text:
# Phil 7.31.18

7:00 – 6:00 ASRC MKT

• Thinking that I need to forward the opinion dynamics part of the work. How heading differs from position and why that matters
• Found a nice adversarial herding chart from The Economist
• Why Do People Share Fake News? A Sociotechnical Model of Media Effects
• Fact-checking sites reflect fundamental misunderstandings about how information circulates online, what function political information plays in social contexts, and how and why people change their political opinions. Fact-checking is in many ways a response to the rapidly changing norms and practices of journalism, news gathering, and public debate. In other words, fact-checking best resembles a movement for reform within journalism, particularly in a moment when many journalists and members of the public believe that news coverage of the 2016 election contributed to the loss of Hillary Clinton. However, fact-checking (and another frequently-proposed solution, media literacy) is ineffectual in many cases and, in other cases, may cause people to “double-down” on their incorrect beliefs, producing a backlash effect.
• Epistemology in the Era of Fake News: An Exploration of Information Verification Behaviors among Social Networking Site Users
• Fake news has recently garnered increased attention across the world. Digital collaboration technologies now enable individuals to share information at unprecedented rates to advance their own ideologies. Much of this sharing occurs via social networking sites (SNSs), whose members may choose to share information without consideration for its authenticity. This research advances our understanding of information verification behaviors among SNS users in the context of fake news. Grounded in literature on the epistemology of testimony and theoretical perspectives on trust, we develop a news verification behavior research model and test six hypotheses with a survey of active SNS users. The empirical results confirm the significance of all proposed hypotheses. Perceptions of news sharers’ network (perceived cognitive homogeneity, social tie variety, and trust), perceptions of news authors (fake news awareness and perceived media credibility), and innate intentions to share all influence information verification behaviors among SNS members. Theoretical implications, as well as implications for SNS users and designers, are presented in the light of these findings.
• Working on plan diagram – done
• Organizing PhD slides. I think I’m getting near finished
• Walked through slides with Aaron. Need to practice the demo. A lot.

# Phil 7.27.18

Ted Underwood

• my research is as much about information science as literary criticism. I’m especially interested in applying machine learning to large digital collections
• Git repo with code for upcoming book: Distant Horizons: Digital Evidence and Literary Change
• Do topic models warp time?
• The key observation I wanted to share is just that topic models produce a kind of curved space when applied to long timelines; if you’re measuring distances between individual topic distributions, it may not be safe to assume that your yardstick means the same thing at every point in time. This is not a reason for despair: there are lots of good ways to address the distortion. The mathematics of cosine distance tend to work better if you average the documents first, and then measure the cosine between the averages (or “centroids”).
• The Historical Significance of Textual Distances
• Measuring similarity is a basic task in information retrieval, and now often a building-block for more complex arguments about cultural change. But do measures of textual similarity and distance really correspond to evidence about cultural proximity and differentiation? To explore that question empirically, this paper compares textual and social measures of the similarities between genres of English-language fiction. Existing measures of textual similarity (cosine similarity on tf-idf vectors or topic vectors) are also compared to new strategies that use supervised learning to anchor textual measurement in a social context.

7:00 – 8:00 ASRC MKT

• Continued on slides. I think I have the basics. Need to start looking for pictures
• Sent response to the SASO folks about who’s presenting what.

• More flailing on A2P UI? Oh, yeah….
• More RNN/LSTM?
• Slow progress. Spent some time cleaning up my single neuron spreadsheet, which does make more sense now.
• Some papers and source pointed to by the text:

# Phil 7.26.18

7:00 – 5:30 ASRC

• This could be interesting. Includes predictive analytics: BigQuery ML
• Working on slides
• Working on RNNs and LSTMS. I would love to build a simple, explanatory model in Excel, but can’t find one.
• Helped Aaron flail on getting tab dates into the A2P GUI

# Phil 7.25.18

7:00 – 3:00 ASRC

• Send out email with meeting time
• Rather than excerpts from the talks, do a demo of the relevant bits with conclusions and implications. Get the laptop running all the pieces. That means Python and TF and all the other bits.
• Submitted tuition expenses
• Submitted Fall 2018 approval
• Got SASO travel approval!
• More DNN study
• Finished CNNs
• Working on embeddings and W2V. Thought I’d try it on the laptop, but keras can’t find it’s back end and I’m getting other weird errors. One of the big ones was that I didn’t install tk with python. Here’s the answer from stackoverflow:
• And now we’re waiting a very long time for a tf ‘hello world’ to run… But it did!
• Had to also install pydot and graphviz-2.38.msi. Then add the graphviz bin directory to the path.
• But now everything runs on the laptop, which will help with the demos!
• Skipped the GloVe and pre-trained embeddings. Ready to start on DNNs tomorrow.

# Phil 7.20.18

• David Peritz
• Political polarization, accompanied by negative partisanship, are striking features of the current political landscape. Perhaps these trends were originally confined to politicians and the media, but we recently reached the point where the majority of Americans report they would consider it more objectionable if their children married across party lines than if they married someone of another faith. Where did this polarization come from? And what it is doing to American democracy, which is housed in institutions that were framed to encourage open deliberation, compromise and consensus formation? In this talk, Professor David Peritz will examine some of the deeper forces in the American economy, the public sphere and media, political institutions, and even moral psychology that best seem to account for the recent rise in popular polarization.

Sent out a Doodle to nail down the time for the PhD review

Went looking for something that talks about the cognitive load for TIT-FOR-TAT in the Iterated Prisoner’s Dilemma and can’t find anything. Did find this though, that is kind of interesting: New tack wins prisoner’s dilemma. It’s a collective intelligence approach:

• Teams could submit multiple strategies, or players, and the Southampton team submitted 60 programs. These, Jennings explained, were all slight variations on a theme and were designed to execute a known series of five to 10 moves by which they could recognize each other. Once two Southampton players recognized each other, they were designed to immediately assume “master and slave” roles – one would sacrifice itself so the other could win repeatedly.
• Nick Jennings
• Professor Jennings is an internationally-recognized authority in the areas of artificial intelligence, autonomous systems, cybersecurity and agent-based computing. His research covers both the science and the engineering of intelligent systems. He has undertaken fundamental research on automated bargaining, mechanism design, trust and reputation, coalition formation, human-agent collectives and crowd sourcing. He has also pioneered the application of multi-agent technology; developing real-world systems in domains such as business process management, smart energy systems, sensor networks, disaster response, telecommunications, citizen science and defence.
• Sarvapali D. (Gopal) Ramchurn
• I am a Professor of Artificial Intelligence in the Agents, Interaction, and Complexity Group (AIC), in the department of Electronics and Computer Science, at the University of Southampton and Chief Scientist for North Star, an AI startup.  I am also the director of the newly created Centre for Machine Intelligence.  I am interested in the development of autonomous agents and multi-agent systems and their application to Cyber Physical Systems (CPS) such as smart energy systems, the Internet of Things (IoT), and disaster response. My research combines a number of techniques from Machine learning, AI, Game theory, and HCI.

7:00 – 4:30 ASRC MKT

• SASO Travel request
• SASO Hotel – done! Aaaaand I booked for August rather than September. Sent a note to try and fix using their form. If nothing by COB try email.
• Potential DME repair?
• Starting Deep Learning with Keras. Done with chapter one
• Two seedbank lstm text examples:
• Generate Shakespeare using tf.keras
• This notebook demonstrates how to generate text using an RNN with tf.keras and eager execution.This notebook is an end-to-end example. When you run it, it will download a dataset of Shakespeare’s writing. The notebook will then train a model, and use it to generate sample output.
• CharRNN
• This notebook will let you input a file containing the text you want your generator to mimic, train your model, see the results, and save it for future use all in one page.

# Phil 7.19.18

7:00 – 3:00 ASRC MKT

• More on augmented athletics: Pinarello Nytro electric road bike review
• WhatsApp Research Awards for Social Science and Misinformation (\$50k – Applications are due by August 12, 2018, 11:59pm PST)
• Setting up meeting with Don for 3:30 Tuesday the 24th. He also gave me some nice leads on potential people for Dance my PhD:
• Dr. Linda Dusman
• Linda Dusman’s compositions and sonic art explore the richness of contemporary life, from the personal to the political. Her work has been awarded by the International Alliance for Women in Music, Meet the Composer, the Swiss Women’s Music Forum, the American Composers Forum, the International Electroacoustic Music Festival of Sao Paulo, Brazil, the Ucross Foundation, and the State of Maryland in 2004, 2006, and 2011 (in both the Music: Composition and the Visual Arts: Media categories). In 2009 she was honored as a Mid- Atlantic Arts Foundation Fellow for a residency at the Virginia Center for the Creative Arts. She was invited to serve as composer in residence at the New England Conservatory’s Summer Institute for Contemporary Piano in 2003. In the fall of 2006 Dr. Dusman was a Visiting Professor at the Conservatorio di musica “G. Nicolini” in Piacenza, Italy, and while there also lectured at the Conservatorio di musica “G. Verdi” in Milano. She recently received a Maryland Innovation Initiative grant for her development of Octava, a real-time program note system (octavaonline.com).
• Doug Hamby
• A choreographer who specializes in works created in collaboration with dancers, composers, visual artists and engineers. Before coming to UMBC he performed in several New York dance companies including the Martha Graham Dance Company and Doug Hamby Dance. He is the co-artistic director of Baltimore Dance Project, a professional dance company in residence at UMBC. Hamby’s work has been presented in New York City at Lincoln Center Out-of-Doors, Riverside Dance Festival, New York International Fringe Festival and in Brooklyn’s Prospect Park. His work has also been seen at Fringe Festivals in Philadelphia, Edinburgh, Scotland and Vancouver, British Columbia, as well as in Alaska. He has received choreography awards from the National Endowment for the Arts, Maryland State Arts Council, New York State Council for the Arts, Arts Council of Montgomery County, and the Baltimore Mayor’s Advisory Committee on Arts and Culture. He has appeared on national television as a giant slice of American Cheese.
• Sent out a note with dates and agenda to the committee for the PhD review thing. Thom can open up August 6th
• Continuing extraction of seed terms for the sentence generation. And it looks like my tasking for next sprint will be to put together a nice framework for plugging in predictive patterns systems like LSTM and multi-layer perceptrons.
• This seems to be working:
agentRelationships GreenFlockSh_1
sampleData 0.0
cell cell_[4, 6]
influences AGENT
influence GreenFlockSh_0 val =  0.8778825396520958
influence GreenFlockSh_2 val =  0.8859173062045552
influence GreenFlockSh_3 val =  0.9390368569108515
influence GreenFlockSh_4 val =  0.9774328763377834
influences SOURCE
influence UL_point val =  0.032906293611796644
• Sprint planning
• VP-613: Develop general TensorFlow/Keras NN format
• LSTM
• MLP
• CNN
• VP-616: SASO Preparation
• Slides
• Poster
• Demo

