text:
# Phil 4.17.18

7:00 – ASRC MKT

• Listening to an interview with Nial Ferguson this morning where he talks about how the Chinese IT model aligns more closely with developing countries because they have solved the payment problem. And the surveillance state apparatus comes along for free. A ML/AI trained in that population will provide even closer alignment and will feel more “native”.
• A ML/AI trained in that population will feel more “native”, and increase the traction of the Chinese IT. The Chinese approach expands its footprint in the developing world because it feels better and solves problems.
• This sets up a conflict between corporate systems in the US and EU and China? In sheer demographics that means that it’s more likely that the dominant ML/AI perspective would reflect the surveillance biases of the Chinese government.
• Payment systems are Socio-cultural user interfaces
• Submitted to SASO. Submission #32. Updated the ArXiv file too. ArXiv “forgets” all the attachments too, so the tarball approach is soooooo much nicer.
• Alt text for screen readers using LaTex
\documentclass{article}
\usepackage{graphicx}
\usepackage{pdfcomment}
\pagestyle{empty}

\begin{document}
one two three

\pdftooltip{\includegraphics{img.png}}{This is the ALT text}%

four five six
\end{document}

# Phil 4.10.18

7:00 – 5:00 ASRC MKT

• Incorporating Wajanat’s changes
• Discovered the csquotes package!
\usepackage[autostyle]{csquotes}

\begin{document}

\enquote{Thanks!}

\end{document}
• Meeting with Drew
• Nice chat. Basically, “use the databases!”
• Also found this:
• A Mechanism for Reasoning about Time and Belief
• Hideki Isozaki
• Several computational frameworks have been proposed to maintain information about the evolving world, which embody a default persistence mechanism; examples include time maps and the event calculus. In multi-agent environments, time and belief both play essential roles. Belief interacts with time in two ways: there is the time at which something is believed, and the time about which it is believed. We augment the default mechanisms proposed for the purely temporal case so as to maintain information not only about the objective world but also about the evolution of beliefs. In the simplest case, this yields a two dimensional map of time, with persistence along each dimension. Since beliefs themselves may refer to other beliefs, we have to think of a statement referring to an agent’s temporal belief about another agent’s temporal belief ( a nested temporal belief statement). It poses both semantical and algorithmic problems. In this paper, we concentrate on the algorithmic aspect of the problems. The general case involves multi-dimensional maps of time called Temporal Belief Maps.
• Register for CI 2018 – done
• Finalize and submit paper by April 27, 2018
• Did not get a go ahead for ONR
• More work on the DHS proposal. Thinking about having a discussion about using latent values and clustering as the initial detection approach, and using ML as the initial simulation approach.
• Then much banging away at keyboards. Good progress, I think
• Neural Artistic Style Transfer: A Comprehensive Look

# Phil 4.9.18

7:00 – ASRC MKT / BD

• The Collective Intelligence 2018 paper was accepted! Now I need to start thinking about the presentation. And lodging, travel, etc.
• Tweaking the SASO paper
• The reasonably current version is on ArXive! Will update after submission to SASO this week.
• This One Simple Trick Disrupts Digital Communities
• This paper describes an agent based simulation used to model human actions in belief space, a high-dimensional subset of information space associated with opinions. Using insights from animal collective behavior, we are able to simulate and identify behavior patterns that are similar to nomadic, flocking and stampeding patterns of animal groups. These behaviors have analogous manifestations in human interaction, emerging as solitary explorers, the fashion-conscious, and members of polarized echo chambers. We demonstrate that a small portion of nomadic agents that widely traverse belief space can disrupt a larger population of stampeding agents. Extending the model, we introduce the concept of Adversarial Herding, where bad actors can exploit properties of technologically mediated communication to artificially create self sustaining runaway polarization. We call this condition the Pishkin Effect as it recalls the large scale buffalo stampedes that could be created by native Americans hunters. We then discuss opportunities for system design that could leverage the ability to recognize these negative patterns, and discuss affordances that may disrupt the formation of natural and deliberate echo chambers.
• Kind of between things, so I wrote up my notes on Influence of augmented humans in online interactions during voting events
• Looks important: Lessons Learned Reproducing a Deep Reinforcement Learning Paper
• Proposal all day today probably
• Fika

