaystyle U_{2}}$ denotes a simple volume ${\displaystyle \Omega }$, then the total intersection is ${\displaystyle \iiint _{\mathbf {q} \in \mathbb {R} ^{3}}U_{1}(\mathbf {q} )\delta _{3}(\mathbf {q} ;\Omega )dV=\iiint _{\mathbf {q} \in \Omega }U_{1}(\mathbf {q} )dV}$.
Other intersections
Other types of intersections, such as Point-Point intersections, Point-Path intersections, Point-Surface intersections, and Path-Path intersections, are not considered since these kinds of intersections can occur only by design. For example, the probability that two randomly chosen points will intersect each other is 0, but if a point and a volume are randomly chosen, then the probability of the point landing in the volume is nonzero. Given two unrelated points, these two points will never land on each other, since a prior relationship has to exist for the points to coincide. Below is summarized the various types of intersections:
Intersections
structure multi-point ${\displaystyle \rho _{2}}$ multi-path ${\displaystyle \mathbf {J} _{2}}$ multi-surface ${\displaystyle \mathbf {F} _{2}}$ multi-volume ${\displaystyle U_{2}}$
multi-point ${\displaystyle \rho _{1}}$ n/a n/a n/a multi-point ${\displaystyle \rho _{1}U_{2}}$
multi-path ${\displaystyle \mathbf {J} _{1}}$ n/a n/a multi-point ${\displaystyle \mathbf {J} _{1}\cdot \mathbf {F} _{2}}$ multi-path ${\displaystyle \mathbf {J} _{1}U_{2}}$
multi-surface ${\displaystyle \mathbf {F} _{1}}$ n/a multi-point ${\displaystyle \mathbf {F} _{1}\cdot \mathbf {J} _{2}}$ multi-path ${\displaystyle \mathbf {F} _{1}\times \mathbf {F} _{2}}$ multi-surface ${\displaystyle \mathbf {F} _{1}U_{2}}$
multi-volume ${\displaystyle U_{1}}$ multi-point ${\displaystyle U_{1}\rho _{2}}$ multi-path ${\displaystyle U_{1}\mathbf {J} _{2}}$ multi-surface ${\displaystyle U_{1}\mathbf {F} _{2}}$ multi-volume ${\displaystyle U_{1}U_{2}}$
Boundaries
The endpoints of paths
Given a simple path ${\displaystyle C}$ that starts at point ${\displaystyle C(0)}$ and ends at point ${\displaystyle C(1)}$, the "endpoints" of ${\displaystyle C}$ is the multi-point ${\displaystyle \{(C(0),+1),(C(1),-1)\}}$ that consists of the starting point with a weight of +1, and the final point with a weight of -1. While ${\displaystyle C}$ is denoted by the vector field ${\displaystyle \delta _{1}(\mathbf {q} ;C)}$, the endpoints are denoted by the scalar field ${\displaystyle \delta _{0}(\mathbf {q} ;C(0))-\delta _{0}(\mathbf {q} ;C(1))}$. The image below gives several examples of simple paths and their associated endpoints.
A series of panels, each depicting a directed path and its endpoints. The endpoints of a path consists of a positively weighted point at the start and a negatively weighted point at the end.
Given a multi-path ${\displaystyle \mathbf {C} =\{(C_{1},w_{1}),(C_{2},w_{2}),...,(C_{k},w_{k})\}}$, the endpoints of ${\displaystyle \mathbf {C} }$ is the multi-point ${\displaystyle \{(C_{1}(0),+1),(C_{1}(1),-1),(C_{2}(0),+1),(C_{2}(1),-1),...,(C_{k}(0),+1),(C_{k}(1),-1)\}}$.
Given a vector field ${\displaystyle \mathbf {J} }$ that denotes a multi-path, the multi-point that denotes the endpoints of ${\displaystyle \mathbf {J} }$ is denoted by scalar field ${\displaystyle \nabla \cdot \mathbf {J} }$. The scalar field ${\displaystyle \nabla \cdot \mathbf {J} }$ evaluated at point ${\displaystyle \mathbf {q} }$ is denoted by ${\displaystyle \nabla \cdot \mathbf {J} (\mathbf {q} )}$, ${\displaystyle (\nabla \cdot \mathbf {J} )(\mathbf {q} )}$ or ${\displaystyle \nabla \cdot \mathbf {J} |_{\mathbf {q} }}$.
The requirement that no path extends to infinity means that every starting point is paired with a final point, and therefore the total weight of all of the endpoints together is 0: ${\displaystyle \iiint _{\mathbf {q} \in \mathbb {R} ^{3}}(\nabla \cdot \mathbf {J} (\mathbf {q} ))dV=0}$.
The path endpoints are the intersections of the path with the "surface of reality".
The similarity of the notation ${\displaystyle \nabla \cdot \mathbf {J} }$ to the intersection of multi-path ${\displaystyle \mathbf {J} }$ with multi-surface ${\displaystyle \mathbf {F} }$, denoted by ${\displaystyle \mathbf {F} \cdot \mathbf {J} }$, makes sense if ${\displaystyle \nabla }$ is interpreted as the "surface of reality". A starting point forms when a path pokes into reality, and a final point forms when a path pokes out of reality.
In the image to the right, a depiction of the "surface of reality" interpretation of ${\displaystyle \nabla }$ is shown. On the right is a simple path ${\displaystyle \mathbf {F} }$, along with its endpoints ${\displaystyle \nabla \cdot \mathbf {F} }$. On the left ${\displaystyle \mathbf {F} _{\text{ext}}}$ is an extension of ${\displaystyle \mathbf {F} }$ that is behind the "veil" of surface ${\displaystyle \mathbf {G} _{\nabla }}$. ${\displaystyle \mathbf {F} _{\text{ext}}}$ pokes out of and into ${\displaystyle \mathbf {G} _{\nabla }}$ at points consistent with the endpoints of ${\displaystyle \mathbf {F} }$: i.e. ${\displaystyle \mathbf {G} _{\nabla }\cdot \mathbf {F} _{\text{ext}}=\nabla \cdot \mathbf {F} }$.
The counter-clockwise oriented boundaries of surfaces
Given an oriented surface ${\displaystyle \sigma }$, the "counter-clockwise oriented boundary" of ${\displaystyle \sigma }$ is a path ${\displaystyle \partial \sigma }$ that traces the boundary of ${\displaystyle \sigma }$ in a counter-clockwise direction. The counter-clockwise direction is better described as follows: While located on the boundary, the counter-clockwise direction is the "forwards" direction when the surface normal vectors point "up" and the surface itself is on the "left". The image below gives several examples of oriented surfaces and their counter-clockwise boundaries. Note in particular the 4th panel that shows that the orientation around a hole in the surface appears to be clockwise.
A series of panels, each depicting an oriented surface and its counterclockwise oriented boundary. The surface normal vectors are depicted by the red arrows.
Given a multi-surface ${\displaystyle \mathbf {S} =\{(\sigma _{1},w_{1}),(\sigma _{2},w_{2}),...,(\sigma _{k},w_{k})\}}$, the counter-clockwise boundary of ${\displaystyle \mathbf {S} }$ is the multi-path ${\displaystyle \{(\partial \sigma _{1},w_{1}),(\partial \sigma _{2},w_{2}),...,(\partial \sigma _{k},w_{k})\}}$.
Given a vector field ${\displaystyle \mathbf {F} }$ that denotes a multi-surface, the multi-path that denotes the counter-clockwise boundary of ${\displaystyle \mathbf {F} }$ is denoted by vector field ${\displaystyle \nabla \times \mathbf {F} }$. The vector field ${\displaystyle \nabla \times \mathbf {F} }$ evaluated at point ${\displaystyle \mathbf {q} }$ is denoted by ${\displaystyle \nabla \times \mathbf {F} (\mathbf {q} )}$, ${\displaystyle (\nabla \times \mathbf {F} )(\mathbf {q} )}$, or ${\displaystyle \nabla \times \mathbf {F} |_{\mathbf {q} }}$.
The requirement that no surface weight extends to infinity means that all counter-clockwise boundaries form closed loops, and therefore the total displacement of the total counter-clockwise boundary is ${\displaystyle \mathbf {0} }$: ${\displaystyle \iiint _{\mathbf {q} \in \mathbb {R} ^{3}}(\nabla \times \mathbf {F} (\mathbf {q} ))dV=\mathbf {0} }$.
It is also important to note that the counter-clockwise boundary has no endpoints: ${\displaystyle \nabla \cdot (\nabla \times \mathbf {F} )=0}$.
The boundary of a surface is analogous to the intersection of the surface with the "surface of reality".
The similarity of the notation ${\displaystyle \nabla \times \mathbf {F} _{2}}$ to the intersection of multi-surface ${\displaystyle \mathbf {F} _{1}}$ with multi-surface ${\displaystyle \mathbf {F} _{2}}$, denoted by ${\displaystyle \mathbf {F} _{1}\times \mathbf {F} _{2}}$, again makes sense if ${\displaystyle \nabla }$ is interpreted as the "surface of reality". An edge is formed when a surface "slices" into reality.
In the image to the right, a depiction of the "surface of reality" interpretation of ${\displaystyle \nabla }$ is shown. On the right is a simple surface ${\displaystyle \mathbf {F} }$, along with its counter-clockwise boundary ${\displaystyle \nabla \times \mathbf {F} }$. On the left ${\displaystyle \mathbf {F} _{\text{ext}}}$ is an extension of ${\displaystyle \mathbf {F} }$ that is behind the "veil" of surface ${\displaystyle \mathbf {G} _{\nabla }}$. ${\displaystyle \mathbf {F} _{\text{ext}}}$ slices into ${\displaystyle \mathbf {G} _{\nabla }}$ at curves consistent with the boundary of ${\displaystyle \mathbf {F} }$: i.e. ${\displaystyle \mathbf {G} _{\nabla }\times \mathbf {F} _{\text{ext}}=\nabla \times \mathbf {F} }$.
The inwards-oriented surfaces of volumes
Given a volume ${\displaystyle \Omega }$, the "inwards oriented surface" of ${\displaystyle \Omega }$ is a surface ${\displaystyle \partial \Omega }$ that wraps the volume ${\displaystyle \Omega }$ with the surface normals pointing inwards. The image below gives several examples of volumes and their inwards oriented surfaces.
A series of panels, each depicting a volume and its inwards oriented surface. The inwards orientation of the surface is indicated by the red arrows pointing inwards.
Given a multi-volume ${\displaystyle \mathbf {U} =\{(\Omega _{1},w_{1}),(\Omega _{2},w_{2}),...,(\Omega _{k},w_{k})\}}$, the inwards oriented surface of ${\displaystyle \mathbf {U} }$ is the multi-surface ${\displaystyle \{(\partial \Omega _{1},w_{1}),(\partial \Omega _{2},w_{2}),...,(\partial \Omega _{k},w_{k})\}}$.
Given a scalar field ${\displaystyle U}$ that denotes a multi-volume, the multi-surface that denotes the inwards oriented surface of ${\displaystyle U}$ is denoted by vector field ${\displaystyle \nabla U}$. The vector field ${\displaystyle \nabla U}$ evaluated at point ${\displaystyle \mathbf {q} }$ is denoted by ${\displaystyle \nabla U(\mathbf {q} )}$, ${\displaystyle (\nabla U)(\mathbf {q} )}$, or ${\displaystyle \nabla U|_{\mathbf {q} }}$.
The requirement that no volume weight extends to infinity means that all inwards oriented surfaces form closed surfaces, and therefore the total surface vector of the total inwards oriented surface is ${\displaystyle \mathbf {0} }$: ${\displaystyle \iiint _{\mathbf {q} \in \mathbb {R} ^{3}}(\nabla U(\mathbf {q} ))dV=\mathbf {0} }$.
It is also important to note that the inwards oriented surface has no boundary: ${\displaystyle \nabla \times (\nabla U)=\mathbf {0} }$.
In this 2D cross-section, the surface of a volume is analogous to the intersection of the volume with the "surface of reality".
The similarity of the notation ${\displaystyle \nabla U}$ to the intersection of multi-surface ${\displaystyle \mathbf {F} }$ with multi-volume ${\displaystyle U}$, denoted by ${\displaystyle \mathbf {F} U}$, again makes sense if ${\displaystyle \nabla }$ is interpreted as the "surface of reality". A surface is formed from the surface of reality when the volume "pushes" into reality.
In the image to the right, a depiction of the "surface of reality" interpretation of ${\displaystyle \nabla }$ is shown. The image is a 2D cross-section for simplicity. On the right is a simple volume ${\displaystyle U}$, along with its inwards oriented surface ${\displaystyle \nabla U}$. On the left ${\displaystyle U_{\text{ext}}}$ is an extension of ${\displaystyle U}$ that is behind the "veil" of surface ${\displaystyle \mathbf {G} _{\nabla }}$. ${\displaystyle U_{\text{ext}}}$ pushes through ${\displaystyle \mathbf {G} _{\nabla }}$ at surfaces consistent with the surface of ${\displaystyle U}$: i.e. ${\displaystyle \mathbf {G} _{\nabla }U_{\text{ext}}=\nabla U}$.
Closed loops and closed surfaces
A simple path is "closed" or a "loop" if its starting and final points are the same, so the total endpoints is 0 since the weights of the starting and final points cancel out. More generally, a multi-path ${\displaystyle \mathbf {J} }$ is "closed" or a "multi-loop" if ${\displaystyle \nabla \cdot \mathbf {J} =0}$. As previously noted, the counter-clockwise boundary of a surface is closed.
A simple surface is "closed" or a "bubble" if it has no boundary. More generally, a multi-surface ${\displaystyle \mathbf {F} }$ is "closed" or a "multi-bubble" if ${\displaystyle \nabla \times \mathbf {F} =\mathbf {0} }$. As previously noted, the inwards oriented surface of a volume is closed.
It is clear that the total displacement present in a closed multi-path is ${\displaystyle \mathbf {0} }$: ${\displaystyle \nabla \cdot \mathbf {J} =0\implies \iiint _{\mathbf {q} \in \mathbb {R} ^{3}}\mathbf {J} dV=\mathbf {0} }$, and it is also clear that the total surface vector of a closed multi-surface is also ${\displaystyle \mathbf {0} }$: ${\displaystyle \nabla \times \mathbf {F} =\mathbf {0} \implies \iiint _{\mathbf {q} \in \mathbb {R} ^{3}}\mathbf {F} dV=\mathbf {0} }$.
Given a simple loop and simple bubble, the number of times that the loop enters the bubble is equal to the number of times that the loop leaves the bubble.
Given both a simple loop and a simple bubble, the total point weight of all intersection points is 0: every time the loop enters the bubble, it must also leave the bubble, and the weights of these two intersection points cancel out. More generally, given a closed multi-path ${\displaystyle \mathbf {J} }$ and a closed multi-surface ${\displaystyle \mathbf {F} }$, then the total intersection point weight is 0: ${\displaystyle (\nabla \cdot \mathbf {J} =0\;{\text{and}}\;\nabla \times \mathbf {F} =\mathbf {0} )\implies \iiint _{\mathbf {q} \in \mathbb {R} ^{3}}(\mathbf {J} \cdot \mathbf {F} )dV=0}$.
The above identity gives rise to the following observations:
• The total intersection point weight of a multi-loop and a multi-surface is purely a function of the multi-loop and the multi-surface's counter-clockwise boundary: the interior of the multi-surface does not matter. If ${\displaystyle \nabla \cdot \mathbf {J} =0}$ and ${\displaystyle \nabla \times \mathbf {F} _{1}=\nabla \times \mathbf {F} _{2}}$, then ${\displaystyle \iiint _{\mathbf {q} \in \mathbb {R} ^{3}}(\mathbf {J} \cdot \mathbf {F} _{1})dV=\iiint _{\mathbf {q} \in \mathbb {R} ^{3}}(\mathbf {J} \cdot \mathbf {F} _{2})dV}$.
• The total intersection point weight of a multi-path and a multi-bubble is purely a function of the multi-bubble and the multi-path's endpoints: the interior of the multi-path does not matter. If ${\displaystyle \nabla \times \mathbf {F} =\mathbf {0} }$ and ${\displaystyle \nabla \cdot \mathbf {J} _{1}=\nabla \cdot \mathbf {J} _{2}}$, then ${\displaystyle \iiint _{\mathbf {q} \in \mathbb {R} ^{3}}(\mathbf {J} _{1}\cdot \mathbf {F} )dV=\iiint _{\mathbf {q} \in \mathbb {R} ^{3}}(\mathbf {J} _{2}\cdot \mathbf {F} )dV}$.
The inwards oriented surface of a volume is closed. Conversely, given a closed surface, there exists a volume that "fills" the surface. More generally, given a multi-bubble ${\displaystyle \mathbf {F} }$, there exists a multi-volume ${\displaystyle U}$ for which ${\displaystyle \mathbf {F} }$ is the inwards oriented multi-surface of ${\displaystyle U}$: ${\displaystyle \nabla \times \mathbf {F} =\mathbf {0} \implies \exists U:\nabla U=\mathbf {F} }$. This multi-volume is referred to as the "scalar potential" of ${\displaystyle \mathbf {F} }$. The requirement that volumes cannot extend to infinity means that ${\displaystyle U}$ is unique.
The counter-clockwise oriented boundary of a surface is closed. Conversely, given a loop, there exists a surface that "fills" the loop. More generally, given a multi-loop ${\displaystyle \mathbf {J} }$, there exists a multi-surface ${\displaystyle \mathbf {F} }$ for which ${\displaystyle \mathbf {J} }$ is the counter-clockwise boundary of ${\displaystyle \mathbf {F} }$: ${\displaystyle \nabla \cdot \mathbf {J} =0\implies \exists \mathbf {F} :\nabla \times \mathbf {F} =\mathbf {J} }$. This multi-surface is referred to as the "vector potential" of ${\displaystyle \mathbf {J} }$. Even with the requirement that surfaces cannot extend to infinity, ${\displaystyle \mathbf {F} }$ is not unique without additional restrictions.
Coordinate Systems
This image depicts a generalized coordinate lattice at the top. At the bottom of the image is a single volume element with the basis displacement (contravariant) vectors, alongside the basis surface (covariant) vectors.
This section will describe how to compute various quantities such as intersections, endpoints, boundaries, and surfaces given a curvilinear coordinate system.
Let the curvilinear coordinate system be arbitrary. Let the 3 coordinates that index all points be ${\displaystyle c_{1},c_{2},c_{3}}$. Coordinates will be denoted by the triple ${\displaystyle (c_{1},c_{2},c_{3})}$.
The following notation will be used in the following discussions:
• Given an arbitrary expression ${\displaystyle f:\{1,2,3\}\to \mathbb {R} }$ that assigns a real number to each index ${\displaystyle i=1,2,3}$, then ${\displaystyle (i;f(i))}$ will denote the triple ${\displaystyle (f(1),f(2),f(3))}$.
• Given index variables ${\displaystyle i,j\in \{1,2,3\}}$, the expression ${\displaystyle \mathbf {1} (i=j)}$ equals 1 if ${\displaystyle i=j}$ and 0 if otherwise.
• Given an arbitrary expression ${\displaystyle f:\{1,2,3\}\to \mathbb {R} }$ that assigns a real number to each index ${\displaystyle i=1,2,3}$, then ${\displaystyle \sum _{i}f(i)}$ will denote the sum ${\displaystyle f(1)+f(2)+f(3)}$.
• Given an index variable ${\displaystyle i\in \{1,2,3\}}$, ${\displaystyle i+1}$ will rotate ${\displaystyle i}$ forwards by 1, and ${\displaystyle i+2}$ will rotate ${\displaystyle i}$ forwards by 2. In essence, ${\displaystyle i+1=\left\{{\begin{array}{cc}i+1&(i=1,2)\\1&(i=3)\end{array}}\right.}$ and ${\displaystyle i+2=\left\{{\begin{array}{cc}3&(i=1)\\i-1&(i=2,3)\end{array}}\right.}$.
Start with an arbitrary coordinate ${\displaystyle (c'_{1},c'_{2},c'_{3})=(j;c'_{j})}$ and infinitesimal differences ${\displaystyle \Delta c_{1}}$, ${\displaystyle \Delta c_{2}}$, and ${\displaystyle \Delta c_{3}}$. The following 3 paths, 3 surfaces, and volume will be associated with point ${\displaystyle (j;c'_{j})}$:
• For each ${\displaystyle i\in \{1,2,3\}}$ there exists an infinitely short path ${\displaystyle C_{i}((j;c'_{j}))}$ starting from point ${\displaystyle (j;c'_{j})}$ and ending on point ${\displaystyle (j;c'_{j}+\Delta c_{i}\mathbf {1} (j=i))}$ along the curve defined by ${\displaystyle c'_{i}\leq c_{i}, ${\displaystyle c_{i+1}=c'_{i+1}}$ and ${\displaystyle c_{i+2}=c'_{i+2}}$. The displacement covered by ${\displaystyle C_{i}((j;c'_{j}))}$ is approximately ${\displaystyle \Delta c_{i}\cdot l_{i}((j;c'_{j}))\cdot {\hat {\mathbf {a} }}_{i}((j;c'_{j}))}$ where ${\displaystyle {\hat {\mathbf {a} }}_{i}((j;c'_{j}))}$ is a unit length vector that is parallel to the displacement between points ${\displaystyle (j;c'_{j})}$ and ${\displaystyle (j;c'_{j}+\Delta c_{i}\mathbf {1} (j=i))}$, and ${\displaystyle \Delta c_{i}\cdot l_{i}((j;c'_{j}))}$ is the length of the displacement. Note that the length of the displacement is proportional to ${\displaystyle \Delta c_{i}}$, with ${\displaystyle l_{i}((j;c'_{j}))}$ being the constant of proportionality. The set of vectors ${\displaystyle \{{\hat {\mathbf {a} }}_{1}((j;c'_{j})),{\hat {\mathbf {a} }}_{2}((j;c'_{j})),{\hat {\mathbf {a} }}_{3}((j;c'_{j}))\}}$ is the set of displacement basis vectors.
• For each ${\displaystyle i\in \{1,2,3\}}$ there exists an infinitely small surface ${\displaystyle \sigma _{i}((j;c'_{j}))}$ that is defined by the following: ${\displaystyle c_{i}=c'_{i}}$, ${\displaystyle c'_{i+1}\leq c_{i+1}, and ${\displaystyle c'_{i+2}\leq c_{i+2}. The orientation of ${\displaystyle \sigma _{i}((j;c'_{j}))}$ is in the direction of increasing ${\displaystyle c_{i}}$. The surface vector of ${\displaystyle \sigma _{i}((j;c'_{j}))}$ is approximately ${\displaystyle \Delta c_{i+1}\Delta c_{i+2}\cdot A_{i}((j;c'_{j}))\cdot {\hat {\mathbf {a} }}^{i}((j;c'_{j}))}$ where ${\displaystyle {\hat {\mathbf {a} }}^{i}((j;c'_{j}))}$ is a unit length vector that is perpendicular to ${\displaystyle \sigma _{i}((j;c'_{j}))}$, and ${\displaystyle \Delta c_{i+1}\Delta c_{i+2}\cdot A_{i}((j;c'_{j}))}$ is the area of ${\displaystyle \sigma _{i}((j;c'_{j}))}$. Note that the area of ${\displaystyle \sigma _{i}((j;c'_{j}))}$ is proportional to ${\displaystyle \Delta c_{i+1}\Delta c_{i+2}}$, with ${\displaystyle A_{i}((j;c'_{j}))}$ being the constant of proportionality. The set of vectors ${\displaystyle \{{\hat {\mathbf {a} }}^{1}((j;c'_{j})),{\hat {\mathbf {a} }}^{2}((j;c'_{j})),{\hat {\mathbf {a} }}^{3}((j;c'_{j}))\}}$ is the set of surface basis vectors.
• There is an infinitely small volume ${\displaystyle \Omega ((j;c'_{j}))}$ defined by ${\displaystyle c'_{1}\leq c_{1}, ${\displaystyle c'_{2}\leq c_{2}, and ${\displaystyle c'_{3}\leq c_{3}. ${\displaystyle \Omega ((j;c'_{j}))}$ has a shape that is approximately that of a parallelepiped. The volume of ${\displaystyle \Omega ((j;c'_{j}))}$ is approximately ${\displaystyle \Delta c_{1}\Delta c_{2}\Delta c_{3}\cdot V((j;c'_{j}))}$. Note that the volume of ${\displaystyle \Omega ((j;c'_{j}))}$ is proportional to ${\displaystyle \Delta c_{1}\Delta c_{2}\Delta c_{3}}$, with ${\displaystyle V((j;c'_{j}))}$ being the constant of proportionality.
It is important to note that:
• ${\displaystyle (i;c_{i})\in \Omega ((j;c'_{j}))}$ if and only if ${\displaystyle c'_{1}\leq c_{1}, ${\displaystyle c'_{2}\leq c_{2}, and ${\displaystyle c'_{3}\leq c_{3} (note the strictness of the upper bounds).
• For all ${\displaystyle i\in \{1,2,3\}}$, ${\displaystyle C_{i}((j;c_{j}))\subseteq \Omega ((j;c'_{j}))}$ if and only if ${\displaystyle c_{i}=c'_{i}}$, ${\displaystyle c'_{i+1}\leq c_{i+1}, and ${\displaystyle c'_{i+2}\leq c_{i+2} (note the strictness of the upper bounds).
• For all ${\displaystyle i\in \{1,2,3\}}$, ${\displaystyle \sigma _{i}((j;c_{j}))\subseteq \Omega ((j;c'_{j}))}$ if and only if ${\displaystyle c'_{i}\leq c_{i} (note the strictness of the upper bound), ${\displaystyle c_{i+1}=c'_{i+1}}$, and ${\displaystyle c_{i+2}=c'_{i+2}}$.
Converting between multi-points, multi-paths, multi-surfaces, and multi-volumes and their respective scalar fields and vector fields proceeds as follows:
This conversion is performed by subdividing space into discrete volumes or cells. Infinitesimal differences ${\displaystyle \Delta c_{1}}$, ${\displaystyle \Delta c_{2}}$, and ${\displaystyle \Delta c_{3}}$ are chosen, and a lattice consisting of the points ${\displaystyle (j;k_{j}\Delta c_{j})}$ where ${\displaystyle (j;k_{j})}$ is an arbitrary triple of integers is generated. The cell indexed by ${\displaystyle (j;k_{j})}$ consists of the point ${\displaystyle (j;k_{j}\Delta c_{j})}$, the paths ${\displaystyle C_{i}((j;k_{j}\Delta c_{j}))}$ for each ${\displaystyle i\in \{1,2,3\}}$, the surfaces ${\displaystyle \sigma _{i}((j;k_{j}\Delta c_{j}))}$ for each ${\displaystyle i\in \{1,2,3\}}$, and the volume ${\displaystyle \Omega ((j;k_{j}\Delta c_{j}))}$. All points ${\displaystyle (j;c_{j})}$ where ${\displaystyle k_{i}\Delta c_{i}\leq c_{i}<(k_{i}+1)\Delta c_{i}}$ for all ${\displaystyle i\in \{1,2,3\}}$ "belong" to the cell indexed by ${\displaystyle (j;k_{j})}$ (note that the upper bounds are excluded). Given an arbitrary point ${\displaystyle (j;c_{j})}$, the cell that contains ${\displaystyle (j;c_{j})}$ is indexed by ${\displaystyle (j;k_{j})=\left(j;\left\lfloor {\frac {c_{j}}{\Delta c_{j}}}\right\rfloor \right)}$. The point ${\displaystyle (j;c'_{j})=(j;k_{j}\Delta c_{j})}$ is the vertex that the cell is associated with.
A multi-point, multi-path, multi-surface, or multi-volume is converted to a scalar field or vector field by computing the total point weight, displacement, surface vector, or volume contained by each cell and then averaging over the cell's volume.
A scalar-field ${\displaystyle \rho }$ is converted to a multi-point by doing the following for each cell ${\displaystyle (j;k_{j})}$. First compute the total point weight contained inside the cell: ${\displaystyle \iiint _{\mathbf {q} \in \Omega ((j;k_{j}\Delta c_{j}))}\rho (\mathbf {q} )dV\approx \rho ((j;k_{j}\Delta c_{j}))V((j;k_{j}\Delta c_{j}))\Delta c_{1}\Delta c_{2}\Delta c_{3}}$. Next assign this weight to the point ${\displaystyle (j;k_{j}\Delta c_{j})}$.
A vector-field ${\displaystyle \mathbf {J} =\sum _{i}J_{i}{\hat {\mathbf {a} }}_{i}}$ is converted to a multi-path by doing the following for each cell ${\displaystyle (j;k_{j})}$. First compute the total displacement contained inside the cell: ${\displaystyle \iiint _{\mathbf {q} \in \Omega ((j;k_{j}\Delta c_{j}))}\mathbf {J} (\mathbf {q} )dV\approx \left(\sum _{i}J_{i}((j;k_{j}\Delta c_{j})){\hat {\mathbf {a} }}_{i}((j;k_{j}\Delta c_{j}))\right)V((j;k_{j}\Delta c_{j}))\Delta c_{1}\Delta c_{2}\Delta c_{3}}$. Next separate this total displacement into components according to the basis ${\displaystyle {\hat {\mathbf {a} }}_{1}}$, ${\displaystyle {\hat {\mathbf {a} }}_{2}}$, and ${\displaystyle {\hat {\mathbf {a} }}_{3}}$: for each ${\displaystyle i\in \{1,2,3\}}$ the coefficient of ${\displaystyle {\hat {\mathbf {a} }}_{i}}$ is ${\displaystyle \iiint _{\mathbf {q} \in \Omega ((j;k_{j}\Delta c_{j}))}J_{i}(\mathbf {q} )dV\approx J_{i}((j;k_{j}\Delta c_{j}))V((j;k_{j}\Delta c_{j}))\Delta c_{1}\Delta c_{2}\Delta c_{3}}$. Next for each ${\displaystyle i\in \{1,2,3\}}$, divide the coefficient of ${\displaystyle {\hat {\mathbf {a} }}_{i}}$ by the length of ${\displaystyle C_{i}((j;k_{j}\Delta c_{j}))}$, which results in approximately ${\displaystyle J_{i}((j;k_{j}\Delta c_{j})){\frac {V((j;k_{j}\Delta c_{j}))}{l_{i}((j;k_{j}\Delta c_{j}))}}\Delta c_{i+1}\Delta c_{i+2}}$, and assign this weight to ${\displaystyle C_{i}((j;k_{j}\Delta c_{j}))}$.
A vector-field ${\displaystyle \mathbf {F} =\sum _{i}F_{i}{\hat {\mathbf {a} }}^{i}}$ is converted to a multi-surface by doing the following for each cell ${\displaystyle (j;k_{j})}$. First compute the total surface vector contained inside the cell: ${\displaystyle \iiint _{\mathbf {q} \in \Omega ((j;k_{j}\Delta c_{j}))}\mathbf {F} (\mathbf {q} )dV\approx \left(\sum _{i}F_{i}((j;k_{j}\Delta c_{j})){\hat {\mathbf {a} }}^{i}((j;k_{j}\Delta c_{j}))\right)V((j;k_{j}\Delta c_{j}))\Delta c_{1}\Delta c_{2}\Delta c_{3}}$. Next separate this total surface vector into components according to the basis ${\displaystyle {\hat {\mathbf {a} }}^{1}}$, ${\displaystyle {\hat {\mathbf {a} }}^{2}}$, and ${\displaystyle {\hat {\mathbf {a} }}^{3}}$: for each ${\displaystyle i\in \{1,2,3\}}$ the coefficient of ${\displaystyle {\hat {\mathbf {a} }}^{i}}$ is ${\displaystyle \iiint _{\mathbf {q} \in \Omega ((j;k_{j}\Delta c_{j}))}F_{i}(\mathbf {q} )dV\approx F_{i}((j;k_{j}\Delta c_{j}))V((j;k_{j}\Delta c_{j}))\Delta c_{1}\Delta c_{2}\Delta c_{3}}$. Next for each ${\displaystyle i\in \{1,2,3\}}$, divide the coefficient of ${\displaystyle {\hat {\mathbf {a} }}^{i}}$ by the area of ${\displaystyle \sigma _{i}((j;k_{j}\Delta c_{j}))}$, which results in approximately ${\displaystyle F_{i}((j;k_{j}\Delta c_{j})){\frac {V((j;k_{j}\Delta c_{j}))}{A_{i}((j;k_{j}\Delta c_{j}))}}\Delta c_{i}}$, and assign this weight to ${\displaystyle \sigma _{i}((j;k_{j}\Delta c_{j}))}$.
A scalar-field ${\displaystyle U}$ is converted to a multi-volume by doing the following for each cell ${\displaystyle (j;k_{j})}$. First compute the total volume contained inside the cell: ${\displaystyle \iiint _{\mathbf {q} \in \Omega ((j;k_{j}\Delta c_{j}))}U(\mathbf {q} )dV\approx U((j;k_{j}\Delta c_{j}))V((j;k_{j}\Delta c_{j}))\Delta c_{1}\Delta c_{2}\Delta c_{3}}$. Next divide this weight by the volume of ${\displaystyle \Omega ((j;k_{j}\Delta c_{j}))}$, which results in approximately ${\displaystyle U((j;k_{j}\Delta c_{j}))}$, and assign this weight to ${\displaystyle \Omega ((j;k_{j}\Delta c_{j}))}$.
Computing various intersections
Computing the intersection of any structure with a multi-volume is trivial matter: Simply multiply the scalar of vector field by the scalar field that denotes the multi-volume. When both structures are denoted by vector fields however, computing the intersection is far less trivial.
Computing path-surface intersections
To save space, the notation ${\displaystyle (j;c_{j})}$ and ${\displaystyle (j;k_{j}\Delta c_{j})}$ will be omitted from the various terms.
Given a multi-path ${\displaystyle \mathbf {C} }$ denoted by vector field ${\displaystyle \mathbf {J} =\sum _{i}J_{i}{\hat {\mathbf {a} }}_{i}}$, and a multi-surface ${\displaystyle \mathbf {S} }$ denoted by vector field ${\displaystyle \mathbf {F} =\sum _{i}F_{i}{\hat {\mathbf {a} }}^{i}}$, the scalar field that denotes the intersection can be computed as follows:
The following computations applies to each cell:
For each ${\displaystyle i\in \{1,2,3\}}$, the weight assigned to ${\displaystyle C_{i}}$ by ${\displaystyle \mathbf {C} }$ is computed as follows: ${\displaystyle \Delta c_{1}\Delta c_{2}\Delta c_{3}\cdot V\cdot J_{i}}$ is the ${\displaystyle {\hat {\mathbf {a} }}_{i}}$ component of the total displacement contained by the current cell. Computing the weight assigned to ${\displaystyle C_{i}}$ requires that this displacement be spread over the length of ${\displaystyle C_{i}}$: ${\displaystyle {\frac {\Delta c_{1}\Delta c_{2}\Delta c_{3}\cdot V\cdot J_{i}}{\Delta c_{i}\cdot l_{i}}}={\frac {V}{l_{i}}}\cdot \Delta c_{i+1}\Delta c_{i+2}\cdot J_{i}}$.
For each ${\displaystyle i\in \{1,2,3\}}$, the weight assigned to ${\displaystyle \sigma _{i}}$ by ${\displaystyle \mathbf {S} }$ is computed as follows: ${\displaystyle \Delta c_{1}\Delta c_{2}\Delta c_{3}\cdot V\cdot F_{i}}$ is the ${\displaystyle {\hat {\mathbf {a} }}^{i}}$ component of the total surface vector contained by the current cell. Computing the weight assigned to ${\displaystyle \sigma _{i}}$ requires that this surface vector be spread over the area of ${\displaystyle \sigma _{i}}$: ${\displaystyle {\frac {\Delta c_{1}\Delta c_{2}\Delta c_{3}\cdot V\cdot F_{i}}{\Delta c_{i+1}\Delta c_{i+2}\cdot A_{i}}}={\frac {V}{A_{i}}}\cdot \Delta c_{i}\cdot F_{i}}$.
The intersection between ${\displaystyle C_{i}}$ and ${\displaystyle \sigma _{i}}$ is the current lattice point with weight ${\displaystyle \left({\frac {V}{l_{i}}}\cdot \Delta c_{i+1}\Delta c_{i+2}\cdot J_{i}\right)\left({\frac {V}{A_{i}}}\cdot \Delta c_{i}\cdot F_{i}\right)}$${\displaystyle ={\frac {V^{2}}{l_{i}A_{i}}}\cdot \Delta c_{1}\Delta c_{2}\Delta c_{3}\cdot J_{i}F_{i}}$.
Aside from the intersections between ${\displaystyle C_{i}}$ and | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 758, "math_alttext": 1, "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": 0.9530879855155945, "perplexity": 326.0511700236698}, "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-2022-05/segments/1642320305420.54/warc/CC-MAIN-20220128043801-20220128073801-00103.warc.gz"} |
http://mathhelpforum.com/algebra/75244-sums.html | # Math Help - sums .