# Phil 5.31.18

7:00 – ASRC MKT

• Via BBC Business Daily, found this interesting post on diversity injection through lunch table size:
• KQED is playing America Abroad – today on russian disinfo ops:
• Sowing Chaos: Russia’s Disinformation Wars
• Revelations of Russian meddling in the 2016 US presidential election were a shock to Americans. But it wasn’t quite as surprising to people in former Soviet states and the EU. For years they’ve been exposed to Russian disinformation and slanted state media; before that Soviet propaganda filtered into the mainstream. We don’t know how effective Russian information warfare was in swaying the US election. But we do know these tactics have roots going back decades and will most likely be used for years to come. This hour, we’ll hear stories of Russian disinformation and attempts to sow chaos in Europe and the United States. We’ll learn how Russia uses its state-run media to give a platform to conspiracy theorists and how it invites viewers to doubt the accuracy of other news outlets. And we’ll look at the evolution of internet trolling from individuals to large troll farms. And — finally — what can be done to counter all this?
• Some interesting papers on the “Naming Game“, a form of coordination where individuals have to agree on a name for something. This means that there is some kind of dimension reduction involved from all the naming possibilities to the agreed-on name.
• The Grounded Colour Naming Game
• Colour naming games are idealised communicative interactions within a population of artificial agents in which a speaker uses a single colour term to draw the attention of a hearer to a particular object in a shared context. Through a series of such games, a colour lexicon can be developed that is sufficiently shared to allow for successful communication, even when the agents start out without any predefined categories. In previous models of colour naming games, the shared context was typically artificially generated from a set of colour stimuli and both agents in the interaction perceive this environment in an identical way. In this paper, we investigate the dynamics of the colour naming game in a robotic setup in which humanoid robots perceive a set of colourful objects from their own perspective. We compare the resulting colour ontologies to those found in human languages and show how these ontologies reflect the environment in which they were developed.
• Group-size Regulation in Self-Organised Aggregation through the Naming Game
• In this paper, we study the interaction effect between the naming game and one of the simplest, yet most important collective behaviour studied in swarm robotics: self-organised aggregation. This collective behaviour can be seen as the building blocks for many others, as it is required in order to gather robots, unable to sense their global position, at a single location. Achieving this collective behaviour is particularly challenging, especially in environments without landmarks. Here, we augment a classical aggregation algorithm with a naming game model. Experiments reveal that this combination extends the capabilities of the naming game as well as of aggregation: It allows the emergence of more than one word, and allows aggregation to form a controllable number of groups. These results are very promising in the context of collective exploration, as it allows robots to divide the environment in different portions and at the same time give a name to each portion, which can be used for more advanced subsequent collective behaviours.
• More Bit by Bit. Could use some worked examples. Also a login so I’m not nagged to buy a book I own.
• Descriptive and injunctive norms – The transsituational influence of social norms.
• Three studies examined the behavioral implications of a conceptual distinction between 2 types of social norms: descriptive norms, which specify what is typically done in a given setting, and injunctive norms, which specify what is typically approved in society. Using the social norm against littering, injunctive norm salience procedures were more robust in their behavioral impact across situations than were descriptive norm salience procedures. Focusing Ss on the injunctive norm suppressed littering regardless of whether the environment was clean or littered (Study 1) and regardless of whether the environment in which Ss could litter was the same as or different from that in which the norm was evoked (Studies 2 and 3). The impact of focusing Ss on the descriptive norm was much less general. Conceptual implications for a focus theory of normative conduct are discussed along with practical implications for increasing socially desirable behavior.
• Construct validity centers around the match between the data and the theoretical constructs. As discussed in chapter 2, constructs are abstract concepts that social scientists reason about. Unfortunately, these abstract concepts don’t always have clear definitions and measurements.
• Simulation is a way of implementing theoretical constructs that are measurable and testable.
• Hyperparameter Optimization with Keras
• Recognizing images from parts Kaggle winner
• White paper
• Storyboard meeting
• The advanced analytics division(?) needs a modeling and simulation department that builds models that feed ML systems.
• Meeting with Steve Specht – adding geospatial to white paper

# Phil 5.25.18

7:00 – 6:00 ASRC MKT

• Starting Bit by Bit
• I realized the hook for the white paper is the military importance of maps. I found A Revolution in Military Cartography?: Europe 1650-1815
• Military cartography is studied in order to approach the role of information in war. This serves as an opportunity to reconsider the Military Revolution and in particular changes in the eighteenth century. Mapping is approached not only in tactical, operational and strategic terms, but also with reference to the mapping of war for public interest. Shifts in the latter reflect changes in the geography of European conflict.
• Reconnoitering sketch from Instructions in the duties of cavalry reconnoitring an enemy; marches; outposts; and reconnaissance of a country; for the use of military cavalry. 1876 (pg 83)
• rutter is a mariner’s handbook of written sailing directions. Before the advent of nautical charts, rutters were the primary store of geographic information for maritime navigation.
• It was known as a periplus (“sailing-around” book) in classical antiquity and a portolano (“port book”) to medieval Italian sailors in the Mediterranean Sea. Portuguese navigators of the 16th century called it a roteiro, the French a routier, from which the English word “rutter” is derived. In Dutch, it was called a leeskarte (“reading chart”), in German a Seebuch (“sea book”), and in Spanish a derroterro
• Example from ancient Greece:
• From the mouth of the Ister called Psilon to the second mouth is sixty stadia.
• Thence to the mouth called Calon forty stadia.
• From Calon to Naracum, which last is the name of the fourth mouth of the Ister, sixty stadia.
• Hence to the fifth mouth a hundred and twenty stadia.
• Hence to the city of Istria five hundred stadia.
• From Istria to the city of Tomea three hundred stadia.
• From Tomea to the city of Callantra, where there is a port, three hundred stadia
• Battlespace
• Cyber-Human Systems (CHS)
• In a world in which computers and networks are increasingly ubiquitous, computing, information, and computation play a central role in how humans work, learn, live, discover, and communicate. Technology is increasingly embedded throughout society, and is becoming commonplace in almost everything we do. The boundaries between humans and technology are shrinking to the point where socio-technical systems are becoming natural extensions to our human experience – second nature, helping us, caring for us, and enhancing us. As a result, computing technologies and human lives, organizations, and societies are co-evolving, transforming each other in the process. Cyber-Human Systems (CHS) research explores potentially transformative and disruptive ideas, novel theories, and technological innovations in computer and information science that accelerate both the creation and understanding of the complex and increasingly coupled relationships between humans and technology with the broad goal of advancing human capabilities: perceptual and cognitive, physical and virtual, social and societal.
• Reworked Section 1 to incorporate all this in a single paragraph
• Long discussion about all of the above with Aaron
• Worked on getting the CoE together by CoB
• Do Diffusion Protocols Govern Cascade Growth?
• Continuing with creating the Simplest LSTM ever
• All work and no play makes jack a dull boy indexes alphabetically as :

# Phil 5.22.18

8:00 – 5:00 ASRC MKT

• EAMS meeting
• Rational
• Sensitivity knn. Marching cubes, or write into space. Pos lat/lon altitude speed lat lon (4 dimensions)
• Do they have flight path?
• Memory
• Retraining (batch)
• inference real time
• How will time be used
• Much discussion of simulation
• End-to-end Machine Learning with Tensorflow on GCP
• In this workshop, we walk through the process of building a complete machine learning pipeline covering ingest, exploration, training, evaluation, deployment, and prediction. Along the way, we will discuss how to explore and split large data sets correctly using BigQuery and Cloud Datalab. The machine learning model in TensorFlow will be developed on a small sample locally. The preprocessing operations will be implemented in Cloud Dataflow, so that the same preprocessing can be applied in streaming mode as well. The training of the model will then be distributed and scaled out on Cloud ML Engine. The trained model will be deployed as a microservice and predictions invoked from a web application. This lab consists of 7 parts and will take you about 3 hours. It goes along with this slide deck
• Slides
• Codelab
• Added in JuryRoom Text rough. Next is Research Browser
• Worked with Aaron on LSTM some more. More ndarray slicing experience:
import numpy as np
dimension = 3
size = 10
dataset1 = np.ndarray(shape=(size, dimension))
dataset2 = np.ndarray(shape=(size, dimension))
for x in range(size):
for y in range(dimension):
val = (y+1) * 10 + x +1
dataset1[x,y] = val
val = (y+1) * 100 + x +1
dataset2[x,y] = val

dataset1[:, 0:1] = dataset2[:, -1:]
print(dataset1)
print(dataset2)
• Results in:
[[301.  21.  31.]
[302.  22.  32.]
[303.  23.  33.]
[304.  24.  34.]
[305.  25.  35.]
[306.  26.  36.]
[307.  27.  37.]
[308.  28.  38.]
[309.  29.  39.]
[310.  30.  40.]]
[[101. 201. 301.]
[102. 202. 302.]
[103. 203. 303.]
[104. 204. 304.]
[105. 205. 305.]
[106. 206. 306.]
[107. 207. 307.]
[108. 208. 308.]
[109. 209. 309.]
[110. 210. 310.]]

# Phil 5.21.18

8:00 – 5:00 ASRC MKT

• Working through the BAA and transposing all the critical terms to the RFI
• A lot of time with Aaron unpacking text-based LSTM an ddoing stupid Python things

# Phil 5.7.18

7:00 – 5:00 ASRC MKT

• Content Sharing within the Alternative Media Echo-System: The Case of the White Helmets
• Kate Starbird
• In June 2017 our lab began a research project looking at online conversations about the Syria Civil Defence (aka the “White Helmets”). Over the last 8–9 months, we have spent hundreds of hours conducting analysis on the tweets, accounts, articles, and websites involved in that discourse. Our first peer-reviewed paper was recently accepted to an upcoming conference (ICWSM-18). That paper focuses on a small piece of the structure and dynamics of this conversation, specifically looking at content sharing across websites. Here, I describe that research and highlight a few of the findings.
• Matt Salganik on Open Review
• Spent a lot of time getting each work to draw differently in the scatterplot. That took some digging into the gensim API to get vectors from the corpora. I then tried to plot the list of arrays, but matplotlib only likes ndarrays (apparently?). I’m now working on placing the words from each text into their own ndarray.
• Also added a filter for short stop words and switched to a hash map for words to avoid redundant points in the plot.
• Fika
• Bryce Peake
• ICA has a computational methods study area. How media lows through different spaces, etc. Python and [R]
• Anne Balsamo – designing culture
• what about language as an anti-colonial interaction
• Human social scraping of data. There can be emergent themes that become important.
• The ability of the user to delete all primary, secondary and tertiary data.
• The third eye project (chyron crawls)

# Phil 5.6.18

Sentiment detection with Keras, word embeddings and LSTM deep learning networks

• Read this blog post to get an overview over SaaS and open source options for sentiment detection. Learn an easy and accurate method relying on word embeddings with LSTMs that allows you to do state of the art sentiment analysis with deep learning in Keras.