# Phil 4.6.18

7:00 – 9:00 ASRC MKT

• Heard a San Francisco comedian refer to Google as “Mordor” to knowing laughter in the audience. That says a lot about the relationship between the SF folks and their technology nation-states to the south. It also makes me rethink what Mordor actually was…
• More ArXive submission
• Tips for submitting to ArXive for the first time
• Make sure that only the used pix are uploaded
• EchoChamberAngle
• Explore-Exploit
• directionpreserving
• SlewAngle
• Explorer
• coloredFlocking
• stampede
• RunawayTrace
• populations
• HerdingImpact
• It may be possible to submit as a single zipped (.gz? .tar?)  package. Will try that next time
• Submitted and pending approval.
• Start on DHS proposal
• Built LaTex document
• The templates provided by ASRC are completely wrong. Fixed in the LaTex template
• Lots of discussion and negotiation on the form of the concept. I think we’re ready to start Monday
• Nice chat with Wajanat about the paper and then her work. It’s interesting to hear how references and metaphors that I think are common get missed when they are read by a non-native english speaker from a different cultural frame. For example, I refer to a “plague of locusts” , which I had to explain as one of the biblical plagues of Egypt. Once explained, Wajanat immediately got it, and mentioned the Arabic word طاعون, We then asked Ali, who’s Iranian. He didn’t know about plagues either, but by using طاعون, he was able to get the entire context. She also suggested improving the screenshot at the beginning of the paper and expanding the transition to the intelligent vehicle stampede section.
• Then a meandering and fun chat with Shimei, mostly about psychology and AI ethics. Left at 9:00

# Phil 4.5.18

7:00 – 5:00 ASRC MKT

• More car stampedes: On one of L.A.’s steepest streets, an app-driven frenzy of spinouts, confusion and crashes
• Working on the first draft of the paper. I think(?) I’m reasonably happy with it.
• Trying to determine the submission guidelines. Are IEEE paper anonymized? If they are, here’s the post on how to do it and my implementation:
\usepackage{xcolor}
\usepackage{soul}

\sethlcolor{black}
\makeatletter
\newif\if@blind
\@blindfalse %use \@blindtrue to anonymize, \@blindfalse on final version
\if@blind \sethlcolor{black}\else
\let\hl\relax
\fi

\begin{document}
this text is \hl{redacted}
\end{document}

• So this clever solution doesn’t work, because you can select under the highlight. This is my much simpler solution:
%\newcommand*{\ANON}{}
\ifdefined\ANON
\author{\IEEEauthorblockN{Anonymous Author(s)}
\IEEEauthorblockA{\textit{this line kept for formatting} \\
\textit{this line kept for formatting}\\
this line kept for formatting \\
this line kept for formatting}
}
\else
\author{\IEEEauthorblockN{Philip Feldman}
\IEEEauthorblockA{\textit{ASRC Federal} \\
Columbia, USA \\
philip.feldman@asrcfederal.com}
}
\fi
• Submitting to Arxive
• Boy, this hit home: The Swamp of Sadness
• Even with Arteyu pulling on his bridle, Artex still had to start walking and keep walking to survive, and so do you. You have to pull yourself out of the swamp. This sucks, because it’s difficult, slow, hand-over-hand, gritty, horrible work, and you will end up very muddy. But I think the muddier the swamp, the better the learning really. I suspect the best kinds of teachers have themselves walked through very horrible swamps.
• You have found the cui2vec explorer. This website will let you interact with embeddings for over 108,000 medical concepts. These embeddings were created using insurance claims for 60 million americans, 1.7 million full-text PubMed articles, and clinical notes from 20 million patients at Stanford. More information about the methods used to create these embeddings can be found in our preprint: https://arxiv.org/abs/1804.01486
• Going to James Foulds’ lecture on Mixed Membership Word Embeddings for Computational Social Science. Send email for meeting! Such JuryRoom! Done!
• Kickoff meeting for the DHS proposal. We have until the 20th to write everything. Sheesh

# Phil 4.4.18

7:00 – 5:00 ASRC MKT

• From zero to research — An introduction to Meta-learning
• Thomas Wolf Machine Learning, Natural Language Processing & Deep learning – Science Lead @ Huggingface  (We’re on a journey to build the first truly social artificial intelligence. Along the way, we contribute to the development of technology for the better.)
• Over the last months, I have been playing and experimenting quite a lot with meta-learning models for Natural Language Processing and will be presenting some of this work at ICLR, next month in Vancouver 🇨🇦 — come say hi! 👋 In this post, I will start by making a very visual introduction to meta-learning, from zero to current research work. Then, we will code a meta-learning model in PyTorch from scratch and I will share some of the lessons learned on this project.