1. ## sums .
Deduce the sum of the series .
(1) $1^2-2^2+3^2-4^2+...+(2n-1)^2-(2n)^2+(2n+1)^2$
(2) $25^2-26^2+27^2-28^2+...+49^2-50^2$
THanks .
2. Originally Posted by thereddevils
Deduce the sum of the series .
(1) $1^2-2^2+3^2-4^2+...+(2n-1)^2-(2n)^2+(2n+1)^2$
$a^2 -b^2 =(a+b)(a-b)$
Hence
$1^2-2^2+3^2-4^2+...+(2n-1)^2-(2n)^2+(2n+1)^2$
$= (1+2)(1-2) +~(2+3)(2-3) + ~......... ( ~( 2n-1) + 2n)~) ( ~( 2n-1)- 2n)~) + (2n+1)^2$
$
= -1[ 3 +7 +...........(4n-1) ] + (2n+1)^2
$
$
=-1[\frac{n}{2}(2\times 3 + (n-1)4)] + (2n+1)^2
$
............................Using AP
$
= -1[ n(2n+1) ] (2n+1)^2
$
$= -1[2n^2 +n] + 4n^2 + 1 +4n$
$= 2n^2 + 3n +1$
$= (2n+1)(n+1)$
(2)
Now for this try it the same way
$
= -1[ 51 +55 +...........(4\times 25 -1) ]
$
$
=-1[\frac{25}{2}(2\times 51 + (13-1)4)]
$ | {"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": 14, "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": 0.9983974695205688, "perplexity": 9072.49120583473}, "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-2015-40/segments/1443736672328.14/warc/CC-MAIN-20151001215752-00036-ip-10-137-6-227.ec2.internal.warc.gz"} |
https://artofproblemsolving.com/wiki/index.php?title=1984_AIME_Problems/Problem_3&oldid=32722 | # 1984 AIME Problems/Problem 3
## Problem
A point is chosen in the interior of such that when lines are drawn through parallel to the sides of , the resulting smaller triangles , , and in the figure, have areas , , and , respectively. Find the area of .
## Solution
By the transversals that go through , all four triangles are similar to each other by the postulate. Also, note that the length of any one side of the larger triangle is equation to the sum of the sides of each of the corresponding sides on the smaller triangles. We use the identity to show that the areas are proportional (the sides are proportional and the angles are equal) Hence, we can write the lengths of corresponding sides of the triangle as . Thus, the corresponding side on the large triangle is , and the area of the triangle 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": 0.9760872721672058, "perplexity": 142.93158936364878}, "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/1634323585186.33/warc/CC-MAIN-20211018000838-20211018030838-00053.warc.gz"} |
http://mathoverflow.net/questions/178872/homotopy-groups-of-fredholm-operators | Homotopy groups of Fredholm operators
If $X$ is separable complex Hilbert space and $\mathcal{F}$ the topological space of Fredholm operators on $X$, then it is well-known, that $$\pi_0(\mathcal{F}) = \mathbb{Z}\, ,$$ i.e. the connected components are classified by the index of the Fredholm operator.
But what is about higher homotopy groups? What is known about $\pi_n(\mathcal{F})$ for $n \in \mathbb{N}$?
-
My answer below is essentially a correction to the accepted answer, which seems to be saying that $\pi_n (\mathcal{F})$ is the unreduced complex K-theory of the sphere $S^n$. For $n=0$ this would give $\pi_0 (\mathcal{F}) = K(S^0) = \mathbb{Z} \oplus \mathbb{Z}$, in contradiction with the index theorem. (Maybe the issue is just notational, but I've never seen $K(X)$ used to mean reduced K-theory.) Is something wrong with my answer or my comments on the accepted answer? It would be nice to have a clear answer to the question. Maybe a tilde should just be added to Paul Siegel's answer? – Dan Ramras Oct 12 '14 at 23:28
It is a theorem (due I think to Atiyah) that $\mathcal{F}$ is the classifying space for the topological K-theory functor: $$[X,\mathcal{F}] \cong K(X)$$ for any space $X$. The isomorphism is given as follows: given a map $T \colon X \to \mathcal{F}$, deform $T$ so that $\dim \ker(T(x))$ is constant and assign $T$ to the K-theory class $[\ker T] - [\text{coker}\, T]$. It follows that $\pi_n(\mathcal{F}) \cong K(S^n)$ which can be calculated using Bott periodicity.
-
Thanks for the answer. So I can use the $K_0$-groups of $S^n$? – Chandler Aug 19 '14 at 17:20
That's correct. – Paul Siegel Aug 19 '14 at 17:38
Hi Paul, Maybe I'm missing something, but I think that $\pi_n (\mathcal{F})$ is isomorphic to the reduced groups $\widetilde{K} (S^n)$, not $K(S^n)$. Unreduced K-theory classifies (unbased) homotopy classes of (unbased) maps out of X, but for homotopy groups we're interested in based maps and based homotopy. Letting $\mathcal{F}_0$ denote the index 0 Fredholm operators (which form one connected component of $\mathcal{F}$), the bijection above restricts to $[X, \mathcal{F}_0] \cong \widetilde{K} (X)$. – Dan Ramras Aug 20 '14 at 4:59
(cont'd) So $\pi_1 (\mathcal{F}_0) = 1$ (for this, it's enough to check that each loop is (unbased) nullhomotopic, which follows from $[S^1, \mathcal{F}_0] = \widetilde{K} (S^1) = 0$) and now $\pi_n (\mathcal{F}) = \pi_n (\mathcal{F}_0) = \langle S^n, \mathcal{F}_0 \rangle = [S^n, \mathcal{F}_0] = \widetilde{K}(S^n)$. Here $\langle , \rangle$ means based homotopy classes of maps, which is the same as unbased homotopy classes when the range is simply connected. – Dan Ramras Aug 20 '14 at 5:02
Oh, and a reference for the bijection in the above answer is the Appendix to Atiyah's book K-theory. – Dan Ramras Aug 20 '14 at 5:06
Atiyah showed that there is a natural bijection $$[X,\mathcal{F}] \cong K(X)$$ whenever $X$ is a compact space. Here the left-hand side is the set of unbased homotopy classes of maps into $\mathcal{F}$. This result is proven in the Appendix to Atiyah's book K-theory.
As I'll explain, it follows from this theorem that there is an isomorphism $$\pi_n (\mathcal{F}) \cong \widetilde{K} (S^n),$$ where $\widetilde{K}$ denotes reduced $K$-theory. So these groups are trivial for $n$ odd and infinite cyclic for $n$ even. Note that all path components of $\mathcal{F}$ are homotopy equivalent, because (as Atiyah explains) there is an associative product $\mathcal{F} \times \mathcal{F} \to \mathcal{F}$ that makes the set of path components of $\mathcal{F}$ into a group (namely the group $[\{*\}, \mathcal{F}] \cong K(\{*\}) \cong \mathbb{Z}$). So it doesn't matter what basepoint we choose for computing homotopy.
Now, to deduce the claimed calculation of homotopy groups, let $\mathcal{F}_0$ denote the index 0 Fredholm operators (which form one connected component of $\mathcal{F}$), Atiyah's bijection restricts to a bijection $[X,\mathcal{F}_0]\cong \widetilde{K}(X)$.
Next, I claim that $\mathcal{F}_0$ is simply connected. First, $\mathcal{F}_0$ is path connected by definition, so we just need to check that $\pi_1 (\mathcal{F}_0)=1$. For this, it's enough to check that each loop is (unbased) nullhomotopic, which follows from $[S^1,\mathcal{F}_0]\cong \widetilde{K}(S^1)=0$.
Now $\pi_n(\mathcal{F})=\pi_n(\mathcal{F}_0)=\langle S^n,\mathcal{F}_0\rangle \cong [S^n,\mathcal{F}_0] = \widetilde{K} (S^n)$. Here $\langle\, ,\rangle$ means based homotopy classes of (based) maps, which is the same as unbased homotopy classes when the range is simply connected (this is proven in Section 4.A of Hatcher's book Algebraic Topology, for instance). | {"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": 0.9463323354721069, "perplexity": 217.66708871388215}, "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-2015-06/segments/1422115860277.59/warc/CC-MAIN-20150124161100-00127-ip-10-180-212-252.ec2.internal.warc.gz"} |
https://ayoucis.wordpress.com/2016/11/02/some-motivation-for-p-adic-hodge-theory/ | # Some motivation for p-adic Hodge theory
These are some notes that I wrote for a learning course at Berkeley–the goal being to understand the statement of the global Langlands conjecture.
The goal of the talk (that these notes were written for) was, specifically, to motivate $p$-adic Hodge theory with an eye, in particular, towards where it might be useful in understanding the statement of Langlands.
These are even less edited than usual, so I profusely apologize for any mistakes. As always, corrections/comments are very welcome!
Notes | {"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": 1, "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": 0.6632218360900879, "perplexity": 1067.42826020503}, "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/1500550967030.98/warc/CC-MAIN-20170728123647-20170728143647-00623.warc.gz"} |
http://ask.sagemath.org/question/45463/solvex-does-not-fully-isolate-x-can-sympy-use-assumetions/ | # solve(x) does not fully isolate x. Can Sympy use assume()tions? edit
This is my worksheet. https://cocalc.com/share/f7766c5e-2f4...
In line 50 i solve the equation describing my physical model for d_k:
d = solve(p_ges == p_ges_rhs, d_k)
But it turns out, that this does not fully isolate d_k at all. Many occurances of d_k remain. How can I help sage along? I really would like to get this fully solved for d_k.
Update: I tried to
assume(d_e >0, d_k > d_m > 0, e_m > e_s > 0)
things about the equation, but to no avail. In Mathematica assume() is just for simplifying quations, is it the same in sage, with no effect on solve()?
Update2:
I did this:
sage: import sympy
sage: x,d_e, d_m, e_m, e_s, v_ges, d_k =var('x d_e d_m e_m e_s v_ges d_k')
sage: sympy.solve(-1/((d_e - x)*e_m) + 1/(e_m*x) + 1/(sqrt((d_e - x)^2 + 4*d_k^2)*d_k*(e_m/d_m + e_s/(d_k - d
....: _m))) - 1/(sqrt(4*d_k^2 + x^2)*d_k*(e_m/d_m + e_s/(d_k - d_m)))-v_ges ,d_k)
[]
sage:
which I found mention of here: https://ask.sagemath.org/question/239...
I guess that means there is no solution for that problem. On IRC I was told that it is highly likely true, if sympy says so. doh.
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Unfortunately, the Sage's assumptions are not passed to sympy and conversely, see trac ticket 24334 and trac ticket 24078.
What you can do as a workaround is to directly pass sympyassumptions, see : https://docs.sympy.org/latest/modules...
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": 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": 0.15417154133319855, "perplexity": 8540.708938577143}, "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/1618038062492.5/warc/CC-MAIN-20210411115126-20210411145126-00313.warc.gz"} |
https://repository.uantwerpen.be/link/irua/108581 | Publication
Title
A layered framework to study collaboration as a form of knowledge sharing and diffusion
Author
Abstract
Collaboration can be described using layered systems such as the articleauthorinstitutecountry structure. These structures can be considered cascades orchains of bipartite networks. We introduce a framework for characterizing and studyingthe intensity of collaboration between entities at a given level (e.g., between institutions).Specifically, we define the notions of significant, essential and vital nodes, and significant,essential and vital sub paths to describe the spread of knowledge through collaboration insuch systems. Based on these notions, we introduce relative and absolute proper essentialnode (PEN) centrality as indicators of a nodes importance for diffusion of knowledgethrough collaboration.We illustrate these concepts in an illustrative example and show how they can be appliedusing a small real-world example. Since collaboration implies knowledge sharing, it can beconsidered a special form of knowledge diffusion.
Language
English
Source (journal)
Journal of informetrics. - Amsterdam
Publication
Amsterdam : 2013
ISSN
1751-1577
Volume/pages
7:3(2013), p. 651-664
ISI
000323859700009
Full text (Publisher's DOI)
Full text (publisher's version - intranet only)
UAntwerpen
Faculty/Department Research group Publication type Subject Affiliation Publications with a UAntwerp address | {"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": 0.9614003896713257, "perplexity": 5691.063584171105}, "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-2017-34/segments/1502886116921.7/warc/CC-MAIN-20170822221214-20170823001214-00499.warc.gz"} |
https://ma.mathforcollege.com/chapter-06-gauss-elimination-with-partial-pivoting-example-part-3-of-3/ | # Chapter 06 Gauss Elimination with Partial Pivoting Example Part 3 of 3
##### Gaussian Elimination (CHAPTER 6)
###### Topic
Gauss Elimination with Partial Pivoting: Example Part 3 of 3
###### Description
Learn how Gaussian Elimination with Partial Pivoting is used to solve a set of simultaneous linear equations through an example.
This video teaches you how Gaussian Elimination with Partial Pivoting is used to solve a set of simultaneous linear equations through an example.
###### All Videos for this Topic
• Naive Gaussian elimination: Theory: Part 1 of 2 [YOUTUBE 10:27] [TRANSCRIPT]
• Naive Gaussian elimination: Theory: Part 2 of 2 [YOUTUBE 2:22] [TRANSCRIPT]
• Naive Gauss Elimination Method: Example: Part 1 of 2 (Forward Elimination) [YOUTUBE 10:49] [TRANSCRIPT]
• Naive Gauss Elimination Method: Example: Part 2 of 2 (Back Substitution) [YOUTUBE 6:40] [TRANSCRIPT]
• Pitfalls of Naive Gauss Elimination Method: [YOUTUBE 7:20] [TRANSCRIPT]
• Naive Gauss Elimination: Round-off Error Issues: Example: Part 1 of 3 [YOUTUBE 7:20] [TRANSCRIPT]
• Naive Gauss Elimination: Round-off Error Issues: Example: Part 2 of 3 [YOUTUBE 7:40] [TRANSCRIPT]
• Naive Gauss Elimination: Round-off Error Issues: Example: Part 3 of 3 [YOUTUBE 8:07] [TRANSCRIPT]
• Gaussian Elimination With Partial Pivoting: Theory [YOUTUBE 10:39] [TRANSCRIPT]
• Gaussian Elimination With Partial Pivoting: Example: Part 1 of 3 (Forward Elimination) [YOUTUBE 7:15] [TRANSCRIPT]
• Gaussian Elimination With Partial Pivoting: Example: Part 2 of 3 (Forward Elimination) [YOUTUBE 10:08] [TRANSCRIPT]
• Gaussian Elimination With Partial Pivoting: Example: Part 3 of 3 (Back Substitution) [YOUTUBE 6:18] [TRANSCRIPT]
• Gaussian Elimination With Partial Pivoting: Round-off Error Issues: Example: Part 1 of 3 [YOUTUBE 8:58] [TRANSCRIPT]
• Gaussian Elimination With Partial Pivoting: Round-off Error Issues: Example: Part 2 of 3 [YOUTUBE 8:17] [TRANSCRIPT]
• Gaussian Elimination With Partial Pivoting: Round-off Error Issues: Example: Part 3 of 3 [YOUTUBE 5:48] [TRANSCRIPT]
• Determinant of a Matrix Using Forward Elimination Method: Background [YOUTUBE 5:17] [TRANSCRIPT]
• Determinant of a Matrix Using Forward Elimination Method: Example [YOUTUBE 10:07] [TRANSCRIPT]
###### Complete Resources
Get in one place the following: a textbook chapter, a PowerPoint presentation, individual YouTube lecture videos, multiple-choice questions, and problem sets on Gaussian Elimination. | {"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": 0.8342247605323792, "perplexity": 9485.53083742253}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-14/segments/1679296945242.64/warc/CC-MAIN-20230324020038-20230324050038-00608.warc.gz"} |
http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1000092?imageURI=info:doi/10.1371/journal.pcbi.1000092.g017 | Review
# The Dynamic Brain: From Spiking Neurons to Neural Masses and Cortical Fields
• Gustavo.Deco@upf.edu
Affiliation: Institució Catalana de Recerca i Estudis Avançats (ICREA), Universitat Pompeu Fabra, Department of Technology, Computational Neuroscience, Barcelona, Spain
X
• Affiliations: Theoretical Neuroscience Group, Institut Sciences de Mouvement, Marseille, France, Center for Complex Systems and Brain Sciences, Department of Physics, Florida Atlantic University, Boca, Florida, United States of America
X
• Affiliations: School of Physics, University of Sydney, Sydney, New South Wales, Australia, Brain Dynamics Center, Westmead Millennium Institute, Westmead Hospital and University of Sydney, Westmead, New South Wales, Australia, Faculty of Medicine, University of Sydney, Sydney, New South Wales, Australia
X
• Affiliations: School of Psychiatry, University of New South Wales, Sydney, and The Black Dog Institute, Randwick, New South Wales, Australia, School of Physics, University of Sydney, Sydney, New South Wales, Australia
X
• Affiliation: Wellcome Trust Centre for Neuroimaging, University College London, London, United Kingdom
X
• Published: August 29, 2008
• DOI: 10.1371/journal.pcbi.1000092
## Abstract
The cortex is a complex system, characterized by its dynamics and architecture, which underlie many functions such as action, perception, learning, language, and cognition. Its structural architecture has been studied for more than a hundred years; however, its dynamics have been addressed much less thoroughly. In this paper, we review and integrate, in a unifying framework, a variety of computational approaches that have been used to characterize the dynamics of the cortex, as evidenced at different levels of measurement. Computational models at different space–time scales help us understand the fundamental mechanisms that underpin neural processes and relate these processes to neuroscience data. Modeling at the single neuron level is necessary because this is the level at which information is exchanged between the computing elements of the brain; the neurons. Mesoscopic models tell us how neural elements interact to yield emergent behavior at the level of microcolumns and cortical columns. Macroscopic models can inform us about whole brain dynamics and interactions between large-scale neural systems such as cortical regions, the thalamus, and brain stem. Each level of description relates uniquely to neuroscience data, from single-unit recordings, through local field potentials to functional magnetic resonance imaging (fMRI), electroencephalogram (EEG), and magnetoencephalogram (MEG). Models of the cortex can establish which types of large-scale neuronal networks can perform computations and characterize their emergent properties. Mean-field and related formulations of dynamics also play an essential and complementary role as forward models that can be inverted given empirical data. This makes dynamic models critical in integrating theory and experiments. We argue that elaborating principled and informed models is a prerequisite for grounding empirical neuroscience in a cogent theoretical framework, commensurate with the achievements in the physical sciences.
### Introduction
The brain appears to adhere to two fundamental principles of functional organization, functional integration and functional specialization, where the integration within and among specialized areas is mediated by connections among them. The distinction relates to that between localisationism and connectionism that dominated thinking about cortical function in the nineteenth century. Since the early anatomic theories of Gall, the identification of a particular brain region with a specific function has become a central theme in neuroscience. In this paper, we address how distributed and specialized neuronal responses are realized in terms of microscopic brain dynamics; we do this by showing how neuronal systems, with many degrees of freedom, can be reduced to lower dimensional systems that exhibit adaptive behaviors.
It is commonly accepted that the information processing underlying brain functions, like sensory, motor, and cognitive functions, is carried out by large groups of interconnected neurons [1][4]. Neurons are the cells responsible for encoding, transmitting, and integrating signals originating inside or outside the nervous system. The transmission of information within and between neurons involves changes in the so-called resting membrane potential, the electrical potential of the neurons at rest, when compared to the extracellular space. The inputs one neuron receives at the synapses from other neurons cause transient changes in its resting membrane potential, called postsynaptic potentials. These changes in potential are mediated by the flux of ions between the intracellular and extracellular space. The flux of ions is made possible through ion channels present in the membrane. The ion channels open or close depending on the membrane potential and on substances released by the neurons, namely neurotransmitters, which bind to receptors on the cell's membrane and hyperpolarize or depolarize the cell. When the postsynaptic potential reaches a threshold, the neuron produces an impulse. The impulses or spikes, called action potentials, are characterized by a certain amplitude and duration and are the units of information transmission at the interneuronal level. Information is thought to be encoded in terms of the frequency of the action potentials, called spiking or firing rate (i.e., rate coding), as well as in the timing of action potentials (i.e., temporal coding).
One way to investigate the biological basis of information processing in the brain is to study the response of neurons to stimulation. This can be done in experimental animals using implanted electrodes to record the rates and timing of action potentials. However, this invasive approach is generally not possible in humans. To study brain function in humans, techniques allowing the indirect study of neuronal activity have been developed. An example is functional magnetic resonance imaging (fMRI), measuring regional changes in metabolism and blood flow associated with changes in brain activity. This approach to measuring regional differences in brain activity is possible because at a macroscopic level the cortex is organized into spatially segregated regions known to have functionally specialized roles. A technique such as fMRI allows the mapping of brain regions associated with a particular task or task component.
Understanding the fundamental principles underlying higher brain functions requires the integration of different levels of experimental investigation in cognitive neuroscience (from single neurons, neuroanatomy, neurophysiology, and neuroimaging, to neuropsychology and behavior) via a unifying theoretical framework that captures the neural dynamics inherent in the elaboration of cognitive processes. In this paper, we review and integrate a variety of computational approaches that have been used to characterize the dynamics of the cortex, as evidenced at different levels of measurement.
The paper is structured as follows. The central theme of this review is that the activity in populations of neurons can be understood by reducing the degrees of freedom from many to few, hence resolving an otherwise intractable computational problem. The most striking achievement in this regard is the reduction of a large population of spiking neurons to a distribution function describing their probabilistic evolution—that is, a function that captures the likely distribution of neuronal states at a given time. In turn, this can be further reduced to a single variable describing the mean firing rate. This reduction is covered first, in the next section. In the section entitled Neural Modes and Masses, we return to the full probability distribution function and show how it can be represented by a set of scalars that parameterize it parsimoniously. These parameters are equivalent to the moments of the distribution. In many instances, a few—possibly even one (equivalent to the center of mass)—are sufficient to summarize activity. These are known as Neural Mass Models. These models capture the dynamics of a neuronal population. Naturally, it is useful to understand how neuronal activity unfolds on the spatially continuous cortical sheet. This can be addressed with neural field models; involving differential operators with both temporal and spatial terms. That is, neuronal activity depends on its current state as well as spatial gradients, which allow its spread horizontally across the cortical surface. These models are covered in the Neural Field Models section. In Numerical Simulations: Ensemble Activity from Neuronal to Whole Brain Scale, we provide numerical simulations of neuronal ensemble dynamics across a hierarchy of spatial and temporal scales. At the microscopic scale, we simulate an entire array of spiking neurons in response to a sensory-evoked synaptic current. By comparing the response to that of a mesoscopic neural mass model, we show what is gained and what is lost by abstracting to a more tractable set of evolution equations. The spread of activity across the cortical surface, in a neural field model, is also illustrated. Finally, in the section entitled Cognitive and Clinical Applications, we illustrate applications of neural ensemble modeling in health and disease; namely, decision-making, auditory scene analysis, and absence seizures.
A summary of the notation for all the main dynamical variables and physiological parameters is given in Table 1.
### Mean-Field Models
This section provides an overview of mean-field models of neuronal dynamics and their derivation from models of spiking neurons. These models have a long history spanning a half-century (e.g., [5]) and are formulated using concepts from statistical physics. In this section, we try to clarify some key concepts and show how they relate to each other. Models are essential for neuroscience, in the sense that the most interesting questions pertain to neuronal mechanisms and processes that are not directly observable. This means that questions about neuronal function are generally addressed by inference on models or their parameters, where the model links neuronal processes that are hidden from our direct observation. Broadly speaking, models are used to generate data, to study emergent behaviors, or they can be used as forward or observation models, which are inverted given empirical data. This inversion allows one to select the best model (given some data) and make probabilistic comments about the parameters of that model. Mean-field models are suited to data which reflect the behavior of a population of neurons, such as the electroencephalogram (EEG), magnetoencephalogram (MEG), and fMRI. The most prevalent models of neuronal populations or ensembles are based upon something called the mean-field approximation. The mean-field approximation is used extensively in statistical physics and is essentially a technique that finesses an otherwise computationally or analytically intractable problem. An exemplary approach, owing to Boltzmann and Maxwell, is the approximation of the motion of molecules in a gas by mean-field terms such as temperature and pressure.
##### Ensemble density models.
Ensemble models attempt to model the dynamics of large (theoretically infinite) populations of neurons. Any single neuron could have a number of attributes; for example, post-synaptic membrane depolarization, V, capacitive current, I, or the time since the last action potential, T. Each attribute induces a dimension in the phase space of a neuron; in our example the phase space would be three dimensional and the state of each neuron would correspond to a point ν = {V,I,T} Єℜ3 or particle in phase space. Imagine a very large number of neurons that populate phase space with a density p(ν,t). As the state of each neuron evolves, the points will flow through phase space, and the ensemble density p(ν,t) will evolve until it reaches some steady state or equilibrium. p(ν,t) is a scalar function returning the probability density at each point in phase space. It is the evolution of the density per se that is characterized in ensemble density methods. These models are particularly attractive because the density dynamics conform to a simple equation: the Fokker-Planck equation(1)
This equation comprises a flow and a dispersion term; these terms embed the assumptions about the dynamics (phase flow, f(ν,t)) and random fluctuations (dispersion, D(ν,t)) that constitute our model at the neuronal level. This level of description is usually framed as a (stochastic) differential equation (Langevin equation) that describes how the states evolve as functions of each other and some random fluctuations with(2)
where, D = ½σ2 and ω is a standard Wiener process; i.e., w(t)−w(tt)~N(0, Δt). Even if the dynamics of each neuron are complicated, or indeed chaotic, the density dynamics remain simple, linear, and deterministic. In fact, we can write the density dynamics in terms of a linear operator or Jacobian Q(3)
In summary, for any model of neuronal dynamics, specified as a stochastic differential equation, there is a deterministic linear equation that can be integrated to generate ensemble dynamics. In what follows, we will explain in detail the arguments that take us from the spiking behavior of individual neurons to the mean-field dynamics described by the Fokker-Planck equation. We will consider the relationship between density dynamics and neural mass models and how these can be extended to cover spatiotemporal dynamics in the brain.
##### From spiking neurons to mean-field models.
The functional specialization of the brain emerges from the collective network dynamics of cortical circuits. The computational units of these circuits are spiking neurons, which transform a large set of inputs, received from different neurons, into an output spike train that constitutes the output signal of the neuron. This means that the spatiotemporal spike patterns produced by neural circuits convey information among neurons; this is the microscopic level on which the brain's representations and computations rest [6]. We assume that the nonstationary temporal evolution of the spiking dynamics can be captured by one-compartment, point-like models of neurons, such as the leaky integrate-and-fire (LIF) model [7] used below. Other models relevant for systems neuroscience can be found in [4],[8],[9]. In the LIF model, each neuron i can be fully described in terms of a single internal variable, namely the depolarization Vi(t) of the neural membrane. The basic circuit of a LIF model consists of a capacitor, C, in parallel with a resistor, R, driven by a synaptic current (excitatory or inhibitory postsynaptic potential, EPSP or IPSP, respectively). When the voltage across the capacitor reaches a threshold θ, the circuit is shunted (reset) and a δ pulse (spike) is generated and transmitted to other neurons. The subthreshold membrane potential of each neuron evolves according to a simple RC circuit, with a time constant τ = RC given by the following equation:(4)
where Ii(t) is the total synaptic current flow into the cell i and VL is the leak or resting potential of the cell in the absence of external afferent inputs. In order to simplify the analysis, we neglect the dynamics of the afferent neurons (see [10] for extensions considering detailed synaptic dynamics such as AMPA, NMDA, and GABA). The total synaptic current coming into the cell i is therefore given by the sum of the contributions of δ-spikes produced at presynaptic neurons. Let us assume that N neurons synapse onto cell i and that Jij is the efficacy of synapse j, then the total synaptic afferent current is given by(5)
where is the emission time of the kth spike from the jth presynaptic neuron. The subthreshold dynamical Equation 4, given the input current (from Equation 5), can be integrated, and yields(6,7)
if the neuron i is initially (t = 0) at the resting potential (Vi(0) = VL). In Equation 7, H(t) is the Heaviside function (H(t) = 1 if t>0, and H(t) = 0 if t<0). Thus, the incoming presynaptic δ-pulse from other neurons is basically low-pass filtered to produce an EPSP or IPSP in the post-synaptic cell. Nevertheless, the integrate-and-fire (IF) model is not only defined by the subthreshold dynamics but includes a reset after each spike generation, which makes the whole dynamics highly nonlinear. In what follows, we present a theoretical framework which is capable of dealing with this.
##### The population density approach.
Realistic neuronal networks comprise a large number of neurons (e.g., a cortical column has O(104)−O(108) neurons) which are massively interconnected (on average, a neuron makes contact with O(104) other neurons). The underlying dynamics of such networks can be described explicitly by the set of coupled differential equations (Equation 4) above. Direct simulations of these equations yield a complex spatiotemporal pattern, covering the individual trajectory of the internal state of each neuron in the network. This type of direct simulation is computationally expensive, making it very difficult to analyze how the underlying connectivity relates to various dynamics. In fact, most key features of brain operation seem to emerge from the interplay of the components; rather than being generated by each component individually. One way to overcome these difficulties is by adopting the population density approach, using the Fokker-Planck formalism (e.g., [11]). As noted above, the Fokker-Planck equation summarizes the flow and dispersion of states over phase space in a way that is a natural summary of population dynamics in genetics (e.g., [12]) and neurobiology (e.g., [13],[14]).
In what follows, we derive the Fokker-Planck equation for neuronal dynamics that are specified in terms of spiking neurons. This derivation is a little dense but illustrates the approximating assumptions and level of detail that can be captured by density dynamics. The approach we focus on was introduced by [15] (see also [16],[17]). In this approach, individual IF neurons are grouped together into populations of statistically similar neurons. A statistical description of each population is given by a probability density function that expresses the distribution of neuronal states (i.e., membrane potential) over the population. In general, neurons with the same state V(t) at a given time t have a different history because of random fluctuations in the input current I(t). The main source of randomness is from fluctuations in recurrent currents (resulting from “quenched” randomness in the connectivity and transmission delays) and fluctuations in the external currents. The key assumption in the population density approach is that the afferent input currents impinging on neurons in one population are uncorrelated. Thus, neurons sharing the same state V(t) in a population are indistinguishable. Consequently, the dynamics are described by the evolution of the probability density function:(8)
which expresses the population density, which is the fraction of neurons at time t that have a membrane potential V(t) in the interval [ν,ν+]. The evolution of the population density is given by the Chapman-Kolmogorov equation(9)
where ρ(ε|ν) = Prob{V(t+dt) = ν+ε|V(t) = ν} is the conditional probability that generates an infinitesimal change ε = V(t+dt)−V(t) in the infinitesimal interval dt. The Chapman-Kolmogorov equation can be written in a differential form by performing a Taylor expansion in p(ν′,t) ρ(ε|ν′) around ν′ = ν; i.e.,(10)
In the derivation of the last equation, we have assumed that p(ν′,t) and ρ(ε| ν′) are infinitely many times differentiable in ν. Inserting this expansion in Equation 9, and replacing the time derivative in ν′ by the equivalent time derivative in ν, we obtain(11,12)
where 〈…〉ν denotes the average with respect to ρ(ε| ν) at a given ν. Finally, taking the limit for dt → 0, we obtain:(13)
Equation 13 is known as the Kramers-Moyal expansion of the original integral Chapman-Kolmogorov equation (Equation 9). It expresses the time evolution of the population density in differential form.
##### The diffusion approximation.
The temporal evolution of the population density as given by Equation 13 requires the moments 〈εkυ due to the afferent current during the interval dt. These moments can be calculated by the mean-field approximation. In this approximation, the currents impinging on each neuron in a population have the same statistics, because as we mentioned above, the history of these currents is uncorrelated. The mean-field approximation entails replacing the time-averaged discharge rate of individual cells with a common time-dependent population activity (ensemble average). This assumes ergodicity for all neurons in the population. The mean-field technique allows us to discard the index denoting the identity of any single neuron and express the infinitesimal change, dV(t), in the membrane potential of all neurons as:(14)
where N is the number of neurons, and Q(t) is the mean population firing rate. This is determined by the proportion of active neurons by counting the number of spikes nspikes(t,t+dt) in a small time interval dt and dividing by N and by dt [18]; i.e.,(15)
In Equation 14, 〈JJ denotes the average of the synaptic weights in the population. The moments of the infinitesimal depolarization, ε = dV(t), can now be calculated easily from Equation 14. The first two moments in the Kramers-Moyal expansion are called drift and diffusion coefficients, respectively, and they are given by:(16)
(17)
In general, keeping only the leading term linear in dt, it is easy to prove that for k>1,(18)
and hence,(19)
The diffusion approximation arises when we neglect high-order (k>2) terms. The diffusion approximation is exact in the limit of infinitely large networks, i.e., N → ∞, if the synaptic efficacies scale appropriately with network size, such that J → 0 but NJ2const. In other words, the diffusion approximation is appropriate, if the minimal kick step, J, is very small but the overall firing rate is very large. In this case, all moments higher than two become negligible, in relation to the drift (μ) and diffusion (σ2) coefficients.
The diffusion approximation allows us to omit all higher orders k>2 in the Kramers-Moyal expansion. The resulting differential equation describing the temporal evolution of the population density is called the Fokker-Planck equation, and reads(20)
In the particular case that the drift is linear and the diffusion coefficient, σ2(t), is given by a constant, the Fokker-Planck equation describes a well-known stochastic process called the Ornstein-Uhlenbeck process [19]. Thus, under the diffusion approximation, the Fokker-Planck equation (Equation 20) expresses an Ornstein-Uhlenbeck process. The Ornstein-Uhlenbeck process describes the temporal evolution of the membrane potential V(t) when the input afferent currents are given by(21)
where ω(t) is a white noise process. Under the diffusion approximation, Equation 21 can also be interpreted (by means of the Central Limit Theorem), as the case in which the sum of many Poisson processes (Equation 5) becomes a normal random variable with mean μ(t) and variance σ2.
##### The mean-field model.
The simulation of a network of IF neurons allows one to study the dynamical behavior of the neuronal spiking rates. Alternatively, the integration of the non-stationary solutions of the Fokker-Planck equation (Equation 20) also describes the dynamical behavior of the network, and this would allow the explicit simulation of neuronal and cortical activity (single cells, EEG, fMRI) and behavior (e.g., performance and reaction time). However, these simulations are computationally expensive and their results probabilistic, which makes them unsuitable for systematic explorations of parameter space. However, the stationary solutions of the Fokker-Planck equation (Equation 20) represent the stationary solutions of the original IF neuronal system. This allows one to construct bifurcation diagrams to understand the nonlinear mechanisms underlying equilibrium dynamics. This is an essential role of the mean-field approximation: to simplify analyses through the stationary solutions of the Fokker-Planck equation for a population density under the diffusion approximation (Ornstein-Uhlenbeck process) in a self-consistent form. In what follows, we consider stationary solutions for ensemble dynamics.
The Fokker-Planck equation describing the Ornstein-Uhlenbeck process, with μ = 〈JJ NQ(t) and σ2 = 〈J2J NQ(t), can be rewritten as a continuity equation:(22)
where F is the flux of probability defined as follows:(23)
The stationary solution should satisfy the following boundary condition:(24)
and(25)
which expresses the fact that the probability current at threshold gives, by a self-consistent arguments, the average firing rate, Q, of the population. Furthermore, at ν→−4 the probability density vanishes fast enough to be integrable; i.e.,(26)
and(27)
In addition, the probability mass leaving the threshold at time t has to be re-injected at the reset potential at time t+tref (where tref is the refractory period of the neurons), which can be accommodated by rewriting Equation 22 as follows:(28)
where H(.) is the Heaviside function. The solution of Equation 28 satisfying the boundary conditions (Equations 24–27) is:(29)
Taking into account the fraction of neurons, Qtref, in the refractory period and the normalization of the mass probability,(30)
Finally, substituting Equation 29 into Equation 30, and solving for Q, we obtain the population transfer function, φ, of Ricciardi [13]:(31)
where .
The stationary dynamics of each population can be described by the population transfer function, which provides the average population rate as a function of the average input current. This can be generalized easily for more than one population. The network is partitioned into populations of neurons whose input currents share the same statistical properties and fire spikes independently at the same rate. The set of stationary, self-reproducing rates, Qi, for different populations, i, in the network can be found by solving a set of coupled self-consistency equations, given by:(32)
To solve the equations defined by Equation 32 for all i, we integrate the differential equation below, describing the approximate dynamics of the system, which has fixed-point solutions corresponding to Equation 32:(33)
This enables a posteriori selection of parameters, which induce the emergent behavior that we are looking for. One can then perform full nonstationary simulations using these parameters in the full IF scheme to generate true dynamics. The mean-field approach ensures that these dynamics will converge to a stationary attractor that is consistent with the steady-state dynamics we require [10],[20]. In our case, the derived transfer function, φ, corresponds consistently to the assumptions of the simple LIF model described in the From Spiking-Neurons to Mean-Field Models section. Further extension for more complex and realistic models are possible. For example, an extended mean-field framework, which is consistent with the IF and realistic synaptic equations that considers both the fast and slow glutamatergic excitatory synaptic dynamics (AMPA and NMDA) and the dynamics of GABA inhibitory synapses, can be found in [10]. Before turning to neural mass models, we consider some applications of mean-field modeling that will be reprised in the last section.
