By using our site, you acknowledge that you have read and understand our Cookie PolicyPrivacy Policyand our Terms of Service. It only takes a minute to sign up. I think that the parameter 2 is near to good and correct. Otherwise you set the option with 1.

See the example below with the parameter 1 :. You can see with a zoom in that you can see the double background, but in the distance it's not obvious. Sign up to join this community. The best answers are voted up and rise to the top.

Home Questions Tags Users Unanswered. Bold pzc for mathmode Ask Question. Asked 21 days ago. Active 20 days ago. Viewed 75 times. Boldface Zapf Chancery is not available. The bold version is not very similar to the italic though, it is much less 'curly'. For my humble opinion you use the best answer of egreg. Active Oldest Votes.

Sebastiano Sebastiano Thank you! The fake bold symbol is the best The Zapf Chancery font or clone thereofis not available in boldface.

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I was editing my answer, but you remain my admiration and esteem. It is a wonderful fake. Sign up or log in Sign up using Google. Sign up using Facebook. Sign up using Email and Password.

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Feedback on Q2 Community Roadmap.The detection of interesting patterns in large high-dimensional datasets is difficult because of their dimensionality and pattern complexity.

Therefore, analysts require automated support for the extraction of relevant patterns. In this paper, we present FDivea visual active learning system that helps to create visually explorable relevance models, assisted by learning a pattern-based similarity. We use a small set of user-provided labels to rank similarity measures, consisting of feature descriptor and distance function combinations, by their ability to distinguish relevant from irrelevant data.

Based on the best-ranked similarity measure, the system calculates an interactive Self-Organizing Map-based relevance model, which classifies data according to the cluster affiliation. It also automatically prompts further relevance feedback to improve its accuracy. Uncertain areas, especially near the decision boundaries, are highlighted and can be refined by the user.

We evaluate our approach by comparison to state-of-the-art feature selection techniques and demonstrate the usefulness of our approach by a case study classifying electron microscopy images of brain cells.


The results show that FDive enhances both the quality and understanding of relevance models and can thus lead to new insights for brain research. Users explore and refine the model by supplying relevance labels in uncertain data regions, especially near the decision boundaries. A primary challenge when analyzing collected data is to distinguish relevant from irrelevant data items.

Large and high-dimensional datasets are not easily analyzed, because of their size, dimensionality, and possible complex patterns. Therefore, analysts need automated support. This support is realized in the form of a relevance model that can help them to make this distinction.

Its task is the retrieval of relevant data items from large high-dimensional datasets that are often associated with many types of analysis scenarios. Similarity models are key to effective data clustering and classification. It is crucial that the model reflects the notion of relevance as it pertains to the analysis task.

More generally, when we are dealing with high-dimensional datasets, we need to automatically and adaptively assess the relevance of data items. Although analysts interact with data for analysis and exploration purposes, their primary goal is to quickly generate new insights and results.

All interactions, such as labeling or relevance feedback, should be focused on yielding insights and need to be as impactful as possible. The fully automatic creation of relevance models is non-trivial.

Classic machine learning techniques depend on a predefined set of features and a given distance function, chosen or even designed by experts based on their experience.

In most real-world scenarios, these labels do not exist and the manual assignment of labels is time consuming, tedious, and expensive.By using our site, you acknowledge that you have read and understand our Cookie PolicyPrivacy Policyand our Terms of Service. The dark mode beta is finally here. Change your preferences any time. Stack Overflow for Teams is a private, secure spot for you and your coworkers to find and share information. Learn more. Ask Question. Asked 10 years, 5 months ago.

Active 2 months ago. Viewed 10k times. Al Jumaily 1 1 gold badge 4 4 silver badges 14 14 bronze badges. Active Oldest Votes. This is using Zapf Chancery which is the standard PostScript calligraphic font.