• Google veteran Jeff Dean takes over as company’s AI chief
• Add some MB framing words to the game theory part of the lit review – done
• Work on the PSA writeup

Our research has indicated that an awareness of nomadic/explorer activity in belief space may help nudge stampeding groups away from a terminal trajectory and back towards “average” beliefs. Tajfel states that groups can exist “in opposition”, so providing counter-narratives may be ineffective. Rather, we think that a practical solution to online polarization is the injection of diversity into user’s feeds, be they social media, search results, videos, etc.  The infrastructure exists for this already in platform’s support of advertising. The precedent is the Public Service Announcement (PSA).

US Broadcasters since 1927, have been obligated to “serve the public interest” in exchange for spectrum rights. One way that this has been addressed is through the creation of the PSA, “the purpose of which is to improve the health, safety, welfare, or enhancement of people’s lives and the more effective and beneficial functioning of their community, state or region”

We believe that PSAs can be repurposed to support diversity injection through the following:

• Random, non-political content designed to expand information horizons, analogous to clicking the “random article” link on Wikipedia.
• Progressive levels of detail starting with an informative “hook” presented in social feeds or search results. Users should be able to explore as much or as little as they want.
• Simultaneous presentation to large populations. Google has been approximating this with their “doodle” since 1998, with widespread positive feedback, which indicates that there may be good receptivity to common serendipitous information.
• Format should reflect the medium, Text, images and videos.
• Content should be easily verifiable, recognizable, and difficult to spoof.

We believe that such diversity injection mechanisms as described above can serve as a “first do no harm” first step in addressing the current crisis of misinformation. By nudging users towards an increased awareness of a wider world, which in turn interferes with the processes that lead to belief stampedes by increasing the number of dimensions, the awareness of different paths that others are taking. As we gain understanding of the mechanisms that influence group behaviors, it may be possible to further refine our designs and interfaces so that they no longer promote extremism while still providing value.

• Done with first draft? Nope. Going to rework the implications section some more.

# Phil 4.3.18

ASRC MKT 7:00 – 5:30

• Integrating airplane notes on Influence of augmented humans in online interactions during voting events
• Follow up on pointing logs
• World Affairs Council (Part II. Part I is Jennifer Kavanagh and Tom Nichols: The End of Authority)
• With so many forces undermining democratic institutions worldwide, we wanted a chance to take a step back and provide some perspective. Russian interference in elections here and in Europe, the rise in fake news and a decline in citizen trust worldwide pose a danger. In this second of a three part series, we look at the role of social media and the ways in which it was exploited for the purpose of sowing distrust. Janine Zacharia, former Jerusalem bureau chief and Middle East correspondent for The Washington Post, and Roger McNamee, managing director at Elevation Partners and an early stage investor in Google and Facebook, are in conversation with World Affairs CEO Jane Wales.
• “The ultimate combination of propaganda and gambling … powered by machine learning”
• The emergence of consensus: a primer (No Moscovici – odd)
• The origin of population-scale coordination has puzzled philosophers and scientists for centuries. Recently, game theory, evolutionary approaches and complex systems science have provided quantitative insights on the mechanisms of social consensus. However, the literature is vast and widely scattered across fields, making it hard for the single researcher to navigate it. This short review aims to provide a compact overview of the main dimensions over which the debate has unfolded and to discuss some representative examples. It focuses on those situations in which consensus emerges ‘spontaneously’ in the absence of centralized institutions and covers topics that include the macroscopic consequences of the different microscopic rules of behavioural contagion, the role of social networks and the mechanisms that prevent the formation of a consensus or alter it after it has emerged. Special attention is devoted to the recent wave of experiments on the emergence of consensus in social systems.
• Need to write up diversity injection proposal
• Basically updated PSAs for social media
• Intent is to expand the information horizon, not to counter anything in particular. So it’s not political
• Presented in a variety of ways (maps, stories and lists)
• Goes identically into everyone’s feed
• Can be blocked, but blockers need to be studied
• More injection as time on site goes up. Particularly with YouTube & FB
• Working on SASO paper. Made it through discussion