Which research results will generalize?

• One approach to AI research is to work directly on applications that matter — say, trying to improve production systems for speech recognition or medical imaging. But most research, even in applied fields like computer vision, is done on highly simplified proxies for the real world. Progress on object recognition benchmarks — from toy-ish ones like MNISTNORB, and Caltech101, to complex and challenging ones like ImageNet and Pascal VOC — isn’t valuable in its own right, but only insofar as it yields insights that help us design better systems for real applications.

Revisiting terms:

• Belief Space – A subset of information space that is associated with opinions. For example, there is little debate about what a table is, but the shape of the table has often been a source of serious diplomatic contention
• Medium – the technology that mediates the communication that coordinates the group. There are properties that seem to matter:
• Reach – How many individuals are connected directly. Evolutionarily we may be best suited to 7 +/- 2
• Directionality – connections can be one way (broadcast) or two way (face to face)
• Transparency – How ‘visible’ is the individual on the other side of the communication? There are immediate perception and historical interaction aspects.
• Friction – How difficult is it to use the medium? For example in physical space, it is trivial to interact with someone nearby, but becomes progressively difficult with distance. Broadcasting makes it trivial for a small number of people to reach large numbers, but not the reverse. Computer mediated designs typically try to reduce the friction of interaction.
• Dimension Reduction – The process by which groups decide where to coordinate. The lower the dimensions, the easier (less calculation) it takes to act together
• State – a multidimensional measure of current belief and interest
• Orientation – A vector constructed of two measures of state. Used to determine alignment with others
• Velocity – The amount of change in state over time
• Diversity Injection – The addition of random, factual information to the Information Retrieval Interfaces (IRIs) using mechanisms currently used to deliver advertising. This differs from Serendipity Injection, which attempts to find stochastically relevant information for an individual’s implicit information needs.
• Level 1: population targeted –  Based on Public Service Announcements (PSAs), information presentation should range from simple, potentially gamified presentations to deep exploration with citations. The same random information is presented by the IRIs to the using population at the same time similarly to the Google Doodle.
• Level 2: group targeted – based on detecting a group’s behaviors. For example, a stampeding group may require information that is more focussed on pointing at where flocking activity is occuring.
• Level 3: individual targeted –  Depending on where in the belief space the individual is, there may be different reactions. In a sparsely traveled space, information that lies in the general direction of travel might be a form of useful serendipity. Conversely, when on a path that often leads to violent radicalization, information associated with disrupting the progression of other individuals with similar vectors could be applied.
• Map – a type of diagram that supports the plotting of trajectories. In this work, maps of belief space are constructed based on the dimension reduction used by humans in discussion. These maps are assumed to be dynamic over time and may consists of many interrelated, though not necessarily congruent, layers.
• Herding – Deliberate creation of stampede conditions in groups. Can be an internal process to consolidate a group, or an external, adversarial process.

# Phil 4.30.18

7:00 – 4:30 ASRC MKT

• Some new papers from ICLR 2018
• Need to write up a quick post for communicating between Angular and a (PHP) server, with an optional IntelliJ configuration section
• JuryRoom this morning and then GANs + Agents this afternoon?
• Next steps for JuryRoom
• Start up the AngularPro course
• Starting Agent/GAN project
• Need to set up an ACM paper to start dumping things into – done.
• Looking for a good source for Jack London. Gutenberg looks nice, but there is a no-scraping rule, so I guess, we’ll do this by hand…
• We will need to check for redundant short stories
• We will need to strip the front and back matter that pertains to project Gutenburg
• *** START OF THIS PROJECT GUTENBERG EBOOK BROWN WOLF AND OTHER JACK ***
• *** END OF THIS PROJECT GUTENBERG EBOOK BROWN WOLF AND OTHER JACK ***
• Fika: Accessibility at the Intersection of Users and Data
• Nice talk and followup discussion with Dr. Hernisa Kacorri, who’s combining machine learning and HCC
• My research goal is to build technologies that address real-world problems by integrating data-driven methods and human-computer interaction. I am interested in investigating human needs and challenges that may benefit from advancements in artificial intelligence. My focus is both in building new models to address these challenges and in designing evaluation methodologies that assess their impact. Typically my research involves application of machine learning and analytics research to benefit people with disabilities, especially assistive technologies that model human communication and behavior such as sign language avatars and independent mobility for the blind.

# Phil 3.28.18

7:00 – 5:00 ASRC MKT

• Aaron found this hyperparameter optimization service: Sigopt
• Improve ML models 100x faster
• SigOpt’s API tunes your model’s parameters through state-of-the-art Bayesian optimization.
• Exponentially faster and more accurate than grid search. Faster, more stable, and easier to use than open source solutions.
• Extracts additional revenue and performance left on the table by conventional tuning.
• A Strategy for Ranking Optimization Methods using Multiple Criteria
• An important component of a suitably automated machine learning process is the automation of the model selection which often contains some optimal selection of hyperparameters. The hyperparameter optimization process is often conducted with a black-box tool, but, because different tools may perform better in different circumstances, automating the machine learning workflow might involve choosing the appropriate optimization method for a given situation. This paper proposes a mechanism for comparing the performance of multiple optimization methods for multiple performance metrics across a range of optimization problems. Using nonparametric statistical tests to convert the metrics recorded for each problem into a partial ranking of optimization methods, results from each problem are then amalgamated through a voting mechanism to generate a final score for each optimization method. Mathematical analysis is provided to motivate decisions within this strategy, and sample results are provided to demonstrate the impact of certain ranking decisions
• World Models: Can agents learn inside of their own dreams?
• We explore building generative neural network models of popular reinforcement learning environments[1]. Our world model can be trained quickly in an unsupervised manner to learn a compressed spatial and temporal representation of the environment. By using features extracted from the world model as inputs to an agent, we can train a very compact and simple policy that can solve the required task. We can even train our agent entirely inside of its own hallucinated dream generated by its world model, and transfer this policy back into the actual environment.
• This came up again: A new optimizer using particle swarm theory (1995)
• The optimization of nonlinear functions using particle swarm methodology is described. Implementations of two paradigms are discussed and compared, including a recently developed locally oriented paradigm. Benchmark testing of both paradigms is described, and applications, including neural network training and robot task learning, are proposed. Relationships between particle swarm optimization and both artificial life and evolutionary computation are reviewed.
• New: Particle swarm optimization for hyper-parameter selection in deep neural networks
• Working with the CIFAR10 data now. Tradeoff between filters and epochs:
NB_EPOCH = 10
NUM_FIRST_FILTERS = int(32/2)
NUM_MIDDLE_FILTERS = int(64/2)
OUTPUT_NEURONS = int(512/2)
Test score: 0.8670728429794311
Test accuracy: 0.6972
Elapsed time =  565.9446044602014

NB_EPOCH = 5
NUM_FIRST_FILTERS = int(32/1)
NUM_MIDDLE_FILTERS = int(64/1)
OUTPUT_NEURONS = int(512/1)
Test score: 0.8821897733688354
Test accuracy: 0.6849
Elapsed time =  514.1915690121759

NB_EPOCH = 10
NUM_FIRST_FILTERS = int(32/1)
NUM_MIDDLE_FILTERS = int(64/1)
OUTPUT_NEURONS = int(512/1)
Test score: 0.7007060846328735
Test accuracy: 0.765
Elapsed time =  1017.0974014300725

Augmented imagery
NB_EPOCH = 10
NUM_FIRST_FILTERS = int(32/1)
NUM_MIDDLE_FILTERS = int(64/1)
OUTPUT_NEURONS = int(512/1)
Test score: 0.7243581249237061
Test accuracy: 0.7514
Elapsed time =  1145.673343808471

• And yet, something is clearly wrong:
• Maybe try this version? samyzaf.com/ML/cifar10/cifar10.html


text:
hexagonal number

A is a figurate number that represents a hexagon. The hexagonal number for $n$ is given by the formula $n(2n-1)$. The first few hexagonal numbers are 1, 6, 15, 28, 45, 66, 91, 120, 153, 190, 231, 276, 325, 378, 435, 496, 561, 630, 703, 780, 861, 946, etc., listed in A000384 of Sloane’s OEIS. Like a triangular number, the base 10 digital root of a hexagonal number can only be 1, 3, 6 or 9. Every hexagonal number is a triangular number, but not every triangular number is a hexagonal number.

Any integer greater than 1791 can be expressed as a sum of at most four hexagonal numbers, a fact proven by Adrien-Marie Legendre in 1830.

Hexagonal numbers should not be confused with centered hexagonal numbers, which model the standard packaging of Vienna sausages.

Title hexagonal number HexagonalNumber 2013-03-22 17:50:51 2013-03-22 17:50:51 PrimeFan (13766) PrimeFan (13766) 4 PrimeFan (13766) Definition msc 11D09

format: plain


text:
# Statistical Mechanics -- partition function, change to polar coords

1. Apr 14, 2017

### binbagsss

1. The problem statement, all variables and given/known data

Hi I have the following definition for the partition function of $N$ particles in $s$ dimensions:

I am looking at computing the partition function for this Hamiltonian:

The solution is here:

2. Relevant equations
above

3. The attempt at a solution

I don't understand the top line of this solution? The definition is to integrate over $\Pi_{i=1}^{i=n} \Pi_{\alpha=1}^{\alpha=2}dP_{i,a}$ not $\Pi_{i=1}^{i=2N} d\vec P_i$

I can change to polar coordinates to get the integration over $d\vec P_i$ (just looking at the integration over $P$ and I have the same result, however in the first line of the solution there are no factors of $2\pi$ from the change of variables to polar coordinates, so how has the definition of the partition function been used? (or is it just by chance I've got the same answer)i.e. $dP_x dP_y \neq d^2\vec P$ does it?:

2. Apr 19, 2017

### PF_Help_Bot

Thanks for the thread! This is an automated courtesy bump. Sorry you aren't generating responses at the moment. Do you have any further information, come to any new conclusions or is it possible to reword the post? The more details the better.


text:
# Pi[x] >=loglogx

1. ### AlbertEinstein

113
I am going through Hardy's book on number theory.The following theorem I do not understand.

theorem 10: pi[x] >= loglog x
where pi[x] is the prime counting function
and >= stands for greater than or equal to

The arguments written in the book are very compact.please help .

2. ### shmoe

1,994
Do you follow any of it?

Do you understand how they derived $$p_{n}<2^{2^n}$$ ?

this is an important step. The rest just follows from pi(x) being increasing, and also $$\pi(p_n)=n$$ which they use but don't explicitly mention.

3. ### CRGreathouse

3,497
Bertrand's postulate?