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Question feed.Can someone recommend a good macro for "little oh" and maybe "big Oh", too? Re: Need a macro for little oh. Something like you defined for Oh is already defined by package physics. No need to trouble yourself. The output for the little oh is somehow expected, since there is no lowercase mathcal alphabet. The smart way: Calm down and take a deep breath, read posts and provided links attentively, try to understand and ask if necessary.

This article suggests that I can download stix. But I cannot figure out what to do from there, so I have not been able to make your suggestion work. You can safely ignore the warnings given by physics. Have a look at the documentation to see why those commands are redefined. Yes, you cannot use fontspec with pdflatex. Another possibility would be XeLaTeX. If you have to stick with pdflatex, you can comment out package fontspec and load fontenc with your appropriate option instead.

Thanks for all your work. I used and it managed to get the symbols for Order and order big and little O.


But can that font be turned on and off? I ask because it is messing with the fonts in the rest of the document. Here is an MWE. But first, note that I have a somewhat reasonable solution in my OP. I don't want to take up more of your time than this is worth to you.The Pazo Math fonts are a family of PostScript fonts suitable for typesetting mathematics in combination with the Palatino family of text fonts.

These contain, in designs that match Palatino, glyphs that are usually not available in Palatino and for which Computer Modern looks odd when combined with Palatino.

These glyphs include the uppercase Greek alphabet in upright and slanted shapes in regular and bold weights, the lowercase Greek alphabet in slanted shape in regular and bold weights, several mathematical glyphs partialdiff, summation, product, coproduct, emptyset, infinity, and proportional in regular and bold weights, other glyphs Euro and dotlessj in upright and slanted shapes in regular and bold weights, and the uppercase letters commonly used to represent various number sets C, I, N, Q, R, and Z in blackboard bold.

L a T e X macro support using package mathpazo. Download the contents of this package in one zip archive Login Join Settings Help. Cover Cover Starting out with T e X Font tables:. Suggestions Maybe you are interested in the following packages as well.Read this paper on arXiv. Here we develop two quantum-computational models for supervised and unsupervised classification tasks in quantum world.

Presuming that the states of a set of given quantum systems or objects belong to one of two known classes, the objective here is to decide to which of these classes each system belongs—without knowing its state. The supervised binary classification algorithm is based on having a training sample of quantum systems whose class memberships are already known.

The unsupervised binary classification algorithm, however, uses a quantum oracle which knows the class memberships of the states of the computational basis. Both algorithms require the ability to evaluate the fidelity between states of the quantum systems with unknown states, for which here we also develop a general scheme.

Statistical classification is an important concern in modern science and technology book:Hastie ; book:Alpaydin. One of the simplest examples of such tasks is to decide to which of a pair of specified target groups a particular object of interest is assigned.

Distinguishing between spam or non-spam emails, determining whether a collection of physical symptoms of a patient is due to an underlying disease or not, and identity verification, along with a diverse set of other relevant applications, are all examples of the problem of binary classification. Binary classification is a special case of the problems where the number of target groups is not necessarily two and can be any natural number or even cardinality of continuume.

Each object O in machine learning is usually represented using a finite sequence of real numbers that can be regarded as a vector v O in a Euclidean space.

Naturally then, resemblance between objects is assessed using the distance of their associated vectors. Performing various steps of a machine leaning algorithm would require computational and processing power, which would increase with complexity of algorithms.

With the advent of quantum computation, quantum information processing, and quantum algorithms book:Nielsenquantum machine learning has also been studied book:QML. Most recent attempts in this line have concerned revisiting earlier classical machine learning algorithms such that one can best employ power of quantum mechanics Adcock ; Schuld ; survey. For example, recently a quantum version of the support vector machine algorithm has been developed Lloyd:PRLwhich in turn relies on a quantum algorithm for solving linear systems of equations Lloyd:linear.

Quantum machine learning can also be categorized into the classes of supervised and unsupervised quantum classification problems. In the case where the quantum states describing the quantum systems of interest are knownthe problem of supervised quantum classification almost perfectly resembles its classical counterpart, except for the manner of representing the objects.