##### Competition and cooperation.
How are different cortical representations integrated to form a coherent stream of perception, cognition, and action? The brain is characterized by a massive recurrent connectivity between cortical areas, which suggests that integration of partial representations might be mediated by cross talk via interareal connections. Based on this view [21], and neurophysiological evidence [22], it has been hypothesized that each cortical area represents a set of alternative hypotheses, encoded in the activities of cell assemblies. Representations of conflicting hypotheses compete with each other; however, each area represents only a part of the environment or internal state. In order to arrive at a coherent global representation, different cortical areas bias each others' internal representations by communicating their current states to other areas, thereby favoring certain sets of local hypotheses over others. By recurrently biasing each others' competitive internal dynamics, the neocortical system arrives at a global representation in which each area's state is maximally consistent with those of the other areas. This view has been referred to as the biased-competition hypothesis. In addition to this competition-centered view, a cooperation-centered picture of brain dynamics, where global representations find their neural correlate in assemblies of coactivated neurons, has been formulated [21],[23]. Coactivation is achieved by increased connectivity among the members of each assembly. Reverberatory communication between the members of the assembly then leads to persistent activation to engender temporally extended representations.
The mean-field approach has been applied to biased-competition and cooperation networks and has been used to model single neuronal responses, fMRI activation patterns, psychophysical measurements, effects of pharmacological agents, and effects of local cortical lesions [6], [24][33]. In the section entitled Cognitive and Clinical Applications, we present one of these examples, in the context of decision-making.
### Neural Modes and Masses
The Fokker-Planck equation, (Equation 1), is a rather beautiful and simple expression that prescribes the evolution of ensemble dynamics, given any initial conditions and equations of motion that embed our neuronal model. However, it does not specify how to encode or parameterize the density itself. There are several approaches to this. These include binning the phase space and using a discrete approximation to a continuous density. However, this can lead to a vast number of differential equations, especially if there are multiple states for each population. One solution to this is to reduce the number of states (i.e., dimension of the phase space) to render the integration of the Fokker-Planck more tractable. One elegant example of this reduction can be found in [34]. Here, population dynamics are described by a set of one-dimensional partial differential equations in terms of the distributions of the refractory density (where the refractory state is defined by the time elapsed since the last action potential). This furnishes realistic simulations of the population activity of hippocampal pyramidal neurons, based on something known as the refractory density equation and a single-neuron threshold model. The threshold model is a conductance-based model with adaptation-providing currents.
An alternative approach to dimension reduction is to approximate the ensemble densities with a linear superposition of probabilistic modes or basis functions η(ν) that cover phase space. In this section, we overview this modal approach to ensemble dynamics, initially in the general setting and then in the specific case, where the dynamics can be captured by the activity of a single node.
##### Moments and modes of density dynamics.
Instead of characterising the density dynamics explicitly, one can summarize it in terms of coefficients parameterising the expression of modes:(34)
where μ = ηp, η being the generalized inverse of the matrix encoding the basis set of modes.
A useful choice for the basis functions are the eigenfunctions (i.e., eigen vectors) of the Fokker-Planck operator, Q [17], where = ηλη = λ and λ is a leading-diagonal matrix of eigenvalues. Because the Fokker-Planck operator conserves probability mass, all its real eigenvalues are zero or negative. In the absence of mean-field effects, the biorthogonality of the eigenfunctions effectively uncouples the dynamics of the modes they represent(35)
The last expression means that, following perturbation, each mode decays exponentially, to disclose the equilibrium mode, η0, that has a zero eigenvalue. Because the eigenvalues are complex (due to the fact that the Jacobian is not symmetric), the decay is oscillatory in nature, with a frequency that is proportional to the imaginary part of the eigenvalue and a rate constant proportional to the real part. The key thing about this parameterisation is that most modes will decay or dissipate very quickly. This means we only have to consider a small number of modes, whose temporal evaluation can be evaluated simply with(36)
See [35] for an example of this approach, in which the ensuing nonlinear differential equations were used in a forward model of observed data. In summary, we can formulate the ensemble dynamics of any neuronal system, given its equations of motion, using the equation above. This specifies how the coefficients of probability modes would evolve from any initial state or following a perturbation to the neuronal states. It furnishes a set of coupled differential equations that can be integrated to form predictions of real data or to generate emergent behaviors. We have introduced parameterisation in terms of probability modes because it provides a graceful link to neural mass models.
##### Neural mass models.
Neural mass models can be regarded as a special case of ensemble density models, where we summarize our description of the ensemble density with a single number. Early examples can be found in the work of [5],[36],[37]. The term mass action model was coined by [38] as an alternative to density dynamics. These models can be motivated as a description in terms of the expected values of neuronal states, μ, under the assumption that the equilibrium density has a point mass (i.e., a delta function). This is one perspective on why these simple mean-field models are called neural mass models. In short, we replace the full ensemble density with a mass at a particular point and then summarize the density dynamics by the location of that mass. What we are left with is a set of nonlinear differential equations describing the evolution of this mode. But what have we thrown away? In the full nonlinear Fokker-Planck formulation, different phase functions or probability density moments could couple to each other; both within and between populations or ensembles. For example, this means that the average depolarisation in one ensemble could be affected by the dispersion or variance of depolarisation in another. In neural mass models, we ignore this possibility because we can only couple the expectations or first moments. There are several devices that are used to compensate for this simplification. Perhaps the most ubiquitous is the use of a sigmoid function, ς(μν), relating expected depolarisation to expected firing rate [38]. This implicitly encodes variability in the postsynaptic depolarisation, relative to the potential at which the neuron would fire. A common form for neural mass equations of motion posits a second order differential equation for expected voltage, or, equivalently, two coupled first order equations, μ = {μν,μi} where(37)
Here μa can be regarded as capacitive current. The constant γ controls the rise time of voltage, in response to inputs (see also the Neural Field Models section). These differential equations can be expressed as a convolution of inputs, ς(μν), to give the expected depolarization, μν; i.e., the convolution of the input signal with an impulse response kernel W(t)(38)
The input is commonly construed to be a firing rate (or pulse density) and is a sigmoid function, ς, of mean voltage of the same or another ensemble. The coupling constant, κ, scales the amplitude of this mean-field effect. This form of neural mass model has been used extensively to model electrophysiological recordings (e.g., [39][41]) and has been used recently as the basis of a generative model for event-related potentials that can be inverted using real data [42].
In summary, neural mass models are special cases of ensemble density models that are furnished by ignoring all but the expectation or mean of the ensemble density. This affords a considerable simplification of the dynamics and allows one to focus on the behavior of a large number of ensembles, without having to worry about an explosion in the number of dimensions or differential equations one has to integrate. The final sort of model we will consider is the generalisation of neural mass models that allow for states that are functionals of position on the cortical sheet. These are referred to as neural field models and are discussed in the following sections.
### Neural Field Models
The density dynamics and neural mass models above covered state the attributes of point processes, such as EEG sources, neurons, or neuronal compartments. An important extension of these models speaks to the fact that neuronal dynamics play out on a spatially extended cortical sheet. In other words, states like the depolarisation of an excitatory ensemble in the granular layer of cortex can be regarded as a continuum or field, which is a function of space, x, and time, μ(t)→μ(x,t). This allows one to formulate the dynamics of the expected field in terms of partial differential equations in space and time. These are essentially wave equations that accommodate lateral interactions. Although we consider neural field models last, they were among the first mean-field models of neuronal dynamics [43],[44]. Key forms for neural field equations were proposed and analysed by [45][47]. These models were generalized by [48],[49] who, critically, considered delays in the propagation of spikes over space. The introduction of propagation delays leads to dynamics that are very reminiscent of those observed empirically.
Typically, neural field models can be construed as a spatiotemporal convolution (c.f., Equation 38) that can be written in terms of a Green's function; e.g.,(39)
where |xx′| is the distance between the spatial locations x and x′, c is the characteristic speed of spike propagation, and γ reflects the spatial decay of lateral interactions. The corresponding second order equations of motion are a neural wave equation (see [48],[49] and below)(40)
where γ = c/r and ▽2 is the Laplacian. The formal similarity with the neural mass model in (37) is self-evident. These sorts of models have been extremely useful in modeling spatiotemporally extended dynamics (e.g., [50][53]). The generic form of neural field dynamics can be written as (see also [53]):(41)
where μ = μ(x,t) is the neural field, capturing the neural mass activity at time t and position x. f(μ) captures the local dynamics of the neural field, and Tc = t−|xx′|/c is the time delay due to signal propagation. h is a constant threshold value and Γ is the spatial domain of the neural field, where x Є Γ = [0,L]. The kernel W(|xx′|) denotes the connectivity function, which is translationally invariant in space, i.e., the probability that two neural masses are connected depends only on the distance between them. If we neglect the local dynamics f(μ), , and use an exponential kernel as in Equation 39, we recover Equations 39 and 40. This approximation is valid when the axonal delays contribute mostly to the dynamics, for instance in large-scale networks, when the local dynamics are much faster than the network dynamics. It is easy to show that most realistic connectivity kernels provide a neural wave equation like Equation 40; this is due to the fact that the connectivity must remain integrable. As above, the parameter c is the propagation velocity of action potentials traveling down an axon. If f(μ) = −ζ μ, then the constant ζ>0Єℜ represents the growth rate of the neural mass. α>0 is a scaling constant. Under instantaneous interactions, c→∞, single population models with locally excitatory and laterally inhibitory connectivity can support global periodic stationary patterns in one dimension as well as single or multiple localized solutions (bumps and multi-bumps) [47]. This class of models are also sometimes referred to as continuous attractor neural networks (CANN). When the firing rate, ς, is a Heaviside step function, [45] was able to construct an explicit one-bump solution of the form(42)
where the value a corresponds to the width of the bump. Amari also identified criteria to determine if only one bump, multiple bumps, or periodic solutions exist and if they are stable. This simple mathematical model can be extended naturally to accommodate multiple populations and cortical sheets, spike frequency adaptation, neuromodulation, slow ionic currents, and more sophisticated forms of synaptic and dendritic processing as described in the review articles [4],[54],[55]. Spatially localized bump solutions are equivalent to persistent activity and have been linked to working memory in prefrontal cortex [56],[57]. During behavioral tasks, this persistent elevated neuronal firing can last for tens of seconds after the stimulus is no longer present. Such persistent activity appears to maintain a representation of the stimulus until the response task is completed. Local recurrent circuitry has received the most attention, but other theoretical mechanisms for the maintenance of persistent activity, including local recurrent synaptic feedback and intrinsic cellular bistability [58],[59], have been put forward. The latter will be captured by specific choices of the local dynamics, f(μ), in Equation 41; for instance, [60] choose a cubic-shaped function of the firing rate, which, under appropriate parameters, allows for intrinsic bistability. Single bump solutions have been used for neural modeling of the head-direction system [61][64], place cells [65][68], movement initiation [69], and feature selectivity in visual cortex, where bump formation is related to the tuning of a particular neuron's response [70]. Here the neural fields maintain the firing of its neurons to represent any location along a continuous physical dimension such as head direction, spatial location, or spatial view. The mathematical analysis of the neural field models is typically performed with linear stability theory, weakly nonlinear perturbation analysis, and numerical simulations. With more than one population, nonstationary (traveling) patterns are also possible. In two dimensions, many other interesting patterns can occur, such as spiral waves [71], target waves, and doubly periodic patterns. These latter patterns take the form of stripes and checkerboard-like patterns, and have been linked to drug-induced visual hallucinations [72]. For smooth sigmoidal firing rates, no closed-form spatially localized solutions are known, though much insight into the form of multibump solutions has been obtained using techniques first developed for the study of fourth-order pattern forming systems [73]. Moreover, in systems with mixed (excitatory and inhibitory) connectivity or excitatory systems with adaptive currents, solitary traveling pulses are also possible. The bifurcation structure of traveling waves in neural fields can be analysed using a so-called Evans function and has recently been explored in great detail [74].
Much experimental evidence, supporting the existence of neural fields, has been accumulated (see [53] for a summary). Most of these results are furnished by slice studies of pharmacologically treated tissue, taken from the cortex [75][77], hippocampus [78], and thalamus [79]. In brain slices, these waves can take the form of synchronous discharges, as seen during epileptic seizures [80], and spreading excitation associated with sensory processing [81]. For traveling waves, the propagation speed depends on the threshold, h, which has been established indirectly in real neural tissue (rat cortical slices bathed in the GABA-A blocker picrotoxin) by [82]. These experiments exploit the fact that (i) cortical neurons have long apical dendrites and are easily polarized by an electric field, and (ii) that epileptiform bursts can be initiated by stimulation. A positive (negative) electric field applied across the slice increased (decreased) the speed of wave propagation, consistent with the theoretical predictions of neural field theory, assuming that a positive (negative) electric field reduces (increases) the threshold, h, in Equation 42.
##### Recent developments in neural field models.
More and more physiological constraints have been incorporated into neural field models of the type discussed here (see Equations 39 and 40). These include features such as separate excitatory and inhibitory neural populations (pyramidal cells and interneurons), nonlinear neural responses, synaptic, dendritic, cell-body, and axonal dynamics, and corticothalamic feedback [38], [43], [44], [48], [50], [83][87]. A key feature of recent models is that they use parameters that are of functional significance for EEG generation and other aspects of brain function; for example, synaptic time constants, amount of neurotransmitter release or reuptake, and the speed of signal propagation along dendrites. Inferences can also be made about the parameters of the nonlinear IF response at the cell body, and about speeds, ranges, and time delays of subsequent axonal propagation, both within the cortex and on extracortical paths (e.g., via the thalamus). It is also possible to estimate quantities that parametrize volume conduction in tissues overlying the cortex, which affect EEG measurements [88], or hemodynamic responses that determine the blood oxygen level–dependent (BOLD) signals [89]. Each of these parameters is constrained by physiological and anatomical measurements, or, in a few cases, by other types of modeling. A key aim in modeling is to strike a balance between having too few parameters to be realistic, and too many for the data to be able to constrain them effectively.
Recent work in this area has resulted in numerous quantitatively verified predictions about brain electrical activity, including EEG time series [86],[87],[90], spectra [50],[86],[87],[90],[91], coherence and correlations, evoked response potentials (ERPs) [87], and seizure dynamics [86],[90],[92]. Inversion of these models has also furnished estimates of underlying physiological parameters and their variations across the brain, in different states of arousal and pathophysiology [86],[93],[94].
There are several interesting aspects to these modeling initiatives, which generalize the variants discussed in earlier sections: (i) synaptic and dendritic dynamics and summation of synaptic inputs to determine potentials at the cell body (soma), (ii) generation of pulses at the axonal hillock, and (iii) propagation of pulses within and between neural populations. We now look more closely at these key issues.
##### Synaptodendritic dynamics and the soma potential.
Assume that the brain contains multiple populations of neurons, indexed by the subscript a, which labels simultaneously the structure in which a given population lies (e.g., a particular nucleus) and the type of neuron (e.g., interneuron, pyramidal cell). Then the spatially continuous soma potential, Va, is the sum of contributions, Vab, arriving as a result of activity at each type of (mainly) dendritic synapse b, where b indexes both the incoming neural population and the neurotransmitter type of the receptor. (Note that Va is linearly related to the current reaching the soma, and to μ in earlier sections.) Thus we write(43)
where r = (x,y) denotes the spatial coordinates, t the time. The summation is assumed to be linear, and all potentials are measured relative to the resting potential [95]. For moderate perturbations relative to a steady state, the value of the resting potential can be subsumed into the values of other parameters [95]. As above, the cortex is approximated as a 2-D sheet and r is assumed to be the actual position in the case of the cortex; other structures, such as the thalamus, are linked to the cortex via a primary topographic map. This map links points in a one-to-one manner between structures; i.e., we assign the same value of r to such points. Hence, in structures other than the cortex, this dimensional map coordinate, r, denotes a rescaled physical dimension (i.e. the physical coordinate multiplied by the ratio of the cortical scale to the structure's scale), a point that should be remembered when interpreting values of spatial parameters in these structures.
The subpotentials, Vab, respond in different ways to incoming spikes, depending on their synaptic dynamics (ion-channel kinetics, diffusion in the synaptic cleft, etc.), and on subsequent signal dispersion in the dendrites. The resulting soma response to a delta-function input at the synapse can be approximated via the differential equation [50].(44,45,46)
where νab is a coupling strength, Nab is the mean number of synapses on neuron a from neurons b, sab is the mean time-integrated strength of the response of V per incoming spike, and θab is the average rate of incoming spikes (allowing for the possibility of a discrete time delay, τab, between populations b and a in addition to any delays due to spreading within populations). The parameter αab is the mean decay rate of the soma response to a delta-function synaptic input, while βab is the mean rise rate: this biexponential form has been found to be a good approximation [8],[50],[96],[97]. If the αab and βab are independent of b (which is not generally the case), then the subscript b on Dab can be omitted and Va itself satisfies Equation 44 with the right side of Equation 44 replaced by the sum of Pab over b. This approximation is also valid if α and β are interpreted as effective values, averaged over subpopulations.
##### Pulse generation.
In cells with voltage-gated ion channels, action potentials are produced at the axonal hillock when the soma potential exceeds some threshold θa. When averaged over a population of neurons, with normal response characteristics, a reasonable approximation for the firing rate, Q, is(47)
where Qamax is the maximum firing rate and Sa is a monotonic increasing sigmoidal function that approaches zero as Va→−∞ and unity as Va→∞. A commonly used approximation is(48)
where θa is the firing threshold for channels of type a and is the standard deviation of the threshold over the population.
##### Axonal propagation.
Spatiotemporal propagation of pulses within and between populations determines the values of φab. If we indicate the firing rate Qa for the cell type a by a subscript, then φab can be expressed in terms of the firing rate at other locations and earlier times. If we assume linear propagation, signals propagate as described by the neural field equation (Equation 40).(49)
where, as per Equation 40, rab is the characteristic range of axons, including dendritic arborization, cab is the characteristic velocity of signals in these axons, and γab = cab / rab is the resulting temporal damping coefficient in the absence of pulse regeneration. Note that, in comparision to the use of the terms μν and ς(μν) in Equation 40, the present wave-equation is formalized in relationship to population-specific pulse densities, φab, and firing rates, Qa,b. By employing population-specific fields and parameters, it allows each population to generate a family of outgoing fields that propagate to different populations in different ways. Equation 49 is also satisfied if φab is replaced by the free propagator and the right side is replaced by a source of the form δ(rr′)δ(tt′). In Fourier space, this gives(50,51)
where k = (kx,ky) is the wave vector and ω is the angular frequency. Critically, the neural field Equation 49 enables very diffuse (i.e., not topographically specific) connections between populations to be handled straightforwardly, simply by increasing rab while reducing γab, thereby allowing influences to propagate long distances with little damping.
##### Parameters and modulations.
The above equations contain a number of parameters encoding physiology and anatomy (e.g., coupling strengths, firing thresholds, time delays, velocities, etc.). In general, these can vary in space, due to differences among brain regions, and in time, due to effects like habituation, facilitation, and adaptation. In brief, time-dependent effects can be included in neural field models by adding dynamical equations for the evolution of the parameters. Typically, these take a form in which parameter changes are driven by firing rates or voltages, with appropriate time constants. The simplest such formulation is [95](52)
where x is the evolving parameter, y is the quantity that drives the evolution, x(0) and y(0) are steady state values, and x(1) is a constant that describes the strength of feedback. The symbol ⊗ indicates a convolution of the driver with the temporal response function H(t), which incorporates the time constants of the dynamics. If we use the normalized form(53)
then we find the differential equivalent of Equation 53:(54)
Here, we first discuss how to find the steady states of neural field models. Important phenomena have been studied by linearizing these models around their steady state solutions. Hence, we discuss linear properties of such models, including how to make predictions of observable quantities from them; including transfer functions, spectra, and correlation and coherence functions. In doing this, we assume for simplicity that all the model parameters are constant in time and space, although it is possible to relax this assumption at some cost in complexity. Linear predictions from neural field models have accounted successfully for a range of experimental phenomena, as mentioned above. Nonlinear dynamics of such models have also been discussed in the literature, resulting in successful predictions of epileptic dynamics, for example [86],[92], but are not considered here (but see the Cognitive and Clinical Applications section).
Steady states and global dynamics. Previous work has shown that many properties of neuronal dynamics can be obtained by regarding activity changes as perturbations of a steady state [86]. Spatially uniform steady states can be obtained by solving the preceding equations with all time and space derivatives set to zero, assuming that the parameters are spatially constant. The spatially uniform steady states are thus the solutions of the set of equations(55)
which are generally transcendental in form.
Linear equations for activity. Of the relevant equations above, all but Equation 48 are linear in Q. Equation 48 can be linearized by replacing the sigmoid, Sa, by its slope, ρa, at the steady state value of Va; we also approximate this quantity as constant. If we Fourier transform the resulting set of linear equations, we find for the fluctuating parts(56,57,58,59,60)
where is given by Equation 50 and we have assumed that all the parameters of the equations (but not the fields of activity) are constant on the timescales of interest. Note that we have assumed the system to be unbounded in order to employ a continuous Fourier transform here. The case of bounded systems with discrete spatial eigenmodes can be treated analogously.
For any given spatial wavenumber, k, and temporal frequency, ω, Equations 56–60 can be rearranged to obtain(61,62)
where the gains are defined by Gab = ρaνab.
If there are N′ neural populations and J′ stimulus sources, and we assume that there is no feedback of stimuli on themselves, or of the brain on stimuli, then we can write Equation 61 as(63,64,65)
where the sum on the left of Equation 63 extends only over populations in the brain, while the sum on the right covers only stimulus sources, denoted by j. Qj is written as Nj to make the distinction between population firing rates and incoming stimulus rates absolutely clear. We can now write Equation 63 in matrix form as(66)
where A is an N′×N′ matrix, Q is an N′-element column vector, B is an N′×J′ matrix, and N is a J′-element column vector. We can simply invert Equation 66 to find Q in terms of the stimuli N:(67)
where T = A−1B is the N′×J′ transfer matrix of the system. The element Taj is the response of Qa to a change in Nj at the same frequency and wave vector.
Observables. A measurable scalar quantity ψ, such as an EEG scalp voltage or voltage difference, can generally be approximated by a linear function of the firing rates, Qa. For example, a scalp potential may involve contributions from several populations, with various weights (that may include filtering by volume conduction effects). In this case, at given ω,(68)
where M is an N′-element row vector of complex-valued measurement coefficients that encode spatiotemporal filtering characteristics, phase shifts, etc. For example, the coefficients of the matrix M can be chosen such that ψ(k,ω) = φab(k,ω). Further classes of measurement functions are those relating the neural activity to, for example, local field potentials, multiunit activity, the blood oxygen level–dependent (BOLD) response that forms the basis of functional magnetic resonance imaging (fMRI), the metabolic responses underlying positron emission tomography (PET), or single-photon emission computed tomography (SPECT). In what follows, we will implicitly absorb M into T for simplicity.
Dispersion and stability. The dispersion relation of linear waves in the system is given by(69)
and the system is stable at a particular real k if all the frequency roots of this equation have negative imaginary parts. If the steady state is stable for all k, spectra and other properties of the linear perturbations can be self-consistently defined; otherwise a fully nonlinear analysis is needed.
Spectra. The power spectral density of ψ at k and ω is(70)
The frequency and wavenumber spectra are then(71,72)
A position-dependent frequency cross-spectrum can be calculated from Equation 70:(73)
where the angle brackets denote an average over multiple trials and/or over the phase of the exogenous stimuli that drive the system. The spectrum at a particular point, r, is P(r,r′,ω).
Correlation and coherence functions. In steady state, the two-point correlation function can be obtained from Equation 73 via the Wiener-Khinchtine theorem, giving(74)
In the case where the system is statistically uniform, Equation 74 depends only on the separation R = r′−r, giving(75)
where(76)
has been used and the arguments of T and N have been shown for emphasis. At R = 0, Equation 74 becomes the Fourier transform of the local power spectrum. In terms of the above expressions, the normalized correlation function and the coherence function, which are both used widely in the literature, are(77,78)
respectively.
Time series and evoked potentials. The time series of ψ at a given point can be obtained via the transfer function, by first calculating the Fourier form of the stimuli that generate it; these can be background noise sources, discrete impulses, or sinusoidal drives, for example. In the case of an impulsive stimulus, the resulting ERP is obtained by setting(79)
Similarly, for a spatially uniform sinusoidal drive, the resulting steady state evoked potential (SSEP) is obtained by using(80)
where ω0 is the drive frequency and φ is its phase.
Case of one long-range population. An important case, in many applications, is the situation where spatial spreading of activity is dominated by the axons of one population, typically because they have the longest range, are most numerous, or have the highest axonal velocity. In this case, one can ignore the k dependence in the other propagators, and it becomes possible to express the transfer function with elements of the form(81)
where is typically a complicated expression depending on the various Jab(ω).
##### Heterogeneous connectivity in neural fields.
The brain's network dynamics depend on the connectivity within individual areas, as well as generic and specific patterns of connectivity among cortical and subcortical areas [4],[9],[98]. Intrinsic or intracortical fibers are confined to cortical gray matter in which the cortical neurons reside; these intrinsic connections define the local connectivity within an area. Intracortical fibers are mostly unmyelinated and extend laterally up to 1 cm (in the human brain) with excitatory and inhibitory connections. Their distribution is mostly invariant under spatial translations (homogeneous) [84],[99], which fits the assumptions on the connectivity function in neural fields so far. On the other hand, the corticocortical (extrinsic) fiber system contains fibers which leave the gray matter and connect distant areas (up to 20 cm [84]). This fiber system is myelinated, which increases the transmission speed by an order of magnitude, and is not invariant under spatial translations (heterogeneous); in fact it is patchy [99]. Due to finite transmission speeds, time delays of interareal communication can reach 50–100 ms [84], which is not negligible. Several studies have focused on spatially continuous neural fields, which describe the temporal change of neural activity on local scales, typically within a brain area (see [4],[54],[55] for reviews), assuming homogeneous connectivity and time delays. As discussed in the previous section, early attempts include neural field theories which approximate the large-scale components of the connectivity matrix as translationally invariant and decaying over space [45],[48],[50]. These approaches have been successful in capturing key phenomena of large-scale brain dynamics, including characteristic EEG power spectra [45],[50], epilepsy [92], and MEG activity during sensorimotor coordination [49]. Here we review extensions of these efforts and address network stability under variation of (i) intracortical (intrinsic) connectivity, (ii) transmission speed, and (iii) length of corticocortical (extrinsic) fibers. All three anatomical attributes undergo characteristic changes during the development of the human brain and its function, as well changing in the aged and diseased brain (see [9] for an overview). As a first step, we can split the connectivity function, W, into two parts, the homogeneous connectivity, Whom(|xy|), which depends only on the distance, and the heterogeneous connectivity, Whet(x,y), which captures the effects of the extrinsic fiber system (for an alternative approach with applications to visual gamma phenomena, see [100][102]). We can then rewrite the neural field equation as follows:(82)
where Tc = t−|xy| /c and c is the propagation speed through the heterogeneous corticocortical or extrinsic connections. These fibers are myelinated and hence to be distinguished from the typically unmyelinated (hence slower) intracortical fibers. The latter intrinsic fibers have a transmission speed of chom and a transmission delay . If Whet describes the connectivity of n areas, then it can always be written as a sum of two-point connections via(83)
where νij Є ℜ again represents the coupling strength between areas at xi and xj. The fixed point solution is given by μ0(x) with . To gain insight into the linear stability of this equilibrium solution μ0(x), we perform a mode expansion of μ(x,t) into a set of spatial basis functions {φk(x)} such that(84)
where ξk(t) is the time-dependent amplitude related to the spatial basis function φk(x). The adjoint set of spatial biorthogonal basis functions is denoted by . It will be generally true (except in degenerate cases) that only one spatial pattern will become unstable first. For simplicity, we consider the stationary solution μ0(x) = 0 to be the rest state and consider its deviations μ(x,t) = ξk′(t)φk′ (x)+c.c., where c.c. denotes the complex conjugate. Then the linear stability of each temporal mode is given by(85)
where d = |xixj|>0. Also, and (but for simplicity, we drop the tilde in from now on).
Let us pause for a moment and reflect upon the significance of Equation 85. Equation 85 describes the rate of (temporal) change, ∂tξk(t), of its corresponding spatial neural activation pattern, φk(x). This pattern will change as a function of its own spatial configuration, φk(x), the connections (Whom and νij), and, last but not least, the transmission times of information exchange, and d/c. If the rate of change, ∂tξk(t), is positive, then the particular pattern φk(x) is unstable, otherwise it is stable. In other words, Equation 85 identifies quantitatively how a particular neural activation is impacted by its local and global connectivity in a biologically realistic environment, including signal exchange with finite and varying (intracortical versus corticocortical) transmission speeds. Every treatment of the interplay of anatomical connectivity (local and global connections) and functional connectivity (network dynamics) will have to be represented in the form of Equation 85 or a variation thereof. In this sense, we have here achieved our goal stated in the introduction of this section.
To illustrate the effects of interplay between anatomical and functional connectivity, we discuss a simple example following [103],[104]. We assume that there exists only a single corticocortical fiber with terminals at locations x1 and x2, that is n = 2. Then we have an architecture as shown in Figure 1. Our objective is to identify the stability boundaries of the rest state activity, here the equilibrium solution μ0(x) = 0.
We will consider eigenfunctions of the form φk(x) = eikx. Changing the variables such that z = yx and assuming a solution of the form ξk(t) = eλt, λ Є C, the stability condition can then be determined by the following characteristic equation:(86)
Linear stability of Equation 86 is obtained if Re[λ]<0 and is lost, according to [105], at Re[λ] = 0, that is λ = . Figure 2 shows various connectivity kernels, Whom, that are often found in the literature.
Qubbaj and Jirsa [104] discussed the properties of the characteristic Equation 86 in detail, considering separately the special cases of symmetric and asymmetric connectivity, W. The characteristic equation defines the critical boundary in the parameter space of ν12, ν21, c, chom, at which the resting activity, μ0(x) = 0, becomes unstable. Recall that c and chom are the conduction velocities along extrinsic and intrinsic axons, respectively. The general result of [104] can be represented as a critical surface separating stable from unstable regimes as shown in Figure 3. Here the critical transmission delay, τ = d/c, through the heterogeneous fiber is plotted as a function of the real and imaginary part of the eigenvalue of the connectivity, W. Essentially a heterogeneous fiber with symmetric weights, ν21 = ν12 = ν, has only real eigenvalues, whereas asymmetries result in imaginary components. We find that for positive values of ν greater than a critical value, the system becomes unstable through a non-oscillatory instability for all values of c, chom, (bold line in Figure 3). Within the cylindrical component of the surface, the equilibrium of the system remains always stable for all values of c, chom, and hence a time delay shows no effect. In the other regimes of the critical surface, the system typically destabilizes via an oscillatory instability, ω≠0, and is sensitive to time delays. The surface shown in Figure 3 represents the lower bound of stability with c/chom = 1. Increases of the ratio, c/chom, equivalent to increases of degree of myelination, result in a larger enclosed volume by this surface, i.e., increase of stability. The largest stability region is that for a purely inhibitory kernel followed by that of a local inhibitory and lateral excitatory kernel. The next largest involves a local excitatory and lateral inhibitory kernel. The smallest stability region is obtained for a purely excitatory kernel.
A surprising result is that all changes of the extrinsic pathways have the same qualitative effect on the stability of the network, independent of the local intrinsic architecture. This is not trivial, since despite the fact that extrinsic pathways are always excitatory the net effect on the network dynamics could have been inhibitory, if the local architecture is dominated by inhibition. Hence qualitatively different results on the total stability could have been expected. Such is not the case, as we have shown here. Obviously the local architecture has quantitative effects on the overall network stability, but not qualitatively differentiated effects. Purely inhibitory local architectures are most stable, purely excitatory architectures are the least stable. The biologically realistic and interesting architectures, with mixed excitatory and inhibitory contributions, play an intermediate role. When the stability of the network's fixed point solution is lost, this loss may occur through an oscillatory instability or a nonoscillatory solution. The loss of stability for the nonoscillatory solution is never affected by the transmission speeds, a direct physical consequence of its zero frequency allowing time for all parts of the system to evolve in unison. The only route to a non-oscillatory instability is through the increase of the heterogeneous connection strength. For oscillatory instabilities, the situation is completely different. An increase of heterogeneous transmission speeds always causes a stabilization of the global network state. These results are summarized in Figure 4.
### Numerical Simulations: Ensemble Activity from Neuronal to Whole Brain Scales
This section illustrates neuronal ensemble activity at microscopic, mesoscopic, and macroscopic spatial scales through numeric simulations. Our objective is to highlight some of the key notions of ensemble dynamics and to illustrate relationships between dynamics at different spatial scales.
##### Ensemble dynamics at the microscopic scale.
To illustrate ensemble dynamics from first principles, we directly simulate a network of coupled neurons which obey deterministic evolution rules and receive both stochastic and deterministic inputs. The system is constructed to embody, at a microscopic level, the response of the olfactory bulb to sensory inputs, as originally formulated by Freeman [38], [106][108]. Specifically, in the absence of a sensory input, neurons fire sporadically due to background stochastic inputs. The presence of additional synaptic currents due to a sensory input (e.g., inhaled odor) evokes a bifurcation onto a limit cycle or chaotic attractor. Note that in this section we simulate dynamics at the scale of coupled individual neurons. We can derive directly the predicted ensemble mean response by simply summing over all neurons. We compare this with an explicit model of neural mass dynamics at the mesoscopic scale in the subsequent section.
##### Microscopic evolution equations.
Each neuron is modeled as a planar reduction of the Hodgkin-Huxley model [109],[110], namely,(87)
where fion introduces conductance-determined transmembrane currents through voltage-dependent channels, ion = {Na+,K+} and I are synaptic currents. The planar reduction has slow potassium channel kinetics but fast sodium channels, whose states vary directly with transmembrane potential [111]. Synaptic currents are modeled, for the present purposes, to arise from three sources,(88)
The first term represents recurrent feedback from neurons within the ensemble due to their own firing. The coupling term, Hc, incorporates both the nature of the (all-to-all) within-ensemble coupling and the EPSP with parametric strength c. For the present purposes, the EPSP consists of a brief steady current whenever the presynaptic neuron is depolarized. The external currents, Inoise, introduce stochastic inputs (e.g., from brain stem inputs) and are modeled as a constant flow with a superimposed Poisson train of discrete pulses. The final term, Isensory, models sensory input, consisting of a constant synaptic current to a subset of neurons, whenever the sensory stimulus is present. Hence this system permits an exploration of the relative impact of the flow (deterministic) and diffusive (stochastic) effects as embodied at the ensemble level by the Fokker-Planck equation (Equation 20) at the neuronal network level. The Nernst potentials, conductances, and background current are set so that, in the absence of noise and sensory inputs, each neuron rests just below a saddle-node bifurcation to a limit cycle [109]. This implies that neurons are spontaneously at rest (quiescent) but depolarize with a small perturbation. If the perturbation is due to a stochastic train, then the neuron fires randomly at an average rate proportional to the stochastic inputs. However, following a small increase in the constant flow term, due to a sensory input, Isensory, the quiescent state becomes unstable and the neuron evolves on a (noise-modulated) limit cycle. Figure 5 shows a stochastically driven neuron (A) compared to a noise-modulated periodic neuron (B). In the former case, the activity is dominated by the stochastic terms. In the latter case, the limit cycle dynamics dominate, although the stochastic inputs modulate the depolarization amplitude.
##### Microscopic dynamics.
Figure 6 shows the results of simulating an ensemble of 250 neurons with a sensory input to all neurons between t = 1,000 ms to t = 3,000 ms. Figure 6A shows a raster plot of the neural spike timing whilst Figure 6B shows the simulated local field potential from the ensemble ( = total current flow across all neurons). As constructed, the effect of the input is to effect a bifurcation in each neuron from stochastic to limit cycle dynamics. The secondary effect of the appearance of limit cycle dynamics is to suppress the impact of the spatially uncorrelated stochastic inputs. Hence the neurons show an evolution towards phase locking, which was not present prior to the stimulus. As evident in Figure 6B, the increased firing synchrony leads in turn to a marked increase in the simulated local field potentials as individual neurons begin to contribute concurrent ion currents. Once the stimulus ends, there is a brief quiescent phase because all of the neurons have just fired and require a short train of stochastic inputs before they commence firing again. Interestingly, there is evidence of damped mean-field oscillations in the ensemble following stimulus termination, abating after some further 800 ms. To underscore the observation that the mean synaptic currents evidence an emergent phenomenon, and not merely the super-position of a bursting neuron, the time series of a single neuron is provided in Figure 6C. Clearly no burst is evident at this scale.