4. ### shmoe

1,994
Nope! the bound of p_n above is much weaker than Bertrand's will give you. It's correspondingly simpler to prove though, it follows from a slight adaptation of Euclid's proof there are infinitely many primes (in case anyone who hasn't seen it wants to give it a stab)

Know someone interested in this topic? Share this thead via email, Google+, Twitter, or Facebook

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text:
# Brownian noise

Last updated
Colors of noise
White
Pink
Red (Brownian)
Purple
Grey

In science, Brownian noise (), also known as Brown noise or red noise, is the kind of signal noise produced by Brownian motion, hence its alternative name of random walk noise. The term "Brown noise" does not come from the color, but after Robert Brown, who documented the erratic motion for multiple types of inanimate particles in water. The term "red noise" comes from the "white noise"/"white light" analogy; red noise is strong in longer wavelengths, similar to the red end of the visible spectrum.

## Explanation

The graphic representation of the sound signal mimics a Brownian pattern. Its spectral density is inversely proportional to f2, meaning it has higher intensity at lower frequencies, even more so than pink noise. It decreases in intensity by 6 dB per octave (20 dB per decade) and, when heard, has a "damped" or "soft" quality compared to white and pink noise. The sound is a low roar resembling a waterfall or heavy rainfall. See also violet noise, which is a 6 dB increase per octave.

Strictly, Brownian motion has a Gaussian probability distribution, but "red noise" could apply to any signal with the 1/f2 frequency spectrum.

## Power spectrum

A Brownian motion, also called a Wiener process, is obtained as the integral of a white noise signal:

${\displaystyle W(t)=\int _{0}^{t}{\frac {dW(\tau )}{d\tau }}d\tau }$

meaning that Brownian motion is the integral of the white noise ${\displaystyle dW(t)}$, whose power spectral density is flat: [1]

${\displaystyle S_{0}=\left|{\mathcal {F}}\left[{\frac {dW(t)}{dt}}\right](\omega )\right|^{2}={\text{const}}.}$

Note that here ${\displaystyle {\mathcal {F}}}$ denotes the Fourier transform, and ${\displaystyle S_{0}}$ is a constant. An important property of this transform is that the derivative of any distribution transforms as [2]

${\displaystyle {\mathcal {F}}\left[{\frac {dW(t)}{dt}}\right](\omega )=i\omega {\mathcal {F}}[W(t)](\omega ),}$

from which we can conclude that the power spectrum of Brownian noise is

${\displaystyle S(\omega )={\big |}{\mathcal {F}}[W(t)](\omega ){\big |}^{2}={\frac {S_{0}}{\omega ^{2}}}.}$

An individual Brownian motion trajectory presents a spectrum ${\displaystyle S(\omega )=S_{0}/\omega ^{2}}$, where the amplitude ${\displaystyle S_{0}}$ is a random variable, even in the limit of an infinitely long trajectory. [3]

## Production

Brown noise can be produced by integrating white noise. [4] [5] That is, whereas (digital) white noise can be produced by randomly choosing each sample independently, Brown noise can be produced by adding a random offset to each sample to obtain the next one. A leaky integrator might be used in audio or electromagnetic applications to ensure the signal does not "wander off", that is, exceed the limits of the system's dynamic range. Note that while the first sample is random across the entire dynamic range that the sound sample can take on, the remaining offsets from there on are a tenth or thereabouts, leaving room for the signal to vary randomly within that range.

## Related Research Articles

Brownian motion, or pedesis, is the random motion of particles suspended in a medium.

In physics, a Langevin equation is a stochastic differential equation describing the time evolution of a subset of the degrees of freedom. These degrees of freedom typically are collective (macroscopic) variables changing only slowly in comparison to the other (microscopic) variables of the system. The fast (microscopic) variables are responsible for the stochastic nature of the Langevin equation. One application is to Brownian motion, calculating the statistics of the random motion of a small particle in a fluid due to collisions with the surrounding molecules in thermal motion.

The power spectrum of a time series describes the distribution of power into frequency components composing that signal. According to Fourier analysis, any physical signal can be decomposed into a number of discrete frequencies, or a spectrum of frequencies over a continuous range. The statistical average of a certain signal or sort of signal as analyzed in terms of its frequency content, is called its spectrum.

In probability theory and statistics, the term Markov property refers to the memoryless property of a stochastic process. It is named after the Russian mathematician Andrey Markov. The term strong Markov property is similar to the Markov property, except that the meaning of "present" is defined in terms of a random variable known as a stopping time.

The Short-time Fourier transform (STFT), is a Fourier-related transform used to determine the sinusoidal frequency and phase content of local sections of a signal as it changes over time. In practice, the procedure for computing STFTs is to divide a longer time signal into shorter segments of equal length and then compute the Fourier transform separately on each shorter segment. This reveals the Fourier spectrum on each shorter segment. One then usually plots the changing spectra as a function of time, known as a spectrogram or waterfall plot, such as commonly used in Software Defined Radio (SDR) based spectrum displays. Full bandwidth displays covering the whole range of an SDR commonly use Fast Fourier Transforms (FFTs) with 2^24 points on desktop computers.

In signal processing, a finite impulse response (FIR) filter is a filter whose impulse response is of finite duration, because it settles to zero in finite time. This is in contrast to infinite impulse response (IIR) filters, which may have internal feedback and may continue to respond indefinitely.

The fluctuation–dissipation theorem (FDT) or fluctuation–dissipation relation (FDR) is a powerful tool in statistical physics for predicting the behavior of systems that obey detailed balance. Given that a system obeys detailed balance, the theorem is a general proof that thermodynamic fluctuations in a physical variable predict the response quantified by the admittance or impedance of the same physical variable, and vice versa. The fluctuation–dissipation theorem applies both to classical and quantum mechanical systems.

In probability theory, in particular in the study of stochastic processes, a stopping time is a specific type of “random time”: a random variable whose value is interpreted as the time at which a given stochastic process exhibits a certain behavior of interest. A stopping time is often defined by a stopping rule, a mechanism for deciding whether to continue or stop a process on the basis of the present position and past events, and which will almost always lead to a decision to stop at some finite time.

In probability theory, fractional Brownian motion (fBm), also called a fractal Brownian motion, is a generalization of Brownian motion. Unlike classical Brownian motion, the increments of fBm need not be independent. fBm is a continuous-time Gaussian process BH(t) on [0, T], that starts at zero, has expectation zero for all t in [0, T], and has the following covariance function:

Instantaneous phase and frequency are important concepts in signal processing that occur in the context of the representation and analysis of time-varying functions. The instantaneous phase of a complex-valued function s(t), is the real-valued function:

In ultrafast optics, spectral phase interferometry for direct electric-field reconstruction (SPIDER) is an ultrashort pulse measurement technique originally developed by Chris Iaconis and Ian Walmsley.

In mathematics, a stopped process is a stochastic process that is forced to assume the same value after a prescribed time.

In many-body theory, the term Green's function is sometimes used interchangeably with correlation function, but refers specifically to correlators of field operators or creation and annihilation operators.

The method of reassignment is a technique for sharpening a time-frequency representation by mapping the data to time-frequency coordinates that are nearer to the true region of support of the analyzed signal. The method has been independently introduced by several parties under various names, including method of reassignment, remapping, time-frequency reassignment, and modified moving-window method. In the case of the spectrogram or the short-time Fourier transform, the method of reassignment sharpens blurry time-frequency data by relocating the data according to local estimates of instantaneous frequency and group delay. This mapping to reassigned time-frequency coordinates is very precise for signals that are separable in time and frequency with respect to the analysis window.

In mathematics — specifically, in stochastic analysis — an Itô diffusion is a solution to a specific type of stochastic differential equation. That equation is similar to the Langevin equation used in physics to describe the Brownian motion of a particle subjected to a potential in a viscous fluid. Itô diffusions are named after the Japanese mathematician Kiyosi Itô.

In statistical signal processing, the goal of spectral density estimation (SDE) is to estimate the spectral density of a random signal from a sequence of time samples of the signal. Intuitively speaking, the spectral density characterizes the frequency content of the signal. One purpose of estimating the spectral density is to detect any periodicities in the data, by observing peaks at the frequencies corresponding to these periodicities.

The narrow escape problem is a ubiquitous problem in biology, biophysics and cellular biology.

In mathematics, the walk-on-spheres method (WoS) is a numerical probabilistic algorithm, or Monte-Carlo method, used mainly in order to approximate the solutions of some specific boundary value problem for partial differential equations (PDEs). The WoS method was first introduced by Mervin E. Muller in 1956 to solve Laplace's equation, and was since then generalized to other problems.

The redundancy principle in biology expresses the need of many copies of the same entity to fulfill a biological function. Examples are numerous: disproportionate numbers of spermatozoa during fertilization compared to one egg, large number of neurotransmitters released during neuronal communication compared to the number of receptors, large numbers of released calcium ions during transient in cells and many more in molecular and cellular transduction or gene activation and cell signaling. This redundancy is particularly relevant when the sites of activation is physically separated from the initial position of the molecular messengers. The redundancy is often generated for the purpose of resolving the time constraint of fast-activating pathways. It can be expressed in terms of the theory of extreme statistics to determine its laws and quantify how shortest paths are selected. The main goal is to estimate these large numbers from physical principles and mathematical derivations.

In many-body physics, the problem of analytic continuation is that of numerically extracting the spectral density of a Green function given its values on the imaginary axis. It is a necessary post-processing step for calculating dynamical properties of physical systems from quantum Monte Carlo simulations, which often compute Green function values only at imaginary-times or Matsubara frequencies.