# Phil 4.2.18

7:00 – 5:00 ASRC MKT

• Someone worked pretty hard on their April Fools joke
• Started cleaning up my TF Dev Conf notes. Need to fill in speaker’s names and contacts – done
• Contact Keith Bennet about “pointing” logs – done
• Started editing the SASO flocking paper. Call is April 16!
• Converted to LaTex and at 11 pages
• But first – expense report…. Done! Forgot the parking though. Add tomorrow!
• Four problems for news and democracy
• To understand these four crises — addiction, economics, bad actors and known bugs — we have to look at how media has changed shape between the 1990s and today. A system that used to be linear and fairly predictable now features feedback loops that lead to complex and unintended consequences. The landscape that is emerging may be one no one completely understands, but it’s one that can be exploited even if not fully understood.
• Humanitarianism’s other technology problem
• Is social media affecting humanitarian crises and conflict in ways that kill people and may ultimately undermine humanitarian response?Fika. Meeting with Wajanat Friday to go over paper

# Phil 3.8.18

7:00 – 5:00 ASRC

• Another nice comment from Joanna Bryson on BBC Business Daily – The bias is seldom in the algorithm. Latent Semantic Indexing is simple arithmetic. The data contains the bias, and that’s from us. Fairness is a negotiated concept, which means that is is complicated. Requiring algorithmic fairness necessitates placing enormous power in the hands of those writing the algorithms.
• The science of fake news (Science magazine)
• The rise of fake news highlights the erosion of long-standing institutional bulwarks against misinformation in the internet age. Concern over the problem is global. However, much remains unknown regarding the vulnerabilities of individuals, institutions, and society to manipulations by malicious actors. A new system of safeguards is needed. Below, we discuss extant social and computer science research regarding belief in fake news and the mechanisms by which it spreads. Fake news has a long history, but we focus on unanswered scientific questions raised by the proliferation of its most recent, politically oriented incarnation. Beyond selected references in the text, suggested further reading can be found in the supplementary materials.
• Incorporating Sy’s comments into a new slide deck
• More ONR
• Meeting with Shimei
• Definitely use the ONR-specified headings
• Research is looking good and interesting! Had to spend quite a while explaining lexical trajectories.
• Ran through the slides with Sy again. Mostly finalized?