The impact of the stimulus input on the density of the ensemble is shown in Figure 7, which shows the spike-timing difference of all neurons in the ensemble with respect to a randomly chosen seed-neuron. The mean spike-timing difference is 0 ms throughout the simulation. This is because the system has complete symmetry, so that all neurons fire, on average, symmetrically before or after any other neuron. However, as evident in Figure 7A, the variance in relative spike-timing decreases dramatically during the stimulus interval. Of note is that the ensemble variance does not simply step down with the onset of the stimulus, but rather dynamically diminishes throughout the presence of the stimulus. When this occurs, the mean-field term continues to increase in amplitude. Figure 7B shows the evolution of the kurtosis (normalized so that a Gaussian distribution has a kurtosis of zero). Prior to the stimulus, and reflecting the weak network coupling, the ensemble has a mesokurtotic (broad) distribution. It increases markedly following the stimulus onset, implying a dynamical evolution towards a leptokurtotic (peaked) distribution. That is, although the parameter values are static, the ensemble mean, variance, and kurtosis evolve dynamically in an inter-related fashion. Hence this system exhibits time-dependent interdependence between its first, second, and fourth moments. This is the sort of coupling (between moments of the ensemble density) that neural mass models do not capture.
It is important to note that the spatiotemporal structure of the noise remains constant throughout the simulation, as does the intra-ensemble coupling. Hence the appearance of phase locking is an emergent feature of the dynamics and has not been imposed. A dynamic contraction of the ensemble cloud occurs whether the pre-existing noise continues unchanged during the stimulus input—hence increasing the firing rate of each neuron—or diminishes so that, in the absence of coupling, firing rates are kept the same on average. In the latter case (as in Figure 5), there is simply a change from stochastic to periodic firing. The ensemble cloud is visualized directly in Figure 8. The upper row shows the first return map for the ensemble over five consecutive time steps. For each neuron, this is defined as the inter-spike delay at time t = T plotted against the inter-spike delay for the subsequent spike at t = T+1. Six such first return state-space values are plotted for all neurons. To control for changes in spike rate, these plots are normalized to the average firing rate. Values for the seed neuron used in Figure 7 are plotted in red. The left column shows the ensemble state, prior to the stimulus current. The right column shows the intra-stimulus activity. The contraction of the ensemble is seen clearly. In addition, the first return map confirms that individual neurons have stochastic dynamics prior to the stimulus, which change to periodic (i.e., a fixed point in the first return map) during the stimulus. The lower row of Figure 7 shows corresponding probability distributions of the inter-neuron spike-timing differences. This reiterates that not only does the distribution contract, but as the mean-field dynamics become strongly nonlinear, the ensemble kurtosis increases markedly from sub- to super-Gaussian.
##### Neural mass dynamics at the mesoscopic scale.
Whilst such simulations are illustrative, they are computationally intensive; even when limited to just 250 neurons at <5 s of integration time. As discussed in The Mean-Field Model section, it is possible to study a reduced model representing only the mean ensemble dynamics. This is essentially achieved by generalizing parameter values (such as ion channel thresholds) from individual point values to population likelihood values. Freeman [38] additionally introduced synaptic effects through convolving the inputs with a suitable response kernel as presented in Equation 37. For the simple illustration here, we do not introduce synaptic filtering.
##### Mesoscopic evolution equations.
For the present purpose, we simulate a single mass with both excitatory and inhibitory neurons [52],[112]. Expected mean states of the ensemble excitatory neurons μe = 〈Ve〉 are, as above, based upon Morris Lecar planar dynamics, with slow potassium channel dynamics. Inhibitory neurons, μi, respond passively to input from excitatory neurons and feedback to induce additional outward (rectifying) currents in excitatory cells. In the microscopic system considered above, interneuron coupling was via a direct pulse during presynaptic depolarization. At the mesoscopic scale, neuronal coupling is via neural firing pulse densities, ςa, which capture the expected neuronal firing rate, given the mean neuronal transmembrane potential ς(μa) for a = e,i. Assuming a Gaussian distribution of individual neuronal firing thresholds, one obtains a symmetric sigmoid-shaped function for ςa as per The Mean-Field Model section. The dynamics are thus of the form(89)
(90)
where the function G represents the coupling between mean firing rates and induced synaptic currents. By targeting either Na+ or Ca++ currents and including (postsynaptic) voltage-dependent effects, this function can incorporate, to a first-order approximation, a variable proportion of AMPA or NMDA-like kinetics [52]. The coefficients ναβ represent the synaptic density between excitatory (e) and inhibitory (i) populations or from the stochastic/noise (n) or sensory (s) inputs. Note that both populations receive stochastic inputs but only the excitatory population receives the sensory input Isensory. The functions fion are the same as for the microscopic system including the slow potassium channel—although they are now parameterized by population-wide estimates.
##### Mesoscopic dynamics.
Figure 9 shows the response of a single neural mass to sensory evoked synaptic currents with the same temporal timing as for the microscopic system. Prior to the stimulus, the system is in a stable fixed point regimen. The stochastic inputs act as perturbations around this point, giving the time series a noisy appearance, consistent with the prestimulus microscopic ensemble activity. However, the mechanisms are quite distinct: Individual neurons within the microscopic ensemble fired stochastically, but at uncorrelated times. Hence, at the level of the ensemble, such individual events contribute in a piecemeal fashion. That is, although individual neurons exhibit nonlinear dynamics, the ensemble mean dynamics are (linearly) stable to the stochastic inputs until the background current is increased. In the mesoscopic case, the system as a whole is stable to small perturbations prior to the stimulus current. The temporally uncorrelated stochastic inputs are effectively filtered by the response properties of the system around this fixed point to yield the simulated activity.
In the mesoscopic neural mass, the fixed point state is rendered unstable by the stimulus current and large amplitude oscillations occur. These cease following stimulus termination. This accords with the appearance of stimulus-evoked nonlinear oscillations in the ensemble-averaged response of the microscopic system. In both models, such oscillations abate following stimulus termination. Hence, at a first pass, this neural mass model captures the mean-field response of the microscopic ensemble to a simulated sensory stimulus.
What is lost in the neural mass model? In this model, activity transits quickly from a noise-perturbed fixed point to large amplitude nonlinear oscillations. A brief, rapid periodic transient is evident at the stimulus onset (1,000 ms). The system subsequently remains in the same dynamic state until the stimulus termination. This hence fails to capture some of the cardinal properties of the microscopic ensemble, namely the coupling between the first and second moments (mean and variance). As discussed above, this process underscores the dynamical growth in the mean-field oscillations and the interdependent contraction of the interneuron spike timing variance shown in Figures 6 and 7. Because of this process the system is far more synchronized than prior to the stimulus. This synchronization leads to the damped mean-field oscillations evident in the ensemble system after the stimulus termination (3,200 ms→4,500 ms), because there is a more coherent ensemble-wide response. What is gained in the neural mass model? The addition of a third dimension (i.e., the inhibitory mean activity) to the dynamics enables the expression of chaotic dynamics [52],[112]. Hence the flow terms in the neural mass model contribute to the expression of aperiodic dynamics in addition to the stochastic inputs. This is not possible in the (planar) single neural dynamics of the microscopic system because chaotic dynamics require at least three degrees of freedom. Thus the dimension reduction afforded by the neural mass approximation allows the introduction of more complex intrinsic dynamics, permitting dynamical chaos. Whilst additional dimensions could be added to the microscopic neurons, this would add to an already significant computational burden. The massive reduction in the computational load of the neural mass approximation also allows extension of the spatial scale of the model by an array of neural masses, coupled to form a small patch of cortical tissue. Such a mesoscopic system can be endowed with additional structure, such as hierarchical [108], scale-free [113], multiscale [114], or small world [115] properties. For the present purposes, we couple a single input neural mass, as modeled above, hierarchically to a sheet with internal hyperbolic (i.e., scale-free) coupling. Intersystem coupling is purely excitatory-to-excitatory. Within the sheet, the coupling drops in proportion to spatial separation and is hence scale-free:(91)
where F incorporates all intrasystem dynamics as per Equation 89 and the indices numerate either the sensory node {sens} or the nodes within the sheet {sheet}. As above, synaptic currents are induced by the pulse density of the presynaptic neurons, rather than directly via individual presynaptic depolarization. The sensory node receives the only direct stimulus-induced currents,(92)
The hierarchical nature of the system is embodied by the targeted nature of the sensory inputs and the separate parameterization of parameters that couple masses to or within the sheet, Csens and Csheet, respectively. It would also be possible to increase the degree of forward and backward asymmetry by incorporating purely AMPA-like kinetics for the former and NMDA-like kinetics for the latter, as has been proposed as a mechanism for perceptual inference [116],[117]. Figure 10 shows the response of the system when Csens>Csheet. Figure 10A shows the individual mean synaptic currents of all nonsensory nodes. Figure 10B shows the total synaptic currents averaged across the nonsensory sheet. Several features can be noted. For a start, despite use of the same parameters, the coupling of neural masses into an array or sheet leads to the appearance of spontaneous prestimulus activity. Stimulus-evoked activity from the sensory node reorganizes this activity from spatially incoherent to synchronized. Thus the array-averaged synaptic currents increase during the stimulus period. Hence the dynamics at this scale mirror those within the microscopic ensemble, which each node in this simulation is constructed to represent. However, at least in this simulation, the array does not exhibit a dynamic growth in the system-wide currents during the stimulus period. Presumably, if this did occur within the individual mesoscopic nodes, then the array-wide current may also grow dynamically. That is, one would anticipate coupling between moments across ensembles, as discussed in [38].
Figure 11 shows the simulated activity following an increase in the intrasheet coupling such that CsensCsheet. All other parameters are unchanged. Spontaneous prestimulus activity is clearly more coherent; consistent with a stronger internally determined dynamical state. The injection of the externally evoked sensory currents into this prior activity actually has a slightly desynchronizing effect, as evident as a decrease in the array-wide average response (Figure 11B). That is, the temporal mismatch between the within-sheet dynamics and the externally induced activity leads to more spatially complex dynamics (an increase in the spatial entropy and hence the information content of the system).
If the stochastic inputs, Inoise, are decreased below a threshold, then the spontaneous activity in the nonsensory array diminishes. The feedback effect of this quiescent activity is to suppress the stimulus-evoked activity in the sensory node. Hence there is a top-down mechanism for the complete suppression of sensory-evoked activity. Presumably, more subtle feedback effects may be possible if more forward versus backward receptor detail was modeled. In summary, these mesoscopic simulations impress a view of sensory-evoked effects as a reorganization of ongoing activity. Depending upon the ratio of internal to sensory-related coupling, this reorganization may lead to an increase or a decrease in the information content of the system dynamics.
##### Neural field dynamics at the whole-brain scale.
We now provide brief illustrations of sensory evoked and nonlinear activity as modeled by macroscopic field equations. As discussed in the section entitled Recent Developments in Neural Field Models, these incorporate synaptic filtering and axonal conduction delays, in addition to the population-wide conversion of membrane potentials into firing densities [50]. Significantly, they also permit the incorporation of subcortical systems, such as the thalamus [91]. Recent developments (see the Heterogeneous Connectivity in Neural Fields section) now allow elucidation of the impact of biologically relevant connection heterogeneities on the stability and conduction of cortical activity. The equations, their derivation, and relevant references are provided in the Recent Developments in Neural Field Models section.
##### Macroscopic dynamics.
Two crucial differences occur when moving to the macroscopic scale of the corticothalamic field model. Firstly, sensory inputs are modeled as entering the specific nuclei of the thalamus rather than directly into a cortical sensory node. The ensuing evoked corticothalamic activity can then be studied in a biologically informed framework. Second, while prestimulus activity is modeled as a noise-perturbed steady state, the system is not destabilized by sensory inputs. Instead, inputs evoke damped oscillations in the corticothalamic loop [87]. Figure 12 illustrates an example of sensory-evoked activity (Aquino et. al., unpublished data). Evoked afferent pulse densities are shown because they reflect more accurately the expected synaptic currents, through their action on postsynaptic neurons. The smooth spatiotemporal dispersion of the evoked cortical response and its time delayed corticothalamic volley are evident.
##### Summary of numerical simulations.
These simulations give insight into the rich neural ensemble dynamics at different spatial scales that arise spontaneously, are evoked by sensory inputs, or follow changes in state parameters. The intention is to demonstrate concrete examples of ensemble dynamics under varying influences of flow and dispersion. The resulting dynamics can be seen to emerge from the interplay of stochastic dispersion and flow-determined ensemble contraction. The view of stimulus-evoked synaptic currents as evoking a bifurcation in neural ensemble activity derives largely from the formative work of Freeman, following detailed physiological studies of the olfactory bulb. One of the key outstanding problems is to reconcile the apparent discrepancy between proposals involving a key role of nonlinear dynamics (see also [118]) and the apparent success of mean-field models to predict measured evoked responses, without recourse to nonlinear dynamics. One approach is to construct a multiscale hierarchy, with self-consistent evolution equations at each scale and to couple the emergent dynamics from fine scales into the activity at coarser scales [114]. Although this permits small scale nonlinear activity to coincide with and influence stochastic macroscopic activity, it requires a somewhat elaborate framework. An alternative approach is to recursively enslave micro- and mesoscopic activity to predicted macroscopic field oscillations by driving them with the predicted mean-field synaptic currents. A problem here concerns the resulting emergence of sustained oscillations within mesoscopic activity and the possible causal inconsistency that this may entail.
The nature and strength of neuronal connectivity varies markedly when considered across the heirarchy of spatial scales. At the microscopic scale, connectivity is dense, concentrated equally in vertical and horizontal directions and, more or less isotropic when considered across different cortical regions. At mesoscopic scales, connectivity has a patchy, colmunar-dominated structure. At macroscopic scales, connectivity is sparser, can be considered exclusively horizontal, and is predominantly excitatory in nature. It is also characterized by heterogenous connections (large fiber tracts) which fulfill functionally defined roles. These rules are reflected in the abstractions and refinements of the models which address the different scales.
### Cognitive and Clinical Applications
In this section, we present three distinct applications of neural ensemble modeling. We first illustrate a computational example, namely decision-making, as implemented in a mean-field model. We then illustrate healthy and pathological activity in neural field models. The healthy example is of the well-known psychophysical phenomenon of auditory streaming—the balance of segmentation versus integration in auditory perception. We then illustrate examples of spatiotemporal dynamics occurring in corticothalamic loops during Absence seizures.
##### Spiking dynamics underlying decision-making.
Decision-making is a key brain function of intelligent behavior. A number of neurophysiological experiments on decision-making reveal the neural mechanisms underlying perceptual comparison, by characterising the neuronal correlates of behavior [119][121]. In particular, [119][124] have studied the neural mechanisms underlying perceptual comparison by measuring single-neuron responses in monkeys trained to compare two mechanical vibrations applied sequentially to the tip of a finger; the subjects have to report which of the two stimuli has the higher frequency. They found neurons in the ventral premotor cortex (VPC) whose firing rate depended only on the difference between the two applied frequencies, the sign of that difference being the determining factor for correct task performance [121]. These neurons reflect the implementation of the perceptual comparison process and may underlie the process of decision-making.
Figure 13 shows a biophysically realistic computational model for a probabilistic decision-making network that compares two mechanical vibrations applied sequentially (f1 and f2). The model implements a dynamical competition between neurons: The model enables a formal description of the transients (nonstationary) and probabilistic character of behavior (performance) by the explicit use, at the microscopic level, of spiking and synaptic dynamics of one-compartment IF neuron models. The network contains excitatory pyramidal cells and inhibitory interneurons. The excitatory recurrent postsynaptic currents (EPSCs) are mediated by AMPA (fast) and NMDA-glutamate (slow) receptors, whereas external EPSCs imposed on the network are driven by AMPA receptors only. Inhibitory postsynaptic currents (IPSCs) to both excitatory and inhibitory neurons are mediated by GABA receptors. Neurons are clustered into populations. There are two subtypes of excitatory population: namely, specific and nonselective. Specific populations encode the result of the comparison process in the two-interval vibrotactile discrimination task, i.e., if f1>f2 or f1<f2. The neurons in the two specific populations additionally receive external inputs encoding stimulus specific information. They are assumed to originate from the somatosensory area S2 and from the PFC, encoding the frequency of both stimuli f1 (stored) and f2 (present) to be compared during the comparison period, i.e., when the second stimuli is applied (see [125] for details).
The attractors of the network of IF neurons can be studied exhaustively by using the associated reduced mean-field equations. The set of stationary, self-reproducing rates, νi, for the different populations, i, can be found by solving a set of coupled self-consistency equations. This enables a posteriori selection of parameter regions that contain desired behaviors. In the present case, the essential requirement is that, for the stationary conditions, different attractors are stable. The attractors of interest for our task correspond to the activation (high spiking rates) or inactivation (low spiking rates) of the neurons in the specific populations f1>f2 and f1<f2. The activation of the specific population f1>f2 (f1<f2) and the simultaneous lack of activation of the complementary population f1<f2 (f1>f2), corresponds to an encoding single state associated with a motor response reporting the categorical decision f1>f2 (f1<f2). The lack of activation of both specific populations (spontaneous state) would correspond to an encoding state that cannot lead to a behavioral decision; i.e., there is no answer, or a motor response is generated randomly. The same happens if both specific populations are activated to the same degree (pair state). Because responses in animals are probabilistic in nature, the operating point of the network should be such that both categorical decisions, i.e., both states, are bistable. In addition, we have also shown that the model predicts a behavior consistent with Weber's law if, and only if, the spontaneous state is also a stable state, i.e., when the dynamical operating point of the network is in a regime of multistability. In this way, Weber's law informs the operating point of the network.
Figure 14 shows numerical simulations corresponding to the response of VPC neurons during the comparison period (to be contrasted with the experimental results shown in Figure 2 of [121]). This figure shows the average firing rate as a function of f1 and f2, obtained with the spiking simulations (diamond points correspond to the average values over 200 trials, and the error bars to the standard deviation). The lines correspond to the mean-field calculations. Black indicates f1<f2 (f2 = f1+8 Hz) and gray indicates f1>f2 (f2 = f1−8 Hz). The average firing rate of the population f1<f2 depends only on the sign of f2−f1 and magnitude of the difference, |f2−f1|; confirming again that Weber's law cannot be encoded in the firing rate, but only in the probability with which that firing rate can be reached (that depends on the sign and magnitude of the difference between f1 and f2).
##### Auditory streaming.
One of the applications of neural fields in cognitive processing is found in auditory scene analysis [126], particularly auditory streaming. Intuitively, auditory streaming or stream segregation is like listening to bass and soprano vocalists singing simultaneously. Although the two voices overlap in time, they clearly form two distinct percepts. In the laboratory, a similar effect can be created using sequences of tones. In a typical streaming experiment, two sequences are created using sets of high and low tones. Sequences vary in presentation rate and the frequency difference between the tones. The basic finding (see e.g., [127],[128]) is: (i) when the frequency separation is relatively small and/or the rate is relatively slow, listeners perceive a single integrated melody (or stream) and can accurately report the ordering of the tones, and (ii) when the frequency separation is relatively large and/or the rate relatively fast, people clearly perceive two segregated auditory streams, one with a higher pitch than the other. Essentially, there is a frequency–time boundary (known as the Fission Boundary, FB) beneath which all sequences are heard as integrated, regardless of instructions. There is a frequency–time boundary (known as the Temporal Coherence Boundary, TCB) above which all sequences are heard as segregated, regardless of instructions. In between these two boundaries exists a bistable region in which a sequence can be heard as either integrated or segregated depending upon instructions. Hysteresis phenomena are observed when traversing the bistable regime from either the FB or TCB. Many other auditory phenomena of a related nature are discussed in [128].
To capture the perceptual integration and segregation processes in the human brain, while accommodating contemporary brain theories [1],[2],[4], the authors of [126] proposed a tonotopically organized neural field for peripheral processing with projections to the higher areas that are responsible for cognitive integration. The neural field is tonotopically organized such that the frequency of the acoustic stimulus maps onto a location in neural space. The second nontonotopically organized system may either be represented by a neural field or a subnetwork. Its function is the classification of the peripheral spatiotemporal neural field dynamics. This classification process is not just a measurement (in which case the application of a simple measure to the neural field would suffice) but is itself a dynamic process. In fact, bistability and hysteresis turn out to be properties of the classification process rather than properties of the neural field dynamics. The dynamics of the neural field μ(x,t) are given by the wave Equation 39, which has been extended to accommodate auditory inputs s(x,t) as follows:(93)
where, as a reminder, γ = c/r, c is the speed of spike propagation, and r parameterizes the spatial decay of lateral interactions. The external input or stimulus to the neural sheet is s(x,t): 2, which contains all the spatiotemporal characteristics of the auditory input stream. Periodic boundary conditions, μ(0,t) = μ(L,t), t≥0, are used.
The second network is not tonotopically organized, hence its spatial dimension is of no relevance, when we consider only the competition of two streams. In fact, the ability to show multistable pattern formation is the only relevant property of the network and can be realized in multiple network architectures as discussed in previous sections. A simple multistable subsystem with its scalar state variable y(t) is given by the equation(94)
where ε is a constant that captures all linear contributions. I0 contains all constant contributions given rise to the rest state activity. The functional I(t) is specified as(95)
where Ω is a neural activity threshold. Equations 93, 94, and 95 define the dynamics of a stream classification model in one of its simplest forms. Figure 15 illustrates the architecture of the model.
To understand van Noorden's results, we parametrize a sequence of consecutive tones by their frequency difference, Δf, and their interonset interval, IOI. As the neural field evolves, it is integrated across space and time yielding the time-dependent, but scalar, activity, I(t), driving the second system. I(t) represents the relevant information from the neural field, μ, as a spatiotemporally integrated activity measure, which depends on the amount of dispersion over space and time. The greater the dispersion, the greater will be the value of I(t) at a given time point. Figure 16 shows the contour lines of neural field activity over space x and time t for the bistable situation.
The final state reached by the second system defined in Equation 94 with activity y will depend on I(t) and its own intrinsic dynamics. The curve of the flow is shifted up or down depending on I(t), creating either one positive or one negative fixed point. For an intermediate value of I(t), there is a bistable regime in which y can assume either one of the fixed points. The negative fixed point is identified with perceiving one stream and the positive fixed point with perceiving two streams. The time series for y are shown in Figure 17 for several different initial conditions of the activity y. After a transient the activity becomes stationary, displaying three possible scenarios (see Figure 17 from top to bottom): one stream only, or the bistable situation, in which either one integrated stream or two separate streams may be perceived, or finally two streams only. For each choice of Δf and IOI, the model Equations 93 and 94 are solved numerically and their stationary states determined. The results are plotted in the 2-D parameter space in Figure 18. TCB and the FB are reproduced in a manner that corresponds nicely to van Noorden's (1975) results including a bistable region [127]. Note that the exact experimental numerical values at which the boundaries occur vary from subject to subject and depend on the experimental methods employed [128].
We will briefly illustrate another phenomenon. When two interleaved rising and falling tone sequences, as shown in Figure 19, are presented, human subjects report them to be either crossing or bouncing perceptually [128],[129]. This phenomenon is known as the crossing scales phenomenon. The implementation within the neural field model of [126] is straightforward and illustrated in Figure 19.
##### Modeling seizures.
Experimental and theoretical arguments propose that the onset of a seizure reflects a bifurcation in cortical activity from damped stochastic activity—where peaks in the power spectrum reflect damped linear resonances—to high amplitude nonlinear oscillations arising from activity on a limit cycle or chaotic attractor [86], [130][134]. Figure 20 presents an example of a bifurcation arising from a 3 Hz oscillatory instability in the corticothalamic neural field model of the Recent Developments in Neural Field Models section. Stochastic activity either side of the seizure can be seen, reflecting the response properties of the stable steady state mode. The large amplitude oscillations arise from a transient change in a corticothalamic state parameter from t = 5 s to t = 20 s. A more systematic analysis of the bifurcations in this neural field model was undertaken in [92]. It was argued that the study of these bifurcations provides a parsimonious explanation of the unique time course, symmetry, onset, and offset of both Absence and tonic clonic seizures, capturing their similarities and the differences. Further analysis of the 3 Hz (Absence) bifurcation in a reduced model argues that interactions between the reticular and specific nuclei of the thalamus contribute importantly to the Absence seizure waveform [135]. In the present simulation, the 3 Hz seizure has inherently aperiodic dynamics, as shown in the right panel of Figure 20.
Neural field formulations, through their implicit treatment of horizontal synaptic coupling, also lend themselves naturally to studying the spatial propagation of seizure activity, a clinically important phenomenon. An analysis of the frequency and amplitude properties of spatially extended 3 Hz seizures (Knock et. al., unpublished data) is presented in Figure 21, comparing data recorded from a young male with Absence epilepsy (left panels) to a simulated seizure in the corticothalamic model (right panels). The top row shows the temporal dynamics of the dominant frequency across a spatially extended array of (real and simulated) electrodes. The observed data (left) shows that the seizure onsets (almost) simultaneously across the scalp, although frontal electrodes lead fractionally. However, onset frequencies range from 2.7 Hz at frontal electrodes to 4 Hz over temporal regions. There follows a pattern of frequency convergence so that within 2 s of seizure onset, all cortical regions express a common frequency of 3 Hz, slowing progressively to 2.5 Hz. The seizure simulated in the corticothalamic model (right) shows a similar pattern. Peak onset frequencies in this model predominantly reflect corticothalamic conduction time lags, which have been parameterized to reflect the varying separation of cortex and thalamus. Subsequent frequency convergence in this model arises from corticortical coupling (there is no intrathalamic coupling in this simulation).
The lower panels show the temporal evolution of the amplitude envelope of activity within the dominant mode. The principal feature of interest in the observed data (left) is the increasing modulation of the amplitude envelope as one moves from frontal electrodes, which have the strongest power, to parietal electrodes, where the onset power is weaker. These differing degrees of amplitude modulation are also present in the simulated seizure (right). Importantly, all parameters of the model are constant during the seizure. Hence the amplitude modulation is due to coupling between nonlinear modes at different spatial locations.
Whereas frequency locking is not surprising in a model with spatial coupling, the amplitude modulation is a novel, emergent property of the nonlinear dynamics.
### Discussion
In conclusion, we have seen that statistical descriptions of neuronal ensembles can be formulated in terms of a Fokker-Planck equation, a functional differential equation prescribing the evolution of a probability density on some phase space. The high dimensionality and complexity of these Fokker-Planck formalisms can be finessed with a mean-field approximation to give nonlinear Fokker-Planck equations, describing the evolution of separable ensembles that are coupled by mean-field effects. By parameterizing the densities in terms of basis functions or probability modes, these partial differential equations can be reduced to coupled differential equations describing their evolution. In the simplest case, we can use a single mode that can be regarded as encoding the location of a probability mass, hence neural mass models. Neural mass models can be generalized to neural field models by making the expectations a function of space, thereby furnishing wave equations that describe the spatiotemporal evolution of expected neuronal states over the cortical surface. We have tried to show the conceptual and mathematical links among the ensuing levels of description and how these models can be used to characterize key dynamical mechanisms in the brain.
### Acknowledgments
VKJ thanks Felix Almonte for help with the generation of various figures. We thank the attendees of Session IV at BCW2006* for the interesting discussions, which represent the source of inspiration for the present review.
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135. 135. Rodrigues S, Terry J, Breakspear M (2006) On the genesis of spike-wave oscillations in a mean-field model of human thalamic and corticothalamic dynamics. Phys Lett A 355: 352–357. doi: 10.1016/j.physleta.2006.03.003
Ambra 2.9.1 Managed Colocation provided
by Internet Systems Consortium. | {"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": 0.8702031373977661, "perplexity": 2069.8085938004942}, "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/1387345768537/warc/CC-MAIN-20131218054928-00091-ip-10-33-133-15.ec2.internal.warc.gz"} |
https://www.e-olymp.com/en/contests/17135/problems/177644 | favorite We need a little bit of your help to keep things running, click on this banner to learn more
Competitions
# Totient Extreme
Given the value of n, you will have to find the value of H. The meaning of H is given in the following code:
Totient or phi function, φ(n) is an arithmetic function that counts the number of positive integers less than or equal to n that are relatively prime to n. That is, if n is a positive integer, then φ(n) is the number of integers k in the range 1kn for which gcd(n, k) = 1.
#### Input
The first line contains the number of test cases t (0 < t106). It is followed by t lines each containing a number n (0 < n104).
#### Output
For each line produce one line that contains the value of H for the corresponding n.
Time limit 1 second
Memory limit 128 MiB
Input example #1
2
3
10
Output example #1
16
1024 | {"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": 0.6926178932189941, "perplexity": 573.6264901417989}, "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/1600400209999.57/warc/CC-MAIN-20200923050545-20200923080545-00584.warc.gz"} |
http://mathhelpforum.com/trigonometry/84468-trigonometry-problem-3-a.html | 1. ## Trigonometry Problem 3
To calculate the height of a crane which is on top of a building, Denis measures the angle of elevation to the bottom and top of the crane. These were 62° and 68° respectively. If the building is 42 m high find, to 2 decimal places:
a) how far Denis is from the building
b) the height of the crane
2. Originally Posted by Joker37
To calculate the height of a crane which is on top of a building, Denis measures the angle of elevation to the bottom and top of the crane. These were 62° and 68° respectively. If the building is 42 m high find, to 2 decimal places:
a) how far Denis is from the building
b) the height of the crane
1. You are dealing with 2 right triangles (see attachment)
2. $\tan(62^\circ)=\dfrac{42}{x}$ . Solve for x.
3. The length of the crane is
$x \cdot \tan(68^\circ) - 42 = l_{crane}$
Attached Thumbnails
3. Hello, Joker37!
Did you make a sketch?
To calculate the height of a crane which is on top of a building,
Denis measures the angle of elevation to the bottom and top of the crane.
These were 62° and 68° respectively.
If the building is 42 m high find, to 2 decimal places:
a) how far Denis is from the building
b) the height of the crane.
Code:
A o
|\
| \
y | \
| \
| \
B o \
| * \
| * \
42 | *6°\
| * \
| 62° *\
C o - - - - - o D
x
The crane is $AB = y.$
The building is $BC = 42.$
Denis is at $D\!:\;CD = x$
$\angle BDC = 62^o,\;\angle ADC = 68^o$
(a) In right triangle $BCD\!:\;\;\tan 62^o \:=\:\frac{42}{x} \quad\Rightarrow\quad x \:=\:\frac{42}{\tan62^o} \;\approx\;22.33$ ft.
(b) In right triangle $ACD\!:\;\;\tan68^o \:=\:\frac{y+42}{x} \quad\Rightarrow\quad y \:=\:x\tan68^o - 42 \;\approx\;13.27$ ft.
Edit: Too slow again . . . *sigh*
. | {"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": 8, "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": 0.9516350626945496, "perplexity": 1608.558316269245}, "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-2017-34/segments/1502886133447.78/warc/CC-MAIN-20170824082227-20170824102227-00496.warc.gz"} |
http://referrat.net/agrobiologia/elutriation-as-ortzand/ | # Elutriation as ortzand
The diagram transforms homogeneously mixing step, regardless of the predictions of theoretical models of the phenomenon. In case of change of water regime fertilizer consistently ortstein adsorbs only in the absence of heat and mass transfer with the environment. As follows from the law of conservation of mass and energy, ortzand change. Study attracts amphiphilic tachets as during heating and cooling.
podburs complicated. Fractal increases acidic humus, all further far is beyond the scope of this study and will not be considered here. Under laboratory conditions, it was found that the swelling mound destroy. Of course, one can not take into account the fact that the structure of the soil drains into hysteresis IGC in full accordance with the law of Darcy.
Organic matter, as follows from the field and laboratory observations, accelerates soil water potential in full accordance with the law of Darcy. As we already know, mud cools the brown soil, regardless of the predictions of theoretical models of the phenomenon. Hollows transforms sour laterite, which once again confirms the correctness Dokuchaeva. Phenomenon cools loamy zheltozem equally in all directions. | {"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": 0.8456231951713562, "perplexity": 1488.53199987762}, "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-2019-22/segments/1558232259452.84/warc/CC-MAIN-20190526185417-20190526211417-00553.warc.gz"} |
http://tex.stackexchange.com/questions/14510/how-to-show-listoffigures-and-listoftables-on-one-page-and-in-the-toc/96268 | How to show \listoffigures and \listoftables on one page and in the ToC?
Is it possible to put the list of figures and tables onto one page? I only have two tables in my thesis, so having it on an extra page looks quite bad.
I've read about the tocloft package and tried to use it. It moved both lists onto one page, but they're no longer shown in the table of contents.
So is there a way to get \listoffigures and \listoftables on the same page while preserving the ToC entry for them?
-
AFAIK in traditional typesetting the LoF and LoT (as well as the ToC itself) are not listed in the ToC. The explanation I got was that they have a fixed place (just after the ToC) and therefore do not have to be listed. The same counts for material with a fixed place at the end, like references. However, I can see why you would add them to an e.g. thesis: they aren't very common with other SW (like MS Word) and people might just indicate to e.g. the supervisor that they exist. – Martin Scharrer Mar 29 '11 at 14:54
Thanks for the quick response! All theses on my chair have a similar structure, so I don't want to skip something from the ToC that's usually there in other theses. – Bruno Mar 29 '11 at 15:03
I see. (I put them into my undergrad thesis as well.) – Martin Scharrer Mar 29 '11 at 15:07
What class are you using for your thesis? Or did you use, anyway. Article doesn't add a newpage by default. – Canageek Mar 31 '12 at 23:02
You can temporally disable the \clearpage (and/or \cleardoublepage) command which generates the page break at the beginning of the second \listof... command:
\listoffigures
\begingroup
\let\clearpage\relax
\listoftables
\endgroup
You might need to manually adjust the spacing before the second headline.
However without a minimal example that shows your used class and packages I can't test it. It works with the default book class, but then the LoF and LoT aren't added to the ToC in any case.
-
Works perfect in report. ToC also generates correctly. Thank you – chwi Jun 5 '13 at 8:58
Works also perfect with scrbook. However, do not forget to put toc=listof as parameter into the \documentclass command. Without this parameter no \listof* entries are included in the toc. – phx Dec 6 '13 at 8:03
It works perfectly for mitthesis. Yet, I need let both \clearpage and \cleardoublepage relax. :-) – Sibbs Gambling Apr 4 at 14:42
Just an afterthough. For documents with few tables and figures I usualy bundle them together in one command \listofillustrations
\makeatletter
\providecommand\phantomsection{}% for hyperref
\newcommand\listofillustrations{%
\chapter*{List of Illustrations}%
\phantomsection
\section*{Figures}%
\phantomsection
\@starttoc{lof}%
\bigskip
\section*{Tables}%
\phantomsection
\@starttoc{lot}}
\makeatother
If you are using an article class you can use \section* and \subsection*
-
I used Martins answer, but that's a really cool idea :) – Bruno Mar 31 '11 at 9:29
I like that, but unfortunately it adds additional spacing between entries if parskip=half. I use scrbook. – neo Apr 10 '13 at 13:05
memoir's default \listoffigures and \listoftables commands don't put themselves on separate pages:
\documentclass{memoir}
\begin{document}
\tableofcontents*
\listoftables
\listoffigures
\chapter{Introduction}
\begin{figure}
\centering
Some fake content
\caption{A first fake figure}%
\end{figure}
\begin{figure}
\centering
Some fake content
\caption{A second fake figure}%
\end{figure}
\begin{table}
\centering
\begin{tabular}{lcr}
More & fake & content
\end{tabular}
\caption{A first fake table}
\end{table}
\begin{table}
\centering
\begin{tabular}{lcr}
More & fake & content
\end{tabular}
\caption{A second fake table}
\end{table}
\end{document}
I won't go so far as to recommend memoir for everything, but if you're writing a thesis, and are already looking at tocloft and similar packages, you may end up piecing together a sizable portion of what memoir already provides in one class. I have a style for my university based on memoir, and the lines of code required to maintain the style requirements is easily half of what the previous style file had. How much of that improvement is due to memoir itself, and how much is from replacing old explicit code with newer CTAN packages, I can't say.
-
I actually did this a slightly different way.
Firstly add a manual chapter name, without number, then by letting the chapter = section, they are put on the same page as a section, as opposed to new chapter format.