## References

1. Gardiner, C. W. Handbook of stochastic methods. Berlin: Springer Verlag.
2. Barnes, J. A. & Allan, D. W. (1966). "A statistical model of flicker noise". Proceedings of the IEEE. 54 (2): 176–178. doi:10.1109/proc.1966.4630. and references therein
3. Krapf, Diego; Marinari, Enzo; Metzler, Ralf; Oshanin, Gleb; Xu, Xinran; Squarcini, Alessio (2018-02-09). "Power spectral density of a single Brownian trajectory: what one can and cannot learn from it". New Journal of Physics. 20 (2): 023029. arXiv:. Bibcode:2018NJPh...20b3029K. doi:.
4. "Integral of White noise". 2005.
5. Bourke, Paul (October 1998). "Generating noise with different power spectra laws".


text:
# American Cinematographer (1926)

### Record Details:

March, L926 AMERICAN CINEMATOGRAPHBR Twenty-three (Continued from Page C) daylight loading. The lens is F 6.5, wide angle, with 20 mm. focus that is fixed. Eastman Kodascope The Eastman Kodascope, the projector which shows the 16 mm. reversible film, weighs 20 pounds, and measures 18}/> by 14% by 10-\x inches in size. Its capacity is 400 feet of 16 mm. film—which gives projection for approximately 16 minutes on the screen. The lens is a SO mm. focus, throwing a picture 30 by 40 inches at 18 feet with a 56-watt lamp, \it a 39 by 52-inch picture at 23 feet with a 200-watt lamp. Source of power and illumi- nation for the Kodascope's electric motor may be taken from any house circuit, alternating or direct current, not over 125 volts nor less than 105, by ''plugging in" on an ordinary bulb socket or wall plug. There is an adjust- able rheostat, with ammeter, to furnish cor- rect voltage for a special 14-volt, 56-watt Mazda lamp or for a 50-volt, 200-watt Mazda lamp. There are provided special rheostats for adaptation to 210-250-volt circuits, or to 32-volt home generators. Pathex Camera The Pathex camera is approximately 3 by 6 inches in size and weighs \ l /\ pounds. It has a fixed focus F 3.5 lens, with an adjustable iris diaphragm; the focal length is 20 mm. The film is supplied in daylight loading magazines which have a capacity of 26 to 30 feet. The Pathex film runs 40 frames to the foot. Development is by the reversible pro- cess, sent to company laboratories, as with the Eastman 16 mm. film. A tripod comes with the Pathex. Pathex Projector The Pathex projector weighs 5 pounds; 5 ounces, and measures 4^ by 7 by 12j/> inches. Power is drawn from the ordinary electric socket. A special Mazda lamp, 12 volts, .5 amperes, furnishes the illumination. Gets Shots that You Couldn't Get ai all Without it ITS ALL 1 IN THE ^LENS use the Ultrastigmat a great deal In commercial work, j I find that I can make inter- iors with it that would require lights with- out it, and get outdoor shots on bad days that I could not get without it." (Signed) QUINCY PEACOCK. 1611 Market St.. Jacksonville, Fla. Write for Folder Gundiach-Manhattan Optical Co. 900 Clinton Street ROCHESTER, N. Y. DEBRIE CAMERA BARGAIN Latest model with complete equipment including all electrical attachments, portable battery, platforms and holding devices 'for using camera without tripod, etc. Most complete DeBrie outfit in America. Priced to sell quickly. 35-50-75-105 m. m. lenses factory mounted. • Address, AMERICAN CIN EM ATOGRAPH ER CLUBBING OFFER Subscribed for separately. Camera Craft and the American Cinematographer will cost a total of $4.50 per year. As a special clubbing offer, both magazines may be had at a total price of$3.40 per year. American Cmematoqrapher 121920 2122 Guaranty Bldq. Hollywood. Calif. (Continued on Pace Z6] Boyle Invents "Close- up Long-Shot" Device < < "ont iniiHil from shots and Jong shots at the same time, and because of its efficiency and inexpensive- ness, Mr. Boyle believes that the device will soon be in common use in all studios. M a n v camera authorities agree with the inventor, who has taken papers of patent out on his mechanical brain- child. Mr. Boyle is at present us- ing this device in photograph- ing fast racing scenes for "Her Second Chance," a First National Him, being di- rected by Lambert Hillyer. The entire circumference of the track will be taken in one shot by this camera. The device was also suc- cessfully used, through the courtesy of Mr. Boyle, by J. I). Jennings, A. S. C, in the filming of "The Million Dol- lar Handicap," a Metropoli- tan production.


text:
Bayes' Rule is the most important rule in data science. It is the mathematical rule that describes how to update a belief, given some evidence. In other words – it describes the act of learning.

The equation itself is not too complex:

There are four parts:

• Posterior probability (updated probability after the evidence is considered)
• Prior probability (the probability before the evidence is considered)
• Likelihood (probability of the evidence, given the belief is true)
• Marginal probability (probability of the evidence, under any circumstance)

Bayes' Rule can answer a variety of probability questions, which help us (and machines) understand the complex world we live in.

It is named after Thomas Bayes, an 18th century English theologian and mathematician. Bayes originally wrote about the concept, but it did not receive much attention during his lifetime.

French mathematician Pierre-Simon Laplace independently published the rule in his 1814 work Essai philosophique sur les probabilités.

Today, Bayes' Rule has numerous applications, from statistical analysis to machine learning.

## Conditional probability

The first concept to understand is conditional probability.

You may already be familiar with probability in general. It lets you reason about uncertain events with the precision and rigour of mathematics.

Conditional probability is the bridge that lets you talk about how multiple uncertain events are related. It lets you talk about how the probability of an event can vary under different conditions.

For example, consider the probability of winning a race, given the condition you didn't sleep the night before. You might expect this probability to be lower than the probability you'd win if you'd had a full night's sleep.

Or, consider the probability that a suspect committed a crime, given that their fingerprints are found at the scene. You'd expect the probability they are guilty to be greater, compared with had their fingerprints not been found.

The notation for conditional probability is usually:

Which is read as "the probability of event A occurring, given event B occurs".

An important thing to remember is that conditional probabilities are not the same as their inverses.

That is, the "probability of event A given event B" is not the same thing as the "probability of event B, given event A".

To remember this, take the following example:

The probability of clouds, given it is raining (100%) is not the same as the probability it is raining, given there are clouds.

## Bayes' Rule in detail

Bayes' Rule tells you how to calculate a conditional probability with information you already have.

It is helpful to think in terms of two events – a hypothesis (which can be true or false) and evidence (which can be present or absent).

However, it can be applied to any type of events, with any number of discrete or continuous outcomes.

Bayes' Rule lets you calculate the posterior (or "updated") probability. This is a conditional probability. It is the probability of the hypothesis being true, if the evidence is present.

Think of the prior (or "previous") probability as your belief in the hypothesis before seeing the new evidence. If you had a strong belief in the hypothesis already, the prior probability will be large.

The prior is multiplied by a fraction. Think of this as the "strength" of the evidence. The posterior probability is greater when the top part (numerator) is big, and the bottom part (denominator) is small.

The numerator is the likelihood. This is another conditional probability. It is the probability of the evidence being present, given the hypothesis is true.

This is not the same as the posterior!

Remember, the "probability of the evidence being present given the hypothesis is true" is not the same as the "probability of the hypothesis being true given the evidence is present".

Now look at the denominator. This is the marginal probability of the evidence. That is, it is the probability of the evidence being present, whether the hypothesis is true or false. The smaller the denominator, the more "convincing" the evidence.

## Worked example of Bayes' Rule

Here's a simple worked example.

Your neighbour is watching their favourite football (or soccer) team. You hear them cheering, and want to estimate the probability their team has scored.

Step 1 – write down the posterior probability of a goal, given cheering

Step 2 – estimate the prior probability of a goal as 2%

Step 3 – estimate the likelihood probability of cheering, given there's a goal as 90% (perhaps your neighbour won't celebrate if their team is losing badly)

Step 4 – estimate the marginal probability of cheering – this could be because:

• a goal has been scored (2% of the time, times 90% probability)
• or any other reason, such as the other team missing a penalty or having a player sent off (98% of the time, times perhaps 1% probability)

Now, piece everything together:

## Use cases for Bayes' Rule and next steps

Bayes' Rule has use cases in many areas:

• Understanding probability problems (including those in medical research)
• Statistical modelling and inference
• Machine learning algorithms (such as Naive Bayes, Expectation Maximisation)
• Quantitative modelling and forecasting

Next, you'll discover how Bayes' Rule can be used to quantify uncertainty and model real world problems. Then, how to reason about "probabilities of probabilities".

The final step will cover how various computational tricks let you make use of Bayes' Rule to solve non-trivial problems.


text:
# Subspace Correction Methods for Total Variation and $\ell_1$-Minimization

Handle URI:
http://hdl.handle.net/10754/599796
Title:
Subspace Correction Methods for Total Variation and $\ell_1$-Minimization
Authors:
Fornasier, Massimo; Schönlieb, Carola-Bibiane
Abstract:
This paper is concerned with the numerical minimization of energy functionals in Hilbert spaces involving convex constraints coinciding with a seminorm for a subspace. The optimization is realized by alternating minimizations of the functional on a sequence of orthogonal subspaces. On each subspace an iterative proximity-map algorithm is implemented via oblique thresholding, which is the main new tool introduced in this work. We provide convergence conditions for the algorithm in order to compute minimizers of the target energy. Analogous results are derived for a parallel variant of the algorithm. Applications are presented in domain decomposition methods for degenerate elliptic PDEs arising in total variation minimization and in accelerated sparse recovery algorithms based on 1-minimization. We include numerical examples which show e.cient solutions to classical problems in signal and image processing. © 2009 Society for Industrial and Applied Physics.
Citation:
Fornasier M, Schönlieb C-B (2009) Subspace Correction Methods for Total Variation and $\ell_1$-Minimization. SIAM J Numer Anal 47: 3397–3428. Available: http://dx.doi.org/10.1137/070710779.
Publisher:
Society for Industrial & Applied Mathematics (SIAM)
Journal:
SIAM Journal on Numerical Analysis
KAUST Grant Number:
KUK-I1-007-43
Issue Date:
Jan-2009
DOI:
10.1137/070710779
Type:
Article
ISSN:
0036-1429; 1095-7170
This work was based on work supported by Award KUK-I1-007-43, made by King Abdullah University of Science and Technology (KAUST).
Appears in Collections:
Publications Acknowledging KAUST Support

DC FieldValue Language
dc.contributor.authorFornasier, Massimoen
dc.contributor.authorSchönlieb, Carola-Bibianeen
dc.date.accessioned2016-02-28T06:10:01Zen
dc.date.available2016-02-28T06:10:01Zen
dc.date.issued2009-01en
dc.identifier.citationFornasier M, Schönlieb C-B (2009) Subspace Correction Methods for Total Variation and $\ell_1$-Minimization. SIAM J Numer Anal 47: 3397–3428. Available: http://dx.doi.org/10.1137/070710779.en
dc.identifier.issn0036-1429en
dc.identifier.issn1095-7170en
dc.identifier.doi10.1137/070710779en
dc.identifier.urihttp://hdl.handle.net/10754/599796en
dc.description.abstractThis paper is concerned with the numerical minimization of energy functionals in Hilbert spaces involving convex constraints coinciding with a seminorm for a subspace. The optimization is realized by alternating minimizations of the functional on a sequence of orthogonal subspaces. On each subspace an iterative proximity-map algorithm is implemented via oblique thresholding, which is the main new tool introduced in this work. We provide convergence conditions for the algorithm in order to compute minimizers of the target energy. Analogous results are derived for a parallel variant of the algorithm. Applications are presented in domain decomposition methods for degenerate elliptic PDEs arising in total variation minimization and in accelerated sparse recovery algorithms based on 1-minimization. We include numerical examples which show e.cient solutions to classical problems in signal and image processing. © 2009 Society for Industrial and Applied Physics.en
dc.description.sponsorshipThis work was based on work supported by Award KUK-I1-007-43, made by King Abdullah University of Science and Technology (KAUST).en
dc.publisherSociety for Industrial & Applied Mathematics (SIAM)en
dc.subject11-Minimizationen
dc.subjectConvex optimizationen
dc.subjectDegenerate elliptic PDEsen
dc.subjectDiscontinuous solutionsen
dc.subjectDomain decomposition methoden
dc.subjectImage and signal processingen
dc.subjectParallel computationen
dc.subjectSubspace correctionsen
dc.subjectTotal variation minimizationen
dc.titleSubspace Correction Methods for Total Variation and $\ell_1$-Minimizationen
dc.typeArticleen
dc.identifier.journalSIAM Journal on Numerical Analysisen
dc.contributor.institutionJohann Radon Institute for Computational and Applied Mathematics, Linz, Austriaen
dc.contributor.institutionUniversity of Cambridge, Cambridge, United Kingdomen
kaust.grant.numberKUK-I1-007-43en


text:
# Prove/Disprove set of even Function with scalar mult and addition forms a Vector space