# Phil 3.7.18

7:00 – 5:00 ASRC MKT

• Some surprising snow
• Meeting with Sy at 1:30 slides
• Meeting with Dr. DesJardins at 4:00
• Nice chat with Wajanat about the presentation of the Saudi Female self in physical and virtual environments
• Sprint planning
• Finish ONR Proposal VP-331
• CHIIR VP-332
• Prep for TF dev conf VP-334
• TF dev conf VP-334
• Working on the ONR proposal
• Oxford Internet Institute – Computational Propaganda Research Project
• The Computational Propaganda Research Project (COMPROP) investigates the interaction of algorithms, automation and politics. This work includes analysis of how tools like social media bots are used to manipulate public opinion by amplifying or repressing political content, disinformation, hate speech, and junk news. We use perspectives from organizational sociology, human computer interaction, communication, information science, and political science to interpret and analyze the evidence we are gathering. Our project is based at the Oxford Internet Institute, University of Oxford.
• Polarization, Partisanship and Junk News Consumption over Social Media in the US
• What kinds of social media users read junk news? We examine the distribution of the most significant sources of junk news in the three months before President Donald Trump’s first State of the Union Address. Drawing on a list of sources that consistently publish political news and information that is extremist, sensationalist, conspiratorial, masked commentary, fake news and other forms of junk news, we find that the distribution of such content is unevenly spread across the ideological spectrum. We demonstrate that (1) on Twitter, a network of Trump supporters shares the widest range of known junk news sources and circulates more junk news than all the other groups put together; (2) on Facebook, extreme hard right pages—distinct from Republican pages—share the widest range of known junk news sources and circulate more junk news than all the other audiences put together; (3) on average, the audiences for junk news on Twitter share a wider range of known junk news sources than audiences on Facebook’s public pages
• Need to look at the variance in the articles. Are these topical stampedes? Or is this source-oriented?
• Understanding and Addressing the Disinformation Ecosystem
• This workshop brings together academics, journalists, fact-checkers, technologists, and funders to better understand the challenges produced by the current disinformation ecosystem. The facilitated discussions will highlight relevant research, share best-practices, identify key questions of scholarly and practical concern regarding the nature and implications of the disinformation ecosystem, and outline a potential research agenda designed to answer these questions.
• More BIC
• The psychology of group identity allows us to understand that group identification can be due to factors that have nothing to do with the individual preferences. Strong interdependence and other forms of common individual interest are one sort of favouring condition, but there are many others, such as comembership of some existing social group, sharing a birthday, and the artificial categories of the minimal group paradigm. (pg 150)
• Wherever we may expect group identity we may also expect team reasoning. The effect of team reasoning on behavior is different from that of individualistic reasoning. We have already seen this for Hi-Lo. This has wide implications. It makes the theory of team reasoning a much more powerful explanatory and predictive theory than it would be if it came on line only in games with th3e right kind of common interest. To take just one example, if management brings it about so that the firm’s employees identify with the firm, we may expect for them to team-reason and so to make choices that are not predicted by the standard theories of rational choice. (pg 150)
• As we have seen, the same person passes through many group identities in the flux of life, and even on a single occasion more than one of these identities may be stimulated. So we will need a model of identity in which the probability of a person’s identification is distributed over not just two alternatives-personal self-identity or identity with a fixed group-but, in principle, arbitrarily many. (pg 151)

# Phil 3.2.18

7:00 – 5:00 ASRC MKT

• Got Wayne’s comments. Will integrate and see if EasyChair will take it
• Work on ONR WhitePaper
• Society for Personality and Social Psychology
• The mission of SPSP is to advance the scienceteaching, and application of social and personality psychology. SPSP members aspire to understand individuals in their social contexts for the benefit of all people.
• Social psychology is the scientific study of how people’s thoughts, feelings, and behaviors are influenced by the actual, imagined, or implied presence of others.
• I am interested in the ways that bias and motivation can affect our reasoning and memory to influence the judgments and decisions that we make.  In particular, I am currently studying how these biases apply to real-world situations, such as political conflicts, hiring decisions, and legal decision-making.  I explore not only how biases affect decision-making but what people think about their own biases and the best ways to help correct them.
• Data from a pre-publication independent replication initiative examining ten moral judgement effects

# Phil 3.1.18

7:00 – 4:30 ASRC MKT

• Anonymize (done) and submit paper – done!
• Finish T’s timeline approach? Finished my version. I think I like it.
• This may be important: https://twitter.com/jack/status/969234275420655616
• We’re committing Twitter to help increase the collective health, openness, and civility of public conversation, and to hold ourselves publicly accountable towards progress.11:33 AM – 1 Mar 2018 from San Francisco, CA
Our friends at @cortico and @socialmachines introduced us to the concept of measuring conversational health. They came up with four indicators: shared attention, shared reality, variety of opinion, and receptivity. Read about their work here: https://www.cortico.ai/blog/2018/2/29/public-sphere-health-indicators
• We simply can’t and don’t want to do this alone. So we’re seeking help by opening up an RFP process to cast the widest net possible for great ideas and implementations. This will take time, and we’re committed to providing all the necessary resources. RFP: https://blog.twitter.com/official/en_us/topics/company/2018/twitter-health-metrics-proposal-submission.html