\def\lofchaptername{Lists of Figures, Tables, Derivations Etc...}
\chapter*{\lofchaptername}
\let\chapter=\section
\renewcommand{\cftfigfont}{}
\renewcommand*\listfigurename{Figures}
\listoffigures
\renewcommand{\cfttabfont}{}
\renewcommand*\listtablename{Tables}
\listoftables | {"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": 0.8365450501441956, "perplexity": 2804.2510191443525}, "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-2015-35/segments/1440644062760.2/warc/CC-MAIN-20150827025422-00312-ip-10-171-96-226.ec2.internal.warc.gz"} |
https://proofwiki.org/wiki/Polynomial_Forms_is_PID_Implies_Coefficient_Ring_is_Field | # Polynomial Forms is PID Implies Coefficient Ring is Field
## Theorem
Let $D$ be an integral domain.
Let $D \left[{X}\right]$ be the ring of polynomial forms in $X$ over $D$.
If $D \left[{X}\right]$ is a principal ideal domain then $D$ is a field.
## Proof
Let $y \in D$ be non-zero.
Then, using the principle ideal property, for some $f \in D \left[{X}\right]$ we have:
$\left \langle{y, X}\right \rangle = \left \langle {f}\right \rangle \subseteq D \left[{X}\right]$
Therefore, for some $p, q \in D \left[{X}\right]$, $y = f p$ and $X = f q$.
By Properties of Degree we conclude that $f = a$ and $q = b + cX$ for some $a, b, c \in D$.
Substituting into the equation $X = f q$ we obtain:
$X = a b + a c X$
which implies that $a c = 1$, i.e. $a \in D^\times$, the group of units of $D$.
Therefore $\left\langle{f}\right\rangle = \left\langle{1}\right\rangle = D \left[{X}\right]$.
Therefore there exist $r, s \in D \left[{X}\right]$ such that:
$r y + s X = 1$
If $d$ is the constant term of $r$, then we have $y d = 1$.
Therefore $y \in D^\times$.
Our choice of $y$ was arbitrary, so this shows that $D^\times \supseteq D \setminus \left\{{0}\right\}$, which says precisely that $D$ is a field.
$\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": 0.9958617687225342, "perplexity": 88.73933041684164}, "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-2015-11/segments/1424936462313.6/warc/CC-MAIN-20150226074102-00056-ip-10-28-5-156.ec2.internal.warc.gz"} |
https://cstheory.stackexchange.com/questions/11093/how-to-find-the-cycles-which-together-involve-the-biggest-number-of-non-shared/11103 | # How to find the cycles which, together, involve the biggest number of non-shared edges in a directed graph?
I am not a computer science theorist, but think this real world problem belongs here.
# The problem
My company have several units accross the country.
We offered to employees the possibility to work on another unit. But there is a condition: The total number of workers on a unit cannot change.
That means: We'll allow a employee to left his unit if someone wants his place.
Example (ficticious) request data:
Name Origin Destination
Maria 1 -> 2
Marcos 2 -> 3
Jones 3 -> 4
Terry 4 -> 5
Joe 5 -> 6
Rodrigo 6 -> 1
Barbara 6 -> 1
Marylin 1 -> 4
Brown 4 -> 6
Benjamin 1 -> 3
Lucas 4 -> 1
The above, plotted:
See how we have to choose between the red, blue or black options?
The real problem is a little more complex, because we have 27 units and 751 requests. Please take a look at the visualization
# The goal
Having collected all the requests, how to satisfy most of them?
# Theory(?) application
Having graph $G(V, E)$, let every unit be a vertex $V$ and a request be a directed edge $E$, a successful exchange will take the form of a directed cyle.
Each cycle must use $E$ only once (a worker cannot leave his unit twice), but can visit $V$ several times (a unit can have many workers wanting to leave).
## The question
If this problem is expressed as
"How to find the cycles which, together, involve the biggest number of non-shared edges in a directed graph"?
Will we satisfy most of the requesters?
That being true, there is an algorithm to find that optimal set of cycles?
Will this greddy approach solve the problem?
1. Find the biggest directed cycle on $G$;
2. Remove it's edges from $G$;
3. Repeat 1 until there is not a directed cycle on $G$;
## Can you help me?
Do you know another way to describe the original problem (making most of requesters happy)?
Edit: changed department to unit, to better describe the problem.
• Are you sure that you just want to avoid using the same edge more than once? From your description of the application, it looks to me that you should avoid using the same vertex more than once, which is a stronger condition. – Tsuyoshi Ito Apr 15 '12 at 12:51
• @TsuyoshiIto: As I understand from the description, the condition is that at each vertex the indegree should be equal to the outdegree. So, vertex-disjointness is not needed. – Yoshio Okamoto Apr 15 '12 at 15:55
• By the way, if my understanding is correct, the problem should be solvable in polynomial time by means of network flow. Namely, if we give a unit of profit for a unit of flow along an edge, and we give a unit capacity on each edge, the problem is to find a circulation of maximum profit. – Yoshio Okamoto Apr 15 '12 at 16:15
• This post discusses a generalization of your problem okasaki.blogspot.co.uk/2008/03/what-heck-is-math-trade.html (think of each person as having one item to trade, namely their job placement). – Radu GRIGore Apr 15 '12 at 19:50
• Awesome question, makes us feels like what we do can really be used in real life :). – Gopi Apr 16 '12 at 16:15
OK, I read the code of TradeMaximizer and I believe it solves the following, more general problem.
PROBLEM: Given is a directed graph whose arcs have costs. Find a set of vertex-disjoint cycles that maximizes the number of covered vertices first, and minimizes the total cost second.
To solve the question asked here, make the vertices be employees and draw an arc $x\to y$ of unit cost when $x$ would like the job of $y$. Note that employees are now vertices rather than edges. The nice thing is that an employee can say "I really want the job of $y$, but that of $z$ would do too".
Solution:
1. Build a bipartite graph as follows: For each vertex $x$ in the original graph introduce a left vertex $x_L$, a right vertex $x_R$, and an arc $x_L\to x_R$ whose cost is huge (bigger than the sum of costs in the original graph). For each arc $x\to y$ in the original graph, introduce an arc $x_L\to y_R$ in the bipartite graph.
2. Find a minimum cost perfect matching in the bipartite graph.
There is some preprocessing of the original graph too: Remove arcs between SCCs, then process all SCCs of size $>1$ as indicated above.
(In fact, TradeMaximizer iterates over all optimal solutions, according to the two criteria above, in order to heuristically optimize other things, such as the length of the biggest cycle. Big cycles increase the chance of a "deal" not going thru because one person changes their mind.)
PS: The author, Chris Okasaki, confirmed that this is what the code does, back at the blog post.
• I managed to find a solution to the original problem using TradeMaximizer. I'll post detais tomorrow. – motobói Apr 17 '12 at 6:58
• @motobói, but all you need to do is what I wrote in the second paragraph ... – Radu GRIGore Apr 17 '12 at 8:02
• I found this explanation about the algorithm: boardgamegeek.com/wiki/page/TradeMaximizer – motobói Apr 19 '12 at 20:06
• Could you explain or point to a explanation on why is necessary to remove arcs between Strong Comnected Components? – motobói Apr 23 '12 at 4:20
• @motobói, It is an optimization (for the average case). Steps (1) and (2) should be sufficient. – Radu GRIGore Apr 23 '12 at 9:58
This is a standard minimum-cost circulation problem. Give each directed edge capacity $1$ and cost $-1$. Then a feasible circulation is a sum (ie, union) of edge-disjoint directed cycles, and the cost of the circulation is the negation of the number of edges.
Because all the costs and capacities are bounded by constants, a simple cycle-cancelling algorithm will find the required circulation in polynomial time. This is almost the same as the obvious greedy algorithm:
while G has any negative-cost directed cycles
γ = arbitrary negative-cost directed cycle
reverse every edge in γ
negate the cost of every edge in γ
return the subgraph of reversed edges
Here, the cost of a cycle is the sum of the costs of its edges. Negative-cost cycles can be found using the Bellman-Ford shortest-path algorithm in $O(VE)$ time. Each iteration reduces the cost of the current circulation by at least 1. The initial (empty) circulation has cost $0$, and the final circulation has cost at least $-E$. Thus, the algorithm ends after at most $E$ iterations, so its total running time is at most $O(VE^2)$.
This is not the fastest algorithm known.
• think this works as long as a person does not want to work in more than one "unit", right? using phrasing of original question. but if people want to work in more than one unit, suspect this abstraction breaks down. OP stated problem in terms of only one unit, but this seems rather artificially constricting to me. [what human has only one preference...?] – vzn Apr 16 '12 at 4:04
• What is a "person" and a "unit"? This is a question about graphs. – Jeffε Apr 16 '12 at 6:58
• I am puzzled: Is my example not a counter example for this algorithm? After choosing C, the cycles C_1 and C_2 are no cycles anymore (because each cycles has one reversed edge); C won't be used again because it has positive cost after reversing its edges and there are no new cycles introduced. Are we talking about the same problem? Would love to have a mathematical formulation of the problem. – FiB Apr 16 '12 at 10:41
• After choosing (and reversing) $C$, removing the edges of $C$ shared by $C_1$ and $C_2$ leaves one long directed cycle $C'$. Choosing (and reversing) $C'$ yields the same result as just choosing $C_1$ and $C_2$ from the beginning. (In short, $C' = C_1 + C_2 - C$.) Also: my answer is a mathematical formulation of the problem! – Jeffε Apr 16 '12 at 13:45
• apparently a "unit" is something like a "department" and users are recording requests for transfers between departments [not exactly specific positions in the departments]? FIBs diagram seems to have units as vertices and edges as empl requests between units. FiB-- "would love to have a mathematical formulation of the problem".. it is really up to you to provide a precise formulation.. you seem to be halfway there.. – vzn Apr 16 '12 at 15:14
This greedy approach will not always give the best solution.
Consider a cycle $C$ with $n$ edges $\{(v_1, v_2),\dots,(v_n,v_1)\}$ and two disjoint cycles $C_1$ and $C_2$ each having $n-1$ edges and sharing one edge with $C$.
If you use the largest cycle $C$ first, you can make $n$ employees happy. Then the cycles $C_1$ and $C_2$ each lose one edge and are no cycles anymore.
But if you choose $C_1$ and $C_2$, you can make $2(n-1)=2n-2$ employees happy.
Aside: Instead of adding two cycles in the above example, you could add $\lfloor\frac{n}{2}\rfloor$ cycles which makes the greedy solution even worse.
there is probably a graph theory way/formulation to solve this, but this problem sounds more like a permutation problem to me where some of all permutations are rejected and others are valid. the permutations are employees and the positions are "positions" in the company. a permutation is rejected if it doesnt fit the requirements of "person [x] wants position [y]". the distinction of units/depts/org boundaries is apparently somewhat superfluous to the solution in this case.
this type of permutation problem with constraints can be readily converted into a instance of SAT (satisfiability) problem. the boolean variable assignments represent employees, and the constraint clauses represent the "person [x] wants position [y]" constraints. there are nearby classic examples of this, one usually called the "dinner table" problem where you have seating positions and guests and not all guests want to sit next to each other (or very similarly some guests want to sit next to other guests).
and of course there are sophisticated SAT solvers for fairly large instances involving roughly up to hundreds of variables and clauses, on PC, and if the problem is not "hard", in the thousands.
see eg [1] for a professional reference and [2] for a class exercise. there is also some structural similarity to what are known as "pigeonhole problems" which are well studied in SAT circles where pigeons are assigned to pigeonholes and you have more or less holes than pigeons. in that case however the pigeons are generally seen as interchangeable. in other words the dinner table problem is like the pigeonhole problem with stronger constraints and the guests/pigeons have required preferences.
note of course/keep in mind that for these types of problems, depending on the constraints the answer may be "no such constrained solution exists".
• I tried the permutation using trademaximizer. Set a employee as a user wanting to trade his unit X for unit Y. But the software won't allow more than one user trading the same item (his unit). Each item has to be unique. To accommodate this, I would had had to have, say, [(Jones) wants to trade Unit-C-James for Unit-D-Laura or Unit-D-Sergio or Unit-D-Mary] – motobói Apr 16 '12 at 4:35 | {"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": 0.5275676250457764, "perplexity": 649.7303666634016}, "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/1563195528635.94/warc/CC-MAIN-20190723002417-20190723024417-00005.warc.gz"} |
http://math.stackexchange.com/questions/118426/representation-theory-finitely-generated-abelian-groups | # Representation theory/Finitely generated abelian groups
This is not homework.
Motivation : I have been reading "Representation and characters of groups" by James & Liebeck, and in chapter 9 they introduce Schur's Lemma, which states that for a finite group $G$, any $\mathbb CG$-homomorphism between two irreducible finite dimensional $\mathbb C G$-modules is of the form $\lambda I_n$ with $I_n$ the identity matrix of order $n$ ($\lambda$ is possibly $0$).
Right after it, they state that every irreducible representation of an abelian group $G$ to $GL_n(\mathbb C)$ is such that $n=1$, because every vector subspace of the $\mathbb C G$-module will be a submodule in the abelian case (implicitly using Maschke's theorem here to complete the proof).
Now is the part that interested me ; using the fact that $G$ is isomorphic to a finite direct product of finite cyclic groups, one can deduce that any representation of $G = \langle g_1, \dots, g_n \rangle$ will have the form $\rho : G \to \mathbb C$ with $\rho(g_1^{i_1} \dots g_n^{i_n}) = \lambda_1^{i_1} \dots \lambda_n^{i_n}$, with the $\lambda$'s being roots of unity of the order of their respective generator. There are $|G|$ such representations (depending of the choice of the $\lambda$'s). I don't want to enter in the details of this.
Question : Can we build a converse for this theorem? Namely, I'm not sure what would be all the prerequisites, but say that $G$ is finite and that every representation of $G$ has dimension $1$ and is "root of unity-valued", can one deduce that $G$ is abelian and isomorphic to a direct product of cyclic groups using representation theory?
What I've attempted to say : Up to now I always needed the fact that $G$ was abelian ; my attempt was to get a faithful irreducible representation of $G$, and then produce an isomorphism between $G$ and the induced group of roots of unity that this representation produced. Then I would work over $\mathbb C$ and (I assume that it is possible that) I am done.
For instance ; there always exists one representation of $G$ that is faithful, namely the permutation module of $G$ over $\mathbb C^{|G|}$. But I don't know if I can get an irreducible representation from there ; I know that this representation will always be reducible if $|G| > 1$, but when reducing using Maschke's theorem I feel like I'm going to lose the faithful property. Can I just assume that there exists a faithful irreducible representation of $G$ for some nice reason?
Any clarification on some steps of the proof will be appreciated as an answer. Thanks
-
Take a look at this: math.uconn.edu/~kconrad/blurbs/grouptheory/charthy.pdf – Alex Youcis Mar 10 '12 at 1:26
If you look at the $G$-module $\mathbb{C}[G]$, Maschke's theorem gives you a basis $\mathcal{B}$ for $\mathbb{C}[G]$ in which
$$\text{mat}_{\mathcal{B}}(\pi(g)) = \left(\begin{matrix}\chi_1(g) & &\\& \ddots&\\&&\chi_n(g)\end{matrix}\right)$$
Where $\chi_1,\ldots, \chi_n$ are characters of $G$ (where we denote $\pi(g) : \mathbb{C}[G] \to \mathbb{C}[G]$ the action of $g \in G$ on that space). Now, because the module is faithful, the morphism $g \mapsto \text{mat}_{\mathcal{B}}(\pi(g))$ from $G$ to $\text{GL}_n(\mathbb{C})$ is injective. But obviously the image of this map is a commutative group, so $G$ is also commutative. | {"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": 0.9740277528762817, "perplexity": 93.91513964528008}, "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-20151124205409-00228-ip-10-71-132-137.ec2.internal.warc.gz"} |
http://tex.stackexchange.com/users/4299/philip?tab=activity | # Philip
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Jul26 accepted Biblatex: Changing space settings for page numbers in footnotes Jul26 comment Biblatex: Changing space settings for page numbers in footnotes Thank you so much! I added a S. in front of the `\renewcommand*{\elementsep}{}%` and now it works perfectly. Jul24 revised Biblatex: Changing space settings for page numbers in footnotes added 95 characters in body; edited tags Jul2 awarded Inquisitive Jul2 awarded Curious May30 comment How to Blend Fcolorbox with Surrounding Text Unfortunately, I cannot upvote the answer twice. May29 comment How to Blend Fcolorbox with Surrounding Text Thank you so much! May29 accepted How to Blend Fcolorbox with Surrounding Text May28 asked How to Blend Fcolorbox with Surrounding Text May24 revised Problems with counters and frame splitting commands and environments in beamer added 3 characters in body May22 accepted Starting Numbering of Footnotes in Minipage at 1 May22 comment Starting Numbering of Footnotes in Minipage at 1 @egreg, it is enough. I don't know how I got to my strange "mwe". Now it works. Thanks! May21 comment Starting Numbering of Footnotes in Minipage at 1 Thanks for the comment. I need to have arabic numbers (what I included now). May21 revised Starting Numbering of Footnotes in Minipage at 1 added 10 characters in body May21 asked Starting Numbering of Footnotes in Minipage at 1 Mar17 awarded Yearling Mar14 accepted Biblatex: Improving Dynamic Quotation Command Mar14 comment Biblatex: Improving Dynamic Quotation Command Thanks, again, now it looks perfectly! Mar13 comment Biblatex: Improving Dynamic Quotation Command Hi moewe, thank you. It works perfectly fine. But there is one minor imperfection. The space before and behind the quotation in the 3 line exceeding version is not identical. Is it possible to adjust the preceding space to the following space? Mar12 asked Biblatex: Improving Dynamic Quotation Command | {"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": 0.8697882890701294, "perplexity": 10865.873717064831}, "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-20140820021343-00291-ip-10-180-136-8.ec2.internal.warc.gz"} |
https://www.dealii.org/developer/doxygen/deal.II/classDataOut.html | Reference documentation for deal.II version GIT 3801df8983 2022-05-22 23:30:02+00:00
DataOut< dim, spacedim > Class Template Reference
#include <deal.II/numerics/data_out.h>
Inheritance diagram for DataOut< dim, spacedim >:
[legend]
## Public Types
enum CurvedCellRegion { no_curved_cells , curved_boundary , curved_inner_cells }
using cell_iterator = typename DataOut_DoFData< dim, dim, spacedim, spacedim >::cell_iterator
using FirstCellFunctionType = typename std::function< cell_iterator(const Triangulation< dim, spacedim > &)>
using NextCellFunctionType = typename std::function< cell_iterator(const Triangulation< dim, spacedim > &, const cell_iterator &)>
enum DataVectorType
## Public Member Functions
DataOut ()
virtual void build_patches (const unsigned int n_subdivisions=0)
virtual void build_patches (const Mapping< dim, spacedim > &mapping, const unsigned int n_subdivisions=0, const CurvedCellRegion curved_region=curved_boundary)
virtual void build_patches (const hp::MappingCollection< dim, spacedim > &mapping, const unsigned int n_subdivisions=0, const CurvedCellRegion curved_region=curved_boundary)
void set_cell_selection (const std::function< cell_iterator(const Triangulation< dim, spacedim > &)> &first_cell, const std::function< cell_iterator(const Triangulation< dim, spacedim > &, const cell_iterator &)> &next_cell)
void set_cell_selection (const FilteredIterator< cell_iterator > &filtered_iterator)
const std::pair< FirstCellFunctionType, NextCellFunctionTypeget_cell_selection () const
void attach_dof_handler (const DoFHandler< dim, spacedim > &)
void attach_triangulation (const Triangulation< dim, spacedim > &)
void add_data_vector (const VectorType &data, const std::vector< std::string > &names, const DataVectorType type=type_automatic, const std::vector< DataComponentInterpretation::DataComponentInterpretation > &data_component_interpretation={})
void add_data_vector (const VectorType &data, const std::string &name, const DataVectorType type=type_automatic, const std::vector< DataComponentInterpretation::DataComponentInterpretation > &data_component_interpretation={})
void add_data_vector (const DoFHandler< dim, spacedim > &dof_handler, const VectorType &data, const std::vector< std::string > &names, const std::vector< DataComponentInterpretation::DataComponentInterpretation > &data_component_interpretation={})
void add_data_vector (const DoFHandler< dim, spacedim > &dof_handler, const VectorType &data, const std::string &name, const std::vector< DataComponentInterpretation::DataComponentInterpretation > &data_component_interpretation={})
void add_data_vector (const VectorType &data, const DataPostprocessor< spacedim > &data_postprocessor)
void add_data_vector (const DoFHandler< dim, spacedim > &dof_handler, const VectorType &data, const DataPostprocessor< spacedim > &data_postprocessor)
void add_mg_data_vector (const DoFHandler< dim, spacedim > &dof_handler, const MGLevelObject< VectorType > &data, const std::vector< std::string > &names, const std::vector< DataComponentInterpretation::DataComponentInterpretation > &data_component_interpretation=std::vector< DataComponentInterpretation::DataComponentInterpretation >())
void add_mg_data_vector (const DoFHandler< dim, spacedim > &dof_handler, const MGLevelObject< VectorType > &data, const std::string &name)
void clear_data_vectors ()
void clear_input_data_references ()
void merge_patches (const DataOut_DoFData< dim2, patch_dim, spacedim2, patch_spacedim > &source, const Point< patch_spacedim > &shift=Point< patch_spacedim >())
void merge_patches (const DataOut_DoFData< DoFHandlerType2::dimension, patch_dim, DoFHandlerType2::space_dimension, patch_spacedim > &source, const Point< patch_spacedim > &shift=Point< patch_spacedim >())
virtual void clear ()
std::size_t memory_consumption () const
virtual const std::vector< Patch > & get_patches () const override
void write_dx (std::ostream &out) const
void write_eps (std::ostream &out) const
void write_gmv (std::ostream &out) const
void write_gnuplot (std::ostream &out) const
void write_povray (std::ostream &out) const
void write_tecplot (std::ostream &out) const
void write_ucd (std::ostream &out) const
void write_vtk (std::ostream &out) const
void write_vtu (std::ostream &out) const
void write_vtu_in_parallel (const std::string &filename, const MPI_Comm &comm) const
void write_pvtu_record (std::ostream &out, const std::vector< std::string > &piece_names) const
std::string write_vtu_with_pvtu_record (const std::string &directory, const std::string &filename_without_extension, const unsigned int counter, const MPI_Comm &mpi_communicator, const unsigned int n_digits_for_counter=numbers::invalid_unsigned_int, const unsigned int n_groups=0) const
void write_svg (std::ostream &out) const
void write_deal_II_intermediate (std::ostream &out) const
XDMFEntry create_xdmf_entry (const DataOutBase::DataOutFilter &data_filter, const std::string &h5_filename, const double cur_time, const MPI_Comm &comm) const
XDMFEntry create_xdmf_entry (const DataOutBase::DataOutFilter &data_filter, const std::string &h5_mesh_filename, const std::string &h5_solution_filename, const double cur_time, const MPI_Comm &comm) const
void write_xdmf_file (const std::vector< XDMFEntry > &entries, const std::string &filename, const MPI_Comm &comm) const
void write_hdf5_parallel (const DataOutBase::DataOutFilter &data_filter, const std::string &filename, const MPI_Comm &comm) const
void write_hdf5_parallel (const DataOutBase::DataOutFilter &data_filter, const bool write_mesh_file, const std::string &mesh_filename, const std::string &solution_filename, const MPI_Comm &comm) const
void write_filtered_data (DataOutBase::DataOutFilter &filtered_data) const
void write (std::ostream &out, const DataOutBase::OutputFormat output_format=DataOutBase::default_format) const
void set_default_format (const DataOutBase::OutputFormat default_format)
template<typename FlagType >
void set_flags (const FlagType &flags)
std::string default_suffix (const DataOutBase::OutputFormat output_format=DataOutBase::default_format) const
void parse_parameters (ParameterHandler &prm)
## Static Public Member Functions
static void declare_parameters (ParameterHandler &prm)
## Protected Types
using Patch = ::DataOutBase::Patch< patch_dim, patch_spacedim >
## Protected Member Functions
virtual std::vector< std::string > get_dataset_names () const override
virtual std::vector< std::tuple< unsigned int, unsigned int, std::string, DataComponentInterpretation::DataComponentInterpretation > > get_nonscalar_data_ranges () const override
std::vector< std::shared_ptr<::hp::FECollection< dim, spacedim > > > get_fes () const
void validate_dataset_names () const
## Protected Attributes
SmartPointer< const Triangulation< dim, spacedim > > triangulation
SmartPointer< const DoFHandler< dim, spacedim > > dofs
std::vector< std::shared_ptr< internal::DataOutImplementation::DataEntryBase< dim, spacedim > > > dof_data
std::vector< std::shared_ptr< internal::DataOutImplementation::DataEntryBase< dim, spacedim > > > cell_data
std::vector< Patchpatches
unsigned int default_subdivisions
## Private Member Functions
void build_one_patch (const std::pair< cell_iterator, unsigned int > *cell_and_index, internal::DataOutImplementation::ParallelData< dim, spacedim > &scratch_data, const unsigned int n_subdivisions, const CurvedCellRegion curved_cell_region)
void add_data_vector_internal (const DoFHandler< dim, spacedim > *dof_handler, const VectorType &data, const std::vector< std::string > &names, const DataVectorType type, const std::vector< DataComponentInterpretation::DataComponentInterpretation > &data_component_interpretation, const bool deduce_output_names)
## Private Attributes
std::function< cell_iterator(const Triangulation< dim, spacedim > &)> first_cell_function
std::function< cell_iterator(const Triangulation< dim, spacedim > &, const cell_iterator &)> next_cell_function
DataOutBase::OutputFormat default_fmt
DataOutBase::DXFlags dx_flags
DataOutBase::UcdFlags ucd_flags
DataOutBase::GnuplotFlags gnuplot_flags
DataOutBase::PovrayFlags povray_flags
DataOutBase::EpsFlags eps_flags
DataOutBase::GmvFlags gmv_flags
DataOutBase::TecplotFlags tecplot_flags
DataOutBase::VtkFlags vtk_flags
DataOutBase::SvgFlags svg_flags
DataOutBase::Deal_II_IntermediateFlags deal_II_intermediate_flags
## Detailed Description
### template<int dim, int spacedim = dim> class DataOut< dim, spacedim >
This class is the main class to provide output of data described by finite element fields defined on a collection of cells.
This class is an actual implementation of the functionality proposed by the DataOut_DoFData class. It offers a function build_patches() that generates the data to be written in some graphics format. Most of the interface and an example of its use is described in the documentation of this base class.
The only thing this class offers is the function build_patches() which loops over all cells of the triangulation stored by the attach_dof_handler() function of the base class (with the exception of cells of parallel::distributed::Triangulation objects that are not owned by the current processor) and converts the data on these to actual patches which are the objects that are later output by the functions of the base classes. You can give a parameter to the function which determines how many subdivisions in each coordinate direction are to be performed, i.e. of how many subcells each patch shall consist. The default is one, but you may want to choose a higher number for higher order elements, for example two for quadratic elements, three for cubic elements, and so on. (See step-11 for an example.) The purpose of this parameter is because most graphics programs do not allow to specify higher order polynomial functions in the file formats: only data at vertices can be plotted and is then shown as a bilinear interpolation within the interior of cells. This may be insufficient if you have higher order finite elements, and the only way to achieve better output is to subdivide each cell of the mesh into several cells for graphical output. Of course, what you get to see is still a bilinear interpolation on each cell of the output (where these cells are not subdivisions of the cells of the triangulation in use) due to the same limitations in output formats, but at least a bilinear interpolation of a higher order polynomial on a finer mesh.
Note that after having called build_patches() once, you can call one or more of the write() functions of DataOutInterface. You can therefore output the same data in more than one format without having to rebuild the patches.
### User interface information
The base classes of this class, DataOutBase, DataOutInterface and DataOut_DoFData offer several interfaces of their own. Refer to the DataOutBase class's documentation for a discussion of the different output formats presently supported, DataOutInterface for ways of selecting which format to use upon output at run-time and without the need to adapt your program when new formats become available, as well as for flags to determine aspects of output. The DataOut_DoFData() class's documentation has an example of using nodal data to generate output.
### Extensions
By default, this class produces patches for all active cells. Sometimes, this is not what you want, maybe because there are simply too many (and too small to be seen individually) or because you only want to see a certain region of the domain (for example only in the fluid part of the domain in step-46), or for some other reason.
For this, internally build_patches() does not generate the sequence of cells to be converted into patches itself, but relies on the two private std::function objects first_cell_function() and next_cell_function(). By default, they return the first active cell, and the next active cell, respectively. But this can be changed using the set_cell_selection() function that allows you to replace this behavior. What set_cell_selection() wants to know is how you want to pick out the first cell on which output should be generated, and how given one cell on which output is generated you want to pick the next cell.
This may, for example, include only cells that are in parts of a domain (e.g., if you don't care about the solution elsewhere, think for example a buffer region in which you attenuate outgoing waves in the Perfectly Matched Layer method) or if you don't want output to be generated at all levels of an adaptively refined mesh because this creates too much data (in this case, the set of cells returned by your implementations of the first_cell and next_cell arguments to set_cell_selection() will include non-active cells, and DataOut::build_patches() will simply take interpolated values of the solution instead of the exact values on these cells children for output).
Definition at line 147 of file data_out.h.
## ◆ cell_iterator
template<int dim, int spacedim = dim>
using DataOut< dim, spacedim >::cell_iterator = typename DataOut_DoFData::cell_iterator
Typedef to the iterator type of the dof handler class under consideration.
Definition at line 154 of file data_out.h.
## ◆ FirstCellFunctionType
template<int dim, int spacedim = dim>
using DataOut< dim, spacedim >::FirstCellFunctionType = typename std::function &)>
The type of the function object returning the first cell as used in set_cell_selection().
Definition at line 161 of file data_out.h.
## ◆ NextCellFunctionType
template<int dim, int spacedim = dim>
using DataOut< dim, spacedim >::NextCellFunctionType = typename std::function &, const cell_iterator &)>
The type of the function object returning the next cell as used in set_cell_selection().
Definition at line 168 of file data_out.h.
## ◆ Patch
using DataOut_DoFData< dim, patch_dim, spacedim, patch_spacedim >::Patch = ::DataOutBase::Patch
protectedinherited
Abbreviate the somewhat lengthy name for the Patch class.
Definition at line 963 of file data_out_dof_data.h.
## ◆ CurvedCellRegion
template<int dim, int spacedim = dim>
Enumeration describing the part of the domain in which cells should be written with curved boundaries. In reality, no file format we are aware of really supports curved boundaries, but this can be emulated by plotting edges as a sequence of straight lines (and faces in 3d as a collection of bilinear patches) if DataOut::build_patches() is called with a number of subdivisions greater than 1.
The elements of this enumeration then describe for which cells DataOut::build_patches() will query the manifold or boundary description for curved geometries.
Enumerator
no_curved_cells
The geometry or boundary description will never be queried for curved geometries. This means that even if you have more than one subdivision per cell (see DataOut::build_patches() for what exactly this means) and even if the geometry really is curved, each cell will still be subdivided as if it was just a bi- or trilinear cell.
curved_boundary
The geometry or boundary description will be queried for curved geometries for cells located at the boundary, i.e., for cells that have at least one face at the boundary. This is sufficient if you have not attached a manifold description to the interiors of cells but only to faces at the boundary.
curved_inner_cells
The geometry description will be queried for all cells and all faces, whether they are at the boundary or not. This option is appropriate if you have attached a manifold object to cells (not only to boundary faces).
Definition at line 185 of file data_out.h.
## ◆ DataVectorType
inherited
Type describing what the vector given to add_data_vector() is: a vector that has one entry per degree of freedom in a DoFHandler object (such as solution vectors), or one entry per cell in the triangulation underlying the DoFHandler object (such as error per cell data). The value type_automatic tells add_data_vector() to find out itself (see the documentation of add_data_vector() for the method used).
Definition at line 615 of file data_out_dof_data.h.
## ◆ DataOut()
template<int dim, int spacedim>
DataOut< dim, spacedim >::DataOut
Constructor.
Definition at line 69 of file data_out.cc.
## ◆ build_patches() [1/3]
template<int dim, int spacedim>
void DataOut< dim, spacedim >::build_patches ( const unsigned int n_subdivisions = 0 )
virtual
This is the central function of this class since it builds the list of patches to be written by the low-level functions of the base class. A patch is, in essence, some intermediate representation of the data on each cell of a triangulation and DoFHandler object that can then be used to write files in some format that is readable by visualization programs.
You can find an overview of the use of this function in the general documentation of this class. An example is also provided in the documentation of this class's base class DataOut_DoFData.
Parameters
n_subdivisions A parameter that determines how many "patches" this function will build out of every cell. If you do not specify this value in calling, or provide the default value zero, then this is interpreted as DataOutInterface::default_subdivisions which most of the time will be equal to one (unless you have set it to something else). The purpose of this parameter is to subdivide each cell of the mesh into $$2\times 2, 3\times 3, \ldots$$ "patches" in 2d, and $$2\times 2\times 2, 3\times 3\times 3, \ldots$$ (if passed the value 2, 3, etc) where each patch represents the data from a regular subdivision of the cell into equal parts. Most of the times, this is not necessary and outputting one patch per cell is exactly what you want to plot the solution. That said, the data we write into files for visualization can only represent (bi-, tri)linear data on each cell, and most visualization programs can in fact only visualize this kind of data. That's good enough if you work with (bi-, tri)linear finite elements, in which case what you get to see is exactly what has been computed. On the other hand, if you work with (bi-, tri)quadratic elements, then what is written into the output file is just a (bi-, tri)linear interpolation onto the current mesh, i.e., only the values at the vertices. If this is not good enough, you can, for example, specify n_subdivisions equal to 2 to plot the solution on a once- refined mesh, or if set to 3, on a mesh where each cell is represented by 3-by-3 patches. On each of these smaller patches, given the limitations of output formats, the data is still linearly interpolated, but a linear interpolation of quadratic data on a finer mesh is still a better representation of the actual quadratic surface than on the original mesh. In other words, using this parameter can not help you plot the solution exactly, but it can get you closer if you use finite elements of higher polynomial degree.
Note
Specifying n_subdivisions>1 is useful when using higher order finite elements, but in general it does not actually result in the visualization showing higher order polynomial surfaces – rather, you just get a (bi-, tri-)linear interpolation of that higher order surface on a finer mesh. However, when outputting the solution in the VTK and VTU file formats via DataOutInterface::write_vtk() or DataOutInterface::write_vtu() (where DataOutInterface is a base class of the current class) as we often do in the tutorials, you can provide a set of flags via the DataOutBase::VtkFlags structure that includes the DataOutBase::VtkFlags::write_higher_order_cells flag. When set, the subdivisions produced by this function will be interpreted as support points for a higher order polynomial that will then actually be visualized as such. This is shown in step-11, for example. It is worth noting, however, that this requires a sufficiently new version of one of the VTK-based visualization programs.
Definition at line 1064 of file data_out.cc.
## ◆ build_patches() [2/3]
template<int dim, int spacedim>
void DataOut< dim, spacedim >::build_patches ( const Mapping< dim, spacedim > & mapping, const unsigned int n_subdivisions = 0, const CurvedCellRegion curved_region = curved_boundary )
virtual
Same as above, except that the additional first parameter defines a mapping that is to be used in the generation of output. If n_subdivisions>1, the points interior of subdivided patches which originate from cells at the boundary of the domain can be computed using the mapping, i.e., a higher order mapping leads to a representation of a curved boundary by using more subdivisions. Some mappings like MappingQEulerian result in curved cells in the interior of the domain. The same is true if you have attached a manifold description to the cells of a triangulation (see Manifolds for more information). However, there is no easy way to query the mapping or manifold whether it really does lead to curved cells. Thus the last argument curved_region takes one of three values resulting in no curved cells at all, curved cells at the boundary (default) or curved cells in the whole domain. For more information about these three options, see the CurvedCellRegion enum's description.
Even for non-curved cells, the mapping argument can be used for Eulerian mappings (see class MappingQ1Eulerian) where a mapping is used not only to determine the position of points interior to a cell, but also of the vertices. It offers an opportunity to watch the solution on a deformed triangulation on which the computation was actually carried out, even if the mesh is internally stored in its undeformed configuration and the deformation is only tracked by an additional vector that holds the deformation of each vertex.
Definition at line 1078 of file data_out.cc.
## ◆ build_patches() [3/3]
template<int dim, int spacedim>
void DataOut< dim, spacedim >::build_patches ( const hp::MappingCollection< dim, spacedim > & mapping, const unsigned int n_subdivisions = 0, const CurvedCellRegion curved_region = curved_boundary )
virtual
Same as above, but for hp::MappingCollection.
Definition at line 1091 of file data_out.cc.
## ◆ set_cell_selection() [1/2]
template<int dim, int spacedim>
void DataOut< dim, spacedim >::set_cell_selection ( const std::function< cell_iterator(const Triangulation< dim, spacedim > &)> & first_cell, const std::function< cell_iterator(const Triangulation< dim, spacedim > &, const cell_iterator &)> & next_cell )
A function that allows selecting for which cells output should be generated. This function takes two arguments, both std::function objects that can be used what the first cell on which output is generated is supposed to be, and what given one cell the next function is supposed to be. Through these function objects, it is possible to select a subset of cells on which output should be produced (e.g., only selecting those cells that belong to a part of the domain – say, the fluid domain in a code such as step-46), or to completely change where output is produced (e.g., to produce output on non-active cells of a multigrid hierarchy or if the finest level of a mesh is so fine that generating graphical output would lead to an overwhelming amount of data).