This difference, however, is not fundamental since there always exists a one-to-one correspondence between the representations of quantum systems in a Hilbert space and vectors of a Euclidean space of the same dimension.

Thus, assuming to be equipped with a quantum- ram RAMany scheme for dividing quantum systems into categories according to their known quantum states is also a tool for revealing patterns in classical data.

Quantum- ram is defined to be a device which is able to provide a mapping from classical vectors in a desired Euclidean space onto the quantum states living in the corresponding Hilbert space RAM. Another example of this criterion, concerned with classifying two-qubit quantum states, can be found in Ref.

Quantum machine learning can also be extended to devise algorithms for recognizing patterns in quantum systems with unknown quantum states Sentis. Such algorithms differ basically from those of the classical machine learning in their manner of treating objects in order to find their hidden structures, besides their performance does not depend on any representations of the objects. Our work here concerns supervised and unsupervised binary classification of a set of quantum systems with unknown quantum states.

Randomised Bayesian Least-Squares Policy Iteration

The supervised classifier operates on the basis of a training set of quantum systems, assuming that each category is associated with a prior set of quantum systems. We relate the problem of evaluating the category membership to the problem of evaluating fidelity, and propose a method for the latter based on the matrix exponentiation and quantum phase estimation qpe algorithms.

By comparing fidelities one can then discern the two classes. In the case of unsupervised classification, we assume we have an oracle which can determine the category membership of the computational basis vectors. This oracle operates as a quantum gate which marks states with one category by shifting their phase, while leaving the rest unchanged.

This property allows us to recast the classification problem as a Grover quantum search problem. Again we employ the method of evaluating and comparing fidelities to distinguish category memberships. The structure of this paper is as follows. In Sec. II we lay out a method for evaluating fidelity of two unknown quantum states based on the techniques of density matrix exponentiation and quantum phase estimation.W hen I was writing a paper, I needed a lot of mathematical variables.

I had already used up so many letters in both plain text and bold face that I needed more styles for English letters. So I looked for ways of using different types of script styles in LaTeX equations. It turns out that a lot of the script styles in math mode are upper case only. I eventually found several ways of using lower case script letters in LaTeX equations, as well as a few other math mode styles that seem useful.

I have listed them in this short tutorial. This is actually the best option I found for making upper and lower case script characters in math mode. More about this can be found on this page about maths script fonts. You now have access to a command called mathfrak. No, it is not meant to help you express your frustration by frakking math. Rather, it is for using the Fraktur font a Gothic script for your mathematical characters.


You can use it like this:. The result is nice, although the upper and lower case Y character are very different from English. The eucal package uses yet another script font Euler script in your equations. First, include the package:. There is yet another script font that can be used in LaTeX for upper case letters.

To use it, include the package:. I found references to a calligra font that is an additional calligraphy font that can be used in equations. I could not get it working in my installation of MikTeX even after installing the calligra pacakge MikTeX tells me it cannot find calligra.

In any case, I am documenting it here for future reference.

pzccal.sty: calligraphic math alphabet with Zapf Chancery

About Peter Yu I am a research and development professional with expertise in the areas of image processing, remote sensing and computer vision. My working experience covers industries ranging from district energy to medical imaging to cinematic visual effects. I like to dabble in 3D artwork, I enjoy cycling recreationally and I am interested in sustainable technology.

More about me Terms of Use Colophon. Another option is to use the amsfonts package. It uses a font derived from Zapf Chancery with metrics adapted to mathematical typesetting. The "eucal" package is no longer available on CTAN. Thanks greatly for this page. It was very helpful. I am surprised at the limited options to get lowercase mathematical letters, but Chancery worked fine. Hi Peter, Thank you for this page. It is very helpful. I would like to know how to include embeshilled calligraphic letters in bold style for instance, those provided by the mathrsfs package.

In your opinion, which is the proper manner to do that? Thank you! Hey, I am new to your site. I found it helpful I looked tor the latex math script.

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