Prove that the set of even function defined on the real line where $x\in \mathbb{R}$with operations of addition and scalar multiplication defined as $$(f+g)(x)=f(x)+g(x); (cf)(x)=c[f(x)]$$ forms a Vector Space

Def of Vector space

A vector space V over field F consists of a set on which 2 operations (addition, scalar multiplication) are defined so that

\begin{aligned} &\forall x,y \in V; x+y\in V && \text{closed add} \\ &\forall a\in F ,x\in V ;\exists \text{ unique } ax\in V && \text{closed mult scalar and vector} \\ &\forall x,y \in V, x+y=y+x && \text{communitive addition} \\ &\forall x,y,z \in V , (x+y)+z=x+(y+z) && \text{associativity of addition} \\ &\forall x\in V, \exists 0_v \in V ; x+0_v=x &&\text{existence of neutral additive element} \\ &\forall x\in V , \exists y\in V ; x+y=0_v && \text{existince of additive inverse} \\ &\forall{x \in V},1x=x &&\text{existence neutral element mult} \\ &\forall a,b\in F,\forall x \in V;(ab)x=a(bx) &&\text{associtive ____} \\ &\forall a\in F, \forall x,y \in V; a(x+y)=ax+ay &&\text{Dist 1}\\ &\forall a,b \in F,\forall x\in V ; (a+b)x=ax+bx && \text{Dist 2} \end{aligned} Def of even function $f(x)=f(-x)$

Attempt

Assuming $F=\mathbb{R}$. Call $V[x]$ The set of all even functions.Let $f(x),g(x) \in V[x], \forall a\in \mathbb{R}$. \begin{aligned} \text{Closed Add} && (f+g)(x)=f(x)+g(x)=f(-x)+g(-x)=(f+g)(-x) \\\text{closed Mult scalar, vector} && (af)(x)=af(x)=af(-x)=(af)(-x) \\ \text{comm. add} && (f+g)(x)=f(x) +g(x)=g(x)+f(x)=(g+f)(x) \end{aligned} Asso. Add \begin{aligned} (f+(g+h))(x)&=f(x)+(g+h)(x)=f(x)+(g(x)+h(x)) =(f(x)+g(x))+h(x)=(f+g)(x)+h(x)\\&=((f+g)+h)(x) \end{aligned}

Let $0_v(x)=0$ be function where $\forall x \in R$ $0_v(x)=0$.$$(f+0_v)(x)=f(x)+0_v(x)=f(x)+0_v=f(x)=(f)(x)$$

\begin{align} \text{existence additive inver.} && (f+-1f)(x)=f(x)+-1f(x)=f(x)*(1-1)=f(x)*(0_v)=0_v \\ \text{Neutral elem. mult.} && (1f)(x)=1f(x)=f(x)=(f)(x) \\ \text{ass.__} && ((ab)f)(x)=(ab)(f(x))=a(bf(x))=(a(bf))x \\ \text{Dist 1} && (a(f+g))(x)=a(f(x)+g(x))=af(x)+bg(x)=(af)(x)+(ag)(x) \\ \text{Dist 2} && ((a+b)f)(x)=(a+b)f(x)=af(x)+bf(x)=(af)(x)+(bf)(x) \end{align}

Just reversed engineered the answer. Not sure if it actually holds. The middle part formatting of the attempt is a little chaotic. I'll try to make it prettier.

Appreciate constructive critique.

• Looks fine. Maybe you should have observed that $0_v$ is even. And maybe (?) many of the verifications can be omitted, since an awful lot of properties are inherited from the mother vector space of all functions from the reals to the reals. Perhaps that has already been proved to be a vector space. – André Nicolas Jan 24 '16 at 18:14
• @AndréNicolas, yes, I think you only need evenness for the closure axioms. The remaining properties are inherited from the more general space of functions on the reals. – Sherif F. Jan 24 '16 at 18:57
• I do understand to check for 4 prop closed add, closed scalar mult, existence of zero, existinence of additive inverse. Like subring test. It will save time but it is on the next section thats why. – Tiger Blood Jan 24 '16 at 19:05

This is correct, except for a minor point under existence of additive inverse: I think $f(x)∗(0_\nu)$ should just be $f(x)∗0$. You haven't defined $f∗g$, where $f$ and $g$ are functions. Also, your expression leads to the number $0$, not the zero function. It's indeed true based on your definitions that $0*f(x) = 0_\nu$.


text:
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Assertion:- If a particle is a...

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If both Assertion & Reason are True & the Reason is a correct explanation of the Assertion.If both Assertion & Reason are True but Reason is not a correct explanation of the Assertiion.If Assertion is True but the Reason is False.If both Assertion & Reason are False

Solution : N//A

Step by step solution by experts to help you in doubt clearance & scoring excellent marks in exams.

Transcript

hello an object is acted upon by external force is Momentum by DT magnitude is always equal to the rate of change of the magnitude of the velocity of the first statement we know that the f x is equals to mass times of acceleration of the centre of mass total mass of the system into acceleration of the centre of mass and if I talk about the momentum of the system it is velocity is the centre of mass by the external force the momentum and relative the external force is equal to the rate of change of the momentum of the

cyst so whenever the external force will act rate the momentum will change external force is not zero then this will be not constant it is changing right it is saying rate of change of this is not that is changing it is not know if you see this statement letters differentiate these Tuta rate if I say this is magnitude of acceleration magnitude just you put a mod in of the rate of change of velocity that is magnitude of acceleration if you see this device

this is this this is what this is the city that it is rate of change of spirit rate of not velocity it is rate of change of that is tangential acceleration so in what direction it as it if I say this is the velocity this is the acceleration so the only company and which is Allah to the velocity is responsible for changing the speed and perpendicular component changes the direction if you see this is a and this is a cos theta is the tangential and is the rate of change of speed as well as changing the magnitude and it is the rate with

the magnitude of change and was responsible for changing the direction of we are not talking about changing the direction so you can differentiate them it is the magnitude of acceleration is the rate of change of that is tangential acceleration is a component of acceleration parallel to the velocity is also true and false is the correct thank you


text:
# Draw a sprite when a key is pressed in LibGDX

I'm working with LibGDX. How can I draw a sprite when a key is pressed? I have tried with the following, but it doesn't seem to work.

if (Gdx.input.isKeyPressed(Input.Keys.X)) {
batch.begin();
sprite.draw(batch);
batch.end();
}

• can you add more details? "doesn't seem to work"? – ronscript Oct 12 '16 at 0:23
• what I mean is that with that code the sprite is not drawn and I don't get it why – MagnusSchuldiner Oct 12 '16 at 19:24
• can you write your whole code – ronscript Oct 12 '16 at 20:33

You could have a boolean that you set to true when the key is pressed in your update method:

 boolean drawSprite;
if (Gdx.input.isKeyPressed(Input.Keys.X)) {
drawSprite = true;
}

And then in your render method:

batch.begin();
if(drawSprite == true) {
sprite.draw(batch);
}
batch.end();

I assume you are using Sprite class from libgdx and the sprite you created is working fine? And the only problem is you cannot show the sprite when a key is pressed.

@Override
public void update() {

// the input is pressed once even you are still holding the button.
if(Gdx.input.isJustKeyPressed(Input.Keys.X)) {
sprite.setVisible(true);
}

batch.begin();
sprite.draw(batch);
batch.end();

}

• should I add it necessary in the update() mehtod? – MagnusSchuldiner Oct 12 '16 at 19:24
• @MagnusSchuldiner yes, if you are gonna toggle show and hide of sprite – ronscript Oct 12 '16 at 20:31


text:
# Line passing through a point and perpendicular to another one

\documentclass[tikz,border=10pt]{standalone}
\usetikzlibrary{calc}

\begin{document}
\begin{tikzpicture}[dot/.style={circle,inner sep=1pt,fill,label={#1},name=#1},
extended line/.style={shorten >=-#1,shorten <=-#1},
extended line/.default=1cm]

\node [dot=A] at (0,0) {};
\node [dot=B] at (3,1) {};
\node [dot=P] at (1.9,-1.6) {};

\draw [extended line=0.5cm] (A) -- (B);
\draw [extended line] ($(A)!(P)!(B)$) -- (P);

\fill [red] ($(A)!(P)!(B)$) circle [radius=2pt];

\end{tikzpicture}
\end{document}

You can use the calc library for this, which allows to do coordinate calculations. The expression ($(A)!(P)!(B)$) yields the projection of (P) on the line from (A) to (B), for example.

You can extend the lines by using the shorten > and shorten < commands with negative values. I’m using them here in a style called extended line that takes an optional argument to set the length by which to extend the line.


text:
I think that my integral is wrong

1. Jul 29, 2007

Robert Mak

Integral of ((Tan x)^6)dx

i think that the solution is:

(1/5)(tan x)^5 + (1/3)(tan x)^3 - (2/3)(tan x)^3 + tan x - x + c

but if i derivate this solution it lead me to that:

(tan x)^4((tan x)^2 + 2)

?????????????????????????

2. Jul 29, 2007

^_^physicist

Yes, your integral is incorrect; however, try expanding the expression and then integrating.

3. Jul 29, 2007

Dick

I think your integral is correct. It must be the differentiation that is causing the problem. But no one can tell you why until you show your work.

4. Jul 30, 2007

cristo

Staff Emeritus
It looks correct to me, also (although, why you haven't collected those terms in tan^3x, I don't know!)

5. Jul 30, 2007

Gib Z

I think he might forgetting to use the Chain Rule.

6. Jul 30, 2007

Robert Mak

Thanks people; i did a mistake of signs lol.


text:
# Quantum Chemistry¶

PennyLane provides the qchem module to perform quantum chemistry simulations. It contains a differentiable Hartree-Fock solver and the functionality to construct a fully-differentiable molecular Hamiltonian that can be used as input to quantum algorithms such as the variational quantum eigensolver (VQE) algorithm. The qchem module also provides tools for building other observables such as molecular dipole moment, spin and particle number observables. The theoretical foundation of the quantum chemistry functionality in PennyLane is explained in our white paper.