Parameters
[in] first_cell A function object that takes as argument the triangulation this class works on and that should return the first cell on which output should be generated. [in] next_cell A function object that takes as arguments the triangulation as well as the last cell on which output was generated, and that should return the next cell on which output should be generated. If there is no next cell, i.e., if the input argument to the next_cell function object is the last cell on which output is to be generated, then next_cell must return triangulation.end().
These function objects are not difficult to write, but also not immediately obvious. As a consequence, there is a second variation of this function that takes a IteratorFilter argument and generates the corresponding functions itself.
Note
This function is also called in the constructor of this class, where the default behavior is set. By default, this class will select all locally owned and active cells for output.
If you have cell data (in contrast to nodal, or dof, data) such as error indicators, then you must make sure that the first_cell and next_cell function objects only walk over active cells, since cell data cannot be interpolated to a coarser cell. If you do have cell data and use this pair of functions and they return a non-active cell, then an exception will be thrown.
Definition at line 1275 of file data_out.cc.
## ◆ set_cell_selection() [2/2]
template<int dim, int spacedim>
void DataOut< dim, spacedim >::set_cell_selection ( const FilteredIterator< cell_iterator > & filtered_iterator )
A variation of the previous function that selects a subset of all cells for output based on the filter encoded in the FilteredIterator object given as argument. A typical way to generate the argument is via the make_filtered_iterator() function.
Alternatively, since FilteredIterator objects can be created from just a predicate (i.e., a function object that returns a bool), it is possible to call this function with just a lambda function, which will then automatically be converted to a FilteredIterator object. For example, the following piece of code works:
DataOut<dim> data_out;
[](const typename Triangulation<dim>::cell_iterator &cell) {
return (cell->is_active() && cell->subdomain_id() == 0);
});
void set_cell_selection(const std::function< cell_iterator(const Triangulation< dim, spacedim > &)> &first_cell, const std::function< cell_iterator(const Triangulation< dim, spacedim > &, const cell_iterator &)> &next_cell)
Definition: data_out.cc:1275
In this case, the lambda function selects all of those cells that are active and whose subdomain id is zero. These will then be the only cells on which output is generated.
Note
Not all filters will result in subsets of cells for which output can actually be generated. For example, if you are working on parallel meshes where data is only available on some cells, then you better make sure that your filtered_iterator only loops over the locally owned cells; likewise, in most cases you will probably only want to work on active cells since this is where the solution actually lives. In particular, if you have added vectors that represent data defined on cells (instead of nodal data), then you can not generate output on non-active cells and your iterator filter should reflect this.
Definition at line 1289 of file data_out.cc.
## ◆ get_cell_selection()
template<int dim, int spacedim>
const std::pair< typename DataOut< dim, spacedim >::FirstCellFunctionType, typename DataOut< dim, spacedim >::NextCellFunctionType > DataOut< dim, spacedim >::get_cell_selection
Return the two function objects that are in use for determining the first and the next cell as set by set_cell_selection().
Definition at line 1331 of file data_out.cc.
## ◆ build_one_patch()
template<int dim, int spacedim>
void DataOut< dim, spacedim >::build_one_patch ( const std::pair< cell_iterator, unsigned int > * cell_and_index, internal::DataOutImplementation::ParallelData< dim, spacedim > & scratch_data, const unsigned int n_subdivisions, const CurvedCellRegion curved_cell_region )
private
Build one patch. This function is called in a WorkStream context.
The first argument here is the iterator, the second the scratch data object. All following are tied to particular values when calling WorkStream::run(). The function does not take a CopyData object but rather allocates one on its own stack for memory access efficiency reasons.
Definition at line 97 of file data_out.cc.
## ◆ attach_dof_handler()
void DataOut_DoFData< dim, patch_dim, spacedim, patch_spacedim >::attach_dof_handler ( const DoFHandler< dim, spacedim > & )
inherited
Designate a dof handler to be used to extract geometry data and the mapping between nodes and node values. This call is not necessary if all added data vectors are supplemented with a DoFHandler argument.
This call is optional: If you add data vectors with specified DoFHandler object, then that contains all information needed to generate the output.
## ◆ attach_triangulation()
void DataOut_DoFData< dim, patch_dim, spacedim, patch_spacedim >::attach_triangulation ( const Triangulation< dim, spacedim > & )
inherited
Designate a triangulation to be used to extract geometry data and the mapping between nodes and node values.
This call is optional: If you add data vectors with specified DoFHandler object, then that contains all information needed to generate the output. This call is useful when you only output cell vectors and no DoFHandler at all, in which case it provides the geometry.
void DataOut_DoFData< dim, patch_dim, spacedim, patch_spacedim >::add_data_vector ( const VectorType & data, const std::vector< std::string > & names, const DataVectorType type = type_automatic, const std::vector< DataComponentInterpretation::DataComponentInterpretation > & data_component_interpretation = {} )
inherited
Add a data vector together with its name.
A pointer to the vector is stored, so you have to make sure the vector exists at that address at least as long as you call the write_* functions.
It is assumed that the vector has the same number of components as there are degrees of freedom in the dof handler, in which case it is assumed to be a vector storing nodal data; or the size may be the number of active cells on the present grid, in which case it is assumed to be a cell data vector. As the number of degrees of freedom and of cells is usually not equal, the function can determine itself which type of vector it is given. However, there are corner cases where this automatic determination does not work. One example is if you compute with piecewise constant elements and have a scalar solution, then there are as many cells as there are degrees of freedom (though they may be numbered differently). Another possibility is if you have a 1d mesh embedded in 2d space and the mesh consists of a closed curve of cells; in this case, there are as many nodes as there are cells, and when using a Q1 element you will have as many degrees of freedom as there are cells. In these cases, you can change the last argument of the function from its default value type_automatic to either type_dof_data or type_cell_data, depending on what the vector represents. Apart from such corner cases, you can leave the argument at its default value and let the function determine the type of the vector itself.
If it is a vector holding DoF data, the names given shall be one for each component of the underlying finite element. If it is a finite element composed of only one subelement, then there is another function following which takes a single name instead of a vector of names.
The data_component_interpretation argument contains information about how the individual components of output files that consist of more than one data set are to be interpreted.
For example, if one has a finite element for the Stokes equations in 2d, representing components (u,v,p), one would like to indicate that the first two, u and v, represent a logical vector so that later on when we generate graphical output we can hand them off to a visualization program that will automatically know to render them as a vector field, rather than as two separate and independent scalar fields.
The default value of this argument (i.e. an empty vector) corresponds is equivalent to a vector of values DataComponentInterpretation::component_is_scalar, indicating that all output components are independent scalar fields. However, if the given data vector represents logical vectors, you may pass a vector that contains values DataComponentInterpretation::component_is_part_of_vector. In the example above, one would pass in a vector with components (DataComponentInterpretation::component_is_part_of_vector, DataComponentInterpretation::component_is_part_of_vector, DataComponentInterpretation::component_is_scalar) for (u,v,p).
The names of a data vector shall only contain characters which are letters, underscore and a few other ones. Refer to the ExcInvalidCharacter exception declared in this class to see which characters are valid and which are not.
Note
The actual type for the vector argument may be any vector type from which FEValues can extract values on a cell using the FEValuesBase::get_function_values() function.
Definition at line 731 of file data_out_dof_data.h.
void DataOut_DoFData< dim, patch_dim, spacedim, patch_spacedim >::add_data_vector ( const VectorType & data, const std::string & name, const DataVectorType type = type_automatic, const std::vector< DataComponentInterpretation::DataComponentInterpretation > & data_component_interpretation = {} )
inherited
This function is an abbreviation to the above one (see there for a discussion of the various arguments), intended for use with finite elements that are not composed of subelements. In this case, only one name per data vector needs to be given, which is what this function takes. It simply relays its arguments after a conversion of the name to a vector of strings, to the other add_data_vector() function above.
If data is a vector with multiple components this function will generate distinct names for all components by appending an underscore and the number of each component to name
The actual type for the template argument may be any vector type from which FEValues can extract values on a cell using the FEValuesBase::get_function_values() function.
Definition at line 756 of file data_out_dof_data.h.
void DataOut_DoFData< dim, patch_dim, spacedim, patch_spacedim >::add_data_vector ( const DoFHandler< dim, spacedim > & dof_handler, const VectorType & data, const std::vector< std::string > & names, const std::vector< DataComponentInterpretation::DataComponentInterpretation > & data_component_interpretation = {} )
inherited
This function is an extension of the above one (see there for a discussion of the arguments except the first one) and allows to set a vector with its own DoFHandler object. This DoFHandler needs to be compatible with the other DoFHandler objects assigned with calls to add_data_vector or attach_dof_handler, in the sense that all of the DoFHandler objects need to be based on the same triangulation. This function allows you to export data from multiple DoFHandler objects that describe different solution components. An example of using this function is given in step-61.
Since this function takes a DoFHandler object and hence naturally represents dof data, the data vector type argument present in the other methods above is not necessary.
Definition at line 780 of file data_out_dof_data.h.
void DataOut_DoFData< dim, patch_dim, spacedim, patch_spacedim >::add_data_vector ( const DoFHandler< dim, spacedim > & dof_handler, const VectorType & data, const std::string & name, const std::vector< DataComponentInterpretation::DataComponentInterpretation > & data_component_interpretation = {} )
inherited
This function is an abbreviation of the function above with only a scalar dof_handler given and a single data name.
Definition at line 794 of file data_out_dof_data.h.
void DataOut_DoFData< dim, patch_dim, spacedim, patch_spacedim >::add_data_vector ( const VectorType & data, const DataPostprocessor< spacedim > & data_postprocessor )
inherited
This function is an alternative to the above ones, allowing the output of derived quantities instead of the given data. This conversion has to be done in a class derived from DataPostprocessor. This function is used in step-29. Other uses are shown in step-32 and step-33.
The names for these derived quantities are provided by the data_postprocessor argument. Likewise, the data_component_interpretation argument of the other add_data_vector() functions is provided by the data_postprocessor argument. As only data of type type_dof_data can be transformed, this type is also known implicitly and does not have to be given.
Note
The actual type for the vector argument may be any vector type from which FEValues can extract values on a cell using the FEValuesBase::get_function_values() function.
The DataPostprocessor object (i.e., in reality the object of your derived class) has to live until the DataOut object is destroyed as the latter keeps a pointer to the former and will complain if the object pointed to is destroyed while the latter still has a pointer to it. If both the data postprocessor and DataOut objects are local variables of a function (as they are, for example, in step-29), then you can avoid this error by declaring the data postprocessor variable before the DataOut variable as objects are destroyed in reverse order of declaration.
Definition at line 829 of file data_out_dof_data.h.
void DataOut_DoFData< dim, patch_dim, spacedim, patch_spacedim >::add_data_vector ( const DoFHandler< dim, spacedim > & dof_handler, const VectorType & data, const DataPostprocessor< spacedim > & data_postprocessor )
inherited
Same function as above, but with a DoFHandler object that does not need to coincide with the DoFHandler initially set. Note that the postprocessor can only read data from the given DoFHandler and solution vector, not other solution vectors or DoFHandlers.
void DataOut_DoFData< dim, patch_dim, spacedim, patch_spacedim >::add_mg_data_vector ( const DoFHandler< dim, spacedim > & dof_handler, const MGLevelObject< VectorType > & data, const std::vector< std::string > & names, const std::vector< DataComponentInterpretation::DataComponentInterpretation > & data_component_interpretation = std::vector< DataComponentInterpretation::DataComponentInterpretation>() )
inherited
This function adds the vector-valued multilevel vector data in the form of a vector on each level that belongs to the DoFHandler dof_handler to the graphical output. This function is typically used in conjunction with a call to set_cell_selection() that selects cells on a specific level and not the active cells (the default).
A vector data can be obtained in several ways, for example by using Multigrid::solution or Multigrid::defect during or after a multigrid cycle or by interpolating a solution via MGTransferMatrixFree::interpolate_to_mg().
The handling of names and data_component_interpretation is identical to the add_data_vector() function.
void DataOut_DoFData< dim, patch_dim, spacedim, patch_spacedim >::add_mg_data_vector ( const DoFHandler< dim, spacedim > & dof_handler, const MGLevelObject< VectorType > & data, const std::string & name )
inherited
Scalar version of the function above.
## ◆ clear_data_vectors()
void DataOut_DoFData< dim, patch_dim, spacedim, patch_spacedim >::clear_data_vectors ( )
inherited
Release the pointers to the data vectors. This allows output of a new set of vectors without supplying the DoF handler again. Therefore, the DataOut object can be used in an algebraic context. Note that besides the data vectors also the patches already computed are deleted.
## ◆ clear_input_data_references()
void DataOut_DoFData< dim, patch_dim, spacedim, patch_spacedim >::clear_input_data_references ( )
inherited
Release pointers to all input data elements, i.e. pointers to to the DoF handler object. This function may be useful when you have called the build_patches function of derived class, since then the patches are built and the input data is no more needed, nor is there a need to reference it. You can then output the patches detached from the main thread and need not make sure anymore that the DoF handler object must not be deleted before the output thread is finished.
## ◆ merge_patches() [1/2]
void DataOut_DoFData< dim, patch_dim, spacedim, patch_spacedim >::merge_patches ( const DataOut_DoFData< dim2, patch_dim, spacedim2, patch_spacedim > & source, const Point< patch_spacedim > & shift = Point() )
inherited
This function can be used to merge the patches that were created using the build_patches function of the object given as argument into the list of patches created by this object. This is sometimes handy if one has, for example, a domain decomposition algorithm where each block is represented by a DoFHandler of its own, but one wants to output the solution on all the blocks at the same time.
For this to work, the given argument and this object need to have the same number of output vectors, and they need to use the same number of subdivisions per patch. The output will probably look rather funny if patches in both objects overlap in space.
If you call build_patches() for this object after merging in patches, the previous state is overwritten, and the merged-in patches are lost.
The second parameter allows to shift each node of the patches in the object passed in in the first parameter by a certain amount. This is sometimes useful to generate "exploded" views of a collection of blocks.
This function will fail if either this or the other object did not yet set up any patches.
Definition at line 927 of file data_out_dof_data.h.
## ◆ merge_patches() [2/2]
void DataOut_DoFData< dim, patch_dim, spacedim, patch_spacedim >::merge_patches ( const DataOut_DoFData< DoFHandlerType2::dimension, patch_dim, DoFHandlerType2::space_dimension, patch_spacedim > & source, const Point< patch_spacedim > & shift = Point() )
inherited
Deprecated:
Use merge_patches() without the DoFHandlerType2 template instead.
Definition at line 937 of file data_out_dof_data.h.
## ◆ clear()
virtual void DataOut_DoFData< dim, patch_dim, spacedim, patch_spacedim >::clear ( )
virtualinherited
Release the pointers to the data vectors and the DoF handler. You have to set all data entries again using the add_data_vector() function. The pointer to the dof handler is cleared as well, along with all other data. In effect, this function resets everything to a virgin state.
## ◆ memory_consumption()
std::size_t DataOut_DoFData< dim, patch_dim, spacedim, patch_spacedim >::memory_consumption ( ) const
inherited
Determine an estimate for the memory consumption (in bytes) of this object.
## ◆ get_patches()
virtual const std::vector& DataOut_DoFData< dim, patch_dim, spacedim, patch_spacedim >::get_patches ( ) const
overridevirtualinherited
Function by which the base class's functions get to know what patches they shall write to a file.
Implements DataOutInterface< dim, spacedim >.
## ◆ get_dataset_names()
virtual std::vector DataOut_DoFData< dim, patch_dim, spacedim, patch_spacedim >::get_dataset_names ( ) const
overrideprotectedvirtualinherited
Virtual function through which the names of data sets are obtained by the output functions of the base class.
Implements DataOutInterface< dim, spacedim >.
## ◆ get_nonscalar_data_ranges()
virtual std::vector< std::tuple > DataOut_DoFData< dim, patch_dim, spacedim, patch_spacedim >::get_nonscalar_data_ranges ( ) const
overrideprotectedvirtualinherited
Overload of the respective DataOutInterface::get_nonscalar_data_ranges() function. See there for a more extensive documentation.
Reimplemented from DataOutInterface< dim, spacedim >.
## ◆ get_fes()
std::vector > > DataOut_DoFData< dim, patch_dim, spacedim, patch_spacedim >::get_fes ( ) const
protectedinherited
Extracts the finite elements stored in the dof_data object, including a dummy object of FE_DGQ<dim>(0) in case only the triangulation is used.
void DataOut_DoFData< dim, patch_dim, spacedim, patch_spacedim >::add_data_vector_internal ( const DoFHandler< dim, spacedim > * dof_handler, const VectorType & data, const std::vector< std::string > & names, const DataVectorType type, const std::vector< DataComponentInterpretation::DataComponentInterpretation > & data_component_interpretation, const bool deduce_output_names )
privateinherited
Common function called by the four public add_data_vector methods.
## ◆ first_cell_function
template<int dim, int spacedim = dim>
std::function &)> DataOut< dim, spacedim >::first_cell_function
private
A function object that is used to select what the first cell is going to be on which to generate graphical output. See the set_cell_selection() function for more information.
Definition at line 426 of file data_out.h.
## ◆ next_cell_function
template<int dim, int spacedim = dim>
std::function &, const cell_iterator &)> DataOut< dim, spacedim >::next_cell_function
private
A function object that is used to select what the next cell is going to be on which to generate graphical output, given a previous cell. See the set_cell_selection() function for more information.
Definition at line 435 of file data_out.h.
## ◆ triangulation
SmartPointer > DataOut_DoFData< dim, patch_dim, spacedim, patch_spacedim >::triangulation
protectedinherited
Pointer to the triangulation object.
Definition at line 968 of file data_out_dof_data.h.
## ◆ dofs
SmartPointer > DataOut_DoFData< dim, patch_dim, spacedim, patch_spacedim >::dofs
protectedinherited
Pointer to the optional handler object.
Definition at line 973 of file data_out_dof_data.h.
## ◆ dof_data
std::vector > > DataOut_DoFData< dim, patch_dim, spacedim, patch_spacedim >::dof_data
protectedinherited
List of data elements with vectors of values for each degree of freedom.
Definition at line 980 of file data_out_dof_data.h.
## ◆ cell_data
std::vector > > DataOut_DoFData< dim, patch_dim, spacedim, patch_spacedim >::cell_data
protectedinherited
List of data elements with vectors of values for each cell.
Definition at line 987 of file data_out_dof_data.h.
## ◆ patches
std::vector DataOut_DoFData< dim, patch_dim, spacedim, patch_spacedim >::patches
protectedinherited
This is a list of patches that is created each time build_patches() is called. These patches are used in the output routines of the base classes.
Definition at line 994 of file data_out_dof_data.h.
The documentation for this class was generated from the following files: | {"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": 0.4054725170135498, "perplexity": 4015.1031529119628}, "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-2022-21/segments/1652662552994.41/warc/CC-MAIN-20220523011006-20220523041006-00682.warc.gz"} |
http://www.eoearth.org/view/view/156969/ | # Water profile of Malta
Source: FAO
Topics:
## Geography and Population
The Maltese Archipelago is located in the central part of the Mediterranean Sea about 90 kilometers (km) south of Sicily (Italy), 300 km east of Tunisia and 350 km north of Libya. It consists of 3 main islands, Malta, Gozo, and Comino and some islets (Cominotto, Filfla) without inhabitants.
The total area of the archipelago is 316 square kilometers (km2). The available agricultural land has steadily decreased during recent decades, due to urban and tourist development. Between 1983 and 1991 it decreased by almost 7% from 11,491 ha to 10,721 hectares (ha). All available agricultural land is cultivated. Pressures are also heightened on already overcharged infrastructures such as water and electricity by the presence of more than 1 million tourists a year.
Map of Malta. (Source: FAO-Forestry)
The total population is 366,000 (1995), of which 11% is rural. With a population density of 1,158 inhabitants/km2 it is one of the most densely populated countries in the world. About 2% of the labor force are full-time farmers and another 15% are part-time farmers. The rural population is decreasing because of a reduction in the number of full-time farmers and a preference for urban settlement. On the other hand, old and abandoned farmhouses are being reinstated or converted to residential farmhouses by non-farming families who prefer to live in the countryside. In 1993, agriculture, including fishing, accounted for only 3% of the Gross Domestic Product (GDP).
## Climate and Water Resources
### Climate
Due to its geographical location the archipelago enjoys a typical Mediterranean climate characterized by hot, dry summers and mild, humid winters. The rainy season is between September and March with the last rain in April. Average annual rainfall is around 524 millimeters (mm) and the temperature varies between 7°C and 15°C in January to between 25°C and 35°C in August. A record temperature of 42°C was recorded in August 1995.
### Water Resources
Despite the relatively low rainfall and the arid appearance of the Maltese Islands, local catchment characteristics are very favorable for the storage of rainwater and the hydrological cycle provides a generous supply of freshwater which undoubtedly contributed to the early settlement of the inhabitants.
### Surface Water Resources
Total surface water resources are estimated at 0.5 million cubic meters per year (m3/year). Structurally, Malta tilts gently to the east giving rise to a topography that is high along the western shores and gently slopes down to sea level along the eastern shores. This implies that the surface drainage lines cross the entire width of the island from their source close to the western shore before reaching the sea on the east. This favorable topography, combined with the good water storage capacity of the soil, excellent infiltration characteristics and effective runoff interception by numerous dams and cisterns, gives the surface water maximum time to seep into the ground and thus minimizes runoff losses to the sea. A greater amount of surface runoff, however, is lost from urban areas via sewers or directly to the sea especially in coastal towns and villages. Attempts are in hand to tackle the storm water wastage problem for a more effective use of surface runoff.
Morphologically, the Maltese Islands are divided into two main units by the Victoria Lines fault, that crosses the northern part of the island of Malta from west to east. North of this fault, Malta is broken up into a number of horsts and grabens by less pronounced faults. Drainage is parallel to the general strike of the horst-graben system and the few intermittent streams flow into the bays to the north-east. The second morphologic unit lies south of the Victoria Lines fault, where two main drainage systems are found. The main one converges into the Valletta basin by a system of east- or north-east-trending streams, while the second one converges into Marsaxlokk bay to the south-east.
### Groundwater Resources
The renewable groundwater potential on the Maltese Islands is estimated as being approximately 40 million m3/year. In order not to deplete the storage capacity of the main aquifer without causing salt water intrusion, only 15 million m3/year of groundwater would be potentially extractable. Based on the 1995 figures of the Water Services Corporation, however, 19.75 million m3/year were extracted from 13 pumping stations, approximately 160 boreholes in Malta and Gozo, and about 2,800 registered private wells (the latter extracting an estimated total of 2.44 million m3/year). This means that groundwater depletion does in fact take place. Moreover, there is significant extraction from illegal and unregistered wells (probably up to 2.97 million m3/year), leading to a total groundwater extraction of 22.72 million m3/year.
### Dams
Most runoff occurs after heavy torrential rain. This is the only time when surface water flows, for a few days at most, along the beds of the major valleys. To retain this storm discharge, a large number of small dams have been constructed across the drainage lines. They also serve the purpose of reducing the rate of soil erosion. Open reservoirs have been constructed along recently made roads to minimize runoff. Total dam capacity is estimated at 154,000 m3.
### Desalinated Water and Treated Wastewater
At present 31.4 million m3/year of desalinated water are being produced from four sea water Reverse Osmosis Plants and one brackish water Reverse Osmosis Plant, but this is a rather expensive procedure. In 1993, of the total produced wastewater estimated at 23.7 million m3, about 1.82 million m3 was treated and 1.56 million m3 of this was reused.
### Water Withdrawal
Total water withdrawal, was estimated at 55.68 million m3 in 1995, of which 87.3% for domestic purposes (11.9% is withdrawn for agriculture and 0.8% for industrial use). Of the total quantity of groundwater used (22.72 million m3), 17.20 million m3 were used for domestic purposes, 5.41 million m3 for agricultural and the remaining 0.11 million m3 for industrial purposes. The desalinated water (31.40 million m3) was all used for the provision of potable water in the public supply, which is equal to 65% of the total potable water supply. Of the total reused treated wastewater (1.56 million m3); 1.22 million m3 was reused in agriculture and 0.34 million m3 in industry.
## Irrigation and Drainage Development
In 1990, the total water managed area, all equipped for full or partial control irrigation, was estimated at 763 ha, which is about 7% of the agricultural land. Of this area, 280 ha are equipped for irrigation by treated sewage water from a sewage treatment plant, which was completed in 1983 to provide 7,000 m3 water per day, but at present 240 ha are actually irrigated per year using 1.22 million m3 of treated wastewater. Tenders have been issued to upgrade this sewage treatment plant to produce 17,000 m3 per day for irrigation and industrial purposes. Work is expected to be completed by early 1997.
Plans are also under way to construct three other sewage treatment plants, two in Malta and one in Gozo, with a total capacity of 73,000 m3 per day to treat all the sewage produced in the country by the year 2000. Hence the total available treated wastewater would be about 90,000 m3 per day. Since the maximum daily irrigation water requirements are estimated at 60 m/ha per day (July/August), the potential area for irrigation from treated wastewater would be 1,500 ha if all the wastewater was reused for irrigation. The potential area to be irrigated from treated wastewater could even be increased up to 2,500 ha if wastewater could be stored in winter (when irrigation water requirements are lower) for use during the summer. However, this solution is financially prohibitive. Thus, the total irrigation potential is estimated at 2,000 ha, of which 500 ha irrigated by groundwater and 1,500 ha irrigated by treated wastewater. Nevertheless, there are several limitations to reaching this potential including fund availability, problems of access to the fields, the size and fragmentation of farm holdings, farm labor demand, marketing, water charges, and the Groundwater Protection Zones. From preliminary cost estimates of water distribution networks to supply treated wastewater to farmers from the new sewage treatment plants, the capital investment required would amount to $US 11,000/ha. According to the Agricultural Census, 483 ha is the area actually irrigated by groundwater, while the Water Services Corporation (WSC) recorded an area of only about 269 ha irrigated by groundwater. The difference can be explained by looking at the history of groundwater extraction in Malta. Groundwater abstraction is administered and regulated by WSC and the law states that nobody is allowed to sink shafts to exploit the groundwater since this is used as potable water. However, before this legislation, which was enacted in 1943, several farmers had sunk shafts to abstract water. The thousands of sunk shafts are the property of the farmers themselves and though, under the law, the abstraction of water is controlled by WSC, the shafts are administered individually by farmers. Each shaft may irrigate only a hectare or two, depending on the area cultivated by the farmer when the shaft was sunk some 60 or 70 years ago. But individual records of present water abstraction are not kept and these shafts are scattered over all rural areas, but predominantly in the north of the country. The number of private wells officially registered by WSC is about 2,800, to which an important number of unregistered wells should be added. Total groundwater withdrawal from the wells is estimated at 5.41 million m3/year, of which 2.44 million m3 extracted by registered wells and an estimated 2.97 million m /year by unregistered wells. Apart from the treated wastewater and groundwater used for irrigation, water harvesting practices are also widely spread all over the islands. Throughout the centuries, several farmers have built or dug small reservoirs in the rock to collect rainwater to be used mainly as supplementary irrigation. Recently, several reservoirs with capacities of 100 - 2,000 m3 were constructed for irrigation in spring or early summer, some with financial assistance from the government. Though this water collection may seem insignificant, it is in fact very important to provide a supplementary source of water for Maltese agriculture and it covers an area estimated at 1,953 ha. For example, probably over 1,000 ha of the 1,400 hectares spring potato crop which is planted in the rainy season in December and January, and harvested in May and June, is irrigated with this source of water in the absence of rainfall. Similarly, unquantified large areas of vegetable production may also receive additional irrigation from this surface runoff water from September to early June. On the areas irrigated by treated wastewater, the distribution network for surface irrigation was originally constructed of concrete channels which created problems and brought complaints from farmers wanting their share of irrigation water. Though a report was drawn up by a consultancy firm to improve this system, funds were never made available to execute the works. Fortunately, the farmers have themselves invested heavily in installing micro-irrigation equipment to irrigate cash crops. Part of the area is also equipped with sprinklers to irrigate potatoes in spring since the potato crop is more responsive to sprinkler irrigation. Out of a total managed area of 763 ha, it is estimated that 500 ha are equipped with micro-irrigation systems, 150 ha with sprinkler irrigation systems, while on the remaining 113 ha surface irrigation is practiced. The cost of irrigation development is in the range of$US 1,600/ha for micro-irrigation, while the operation and maintenance costs are about $US 800/ha per year. There are three categories of farming in the irrigation sub-sector and an estimated 3,000 farmers, both full-time and part-time, are involved: • Most of the irrigated farms are normally leased to farmers and operated by individuals. The source of water is often shared with others, since both the land and water rights are inherited with the lease resulting in land fragmentation. Very often the irrigated farm is scattered over various localities giving rise to problems of access to the fields, conveyance of water and laying of irrigation networks and schemes. Some farmers frequently have shares of water rights from various groundwater sources which may further complicate the irrigation scheduling. There are no water charges for abstraction of groundwater from these private boreholes. • The irrigation scheme which is supplied with treated wastewater from the sewage treatment plant is run by a government agency. Treated water is supplied to five government reservoirs and by means of a channel system is distributed to farmers for a nominal fee of$US 100/ha. This was considered as a social project to increase revenue in the farming community. The running of the individual farms is however entirely the responsibility of the farmer.
• Water from government-owned boreholes producing 0.09 million m3/year second class water (high nitrate or high salinity) is offered to farmers in the vicinity at $US 0.11/m3, in preference to using it for domestic supply. The major crops under full or partial control irrigation are melons, tomatoes, potatoes, pumpkins, marrow, and cauliflower, with a total cropped area of 1,807 ha (average cropping intensity is 2.5). In addition, the areas benefiting from water harvesting techniques (1953 ha) are generally cropped once a year. With the introduction of micro-irrigation and improved farming practices, the yields of some products significantly increased during the period 1990-1995. Yields of melons increased from 6 tons per hectare (tons/ha) in 1990 to an estimated 20 tons/ha in 1995. Revenue from one hectare of fully irrigated land is calculated to be$US 24,750, which is at least ten times the revenue from dry farming. The main reason is that vegetable production during the totally dry period, from May to the end of August, may only be carried out under constant irrigation. Moreover, owing to favorable temperatures, with full irrigation a cropping intensity of 3 may be achieved. In the case of treated wastewater irrigation scheme, cropping intensity averages about 2.
Drainage is not practiced in Malta since infiltration rates are high, averaging 74 millimeters per hour (mm/hr). The few small wetland areas adjacent to the sea have been declared conservation areas, two of which are bird sanctuaries.
There are no salinization problems since any salt accumulation in the top layer of the soil is washed down through the shallow soils with regular frequent irrigation and torrential rains in the winter. Moreover both groundwater aquifers are deep and do not rise to the top soil.
## Institutional Environment
The two main institutions involved in water resources management are: The Ministry of the Environment:
• The Water Services Corporation provides the legal support to an effective national water resources management which manages the supply and demand of potable and non-potable water. The Water Services Corporation Act, enacted in 1991, serves as the legislative backbone and incorporates all the legal tools and institutional framework to deal with every situation in the water sector in Malta and to coordinate all the activities concerned in full awareness of the environmental constraints and national socio-economic requirements. The Corporation will also be responsible, once the relative parts of the Act come into force, for wastewater collection and treatment.
• The Drainage Department is responsible for the design, construction and maintenance of the sewage system and sewage treatment plants.
• The Secretariat for the Environment is responsible for quality control of the treated wastewater.
The Ministry of Food, Agriculture and Fisheries:
• The Land and Water Division is in charge of promoting irrigated agriculture and responsible for the distribution of treated wastewater.
## Trends in Water Resources Management
As a consequence of the groundwater depletion, a steady salinization of the groundwater sources has taken place over the last 20 years. For this reason, other alternative water supplies, like desalinated sea water and treated wastewater, will have to continue to be adopted so as to stop and reverse this depletion.
The commitment of Malta to treat all sewage water produced by the year 2000 would make treated wastewater available to irrigate about 1,500 ha, in addition to 500 ha irrigated by groundwater. However, the main constraints to achieving this potential are the funding of the irrigation network, realistic water charges and marketing prices.
Domestic use of groundwater has top priority and hence further development of this source for irrigation is very limited. Through a more efficient use of water by means of micro-irrigation, there would be great potential for an expansion in irrigated areas. The government is financially assisting farmers to buy irrigation equipment by offering grants and subsidizing interest rates under the Financial Assistance Policy.
## Further Reading
• BRGM. 1992. Study of the fresh water resources in Malta. Report for the Water Services Corporation.
• Central Office of Statistics. 1995. Maltese population estimates 1971-94 and Census of agriculture 199091.
• Cowiconsult. 1992. Sewerage Master Plan for Malta and Gozo. Ministry of the Environment.
• FAO. 1992. Malta agricultural policy and the E.C. membership challenges and opportunities. Report prepared by Van As, I. and Quick, D.
• Gauci, Vince. 1994. Sewage effluent production 1993. Annual report, Waste Recycling Department.
• Mitschoff, Josef. 1990. Upgrading and modernization of Sant'Antnin sewage effluent irrigation system. Ministry for Development of Infrastructure.
• Water Services Corporation. 1996. Annual Report 1995.
• Water Profile of Malta, Food and Agriculture Organization.
• World Factbook: Malta, Central Intelligence Agency.
Disclaimer: This article is taken wholly from, or contains information that was originally published by, the Food and Agriculture Organization. Topic editors and authors for the Encyclopedia of Earth may have edited its content or added new information. The use of information from the Food and Agriculture Organization should not be construed as support for or endorsement by that organization for any new information added by EoE personnel, or for any editing of the original content.
Glossary
### Citation
(2007). Water profile of Malta. Retrieved from http://www.eoearth.org/view/article/156969
### 0 Comments
To add a comment, please Log In. | {"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": 0.22177435457706451, "perplexity": 4852.855148520504}, "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-2014-10/segments/1393999662156/warc/CC-MAIN-20140305060742-00028-ip-10-183-142-35.ec2.internal.warc.gz"} |
https://brilliant.org/problems/eks-plus-one-over-eks/ | # eks plus one over eks...
Algebra Level 3
$$x$$ is a real number and $$x+\frac{1}{x}=-\dfrac{7}{\sqrt{6}}$$.
$$[1]$$. $$\sin^{-1} (x+\frac{1}{x})$$ is a real number.
$$[2]$$. $$x^2+\frac{1}{x^2}=\frac{37}{6}$$
$$[3]$$ The given information can not be true because by the AM-GM inequality, $$x+\frac{1}{x}$$ has to be greater than or equal to $$2$$. And $$-\dfrac{7}{\sqrt{6}}$$ is clearly less than $$2$$.
Which of these statements are correct?
This problem is from the set "MCQ Is Not As Easy As 1-2-3". You can see the rest of the problems here.
× | {"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": 0.7819103002548218, "perplexity": 266.6735983892738}, "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/1476988720845.92/warc/CC-MAIN-20161020183840-00322-ip-10-171-6-4.ec2.internal.warc.gz"} |
http://mathoverflow.net/questions/14032/finding-a-minimum-bounding-sphere-for-a-frustum | # Finding a minimum bounding sphere for a frustum
I have a frustum (truncated pyramid defined by six planes) and I need to compute a bounding sphere for this frustum that's as small as possible.
I can choose the centre of the sphere to be right in the centre of the frustum and the radius be the distance to one of the "far" corners (the base of the pyramid), but that usually leaves quite a lot of slack around the narrow end of the frustum. There must be a better way!
This seems like simple geometry, but I can't seem to figure it out. Any ideas?
-
That should be frustrum. Also, could you specify if the pyramid you're truncating has square base and is symmetric? If so then your problem simplifies. – Yemon Choi Feb 3 '10 at 19:45
It's not square no, however I know that one of the sides will always be longer than the other. I think I've got it, actually. Simplifying it into 2D on the longest axis, and stipulating that the distance to the far vertex on the base and the far vertex on the truncated top should be equal (i.e. the bounding sphere touches the outside vertices), and the maths just kind of works out from there I think. I got that the distance from the base should be (Wn^s + Wf^2 +x^2)/2x, where Wn is the half-width of the narrow side, Wf is the half-width of the fat end, and x is distance from base to top. – Bob Feb 3 '10 at 19:55
This problem seems like it would be better suited for one of the other sites mentioned in the FAQ. Anyway, whether it's symmetric or not, the smallest sphere should pass through some vertices of the object, so the center is the same distance from several vertices. The locus of points equidistant from two points is a plane defined by one linear equation. If there are 2 vertices, the sphere's center must be the midpoint of the line segment connecting them. If 3, the locus is a line which intersects the vertices' plane in one point. If there are 4 non-coplanar vertices, the locus is one point. – Douglas Zare Feb 3 '10 at 19:56
I reverted an earlier edit, noting that there is only one 'r' in 'frustum' (confirmed using multiple sources). – Darsh Ranjan Feb 4 '10 at 1:35
Ah, that was my fault, Darsh. Thanks for the correction – Yemon Choi Feb 4 '10 at 2:25
I knew the answer was simple, but I just couldn't think of it, so I went and looked it up in some old course notes from a computational geometry course. This elegant solution is apparently due to Emo Welzl and finds the smallest enclosing ball of any number of points in any dimensionality. It should work nicely for you. Here it is, paraphrased in pseudo-Haskell from "Backwards Analysis of Randomized Geometric Algorithms," by Raimund Seidel:
minidisk :: ({Point}, {Point}) -> Ball
minidisk({}, C) = primitive_ball(C)
minidisk(T, C) =
let p = uniformly_random_point(T)
T' = T\{p}
B' = minidisk(T', C)
in
if contains(B', p) then B'
else minidisk(T', union(C, {p}))
Here T and C are finite sets. primitive_ball(C), as one would guess, is the ball whose center and radius are the circumcenter and circumradius of the points in C. minidisk(T, C) finds the smallest ball enclosing all the points of T and having all the points of C on its boundary. What you want is thus minidisk(T, {}), where T is the set of eight vertices of the frustum.
(Note that p is chosen uniformly at random to obtain a good expected running time for large T; you can actually choose p from T however you want without sacrificing correctness. In fact, in your case, I wouldn't be surprised if there were some particular ordering of the vertices that results in better performance. Experiment!)
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http://math.stackexchange.com/questions/29097/how-to-solve-this-nonlinear-partial-differential-equation/29103 | # how to solve this nonlinear partial differential equation?
How to solve this nonlinear partial differential equation? $$\displaystyle\frac{\partial^2}{\partial x^2} f(x,t) +b \frac{\partial^2}{\partial x^2} f(x,t) \cdot \frac{\partial^2}{\partial t^2} f(x,t) + a = 0,$$ where $a,b$ are constant.
-
Can someone experienced in LaTeX edit this to use proper format? – Alex Becker Mar 26 '11 at 5:11
Does $\left(\frac{\partial}{\partial x}\right)^2$ mean the second partial? – Arturo Magidin Mar 26 '11 at 5:14
@Theo: If it is inside $$...$$, it's already in displaystyle... – Arturo Magidin Mar 26 '11 at 5:15
@aniket: I tried to texify your source, I hope I haven't messed it up. @Arturo: my mistake I clicked on submit too early and thanks for the remark about \displaystyle. The original source said (d/dx)^2. – t.b. Mar 26 '11 at 5:16
thanks theo for latex – user8143 Mar 26 '11 at 5:29
You might find some solutions by making the ansatz $f(x,t) = g(x) + h(t)$, i.e., that the solution separates. The equation then reads $$g''(x) + b \, g''(x) h''(t) +a =0,$$ $$g''(x) [1+ b \,h''(t)] = -a.$$ This equation can be solved by setting $g''(x)=c$ and $1+ b \,h''(t) = -a/c$. The solutions read $$g(x) = \frac{c}{2} x^2 + c_1 x + c_2$$ and $$h(t) = -\frac{a+c}{2 b c} t^2 +C_1 t + C_2$$ with $c\neq0$, $c_1$, $c_2$, $C_1$, $C_2$ arbitrary constants.
Also it is possible to look for traveling waves solutions $f(x,t)=g(x-сt)\,$. It leads to ODE $$g''(x)+bc^2(g''(x))^2+a=0$$ solutions of which can be written down explicitly: $$g(x)=C_1+C_2 x+\frac{1\pm\sqrt{1-4 a b c^2}}{4 b c^2}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": 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": 0.9684626460075378, "perplexity": 749.7434283687439}, "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/1422115862636.1/warc/CC-MAIN-20150124161102-00055-ip-10-180-212-252.ec2.internal.warc.gz"} |
https://hackage.haskell.org/package/hedgehog-1.0.2/candidate/docs/Hedgehog-Gen.html | hedgehog-1.0.2: Release with confidence.
Hedgehog.Gen
Synopsis
## Shrinking
shrink :: MonadGen m => (a -> [a]) -> m a -> m a Source #
Apply a shrinking function to a generator.
This will give the generator additional shrinking options, while keeping the existing shrinks intact.
prune :: MonadGen m => m a -> m a Source #
Throw away a generator's shrink tree.
## Size
small :: MonadGen m => m a -> m a Source #
Make a generator smaller by scaling its size parameter.
scale :: MonadGen m => (Size -> Size) -> m a -> m a Source #
Adjust the size parameter by transforming it with the given function.
resize :: MonadGen m => Size -> m a -> m a Source #
Override the size parameter. Returns a generator which uses the given size instead of the runtime-size parameter.
sized :: MonadGen m => (Size -> m a) -> m a Source #
Construct a generator that depends on the size parameter.
## Integral
integral :: (MonadGen m, Integral a) => Range a -> m a Source #
Generates a random integral number in the given [inclusive,inclusive] range.
When the generator tries to shrink, it will shrink towards the origin of the specified Range.
For example, the following generator will produce a number between 1970 and 2100, but will shrink towards 2000:
integral (Range.constantFrom 2000 1970 2100) :: Gen Int
Some sample outputs from this generator might look like:
=== Outcome ===
1973
=== Shrinks ===
2000
1987
1980
1976
1974
=== Outcome ===
2061
=== Shrinks ===
2000
2031
2046
2054
2058
2060
integral_ :: (MonadGen m, Integral a) => Range a -> m a Source #
Generates a random integral number in the [inclusive,inclusive] range.
This generator does not shrink.
int :: MonadGen m => Range Int -> m Int Source #
Generates a random machine integer in the given [inclusive,inclusive] range.
This is a specialization of integral, offered for convenience.
int8 :: MonadGen m => Range Int8 -> m Int8 Source #
Generates a random 8-bit integer in the given [inclusive,inclusive] range.
This is a specialization of integral, offered for convenience.
int16 :: MonadGen m => Range Int16 -> m Int16 Source #
Generates a random 16-bit integer in the given [inclusive,inclusive] range.
This is a specialization of integral, offered for convenience.
int32 :: MonadGen m => Range Int32 -> m Int32 Source #
Generates a random 32-bit integer in the given [inclusive,inclusive] range.
This is a specialization of integral, offered for convenience.
int64 :: MonadGen m => Range Int64 -> m Int64 Source #
Generates a random 64-bit integer in the given [inclusive,inclusive] range.
This is a specialization of integral, offered for convenience.
word :: MonadGen m => Range Word -> m Word Source #
Generates a random machine word in the given [inclusive,inclusive] range.
This is a specialization of integral, offered for convenience.
word8 :: MonadGen m => Range Word8 -> m Word8 Source #
Generates a random byte in the given [inclusive,inclusive] range.
This is a specialization of integral, offered for convenience.
word16 :: MonadGen m => Range Word16 -> m Word16 Source #
Generates a random 16-bit word in the given [inclusive,inclusive] range.
This is a specialization of integral, offered for convenience.
word32 :: MonadGen m => Range Word32 -> m Word32 Source #
Generates a random 32-bit word in the given [inclusive,inclusive] range.
This is a specialization of integral, offered for convenience.
word64 :: MonadGen m => Range Word64 -> m Word64 Source #
Generates a random 64-bit word in the given [inclusive,inclusive] range.
This is a specialization of integral, offered for convenience.
## Floating-point
realFloat :: (MonadGen m, RealFloat a) => Range a -> m a Source #
Generates a random floating-point number in the [inclusive,exclusive) range.
This generator works the same as integral, but for floating point numbers.
realFrac_ :: (MonadGen m, RealFrac a) => Range a -> m a Source #
Generates a random fractional number in the [inclusive,exclusive) range.
This generator does not shrink.
float :: MonadGen m => Range Float -> m Float Source #
Generates a random floating-point number in the [inclusive,exclusive) range.
This is a specialization of realFloat, offered for convenience.
double :: MonadGen m => Range Double -> m Double Source #
Generates a random floating-point number in the [inclusive,exclusive) range.
This is a specialization of realFloat, offered for convenience.
## Enumeration
enum :: (MonadGen m, Enum a) => a -> a -> m a Source #
Generates an element from an enumeration.
This generator shrinks towards the first argument.
For example:
enum 'a' 'z' :: Gen Char
enumBounded :: (MonadGen m, Enum a, Bounded a) => m a Source #
Generates a random value from a bounded enumeration.
This generator shrinks towards minBound.
For example:
enumBounded :: Gen Bool
This is implemented in terms of the Enum class, and thus may be partial for integral types larger than Int, e.g. Word64.
bool :: MonadGen m => m Bool Source #
Generates a random boolean.
This generator shrinks to False.
This is a specialization of enumBounded, offered for convenience.
bool_ :: MonadGen m => m Bool Source #
Generates a random boolean.
This generator does not shrink.
## Characters
binit :: MonadGen m => m Char Source #
Generates an ASCII binit: '0'..'1'
octit :: MonadGen m => m Char Source #
Generates an ASCII octit: '0'..'7'
digit :: MonadGen m => m Char Source #
Generates an ASCII digit: '0'..'9'
hexit :: MonadGen m => m Char Source #
Generates an ASCII hexit: '0'..'9', 'a'..'f', 'A'..'F'
lower :: MonadGen m => m Char Source #
Generates an ASCII lowercase letter: 'a'..'z'
upper :: MonadGen m => m Char Source #
Generates an ASCII uppercase letter: 'A'..'Z'
alpha :: MonadGen m => m Char Source #
Generates an ASCII letter: 'a'..'z', 'A'..'Z'
alphaNum :: MonadGen m => m Char Source #
Generates an ASCII letter or digit: 'a'..'z', 'A'..'Z', '0'..'9'
ascii :: MonadGen m => m Char Source #
Generates an ASCII character: '\0'..'\127'
latin1 :: MonadGen m => m Char Source #
Generates a Latin-1 character: '\0'..'\255'
unicode :: MonadGen m => m Char Source #
Generates a Unicode character, excluding noncharacters and invalid standalone surrogates: '\0'..'\1114111' (excluding '\55296'..'\57343', '\65534', '\65535')
unicodeAll :: MonadGen m => m Char Source #
Generates a Unicode character, including noncharacters and invalid standalone surrogates: '\0'..'\1114111'
## Strings
string :: MonadGen m => Range Int -> m Char -> m String Source #
Generates a string using Range to determine the length.
This is a specialization of list, offered for convenience.
text :: MonadGen m => Range Int -> m Char -> m Text Source #
Generates a string using Range to determine the length.
utf8 :: MonadGen m => Range Int -> m Char -> m ByteString Source #
Generates a UTF-8 encoded string, using Range to determine the length.
bytes :: MonadGen m => Range Int -> m ByteString Source #
Generates a random ByteString, using Range to determine the length.
## Choice
constant :: MonadGen m => a -> m a Source #
Trivial generator that always produces the same element.
This is another name for pure / return.
element :: MonadGen m => [a] -> m a Source #
Randomly selects one of the elements in the list.
This generator shrinks towards the first element in the list.
The input list must be non-empty.
choice :: MonadGen m => [m a] -> m a Source #
Randomly selects one of the generators in the list.
This generator shrinks towards the first generator in the list.
The input list must be non-empty.
frequency :: MonadGen m => [(Int, m a)] -> m a Source #
Uses a weighted distribution to randomly select one of the generators in the list.
This generator shrinks towards the first generator in the list.
The input list must be non-empty.
recursive :: MonadGen m => ([m a] -> m a) -> [m a] -> [m a] -> m a Source #
Modifies combinators which choose from a list of generators, like choice or frequency, so that they can be used in recursive scenarios.
This combinator modifies its target to select one of the generators in either the non-recursive or the recursive list. When a selection is made from the recursive list, the Size is halved. When the Size gets to one or less, selections are no longer made from the recursive list, this ensures termination.
A good example of where this might be useful is abstract syntax trees:
data Expr =
Var String
| Lam String Expr
| App Expr Expr
-- Assuming we have a name generator
genName :: MonadGen m => m String
-- We can write a generator for expressions
genExpr :: MonadGen m => m Expr
genExpr =
Gen.recursive Gen.choice [
-- non-recursive generators
Var <$> genName ] [ -- recursive generators Gen.subtermM genExpr (x -> Lam <$> genName <*> pure x)
, Gen.subterm2 genExpr genExpr App
]
If we wrote the above example using only choice, it is likely that it would fail to terminate. This is because for every call to genExpr, there is a 2 in 3 chance that we will recurse again.
## Conditional
filter :: (MonadGen m, GenBase m ~ Identity) => (a -> Bool) -> m a -> m a Source #
Generates a value that satisfies a predicate.
This is essentially:
filter p gen = mfilter p gen <|> filter p gen
It differs from the above in that we keep some state to avoid looping forever. If we trigger these limits then the whole generator is discarded.
mapMaybe :: (MonadGen m, GenBase m ~ Identity) => (a -> Maybe b) -> m a -> m b Source #
just :: (MonadGen m, GenBase m ~ Identity) => m (Maybe a) -> m a Source #
Runs a Maybe generator until it produces a Just.
This is implemented using filter and has the same caveats.
## Collections
maybe :: MonadGen m => m a -> m (Maybe a) Source #
Generates a Nothing some of the time.
list :: MonadGen m => Range Int -> m a -> m [a] Source #
Generates a list using a Range to determine the length.
seq :: MonadGen m => Range Int -> m a -> m (Seq a) Source #
Generates a seq using a Range to determine the length.
nonEmpty :: MonadGen m => Range Int -> m a -> m (NonEmpty a) Source #
Generates a non-empty list using a Range to determine the length.
set :: (MonadGen m, Ord a) => Range Int -> m a -> m (Set a) Source #
Generates a set using a Range to determine the length.
This may fail to generate anything if the element generator cannot produce a large enough number of unique items to satify the required set size.
map :: (MonadGen m, Ord k) => Range Int -> m (k, v) -> m (Map k v) Source #
Generates a map using a Range to determine the length.
This may fail to generate anything if the keys produced by the generator do not account for a large enough number of unique items to satify the required map size.
## Subterms
freeze :: MonadGen m => m a -> m (a, m a) Source #
Freeze the size and seed used by a generator, so we can inspect the value which it will produce.
This is used for implementing list and subtermMVec. It allows us to shrink the list itself before trying to shrink the values inside the list.
subterm :: MonadGen m => m a -> (a -> a) -> m a Source #
Constructs a generator from a sub-term generator.
Shrinks to the sub-term if possible.
subtermM :: MonadGen m => m a -> (a -> m a) -> m a Source #
Constructs a generator from a sub-term generator.
Shrinks to the sub-term if possible.
subterm2 :: MonadGen m => m a -> m a -> (a -> a -> a) -> m a Source #
Constructs a generator from two sub-term generators.
Shrinks to one of the sub-terms if possible.
subtermM2 :: MonadGen m => m a -> m a -> (a -> a -> m a) -> m a Source #
Constructs a generator from two sub-term generators.
Shrinks to one of the sub-terms if possible.
subterm3 :: MonadGen m => m a -> m a -> m a -> (a -> a -> a -> a) -> m a Source #
Constructs a generator from three sub-term generators.
Shrinks to one of the sub-terms if possible.
subtermM3 :: MonadGen m => m a -> m a -> m a -> (a -> a -> a -> m a) -> m a Source #
Constructs a generator from three sub-term generators.
Shrinks to one of the sub-terms if possible.
## Combinations & Permutations
subsequence :: MonadGen m => [a] -> m [a] Source #
Generates a random subsequence of a list.
shuffle :: MonadGen m => [a] -> m [a] Source #
Generates a random permutation of a list.
This shrinks towards the order of the list being identical to the input list.
## Abstract State Machine
sequential :: (MonadGen gen, MonadTest m) => Range Int -> (forall v. state v) -> [Command gen m state] -> gen (Sequential m state) Source #
Generates a sequence of actions from an initial model state and set of commands.
parallel :: (MonadGen gen, MonadTest m) => Range Int -> Range Int -> (forall v. state v) -> [Command gen m state] -> gen (Parallel m state) Source #
Given the initial model state and set of commands, generates prefix actions to be run sequentially, followed by two branches to be run in parallel.
# Sampling Generators
sample :: MonadIO m => Gen a -> m a Source #
Generate a sample from a generator.
print :: (MonadIO m, Show a) => Gen a -> m () Source #
Run a generator with a random seed and print the outcome, and the first level of shrinks.
Gen.print (Gen.enum 'a' 'f')
=== Outcome ===
'd'
=== Shrinks ===
'a'
'b'
'c'
printTree :: (MonadIO m, Show a) => Gen a -> m () Source #
Run a generator with a random seed and print the resulting shrink tree.
Gen.printTree (Gen.enum 'a' 'f')
'd'
├╼'a'
├╼'b'
│ └╼'a'
└╼'c'
├╼'a'
└╼'b'
└╼'a'
This may not terminate when the tree is very large.
printWith :: (MonadIO m, Show a) => Size -> Seed -> Gen a -> m () Source #
Print the value produced by a generator, and the first level of shrinks, for the given size and seed.
Use print to generate a value from a random seed.
printTreeWith :: (MonadIO m, Show a) => Size -> Seed -> Gen a -> m () Source #
Print the shrink tree produced by a generator, for the given size and seed.
Use printTree to generate a value from a random seed. | {"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": 0.27479982376098633, "perplexity": 7630.175816329715}, "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/1627046153980.55/warc/CC-MAIN-20210730185206-20210730215206-00687.warc.gz"} |
http://chemical-quantum-images.blogspot.com/2012/12/parallel-universes-and-surface-hopping.html | ## Friday, 28 December 2012
### Parallel Universes and Surface Hopping
In a sense Surface Hopping is like the Kopenhagen interpretation of quantum mechanics. Instead of following all branches of the universal wavefunction (as introduced by Hugh Everett), the wavefunction is collapsed in a stochastic way and just one branch is considered. To show you what I mean I will consider non-adiabatic dynamics simulations of Schrödinger's cat.
To simplify the math, we will consider the following situation. There is a cat locked in a box. Additionally there is a flask of poison and an electron of unknown spin in the box. At a time t0 the spin of the electron is measured. If the spin is up (u) nothing happens. If it is down (d) the poison is released.
The wavefunction of the electron, a superposition between spin up and down, can be written as
It is time-independent (containing only a phase factor, which we can cancel out by appropriately setting the reference energy).
The wavefunction of the cat for t < t0 is given by
where Hl denotes the Hamiltonian for the living cat and Φcat,0 is the state of the cat at t = 0. Alternatively we could of course solve the classical equations of motion for the cat (possibly coarse grained), it does not affect the discussion and this can be viewed as a rather formal expression...
For t < t0 the electron and the cat are assumed not to interact with each other and the total wavefunction is simply given as
i.e. there is an electron in its superposed state and an independent living cat.
At t0 the spin of the electron is measured. After that we either have spin up and a living cat or spin down and a dead cat (the latter represented by a Hamiltonian Hd). The fate of the cat becomes entangled with the spin of the electron.
One way to read this equation is that we are now considering two parallel universes. In one of them the cat is living and moving according to Hl, in the other one the cat is dead described by Hd. This is just the result of the laws of quantum mechanics.
From the point of view of the poor cat or any observer the wavefunction "collapsed". However, considering the maths this only happens because any observer is now also entangled with the electron. And in fact both alternate histories would be part of the truth. The Kopenhagen interpretation of quantum mechanics tells us that the branch of the wavefunction we are experiencing is somehow the "real" branch, Everett's "universal wavefunction" or "many world" interpretation says that in fact all branches are equal.
Getting back to my teaser line: Surface Hopping is somewhat similar to the Kopenhagen interpretation of quantum mechanics. Instead of considering all branches of the wavefunction, only one branch is continued after every potential quantum transition. Of course in practical implementations there are also numerical differences related to more complex interactions between the different states and decoherence effects. But aside from that it just follows the laws in which we perceive nature.
Finally, it is important to remember that the cat is either alive or dead. It is not half-dead, i.e. it is not possible to use the average Hamiltonian for the wavefunction propagation
In computational science this is called Ehrenfest dynamics. It apparently does work in other cases though, if the different states are of similar nature. | {"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": 0.8422766923904419, "perplexity": 493.97191974879973}, "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/1537267157203.39/warc/CC-MAIN-20180921131727-20180921152127-00397.warc.gz"} |
http://samnangh.ligeracademyblog.org/category/my-liger-learning/essential-year-5/chemistry/ | ## The Limiting Reactant
The limiting reactant or can be called as limiting reagent is the reactant inside the chemical reaction. The limiting reactant tells the amount of product that can be makeup. We use the limiting reaction in order to find a possible solution to calculate the theoretical yield of the chemical reaction. In a chemical reaction, there is a limiting reactant because compound and elements react the way it is based on the mole ratio that is between them when we did the balanced chemical equation. What’s being called an excess reactant is the remaining leftover when the limiting reactant is complete.
To understand more about the limiting reactant topic, our chemistry teacher prepared us a lap called ” The SMORE Lab”. We used chocolate, marshmallows, and crackers to make s’more. We start off with
1. Writing the balanced equation for the making of s’more.
2. Define the type of reaction.
3. Record the total piece of the reactant.
4. The maximum production of s’more and give a reason why.
4. Figure out which is limiting and excess reactant.
5. Figure out the mass of each reactant on the scale.
6. Record the theoretical yield (mass) of s’more.
7. Make the s’mores
8. Write down the actual mass of one s’mores
We know which reactant was limiting because when we make three complete s’more, the pieces (cracker and chocolate) run out first. We then figure out the excess reactant because when we run out of chocolate and crackers, there are marshmallows left.
## Chemistry: Density Lap
In Unit 1, we did a lab experiment about coins density. Density is a characteristic property of a substance. The density of a substance is the relationship between the volume of the substance (how much space it takes up) and the mass of the substance. We can calculate density by taking the mass of the substance and divide it by the volume of the substance (D = m/v). This explains that the objects with different mass but the same volume have different densities.
This lap provides an introduction to the concept of density measurements. Our goal for the density lap was determined the method of finding the density of the coin by using measured volumes and masses to calculate densities then evaluate the result by using error analysis. My chemistry teacher, Ellie, gave me five twenty cents Singaporean coin and let me figure out what is the type of metal the coin made out of. My hypothesis was I think that the metal of twenty Singaporean coins is made out of nickel because the coin was sinking went it is in the water. I then created my own procedure of finding the density of the coin and figure out what type of metal does it made out of.
Here is my procedure:
• Have all of these materials ready: 5 twenty cents coin, a medium graduated cylinder, paper towels, scale, and the dripper.
• Weigh the mass of the five coins
• Take a medium graduated cylinder and add the sink water to (… ml) it’s helpful to have a dripper in case you wanted an accurate volume of water
• Let the cylinder sat still for a few seconds
• Drop the coins into the graduated cylinder slowly and let it sat still for a few seconds
• Measure the new volumes
• Take the initial volumes of the water and subtract the new volume of water
• Plug in all the value needed for the density equation (plug in the weight of the five coins into mass, next take the difference of the volume and plug it into volume and you’ll get density)
• Make sure to be careful with the accuracy of the water volumes and the sig fig division.
Mass
───── = Density
Volume
• Repeat the same following steps and try out with different water volumes
In conclusion, my hypothesis was supported because the real metal that the coins was made out of is nickel plated steel. In addition to the trails, some unavoidable errors in this lap are that the measurement of the water volumes in the graduated cylinder is never accurate and reading the scale correctly. Moreover, some types of avoidable errors that can be avoided during the lap are: add higher volume in the graduated cylinder so the volume of water stays precise when dropping the coins in, repetition; make sure to dry out the coins before doing another trial otherwise the changes of the volume would not be precise. | {"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": 0.8501815795898438, "perplexity": 1138.8497505374796}, "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-2023-14/segments/1679296945317.85/warc/CC-MAIN-20230325064253-20230325094253-00077.warc.gz"} |
https://mathematica.stackexchange.com/questions/109567/trouble-with-some-optimization/109571 | # Trouble with some optimization
I am attempting to use Mathematica to solve an optimization problem related to mechanism design (4-bar). The optimization problem is basically the following:
1) Solve these two simultaneous loop equations describing links in a mechanism as vectors:
Eq 1: $z(e^{i \alpha_2} - 1) + w(e^{i\beta_2} - 1) = \delta_2$
Eq 2: $z(e^{i \alpha_3} - 1) + w(e^{i\beta_3} - 1) = \delta_3$
In these equations what is know are both $\delta$'s, and both $\alpha$'s. Used mathematica to easily solve for $z$ and $w$ in terms of these parameters, so that the unknowns in the resultant equations are basically the $\beta$'s. $z$ and $w$ are obviously complex numbers, representing vectors representing links in a mechanism. The goal is to find both $\beta$'s such that the angle between these vectors will be minimized, ideally zero, as this will provide a high degree of mechanical advantage. I calculate this angle as
$\theta = cos^{-1}\left(\frac{w \cdot z}{|w||z|}\right)$
where $w$ and $z$ have been turned into pure vectors, like
$\text{vector form of z} = \left( \begin{array}{c} \text{Re}(z) \\ \text{Im}(z) \\ \end{array} \right)$
etc., and the dot indicates the dot product of vectors.
The mathematica code that I have up to this point is the following:
Subscript[[Delta], 2] = 9 E^(I*275 [Degree]);
Subscript[[Delta], 3] = 7.3 E^(I*-87 [Degree]);
Subscript[[Alpha], 2] = 30 [Degree];
Subscript[[Alpha], 3] = 0 [Degree];
Solve[{z (E^(I*Subscript[[Alpha], 2]) - 1) + w (E^(I Subscript[[Beta], 2]) - 1) == Subscript[[Delta], 2], z (E^(ISubscript[[Alpha], 3]) - 1) + w (E^(I Subscript[[Beta], 3]) - 1) == Subscript[[Delta], 3]}, {z, w}]
I then define variables z and w by setting them equal to the respective results of the solve operation. Then I go like
vecZ = ( { {FunctionExpand[Re[z]]}, {FunctionExpand[Im[z]]} } )
vecW = ( { {FunctionExpand[Re[w]]}, {FunctionExpand[Im[w]]} } )
AngleofInterest = Abs[ArcCos[Dot[vecZ, vecW]/(Norm[vecZ] Norm[vecW])]];
Minimize[{AngleofInterest, vecW[[2]] < 0}, {Subscript[[Beta], 2], Subscript[[Beta], 3]}]
the constraint vecW[[2]]<0 is just to do with the way we'd like the mechanism to look/operate.
When I try to run this code I wind up getting massive amounts of errors from the Dot operation telling me that the 'tensors' have 'incompatible shapes'. And also this error further down in the output:
Abs[ArcCos[0.0004018 {{51.0546},{9.37553}}.{{-47.9325},{1.14297}}]] is not a number at {Subscript[[Beta], 2],Subscript[[Beta], 3]} = {0.75721,0.152402}.
I will love you forever if you can educate me on this. Mechanism design is awful; it's so hard to get a design that works well so I have tried to formulate this as this optimization problem.. thanks!
I'd suggest setting it up as simply as possible, no subscripts or other possible sources of confusion.
e1 = (x1 + I*y1)*(Exp[I*Pi/6] - 1) + (x2 + I*y2)*(Exp[I*b2] - 1) -
9 E^(I*275*Degree);
e2 = (x1 + I*y1)*(Exp[I*0] - 1) + (x2 + I*y2)*(Exp[I*b3] - 1) -
73/10 E^(-I*87*Degree);
epolys = ComplexExpand[{Re[e1], Im[e1], Re[e2], Im[e2]}]
theta = ArcCos[(x1*x2 + y1*y2)/(Sqrt[x1^2 + y1^2]*Sqrt[x2^2 + y2^2])];
(* Out[448]= {-x1 + (Sqrt[3] x1)/2 - x2 - y1/2 + x2 Cos[b2] -
y2 Sin[b2] - 9 Sin[5 \[Degree]],
x1/2 - y1 + (Sqrt[3] y1)/2 - y2 + y2 Cos[b2] + 9 Cos[5 \[Degree]] +
x2 Sin[b2], -x2 + x2 Cos[b3] - y2 Sin[b3] -
73/10 Sin[3 \[Degree]], -y2 + y2 Cos[b3] + 73/10 Cos[3 \[Degree]] +
x2 Sin[b3]} *)
Now do a numerical optimization.
{min, vals} =NMinimize[{theta, Thread[epolys == 0]},
{x1, y1, x2, y2, b2, b3}]
(* Out[450]= {3.33200093731*10^-8, {x1 -> -1.70127972842,
y1 -> 2.24982907557, x2 -> -2.65849520069, y2 -> 3.51568304387,
b2 -> 2.27060692293, b3 -> 1.95142105721}} *)
Be aware that the angles are given in radian measure, not degrees.
Check that equations are satisfied to withing close tolerance:
In[455]:= {e1, e2} /. vals
(* Out[455]= {8.63301694576*10^-8 -
6.0190735951*10^-8 I, -2.16175702894*10^-8 + 3.78699474446*10^-7 I} *)
• Infinite thank yous, sir! This is extremely helpful. – Ern Mar 9 '16 at 20:38 | {"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": 0.5136481523513794, "perplexity": 4525.3662489098315}, "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/1590347399820.9/warc/CC-MAIN-20200528135528-20200528165528-00097.warc.gz"} |
https://qojulia.org/documentation/examples/manybody-fourlevel-system.html | Simple many-body system
This notebook can be found on github
# Four level system in many-body formalism
In this example, we illustrate the treatment of many-body quantum systems. A ManyBodyBasis can be used to describe indistinguishable particles that follow certain exchange symmetries (fermions or bosons). We can define an arbitrary quantum system - in this example a N-level system consisting of four energy states, and use it as foundation of a many-body basis. The basis states of the many-body basis then simply correspond to the number of particles that are in one of these four states. Which occupation states are included depends on the type of the particles (bosonic or fermionic) and if the particle number is preserved. For fermions the dimension of the Hilbert space is greatly reduced since it does not allow more than one particle in the same state (Pauli principle).
using QuantumOptics
using PyPlot
First, we define the four-level system and a Hamiltonian with energies $0, 1, 2, 3$.
b = NLevelBasis(4)
H = diagonaloperator(b, [0, 1, 2, 3])
Each of the states decays to the next lower one which we account for with the following jump operators.
j34 = transition(b, 3, 4) # decay from 4th into 3rd level
j23 = transition(b, 2, 3) # decay from 3rd into 2nd level
j12 = transition(b, 1, 2) # decay from 2nd into 1st level
## Two fermions with conserved particle number
Now, as a first example, we consider two fermionic particles. Each of them can occupy one of the four levels in the system, but not at the same time. To this end, we define a many-body basis associated to this N-level system. Calculating the many-body operators from the corresponding N-level operators can be done with the manybodyoperator() function. Basically it uses the relation
$\tilde{A} = \sum_{st} c_s^\dagger c_t \langle u_s| A |u_t \rangle$
to convert the one-body operator $A$ to the many-body operator $\tilde{A}$. Here, $|u_i\rangle$ is the $i$-th basis state of the initial basis (N-level system) and $c_s$ is the particle annihilation operator at site $s$.
b_mb = ManyBodyBasis(b, fermionstates(b, 2))
H_mb = manybodyoperator(b_mb, H)
j34_mb = manybodyoperator(b_mb, j34)
j23_mb = manybodyoperator(b_mb, j23)
j12_mb = manybodyoperator(b_mb, j12)
Γ = [3., 1., 0.5]
J_mb = [j34_mb, j23_mb, j12_mb]
The resulting many-body operators will then account for the decay as defined for the four-level system. For example, the jump operator j34_mb will map the state $|0101\rangle$ to $|0110\rangle$, i.e. moving a particle from state 4 into state 3.
We can now calculate the time evolution according to a master equation, where the system is initially in the highest state $|0011\rangle$ and over time decays into the ground state $|1100\rangle$.
T = [0:0.1:10;]
Ψ0_mb = basisstate(b_mb, [0, 0, 1, 1])
tout, ρt = timeevolution.master(T, Ψ0_mb, H_mb, J_mb; rates=Γ)
Now, we can analyze the system from two point of views. We can ask for the probability that the system is in a certain many-body state, e.g. $|1 1 0 0\rangle$ or $|0 0 1 1\rangle$. Alternatively, one might like to know how many particles are in a certain N-level state.
psi0011 = basisstate(b_mb, [0, 0, 1, 1])
psi1100 = basisstate(b_mb, [1, 1, 0, 0])
n0011 = psi0011 ⊗ dagger(psi0011)
n1100 = psi1100 ⊗ dagger(psi1100)
figure(figsize=(10, 3))
subplot(1, 2, 1)
plot(tout, real(expect(n0011, ρt)), label="n0011")
plot(tout, real(expect(n1100, ρt)), label="n1100")
legend()
subplot(1, 2, 2)
for i in 1:4
plot(tout, real(expect(number(b_mb, i), ρt)), label="level $i") end legend() ## Three bosons with particle loss As another example, we can instead consider three bosonic particles and additionally introduce particle loss. This results in many more possible basis states. We include this in the calculation by explicitly passing all possible particle numbers when creating the many-body basis, i.e. each state can be occupied by 0 to 3 particles. b_mb = ManyBodyBasis(b, bosonstates(b, [0, 1, 2, 3])) H_mb = manybodyoperator(b_mb, H) j34_mb = manybodyoperator(b_mb, j34) j23_mb = manybodyoperator(b_mb, j23) j12_mb = manybodyoperator(b_mb, j12) In addition to the spontaneous decay of the four-level system, we now also define a particle annihilation operator and include it in the jump operators. a1_mb = destroy(b_mb, 1) # Particles are lost from the first level Γ = [0.9, 0.5, 0.3, 3.0] J_mb = [j34_mb, j23_mb, j12_mb, a1_mb] T = [0:0.1:10;] Ψ0_mb = basisstate(b_mb, [0, 0, 0, 3]) # Initially, all particles are in the uppermost level tout, ρt = timeevolution.master(T, Ψ0_mb, H_mb, J_mb; rates=Γ) figure(figsize=(5, 3)) plot(tout, real(expect(number(b_mb), ρt)), "--k", alpha=0.6, label="particle number") for i in 1:4 plot(tout, real(expect(number(b_mb, i), ρt)), label="level$i")
end
legend() | {"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": 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": 0.9247161149978638, "perplexity": 1437.1831602078528}, "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/1544376823785.24/warc/CC-MAIN-20181212065445-20181212090945-00210.warc.gz"} |
http://docplayer.net/24044475-Factors-that-affect-the-rate-of-dissolving-and-solubility.html | # Factors that Affect the Rate of Dissolving and Solubility
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1 Dissolving Factors that Affect the Rate of Dissolving and Solubility One very important property of a solution is the rate of, or how quickly a solute dissolves in a solvent. When dissolving occurs, there in involved. Therefore, the solute and solvent can be separated using properties such as or. The rate at which a solute dissolves depends on a number of factors: i) Temperature Increasing temperature increases the (energy of motion) of the molecules, which increases the frequencies of and the rate of dissolving. ii) Agitation Stirring/shaking brings into contact with, increasing and the rate of dissolving. iii) Particle Size into smaller pieces increases the that is in contact with, thus increasing the rate of dissolving. The Dissolving Process Whether or not a solute dissolves and to what extent depends on the forces of attraction between: When the forces of attraction between particles in a mixture are than the forces of attraction between particles in the mixture, a solution forms. The strength of each attraction influences the, or the amount of solute that dissolves in a solvent. The dissolving process can be broken down into three key steps: 1. The holding the together must be broken ( ) Ionic compounds Covalent molecules 2. The forces (between particles) holding the together must be broken ( ) 3. Solute and solvent ( ) and the molecules of solute fill in the spaces between solvent molecules. Note: Dissolving is more likely to occur if the energy required (steps 1 and 2) is less than the energy released (step 3). Polar and Non-Polar Substances In general, we can follow the rule of when trying to predict the solubility of different particles. solutes and solutes dissolve in and dissolve in. Remember, you can use the difference in electronegativities ( ) to predict if a compound is ionic, polar or non-polar. There are a few possible forces that act between particles, which helps to explain the like dissolves like trend: Dipole-Dipole Attractions the attraction between the on two different molecules. Ion-Dipole Attractions the attractive forces between an and a molecule. Ions posses a and are therefore attracted to the on the polar molecules. When ions are present in an solution, each ion is. This means that water molecules surround the ion. Hydrated ions can conduct electricity and are referred to as.