## Building the electronic Hamiltonian¶

The qchem module provides access to a driver function molecular_hamiltonian() to generate the electronic Hamiltonian in a single call. For example,

import pennylane as qml
from pennylane import numpy as np

symbols = ["H", "H"]
geometry = np.array([[0., 0., -0.66140414], [0., 0., 0.66140414]])
hamiltonian, qubits = qml.qchem.molecular_hamiltonian(symbols, geometry)

where:

• hamiltonian is the qubit Hamiltonian of the molecule represented as a PennyLane Hamiltonian and

• qubits is the number of qubits needed to perform the quantum simulation.

The molecular_hamiltonian() function can also be used to construct the molecular Hamiltonian with an external backend that uses the OpenFermion-PySCF plugin interfaced with the electronic structure package PySCF, which requires separate installation. This backend is non-differentiable and can be selected by setting method='pyscf' in molecular_hamiltonian(). Additionally, if the electronic Hamiltonian is built independently using OpenFermion tools, it can be readily converted to a PennyLane observable using the import_operator() function.

Furthermore, the net charge, the spin multiplicity, the atomic basis functions and the active space can also be specified for each backend.

hamiltonian, qubits = qml.qchem.molecular_hamiltonian(
symbols,
geometry,
charge=0,
mult=1,
basis='sto-3g',
method='pyscf',
active_electrons=2,
active_orbitals=2
)

### Importing molecular structure data¶

The atomic structure of a molecule can be either defined as an array or imported from an external file using the read_structure() function:

symbols, geometry = qml.qchem.read_structure('h2.xyz')

## VQE simulations¶

The Variational Quantum Eigensolver (VQE) is a hybrid quantum-classical computational scheme, where a quantum computer is used to prepare the trial wave function of a molecule and to measure the expectation value of the electronic Hamiltonian, while a classical optimizer is used to find its ground state.

PennyLane supports treating Hamiltonians just like any other observable, and the expectation value of a Hamiltonian can be calculated using qml.expval:

dev = qml.device('default.qubit', wires=4)

symbols = ["H", "H"]
geometry = np.array([[0., 0., -0.66140414], [0., 0., 0.66140414]])
hamiltonian, qubits = qml.qchem.molecular_hamiltonian(symbols, geometry)

@qml.qnode(dev)
def circuit(params):
qml.BasisState(np.array([1, 1, 0, 0]), wires=[0, 1, 2, 3])
qml.DoubleExcitation(params, wires=[0, 1, 2, 3])
return qml.expval(hamiltonian)

circuit(params)

tensor(-1.13618912, requires_grad=True)

The circuit parameter can be optimized using the interface of choice.

Note

For more details on VQE and the quantum chemistry functionality available in qchem, check out the PennyLane quantum chemistry tutorials.

## Quantum chemistry functions and classes¶

PennyLane supports the following quantum chemistry functions and classes.

### Molecular integrals and matrices¶

 attraction_integral Return a function that computes the nuclear attraction integral for two contracted Gaussian functions. attraction_matrix Return a function that computes the electron-nuclear attraction matrix for a given set of basis functions. contracted_norm Compute the normalization constant for a contracted Gaussian function. core_matrix Return a function that computes the core matrix for a given set of basis functions. dipole_integrals Return a function that computes the dipole moment integrals over the molecular orbitals. electron_integrals Return a function that computes the one- and two-electron integrals in the molecular orbital basis. electron_repulsion Compute the electron-electron repulsion integral between four primitive Gaussian functions. expansion Compute Hermite Gaussian expansion coefficients recursively for two Gaussian functions. gaussian_kinetic Compute the kinetic integral for two primitive Gaussian functions. gaussian_moment Compute the one-dimensional multipole moment integral for two primitive Gaussian functions. gaussian_overlap Compute overlap integral for two primitive Gaussian functions. hermite_moment Compute the Hermite moment integral recursively. kinetic_integral Return a function that computes the kinetic integral for two contracted Gaussian functions. kinetic_matrix Return a function that computes the kinetic matrix for a given set of basis functions. mol_density_matrix Compute the molecular density matrix. moment_integral Return a function that computes the multipole moment integral for two contracted Gaussians. moment_matrix Return a function that computes the multipole moment matrix for a set of basis functions. nuclear_attraction Compute nuclear attraction integral between primitive Gaussian functions. overlap_integral Return a function that computes the overlap integral for two contracted Gaussian functions. overlap_matrix Return a function that computes the overlap matrix for a given set of basis functions. primitive_norm Compute the normalization constant for a primitive Gaussian function. repulsion_integral Return a function that computes the electron-electron repulsion integral for four contracted Gaussian functions. repulsion_tensor Return a function that computes the electron repulsion tensor for a given set of basis functions.

### Differentiable Hartree-Fock¶

 hf_energy Return a function that computes the Hartree-Fock energy. nuclear_energy Return a function that computes the nuclear-repulsion energy. scf Return a function that performs the self-consistent-field calculations.

### Hartree-Fock with external packages¶

 decompose Decomposes the molecular Hamiltonian into a linear combination of Pauli operators using OpenFermion tools. meanfield Generates a file from which the mean field electronic structure of the molecule can be retrieved. one_particle Generates the FermionOperator representing a given one-particle operator required to build many-body qubit observables. two_particle Generates the FermionOperator representing a given two-particle operator required to build many-body qubit observables.

### Differentiable observables¶

 diff_hamiltonian Return a function that computes the qubit Hamiltonian. dipole_moment Return a function that computes the qubit dipole moment observable. fermionic_dipole Return a function that builds the fermionic dipole moment observable. fermionic_hamiltonian Return a function that computes the fermionic Hamiltonian. fermionic_observable Create a fermionic observable from molecular orbital integrals. jordan_wigner Convert a fermionic operator to a qubit operator using the Jordan-Wigner mapping. molecular_hamiltonian Generate the qubit Hamiltonian of a molecule. qubit_observable Convert a fermionic observable to a PennyLane qubit observable.

### Other observables¶

 dipole_of Computes the electric dipole moment operator in the Pauli basis. observable Builds the fermionic many-body observable whose expectation value can be measured in PennyLane. particle_number Compute the particle number observable $$\hat{N}=\sum_\alpha \hat{n}_\alpha$$ in the Pauli basis. spin2 Compute the total spin observable $$\hat{S}^2$$. spinz Computes the total spin projection observable $$\hat{S}_z$$.

### Qubit tapering¶

 clifford Compute a Clifford operator from a set of generators and Pauli-X operators. optimal_sector Get the optimal sector which contains the ground state. paulix_ops Generate the single qubit Pauli-X operators $$\sigma^{x}_{i}$$ for each symmetry $$\tau_j$$, such that it anti-commutes with $$\tau_j$$ and commutes with all others symmetries $$\tau_{k\neq j}$$. symmetry_generators Compute the generators $$\{\tau_1, \ldots, \tau_k\}$$ for a Hamiltonian over the binary field $$\mathbb{Z}_2$$. taper Transform a Hamiltonian with a Clifford operator and then taper qubits. taper_hf Transform a Hartree-Fock state with a Clifford operator and then taper qubits. taper_operation Transform a gate operation with a Clifford operator and then taper qubits.

### Utility functions¶

 active_space Build the active space for a given number of active electrons and active orbitals. excitations Generate single and double excitations from a Hartree-Fock reference state. excitations_to_wires Map the indices representing the single and double excitations generated with the function excitations() to the wires that the Unitary Coupled-Cluster (UCCSD) template will act on. factorize Return the double-factorized form of a two-electron integral tensor. hf_state Generate the occupation-number vector representing the Hartree-Fock state. import_operator Convert an external operator to a PennyLane operator. read_structure Read the structure of the polyatomic system from a file and returns a list with the symbols of the atoms in the molecule and a 1D array with their positions $$[x_1, y_1, z_1, x_2, y_2, z_2, \dots]$$ in atomic units (Bohr radius = 1).

### Molecule class and basis functions¶

 atom_basis_data Generate default basis set parameters for an atom. BasisFunction Create a basis function object. Molecule Create a molecule object that stores molecular information and default basis set parameters. mol_basis_data Generates default basis set parameters for a molecule.


text:
0
RESEARCH PAPERS: Two-Phase Flow and Heat Transfer

# On the Transient Analysis of a V-Shaped Microgrooved Heat Pipe

[+] Author and Article Information
Balram Suman1

Department of Chemical Engineering and Materials Science, University of Minnesota, 151 Amundson Hall, 421 Washington Avenue SE, Minneapolis, MN 55455suman@cems.umn.edu

Nazish Hoda

Department of Chemical Engineering and Materials Science, University of Minnesota, 151 Amundson Hall, 421 Washington Avenue SE, Minneapolis, MN 55455

1

Corresponding author.

J. Heat Transfer 129(11), 1584-1591 (Mar 05, 2007) (8 pages) doi:10.1115/1.2759975 History: Received December 14, 2006; Revised March 05, 2007

## Abstract

In this paper, we present a transient mathematical model for a V-shaped microgrooved heat pipe considering the temporal variations in the fluid flow, and heat and mass transfer, and utilizing a macroscopic approach. Unlike other heat pipe models, the shear stress at the liquid-vapor interface and the disjoining pressure have been used in the momentum balance equation of the model. The sensible heat used by the substrate is also taken into account using a pseudo-lump capacity model. The coupled nonlinear partial differential equations governing the transient fluid flow, heat and mass transfer have been solved numerically. The transient and steady-state profiles for the radius of curvature, liquid and vapor velocity, liquid pressure, and substrate temperature have been obtained. The mathematical model is capable of predicting the time required for the onset of dry out at the hot end, and for a micro heat pipe to reach steady state. The time required to reach steady state is independent of heat input, heat pipe inclination, groove angle, and $Qss$ profile. However, the time required for the onset of dry out at the hot end decreases with increasing heat input, inclination, and groove angle. The model predicted results have been successfully compared to the results from the literature. The general nature of this model and the associated study can be useful for many practical applications in the microscale heat exchange.

<>

## Figures

Figure 1

A V-groove showing heat pipe dimensions and flow directions

Figure 2

Volume element of a V-shaped micro heat pipe with all forces specified

Figure 3

Variation of the substrate temperature, Ts(°C) with the dimensionless position, X* at different times (s)

Figure 4

Variation of the dimensionless radius of curvature, R* with the dimensionless position, X* at different times (s)

Figure 5

Variation of the dimensionless radius of curvature, R* with time (s) for different positions, X*=0.32,0.5, and 0.68

Figure 6

Variation of the dimensionless liquid pressure, Pl* with the dimensionless position, X* at different times (s)

Figure 7

Variation of the dimensionless liquid velocity, Vl* with the dimensionless position, X* at different times (s)

Figure 8

Variation of the dimensionless vapor velocity, Vg* with the dimensionless position, X* at different times (s)

Figure 9

Steady-state dimensionless radius of curvature (R*) with the dimensionless position, X* for different values of Hamaker constant

Figure 10

Comparison of the theoretical and the experimental (23) dimensionless steady-state substrate temperature (Ts*) with position X*. The points are the experimental data and the solid lines are the theoretical predictions. The reference temperatures for 0deg and 14.93deg inclinations are 35°C and 32.6°C, respectively.