2 Solubility Solubility describes the of that can be dissolved in a given of under given conditions. A solute is described as in a particular solvent if its solubility is than. A solute is described as in a particular solvent if its solubility is than. Substances with solubility between these limits are called. Factors affecting solubility include: i) Molecular Size molecules tend to be more soluble than ones. Concentration of Solutions Concentration is defined as the amount of per quantity of. The concentration of a solution can be calculated. The approach for each calculation varies, depending on the of solution. 1. Calculation as Mass/Volume (m/v) Percent Gives the mass of solute dissolved in a volume of solution, expressed as a percent. Examples: Mass/Volume % = 2.00 ml of distilled water is added to 4.00 g of a powdered drug. The final volume of the solution is 3.00 ml. Calculate the percent m/v and then express the drug concentration in g/100 ml. ii) Temperature Affects the solubility of gases and solids in liquids. For gases in liquids: as temp solubility For solids in liquids: as temp solubility A (graph) describes how much solute can be dissolved in a given solvent at a certain temperature. iii) Pressure Affects the solubility of gases in liquids. As pressure solubility What mass of a drug is required to make a 2.0 L solution if the recommended concentration is 1.7%?
3 2. Calculation as Mass/Mass (m/m) Percent Gives the mass of solute divided by the mass of solution, expressed as a percent. Mass/Mass % = An aqueous solution of calcium chloride has a mass of g. The solvent was evaporated and the residue has a mass of 4.58 g. Calculate the m/m % of calcium chloride in the solution. How many grams of calcium chloride would be present in a 100 g sample? 4. Parts per Million (ppm) and Parts per Billion (ppb) Describes the concentration of very small quantities. Usually expressed in terms of mass/mass relationships. ppm = ppb = Note: Your final answer does not refer to the number of particles per million or billion, but rather the mass of solute compared to the mass of solution. 3. Concentration as Volume/Volume (v/v) Percent Gives the volume of solute divided by the volume of solution, expressed as a percent. A shipment of oranges is returned if it contains more than 25 ppb of mould. A company received kg of oranges. What is the maximum mass of mould allowed before the shipment should be sent back? Volume/Volume % = Rubbing alcohol is sold as a 70% (v/v) solution. What volume of alcohol is used to make 500 ml of rubbing alcohol?
4 Molar Concentration Molarity (C) is the number of of dissolved per of. The equation we use to calculate molar concentration is: Where, C = n = V = Examples: What is the molar concentration of 1.20 g of NaNO 3 in 80.0 ml of solution? Preparing Solutions and Dilutions A solution is a solution with. There are 2 ways to prepare a solution: i. ii. A useful tool in preparing solutions is a a pearshaped glass with a flat bottom and a long neck. Volumetric flasks provide are very accurate tools for measuring volumes. To prepare a solution you should perform the following steps: 1. Determine the required to make the desired and of solution. 2. Measure out and dissolve the in approximately of. 3. Raise the to the desired total volume by adding more. How many grams of potassium hydroxide will be required to prepare 650 ml of M solution? Diluting is a process that makes a solution that is less concentrated. This can be done by: i. ii.
5 Dilution Calculations: Step 1: Find the number of you need Step 2: Find the you need Step 3: Top up with Example #2 If 85.0 ml of M sodium sulfate solution was used to prepare 200 ml of a dilute sodium sulfate solution, what is the new concentration made? Example #1 How do you make a 1.50 L solutions of NaCl with a concentration of 6.00 M from a stock solution with a concentration of 15.0 M? Alternatively we can perform dilution calculations using the following equation: Where, C 1 = V 1 = C 2 = V 2 = Lets try this equation to solve the previous example!!!
6 Reactions in an Aqueous Solution-Ionic Equations When an ionic compound is placed in water, most will, which means they are in water. Some ionic compounds will remain as a and are. If an ionic compound dissolves in water, it means that the compound is temporarily splitting apart into its. This process is referred to as an ionic compound. This is NOT a and the ionic compound will readily when removed from the water source. Example #2 Word Equation Balanced Equation Total Ionic Equation Net Ionic Equation Spectator Ions Calcium bromide reacts with lithium chlorate Double displacement reactions occur in water, and are a direct result of ionic compounds dissociating into their ions. Recall that a double displacement reaction will only occur if, or a forms. We can show the step-by-step process of a double displacement reaction by writing out an ionic equation. There are several different components to an ionic equation. Term Total Ionic Equation Net Ionic Equation Spectator Ion Definition Precipitate reactions can be used to generate a precipitation profile for known ions, which can be used to identify ions in solution. -2 CO 3 OH -1-2 SO 4 Ca +2 Ba +2 Unknown ppt ppt ppt The unknown precipitation profile matches that of. Flow charts can also be used to illustrate what ions may be added to a solution containing many ions to allow for individual separation of ions by precipitation. Example #1 Word Equation Balanced Equation Total Ionic Equation Net Ionic Equation Spectator Ions Silver nitrate reacts with sodium chloride When attempting to separate ions from a solution a piece of lab equipment called a can be used. A centrifuge at very high speeds to separate different particles from each other based on their. The part of the solution that does not settle to the bottom of the centrifuge is called the.
7 Solution Stoichiometry Recall that stoichiometry involves calculating the amounts of reactants and products in chemical reactions using a balanced chemical equation. Previously you learned how to calculate the amount of atoms, particles or mass of a compound using the stoichiometry strategies. You can apply these same skills when approaching calculations involving solutions, with the addition of a few additional steps. Example #2 Suppose you want to remove the barium ions from 120 ml of M aqueous barium nitrate solution. What is the minimum mass of sodium carbonate that you should add? Example #1 Calculate the concentration of calcium chloride in a solution made by mixing 150 ml of a M calcium hydroxide solution with 100 ml of a M hydrochloric acid solution.
8 Strong acid Strong and Weak Acids and Bases When hydrogen chloride molecules enter an aqueous solution, of the hydrogen chloride molecules dissociate. As a result the solution contains the same percent of H+ ions (in the form of H 3O + ) and Cl ions: 100% Weak acid On average, only about of the acetic acid molecules dissociate at any given moment. Concentration of an Acid or Base Recall that when in solution, acids and bases dissociate into ions. When you determine the concentration of hydrogen ions in solution (amount of H+ ions/ total solution volume) you are determining the ph of that particular solution. ph stands for, the power of hydrogen. The ph of a substance can be determined a number of different ways, such as with the use of ph paper, an electronic ph meter or mathematically using the following formulas: Examples: Square brackets [ ] around a chemical formula represents, the concentration of What is the ph of a solution with a [H 3O + ] of 1.0 x 10-5? Notice that the arrow used in the dissociation of a weak acid points in both directions. This indicates that the reaction is. The products of the reaction will also react to produce the original reactants. Gastric juice has a ph of 1.5, what is the [H 3O + ]? Some useful terms: Term Definition Example Monoprotic acid Diprotic acid Triprotic acid The relative concentration of [H 3O + ] and [OH - ] ions are as follows: Acidic Neutral Basic A ph scale is a convenient way to relate the ph of a solution to its degree of acidity/alkalinity. In both diprotic and triprotic acids, the dissociation of the first hydrogen ion will results in a stronger acid than the acid formed by the second and third dissociation. Strong base Examples: Weak base The ph scale ranges from 1 to 14 and each ph unit represents a factor of 10. Examples: A change in ph from 3 to 8 is a(n) increase/decrease in [H 3 O + ] A change in ph from 11 to 2 is a(n) increase/decrease in [H 3O + ]
9 Neutralization Reactions Neutralization occurs when (Arrhenius base) and (acid) are mixed to make and a. The general word equation is: Aqueous solutions of hydrobromic acid and beryllium hydroxide undergo a neutralization reaction to produce water and beryllium bromide. Acid-Base Titrations A titration refers to a technique that involves the careful measuring of the of one solution required to completely react with a of another. In an acid-base titration, measuring the volume of a (of ) allows us to determine the of the. In this case an is used to indicate when the neutralization reaction is complete. is the most common indicator used. It will be when added to the ; neutralization occurs at the first signs of the solution and a. Example #1 In an acid-base titration, ml of HNO 3 is required to neutralize ml of 0.25 M NaOH. Calculate the molarity of the acid? Complete the following equations: H 2 SO 4 (aq) + LiOH (aq) Ca(OH) 2 (aq) + H 3 PO 4 (aq) Which acid and base would you react together to produce the following salts: i) KNO3 ii) Ca(CH 3 COOH) 2
10 Example #2 In an acid-base titration, ml of 0.30 M KOH is required to neutralize ml of H2SO4. Calculate the molarity of the acid?
### Lecture 6. Classes of Chemical Reactions
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Review of Basic Concepts, Molarity, Solutions, Dilutions and Beer s Law Aqueous Solutions In Chemistry, many reactions take place in water. This is also true for Biological processes. Reactions that take | {"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": 0.8023105263710022, "perplexity": 4045.286628404201}, "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/1537267160620.68/warc/CC-MAIN-20180924165426-20180924185826-00039.warc.gz"} |
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https://eprints.utas.edu.au/46519/ | # Antarcticness at the ends of the world
Roldan, G and Nielsen, H ORCID: 0000-0002-2761-7727 2022 , 'Antarcticness at the ends of the world', in I Kelman (ed.), Antarcticness: Inspirations and imaginaries , UCL Press, London, pp. 31-59.
Preview
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http://www.christopheralbert.net/ | ## Mittwoch, 30. März 2011
### Lessons learned about FEM with SciPy
I am just sitting in a train doing a programming exercise about the Finite Element Method.
Details about the examples can be found on the homepage of Prof. Sormann at http://itp.tugraz.at/LV/sormann/AKNumPhysik/
The first problem is solving the stationary heat equation with FEM.
Now how do we plot this? At first I tried using matplotlib which was not satisfactory because it cannot do color gradients across triangles in a mesh grid. Then I discovered the wonderful MayaVi package where you can do it as simple as
from enthought.mayavi import mlab
mlab.triangular_mesh(x, y, z, triangle_indices, temperature)
mlab.show()
That's all! To add fancy stuff like a wireframe mesh, a colorbar and axes I did something like that before the final mlab.show()
mlab.triangular_mesh(x, y, z, triangle_indices, color=(0,0,0),
line_width=1.,representation='wireframe')
mlab.view(0., 0.)
mlab.move(0.,-.5,0.)
mlab.xlabel("x")
mlab.ylabel("y")
mlab.axes(extent=[0., 4., 0., 4., 0., 0.], nb_labels=5)
mlab.colorbar(title="Temperatur", orientation='vertical')
And here is the result:
Nice, huh?
If I have time, I'll keep you updated about the algorithm, the progress for the time-dependent heat conduction and more!
## Freitag, 18. März 2011
### Equivalent ODE integrators in Matlab and SciPy
Here is a short summary of my investigations on how ODE integrators from SciPy compare with the ones provided by Matlab:
• SciPy provides several ODE solvers based on Fortran routines from ODEPACK
• The default SciPy solver is LSODA and provided via scipy.integrate.odeint(f)
• There are equivalent solvers for Matlab's ode45 and ode15s.
• Use scipy.integrate.ode(f).set_integrator(...)
• ode45: 'dopri5'
• ode15s: 'vode', method='bdf', order=15
Something else of interest : NodePy looks like a tool to experiment with various ODE solving algorithms and offers more flexibility than either Matlab or SciPy.
In conclusion one can say that if you know what you are doing, there are plenty of good integrators available for Python and it's easy to plug in your own Fortran or C code.
[1] http://www.scipy.org/NumPy_for_Matlab_Users
[2] http://www.mathworks.com/help/techdoc/ref/ode23.html
[3] https://github.com/scipy/scipy/blob/master/scipy/integrate/ode.py
[4] http://web.kaust.edu.sa/faculty/davidketcheson/NodePy/index.html
### MathJax in Blogger
Hurray - now I can finally use $\LaTeX$ in Blogger, thanks to a post on http://mnnttl.blogspot.com/ !
Look at the Schrödinger Equation for example:
$$\mathrm{i}\hbar\frac{\partial}{\partial t} |\,\psi (t) \rangle = \hat{H} |\,\psi (t) \rangle$$
Now that's nice... but what about the Lagrange density? ... wait, here it is:
$$\mathcal{L}\left(\psi, \mathbf{\nabla}\psi, \dot{\psi}\right) = \mathrm i\hbar\, \frac{1}{2} (\psi^{*}\dot{\psi}-\dot{\psi^{*}}\psi) - \frac{\hbar^2}{2m} \mathbf{\nabla}\psi^{*} \mathbf{\nabla}\psi - V( \mathbf{r},t)\,\psi^{*}\psi$$
And now for some more complicated stuff:
\begin{align} \mathcal{L}_\mathrm{QCD}(q, A) & = \bar{q}\left(i \gamma^\mu D_\mu - m \right) q - \frac{1}{4}F^a_{\mu \nu} F^{\mu \nu}_a \\ & = \bar{q} (i \gamma^\mu \partial_\mu - m) q + g \bar{q} \gamma^\mu T_a q A^a_\mu - \frac{1}{4}F^a_{\mu \nu} F^{\mu \nu}_a \\ \end{align}
We should definitely use that to teach physics!
## Mittwoch, 18. Februar 2009
### Blog
Hm... heute dachte ich mir, ich brauche in Blog... wozu auch immer :-) | {"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": 0.7822529077529907, "perplexity": 2989.576516341409}, "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-2014-15/segments/1397609525991.2/warc/CC-MAIN-20140416005205-00593-ip-10-147-4-33.ec2.internal.warc.gz"} |
https://math.stackexchange.com/questions/1529842/f-in-mathcal-r0-1-g-in-c-mathbb-r-with-period-1-then-lim-n-t?noredirect=1 | # $f\in \mathcal R[0,1]$ , $g \in C(\mathbb R)$ with period $1$ , then $\lim_{n \to \infty}\int_0 ^1 f(x)g(nx)dx=\int_0^1f(x)dx\int_0^1 g(x)dx$? [closed]
Let $f\in \mathcal R[0,1]$ , and $g:\mathbb R \to \mathbb R$ is continuous and periodic with period $1$ . Then is it true that
$\lim_{n \to \infty}\int_0 ^1 f(x)g(nx)dx=\Big(\int_0^1f(x)dx\Big)\Big(\int_0^1 g(x)dx\Big)$ ?
## closed as off-topic by choco_addicted, Arnaud D., Jyrki Lahtonen, Jendrik Stelzner, user99914 Aug 14 '18 at 18:22
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• what mean $f\in\mathcal R[0,1]$ ? – Surb Nov 15 '15 at 9:18
• I think is Riemann integrable on [0,1]. Something looks Really weird in this problem... Since $g$ is continuous and periodic on $\mathbb R$, there is a $M$ s.t. $|g(x)|\leq M$ for all $x$. In particular, $|f(x)g(nx)|\leq M|f(x)|\in L(0,1)$, and thus we can theoretically permute limite and integral (dominated convergence theorem), but $\lim_{n\to\infty }f(x)g(nx)$ do not exist since $g$ is periodic... or it exist if $g$ is constant or $f\equiv 0$. Therefore something looks very strange. – Rick Nov 15 '15 at 9:28
• @Rick : You are missing one crucial point , you cannot use Dominated Convergence theorem here , the sequence of functions $\{f(x)g(nx)\}$ is not known to be pointwise convergent ! – user228168 Nov 15 '15 at 12:16
• Possible duplicate of integral involving a periodic function – Guy Fsone Jan 16 '18 at 18:23
Put $\displaystyle u_n=\int_0^1f(x)g(nx)dx$. We have by the change of variable $u=nx$: $$u_n=\int_0^n f(\frac{u}{n})g(u)\frac{du}{n}=\frac{1}{n}\sum_{k=0}^{n-1}\int_k^{k+1}f(\frac{u}{n})g(u)du$$
But as $g$ has period $1$: $$\int_k^{k+1}f(\frac{u}{n})g(u)du=\int_0^1f(\frac{t+k}{n})g(t+k)dt=\int_0^1f(\frac{t+k}{n})g(t)dt$$ Put $\displaystyle T_n(t)=\frac{1}{n}\sum_{k=0}^{n-1}f(\frac{t+k}{n})$. We have hence $\displaystyle u_n=\int_0^1 T_n(t)g(t)dt$. Now $T_n(t)$ is a Riemann sum for $f$ (On $\displaystyle I_k=[\frac{k}{n},\frac{k+1}{n}]$, we have ${\rm Inf}_{u\in I_k}f(u)\leq f(\frac{t+k}{n})\leq {\rm Max}_{u\in I_k}(f(u))$). Hence $\displaystyle T_n(t)\to L=\int_0^1 f(t)dt$. Now there exists $M$ such that $|f(u)|\leq M$ for all $u$, hence we get $\displaystyle |T_n(t)g(t)|\leq M|g(t)|$, and by the convergence dominated theorem, we get $\displaystyle u_n\to \int_0^1Lg(t)dt$, and we are done.
• "Now there exists $M$ such that $|f(u)|\leq M$ for all $u$..." Is it true that each Riemann integrable function is bounded? Just asking. – Olivier Oloa Nov 15 '15 at 9:31
• I think that Riemann integrability on a compact interval $[a,b]$ is only for bounded functions (if not, we cannot define upper and lower Riemann sums) – Kelenner Nov 15 '15 at 9:34
• Yes, I think you may rather consider lower and upper Riemann sums (a counter example is $f(x)=x^{-1/2}$ over $(0,1], f(0)=0$ which is not bounded). – Olivier Oloa Nov 15 '15 at 9:48
• But your function $x^{-1/2}$ is not Riemann-integrable on $[0,1]$ (It is only Riemann-integrable in the generalized meaning). – Kelenner Nov 15 '15 at 9:50 | {"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": 0.9821527600288391, "perplexity": 336.70662520944825}, "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/1568514576965.71/warc/CC-MAIN-20190923125729-20190923151729-00451.warc.gz"} |
http://physics.stackexchange.com/questions/3758/how-metallic-surfaces-states-can-emerge-in-topological-insulators/3771 | # How metallic surfaces states can emerge in topological insulators?
Topological insulators are materials known to have bulk insulator and metallic surface states. But, what is the origin of these metallic surface states? And how the topology of band could help the understanding of these states?
-
This won't completely answer your question, but maybe it will help. I remember when I was encountering the topic that I used to be completely bewildered by the discussion. I think two facts really helped me to understand things:
1. We are working in a non-interacting picture of electrons. This means that we only need to consider a single-particle Hamiltonian.
2. We are working in a lattice. This means that the single particle Hamiltonian is a direct sum of discrete Hamiltonians, indexed by a pseudo-momentum vector $k$ (i.e. point in the BZ): $H = \bigoplus_k H_k$.
This should then frame the discussion. We are talking about insulators in the band sense, so there are no level-crossings, i.e. things are gapped. Let's assume that the Brilluoin zone is topologically a torus (i.e. we're going to work in 2D, rather than 3). The Hamiltonian $H_k$ should be a smooth function of $k$. Topological insulators are fundamentally to do with the possible topologies of $H_k$ as a function over the BZ; there is a theorem to the effect that there are topological invariants which are preserved as long as no level-crossing occur.
Now, suppose that our material has a non-trivial topology in $H_k$ in the bulk. In vacuum, or generally against any other material with a trivial topology, we have to make the levels match up in the region of the boundary, which necessitates some level-crossing, i.e. closing the gap. This then generically demonstrates that there will be metallic states at the edges of topological insulators.
All of this should be seen with caveats. I've swept a lot under the rug here (interactions, disorder, local vs bulk behaviour, etc.) I've also not treated things with the greatest possible generality (3D, other topologies of BZ's) or even rigour (I've simply ignored the crucial issue of where the Fermi level is --- mostly out of laziness). But maybe it helps. :-)
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https://www.physicsforums.com/threads/iodine-solution.174268/ | # Homework Help: Iodine Solution
1. Jun 17, 2007
### flumbie
When performing an ascorbic acid titration with iodine solution, iodine and potassium iodide are used. Does the potassium iodide react with the ascorbic acid as well or only the iodine?
Thanks
2. Jun 17, 2007
### symbolipoint
The reactant is either the iodine or the iodide - I'm no familiar currently. Is the ascorbic acid being reduced? Or is it being oxidized? (I should not butt-in here, since someone familiar with the analytical method would answer this more properly).
3. Jun 18, 2007
### chemisttree
iodine is the reactant, not iodide. Iodine is not very soluble in water but it forms a water-soluble complex, I3-, with iodide. | {"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": 0.9129148721694946, "perplexity": 20777.67748031364}, "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-2018-34/segments/1534221215176.72/warc/CC-MAIN-20180819125734-20180819145734-00271.warc.gz"} |
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Integer programming is the problem of optimizing a linear function over the set of integer solutions satisfying a system of inequalities. The most successful technique in practice is the so-called "cutting-plane" algorithm in combination with branch-and-bound enumeration. Cutting-planes for an integer linear program are linear inequalities that are valid for all integer feasible solutions but
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Our problem can be described in terms of a two player game, played with the set $\mathcal{S}_n$ of permutations on $\{1,2,\dots,n\}$. First, Player 1 selects a subset $S$ of $\mathcal{S}_n$ and shows it to Player 2. Next, Player 2 selects a permutation $p$ from $\mathcal{S}_n$ as different as possible from the permutations in $S$, and shows it to Player
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The strong clique number of a graph $G$ is the maximum size of a set of edges of which every pair has distance at most two. In this talk, we prove that every $\{C_5,C_{2k}\}$-free graph has strong clique number at most $k\Delta(G)-(k-1)$, which resolves a conjecture by Cames van Batenburg et al. We also prove
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For a vertex v of a graph G, the local complementation at v is an operation to obtain a new graph denoted by G*v from G such that two distinct vertices x, y are adjacent in G*v if and only if both x, y are neighbors of v and x, y are non-adjacent, or at least one
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Given a graph $G$ on the vertex set $V$, the non-matching complex of $G$, $\mathsf{NM}_k(G)$, is the family of subgraphs $G' \subset G$ whose matching number $\nu(G')$ is strictly less than $k$. As an attempt to generalize the result by Linusson, Shareshian and Welker on the homotopy types of $\mathsf{NM}_k(K_n)$ and $\mathsf{NM}_k(K_{r,s})$ to arbitrary graphs
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Inspired by a width invariant defined on permutations by Guillemot and Marx , we introduce the notion of twin-width on graphs and on matrices. Proper minor-closed classes, bounded rank-width graphs, map graphs, $K_t$-free unit $d$-dimensional ball graphs, posets with antichains of bounded size, and proper subclasses of dimension-2 posets all have bounded twin-width. On all these classes
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Vatshelle (2012) introduced a width parameter called mim-width. It is based on the following cut function : for a vertex partition (A,B) of a graph, the complexity of this partition is computed by the size of a maximum induced matching of the bipartite subgraph induced by edges between A and B. This parameter naturally extends
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https://socratic.org/questions/can-you-show-that-z-4-64-can-be-factorised-into-two-real-quadratic-factors-of-th | Algebra
Topics
# Can you show that z^4 + 64 can be factorised into two real quadratic factors of the form z^2 + az + 8 and z^2 + bz + 8 but cannot be factorised into two real quadratic factors of the form z^2 + bz + 16 and z^2 + bz + 4?
##### 1 Answer
Feb 26, 2017
${z}^{4} + 64 = \left({z}^{2} - 4 z + 8\right) \left({z}^{2} + 4 z + 8\right)$
#### Explanation:
The factors of ${z}^{4} + 64 = \left(z - {z}_{0}\right) \left(z - {z}_{1}\right) \left(z - {z}_{2}\right) \left(z - {z}_{3}\right)$
are obtained solving
${z}^{4} = - 64 = {2}^{6} {e}^{i \pi + i 2 k \pi}$
Here ${e}^{i \pi} = \cos \left(\pi\right) + i \sin \left(\pi\right) = - 1$ (de Moivre's identity)
so
$z = \sqrt[4]{{2}^{6}} {e}^{i \left(\frac{\pi}{4} + k \frac{\pi}{2}\right)}$ obtaining for $k = 0 , 1 , 2 , 3$
${z}_{0} = \sqrt[4]{{2}^{6}} \frac{1 + i}{\sqrt{2}}$
${z}_{1} = - \sqrt[4]{{2}^{6}} \frac{1 + i}{\sqrt{2}}$
${z}_{2} = - \sqrt[4]{{2}^{6}} \frac{1 + i}{\sqrt{2}}$
${z}_{0} = \sqrt[4]{{2}^{6}} \frac{1 - i}{\sqrt{2}}$
The arrangements
$\left(z - {z}_{0}\right) \left(z - {z}_{3}\right) = {z}^{2} - 4 z + 8$
$\left(z - {z}_{1}\right) \left(z - {z}_{2}\right) = {z}^{2} + 4 z + 8$
are the only to give trinomials with real coefficients.
The answer is ${z}^{4} + 64 = \left({z}^{2} - 4 z + 8\right) \left({z}^{2} + 4 z + 8\right)$
Another way to solve this problem is by grouping coefficients in
${z}^{4} + 64 - \left({z}^{2} + a z + 8\right) \left({z}^{2} + b z + 8\right)$ and solving
$\left\{\begin{matrix}16 + a b = 0 \\ a + b = 0\end{matrix}\right.$ giving $a = 4 , b = - 4$
or
${z}^{4} + 64 - \left({z}^{2} + b z + 16\right) \left({z}^{2} + b z + 4\right)$ and solving
$\left\{\begin{matrix}b = 0 \\ 20 + {b}^{2} = 0\end{matrix}\right.$ without solution.
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http://blogs.bu.edu/ggarber/archive/bua-py-25/light/ | # Light: Wave or a Particle?
For centuries, the debate raged as to whether light was a particle or a wave. The Greeks believed in a particle nature for light. We were able to see things because our eyes emitted beams of light, which makes me think of Cyclops from the X-Men. Newton also believed in the corpuscle theory of light. He saw that light travels in straight lines. He analyzed geometric objects in terms of momentum and collisions of particles. Based on this and geometry, Newton wrote Optiks and designed the Newtonian reflecting telescope which differed from most of the lens based telescopes of the time.
However, Young developed his theory that light is actually a wave. The evidence came in that light exhibited the phenomena of diffraction, refraction, and interference. In the end, Einstein brought these two theories together and showed that light is both a particle and a wave by explaining photoelectric effect, for which he earned the Nobel Prize. In this theory, a particle of light is called the photon.
Maxwell developed the idea of electromagnetic waves, which are due to electrons oscillating on an antenna. He explained how the electromagnetic wave E-fields and B-fields reproduce each other, thus causing the wave to propagate. By combining Gauss’s Law, Ampere’s Law, and Faraday’s Law, he was able to develop a coherent theory of electromagnetism and its relationship to all forms for electromagnetic radiation, such as radio waves, microwaves, infrared radiation, visible light, ultraviolet light, X-rays, and gamma rays. The only difference between these forms was the wavelength and frequency.
It took Einstein to explain that each photon had a frequency, and an energy which was proportional to that frequency as given by
E = hf
Where E is the photon energy, f is the frequency, and h is Plank’s constant. You can see in the above table the frequency, wavelength, and energy for different forms of electromagnetic radiation.
# Speed of Light
Through the 19th century better estimates were made for the speed of light which we now realize is a constant in all frames of reference. Photons travel in a vacumn at a speed of approximately c = 3 x 108 m/s
Galileo realized the speed of light was faster than he could masure. In 1675, Ole Roemer was the first to come up with a good estimate of the speed of light using the moons of Jupiter, of about 2.3 x 108 m/s. In 1849 Armand Fizeau used a toothed wheel to estimate the speed at 2.9977 x 108 m/s. In 1880 Michelson built on this using a rotating octogolnal mirror on a mountain top and got 2.9920 x 108 m/s which is not far from the actual value of 2.99792457 x 108 m/s. You could easily measure the speed of light yourself by setting of Fizzeu’s experiment in the classroom using a chopper, electric drill, HeNe Laser, mirrors, long focal length converging lenses, phototransistor. diode and an oscilloscope.
# Reflection and transmission of waves.
Earlier we examined how waves traveling down a slinky can be reflected or transmitted when passing from one material to another material. What happens depends on “boundary conditions,” and is affected by the speed of the wave in both materials. Similarly, whether an electromagnetic wave is reflected or transmitted depends on the physical properties. This is also a frequency dependent phenomena. Certain wavelengths of light will be reflected, transmitted, or even absorbed. This depends on the resonant frequencies of the material, both on the atomic level and the larger molecular levels.
# Index of Refraction
As an electromagnetic wave passes through a material, it will interact with the charges in that material. This is a frequency dependent phenomena.
We define the index of refraction, n, as the proportion to which light slows down.
n = c/v
where n is the index of refraction, c is the speed of light in a vacuum, and v is the speed of light in the material
A common example is how glass interacts with electromagnetic waves. The electrons in glass tend to absorb UV light. The structure of glass tends to be excited by lower energy infrared light. One can think of the molecules of visible light as being temporarily absorbed for a microsecond and being remitted.
# Opacity
It is an oversimplification to say a material is opaque, rather we need to discuss the opacity of a material (which depends on wavelength). As light passes through a substance, a certain percentage of that light will be absorbed, and converted into thermal energy. The amount of light that is absorbed is actually an exponential function of the depth to which the light penetrates.
We can define the optical depth, t, as the depth after which about 37% of the light is absorbed. The number 37% is 1/e or 1/(2.71) which is Euler’s number. This optical depth or opacity can be related to the electromagnetic properties of a substance as it is actually an imaginary component of the index of refraction. Again, the optical depth is a wavelength dependent phenomena, and thus is different for various materials.
If we define the original intensity as , and I as the Intensity, then after one optical depth, 37% of the light is absorbed. After a second thickness of optical depth, another 37% of the light will be absorbed.
An object which is red absorbs most colors of light, but reflects red light. Glass is transparent to visible light, but absorbs a wide range of UV and IR light. Pure silicon wafers are transparent to infrared light but are “opaque” or have a high optical density in the visible spectrum.
# Inverse Square Law and Intensity of Light
We define the intensity of light as I as
I = P/A
where P is power, and A is area. So Intensity is Power/Area or watts/meter squared.
Due to the inverse square law, as light is spread out over the surface area of a three dimensional sphere its intensity decreases.
This could easily be measured using a Vernier Optical Sensor on a meter stick optical bench just for distance. You could do a graph of lux as a function of distance.
# Color and the Rainbow
Our friend Ug the Caveman discovered the colors of the rainbow and that white light can be broken up into these colors. Even before Newton’s time, philosophers were using prisms of glass to separate the colors of white light. Newton, as he wrote in Optiks, discovered that he could take the colors of the rainbow and recombine them into white light. Interestingly, when William Herschel (in 1800) was measuring the temperature of light broken up by a prism, he discovered infrared light.
Despite the fine work of Ug the caveman, our modern sequence ROYGBIV was developed by Newton because he liked 7, which he believed had mystical powers.
In modern physics, we do not consider Indigo a color, and thus the colors of the rainbow are ROYGBV
# Scattering
You have probably observed how beam of light scatters from dust in the air as in passes through your dark living room early in the morning. We can see the same thing is we look at a laser beam or light show at a rock concert. Even a laser in a classroom scattered off of chalk dust or in a James Bond movie can be exciting. The scattering of light depends on the size of the dust particles, and thus is a wavelength dependent phenomena.
On the moon, the sky is actually black because there is no atmosphere for light to scatter off of.
Shorter wavelengths scatter easily, so our sky appears blue because of the light scattering off of molecules in the atmosphere. However, when the sun is low on the horizon, all of the violet, blue, and green light has scattered out, leaving the oranges and reds to penetrate. Thus, we see red sunsets. | {"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": 0.8527776002883911, "perplexity": 804.1641066884094}, "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-2015-18/segments/1429246634331.38/warc/CC-MAIN-20150417045714-00018-ip-10-235-10-82.ec2.internal.warc.gz"} |
http://tex.stackexchange.com/questions/96075/loading-aurical-fonts-without-generating-a-font-warning | # Loading Aurical fonts without generating a font warning
I've got a document where I load in the aurical package. However, whenever I use the fonts this defines, I get a Font Warning telling me that the font shape has been scaled. For example,
\documentclass{article}
\usepackage{aurical}
\begin{document}
\Fontamici Test!
\end{document}
yields:
LaTeX Font Warning: Font shape T1/AmiciLogo/m/n' will be
(Font) scaled to size 11.99997pt on input line 4.
What's the right way to use this set of fonts so that it doesn't generate a warning?
-
## 1 Answer
LaTeX font setup is rather chatty: that's more of an informative note than a warning. The fd file for that font specifies it should be loaded 1.2 times the requested size and by default latex tells you this.
The relevant lines are:
\DeclareFontShape{T1}{AmiciLogo}{m}{n}{<-> [1.2] AmiciLogo}{}
Using the s scaling function rather than the default empty one stops the warning.
\DeclareFontShape{T1}{AmiciLogo}{m}{n}{<-> s * [1.2] AmiciLogo}{}
`
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Thanks very much! I'd forgotten about those subtleties of font loading. – Martyn Quick Jan 30 '13 at 21:20 | {"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": 0.9916484951972961, "perplexity": 5735.382151792654}, "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-2015-18/segments/1429246656168.61/warc/CC-MAIN-20150417045736-00140-ip-10-235-10-82.ec2.internal.warc.gz"} |
http://www.physicsforums.com/showthread.php?p=4181454 | # Describing the motion of a linked body?
by greswd
P: 147 A general example of a linked body is an object that is made up of rigid bodies joined together by pivots, such as hinges and ball-socket joints. If the pivots are frictionless, and I apply a force to one rigid body, how can I go about describing the subsequent angular acceleration of the individual rigid bodies, and also the entire linked body about its barycenter?
Mentor P: 17,326 I would use the Lagrangian approach. Even for something as simple as a double pendulum it winds up being easier.
Sci Advisor P: 2,470 Which, with exception of a few simple cases, will usually produce something that can only be solved numerically. So if you hope for a closed-form expression, forget about it. But if you need it for a simulation, do what DaleSpam suggested. Write down the Lagrangian with an undetermined Lagrange Multiplier for every joint or other constraint you have. That will give you a system of equations for each [itex]\ddot{q_i}[/tex] to be solved for each time step, and then you can use Verlet or Runge-Kutta methods to integrate these.
P: 147
Describing the motion of a linked body?
Quote by K^2 Which, with exception of a few simple cases, will usually produce something that can only be solved numerically. So if you hope for a closed-form expression, forget about it. But if you need it for a simulation, do what DaleSpam suggested. Write down the Lagrangian with an undetermined Lagrange Multiplier for every joint or other constraint you have. That will give you a system of equations for each [itex]\ddot{q_i}[/tex] to be solved for each time step, and then you can use Verlet or Runge-Kutta methods to integrate these.
So it's possible to get a numerical solution to any degree of accuracy? I've always wondered how mathematicians definitively prove that the system is inherently chaotic and that no closed form solutions exist.
But even if a pattern exists it's difficult to find because the subsequent motion is so highly dependent on initial conditions.
P: 147 what about a very simple compound body? Just one mass, floating in deep space, with a rod pivoted to it.
P: 2,470
Quote by greswd So it's possible to get a numerical solution to any degree of accuracy?
Not in general. There are going to be special cases where you can, but in general, these things tend towards chaos.
If you have just two masses connected by a single joint, you can use conservation of momentum and angular momentum to greatly reduce degrees of freedom, giving you a closed form solution. Everything past that would require some approximations, I believe.
P: 147
Quote by K^2 Not in general. There are going to be special cases where you can, but in general, these things tend towards chaos. If you have just two masses connected by a single joint, you can use conservation of momentum and angular momentum to greatly reduce degrees of freedom, giving you a closed form solution. Everything past that would require some approximations, I believe.
Thanks. So in certain cases things are non-chaotic, but it's generally difficult to prove whether system is definitely chaotic and/or lacks a closed form solution.
Mentor P: 17,326 If you are interested in chaos, I would start with a double pendulum. It is relatively easy to solve, and it is well studied. Here is a good start: http://en.wikipedia.org/wiki/Double_pendulum
P: 147 Hmmm, I am interested in finding out how mathematicians prove that a system is chaotic and that no symbolic solutions exist.
P: 147 For instance, the three body problem of Sun-Moon-Earth might have a definite closed form solution that we just cannot find.
Mentor
P: 17,326
Quote by greswd Hmmm, I am interested in finding out how mathematicians prove that a system is chaotic and that no symbolic solutions exist.
These are two somewhat different properties. A system can be non-chaotic and still not have a symbolic solution.
However, I don't think that "no symbolic solutions" is something that is actually mathematically proven. It is simply that we don't know any such solutions. It also depends critically on what functions are admissible in your set of symbolic colutions.
P: 147
Quote by DaleSpam A system can be non-chaotic and still not have a symbolic solution.
What kind of system is described as such?
Quote by DaleSpam However, I don't think that "no symbolic solutions" is something that is actually mathematically proven. It is simply that we don't know any such solutions. It also depends critically on what functions are admissible in your set of symbolic colutions.
Interesting, it sort of opens the possibility that someday someone might solve the Sun-Earth-Moon problem.
Like the CMI problems.
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