## Errata

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### Related Content

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text:
# Calabi-Yau and Hanson’s surfaces

I have a glass cube on my office windowsill containing a slice of a Calabi-Yau manifold, one of Bathsheba Grossman’s wonderful creations. It is an intricate, self-intersecting surface with lots of unexpected symmetries. A visiting friend got me into trying to make my own version of the surface.

First, what is the equation for it? Grossman-Hanson’s explanation is somewhat involved, but basically what we are seeing is a 2D slice through a 6-dimensional manifold in a projective space expressed as the 4D manifold $z_1^5+z_2^5=1$, where the variables are complex. Hanson shows that this is a kind of complex superquadric in this paper. This leads to the formulae:

$z_1(\theta,\xi,k_1)=e^{2\pi i k_1 / n}\cosh(\theta+\xi i)^{2/n}$

$z_2(\theta,\xi,k_2)=e^{2 \pi i k_2 / n}\sinh(\theta+\xi i)^{2/n}/i$

where the k’s run through $0 \leq k \leq (n-1)$. Each pair $k_1,k_2$ corresponds to one patch of what is essentially a complex catenoid. This is still a 4D object. To plot it, we plot the points

$(\Re(z_1),\Re(z_2),\cos(\alpha)\Im(z_1)+\sin(\alpha)\Im(z_2))$

where $\alpha$ is some suitable angle to tilt the projection into 3-space. Hanson’s explanation is very clear; I originally reverse-engineered the same formula from the code at Ziyi Zhang’s site.

The result is pretty nifty. It is tricky to see how it hangs together in 2D; rotating it in 3D helps a bit. It is composed of 16 identical patches:

The boundary of the patches meet other patches except along two open borders (corresponding to large or small values of $\theta$): these form the edges of the manifold and strictly speaking I ought to have rendered them to infinity. That would have made it unbounded and somewhat boring to look at: four disks meeting at an angle, with the interesting part hidden inside. By marking the edges we can see that the boundary are four linked wobbly circles:

A surface bounded by a knot or a link is called a Seifert surface. While these surfaces look a lot like minimal surfaces they are not exactly minimal when I estimate the mean curvature (it should be exactly zero); while this could be because of lack of numerical precision I think it is real: while minimal surfaces are Ricci-flat, the converse is not necessarily true.

Changing N produces other surfaces. N=2 is basically a catenoid (tilted and self-intersecting). As N increases it becomes more like a barrel or a pufferfish, with one direction dominated by circular saddle regions, one showing a meshwork of spaces reminiscent of spacefilling minimal surfaces, and one a lot of overlapping “barbs”.

Note that just like for minimal surfaces one can multiply $z_1, z_2$ by $e^{i\omega}$ to get another surface in an associate family. In this case it circulates the patches along their circles without changing the surface much.

Hanson also notes that by changing the formula to $z_1^{n_1}+z_2^{n_2}=1$ we can get boundaries that are torus-knot-like. This leads to the formulae:

$z_1(\theta,\xi,k_1)=e^{2\pi i k_1 / n_1}\cosh(\theta+\xi i)^{2/n_1}$

$z_2(\theta,\xi,k_2)=e^{2 \pi i k_2 / n_2}\sinh(\theta+\xi i)^{2/n_2}/i$

## Appendix: Matlab code

%% Initialization
edge=0; % Mark edge?
coloring=1; % Patch coloring type
n=4;
s=0.1; % Gridsize
alp=1; ca=cos(alp); sa=sin(alp); % Projection
[theta,xi]=meshgrid(-1.5:s:1.5,1*(pi/2)*(0:1:16)/16);
z=theta+xi*i;
% Color scheme
tt=2*pi*(1:200)'/200; co=.5+.5*[cos(tt) cos(tt+1) cos(tt+2)];
colormap(co)
%% Plot
clf
hold on
for k1=0:(n-1)
for k2=0:(n-1)
z1=exp(k1*2*pi*i/n)*cosh(z).^(2/n);
z2=exp(k2*2*pi*i/n)*(1/i)*sinh(z).^(2/n);
X=real(z1);
Y=real(z2);
Z=ca*imag(z1)+sa*imag(z2);
if (coloring==0)
surf(X,Y,Z);
else
switch (coloring)
case 1
C=z1*0+(k1+k2*n); % Color by patch
case 2
C=abs(z1);
case 3
C=theta;
case 4
C=xi;
case 5
C=angle(z1);
case 6
C=z1*0+1;
end
h=surf(X,Y,Z,C);
set(h,'EdgeAlpha',0.4)
end
if (edge>0)
plot3(X(:,end),Y(:,end),Z(:,end),'r','LineWidth',2)
plot3(X(:,1),Y(:,1),Z(:,1),'r','LineWidth',2)
end
end
end
view([2 3 1])
camlight
h=camlight('left');
set(h,'Color',[1 1 1]*.5)
axis equal
axis vis3d
axis off


text:
auctex
[Top][All Lists]

## Re: [AUCTeX] (New?) No indentation in some circumstances

 From: Mosè Giordano Subject: Re: [AUCTeX] (New?) No indentation in some circumstances Date: Sun, 19 Jun 2016 23:24:01 +0200

Hi Denise,

2016-06-19 18:18 GMT+02:00 Denis Bitouzé <address@hidden>:
> Hi,
>
> consider the following minimal `.dtx' example:
>
> --8<---------------cut here---------------start------------->8---
> %    \begin{macrocode}
> \newcommand{\blah}{%
>   \textbf{%
>     blah%
>   }%
> }
> \newcommand*{\bleh}{%
>     \begin{tabular}{l}
>       }{%
>       \begin{tabular}{r}
>         }%
>         bleh
>       \end{tabular}
>       }
>       \newcommand{\blih}[1]{%
>       \textbf{%
>       blih%
>       }%
>       }
> %    \end{macrocode}
> --8<---------------cut here---------------end--------------->8---
>
> The content of the \blah macro can be indented as usually with the TAB
> key.
>
> But, I guess because of the disruptive two \begin{tabular} for only one
> \end{tabular}, the content of the \blih macro cannot be properly
> indented.
>
> IIRC, indentation used to work properly in both cases.

Are you sure it used to work in this case?  If you could provide a
version where it worked we could try to look for the culprit.

> Do you know what's going on?

I think you got it right: unbalanced "\begin" and "\end" are a
problem.  A couple of possible dirty workarounds: if possible, move
the offending code in a separate file in order not to break
indentation for the rest of the code; make "\newcommand" a verbatim
command (I don't remember it it's possible to do it for two-argument
macros, though).  In addition, can't you do the conditional test on
the argument of "\begin{tabular}" only and call "\begin{tabular}" just
once?

In any case, I'm not sure it's good LaTeX-style to define commands
that fiddle with "\begin" and "\end".  Shouldn't this be a task of
"\newenvironment"?

Bye,
Mosè


text:
# zbMATH — the first resource for mathematics

Integral representations for solutions of exponential Gauß-Manin systems. (English) Zbl 1171.32019
The Gauss-Manin systems of a function $$f$$ on a smooth affine complex variety $$U$$ is generalised by considering an additional regular function $$g$$. Consider on $$\mathcal O_U$$ the flat connection $$\nabla u = du+dg\cdot u$$ and let $$\mathcal O_U e^g$$ be the associated holonomic $$\mathcal D_U$$-module. The exponential Gauss-Manin systems are defined to be the cohomology sheaves of the direct image $$f_+(\mathcal O_U e^g)$$. If $$g\neq 0$$, the connection is irregular singular at infinity.
The authors show that holomorphic solutions admit representations in terms of period integrals over topological chains in an appropriate homology theory: chains with possibly closed support and with rapid decay condition.

##### MSC:
 32S40 Monodromy; relations with differential equations and $$D$$-modules (complex-analytic aspects) 14F40 de Rham cohomology and algebraic geometry 32C38 Sheaves of differential operators and their modules, $$D$$-modules
##### Keywords:
Gauss-Manin systems: D-modules
Full Text:


text:
# Why is 50ohm sometimes used as a differential impedance?

I'm creating a design where I convert an RF single-ended signal to a differential signal with a 5400BL15B050E RF balun that is then fed to a ADL5802 RF mixer. The balun datasheet specifies the single ended characteristic impedance should be matched to $$\50\,\Omega\$$ and the differential balanced impedance should also be matched to $$\50\,\Omega\$$. Why would the balun choose a balanced differential impedance of $$\50\,\Omega\$$ and not $$\100\,\Omega\$$? Practically, this means that my differential microstrip traces need to be much wider than the single-ended traces (in my case almost 3x as wide). This makes routing trickier since (at least for my PCB stackup) the trace width is larger than the mixer pin spacing, and so I need to add tapering to make all the connections. Would it not have been more sensible to have the differential impedance be $$\100\,\Omega\$$ so that the balanced trace widths could be roughly the same as the single-ended ones?

Is there a reason why $$\50\,\Omega\$$ makes sense here?

Edit

Prompted by pericynthion's comment below, I'd also be interested to know why the mixer would use a $$\50\,\Omega\$$ differential impedance.

• Baluns are available with a variety of impedance ratios. Instead of asking "why would the balun choose a balanced differential impedance of 50 Ω and not 100 Ω" I think it would be better to ask why the active mixer IC designers chose to match its input ports to 50 Ω diff. – pericynthion Mar 29 at 4:00
• @pericynthion that's a fair point. Any thoughts on that, or that seems strange to you as well? – MattHusz Mar 29 at 4:05
• No, I'm curious though.. – pericynthion Mar 29 at 5:05
• @pericynthion I've added that into the main question. – MattHusz Mar 29 at 5:50


text:
# Math Help - Calculating surface area

1. ## Calculating surface area

An ingot 80x10x300mm long is cast into a cyclinder 120mm diameter. Calculate its length and total surface area.

an open top cyclinder diameter 84mm x 150mm.

Any help would be great

Cheers

Luke

2. An ingot 80x10x300mm long is cast into a cyclinder 120mm diameter. Calculate its length and total surface area.
The first step is to calculate the volume of the ingot. This will be the same as the volume of the cylinder. You will need to know that for a cylinder, $V=2\pi rh$.

I assume the other information in your post is related to some other question; I can't make head nor tail of it.