• Interactive topic hierarchy revision for exploring a collection of online conversations
• In the last decade, there has been an exponential growth of asynchronous online conversations (e.g. blogs), thanks to the rise of social media. Analyzing and gaining insights from such discussions can be quite challenging for a user, especially when the user deals with hundreds of comments that are scattered around multiple different conversations. A promising solution to this problem is to automatically mine the major topics from conversations and organize them into a hierarchical structure. However, the resultant topic hierarchy can be noisy and/or it may not match the user’s current information needs. To address this problem, we introduce a novel human-in-the-loop approach that allows the user to revise the topic hierarchy based on her feedback. We incorporate this approach within a visual text analytics system that helps users in analyzing and getting insights from conversations by exploring and revising the topic hierarchy. We evaluated the resulting system with real users in a lab-based study. The results from the user study, when compared to its counterpart that does not support interactive revisions of a hierarchical topic model, provide empirical evidence of the potential utility of our system in terms of both performance and subjective measures. Finally, we summarize generalizable lessons for introducing human-in-the-loop computation within a visual text analytics system
• Understanding the Promise and Limits of Automated Fact-Checking
• The furor over so-called ‘fake news’ has exacerbated long-standing concerns about political lying and online rumors in a fragmented media environment, drawing attention to the potential of various automated fact-checking (AFC) technologies to combat online misinformation. This factsheet gives an overview of current efforts to automatically police false claims and misleading content online. Based on a review of recent research and interviews with both fact-checkers and computer scientists working in this area, we find that:
• Much of the terrain covered by human fact-checkers requires a kind of judgement and sensitivity to context that remains far out of reach for fully automated verification.
• Despite progress in automatic verification of a narrow range of simple factual claims, AFC systems will require human supervision for the foreseeable future.
• The promise of AFC technologies for now lies in tools to assist fact-checkers to identify and investigate claims, and to deliver their conclusions, as effectively as possible.
• More BIC
• Now it is the case, and increasingly widely recognized to be, that in games in general there’s no way players can rationally deliberate to a Nash equilibrium. Rather, classical canons of rationality do not in general support playing in Nash equilibria. So it looks as though shared intentions cannot, in the general run of games, by classical canons, be rationally formed! And that means in the general run of life as well. This is highly paradoxical if you think that rational people can have shared intentions. The paradox is not resolved by the thought that when they do, the context is not a game: any situation in which people have to make the sorts of decisions that issue in shared intentions must be a game, which is, after all, just a situation in which combinations of actions matter to the combining parties. (pg 139)
• Turn to the idea that a joint intention to do (x,y) is rationally produced in 1 and 2 by common knowledge of two conditional intentions: Pl has the intention expressed by ‘I’ll do x if and only if she does y’, and P2 the counterpart one. Clearly P1 doesn’t have the intention to do x if and. only if P2 in fact does y whether or not Pl believes P2 will do y; the right condition must be along the lines of:
(C1) P1 intends to do x if and only if she believes P2 will do y. (pg 139)

• So this is in belief space, and belief is based on awareness and trust
• There are two obstacles to showing this, one superable, the other not, I think. First, there are two Nash equilibria, and nothing in the setup to suggest that some standard refinement (strengthening) of the Nash equilibrium condition will eliminate one. However, I suspect that my description of the situation could be refined without ‘changing the subject’. Perhaps the conditional intention Cl should really be ‘I’ll do x if and only if she’ll do y, and that’s what I would like best’. For example, if x and y are the two obligations in a contract being discussed, it is natural to suppose that Pl thinks that both signing would be better than neither signing. If we accept this gloss then the payoff structure becomes a Stag Hunt – Hi-Lo if both are worse off out of equilibrium than in the poor equilibrium (x’ ,y’). To help the cause of rationally deriving the joint intention (x,y), assume the Hi-Lo case. What are the prospects now? As I have shown in chapter 1, there is no chance of deriving (x,y) by the classical canons, and the only (so far proposed) way of doing to is by team reasoning. (pg 140)
• The nature of team reasoning, and of the conditions under which it is likely to be primed in individual agents, has a consequence that gives further support to this claim. This is that joint intentions arrived at by the route of team reasoning involve, in the individual agents, a ‘sense of collectivity’. The nature of team reasoning has this effect, because the team reasoner asks herself not ‘What should I do?’ but ‘What should we do?’ So, to team-reason, you must already be in a frame in which first-person plural concepts are activated. The priming conditions for team reasoning have this effect because, as we shall see later in this chapter, team reasoning, for a shared objective, is likely to arise spontaneously in an individual who is in the psychological state of group-identifying with the set of interdependent actors; and to self-identify as a member of a group essentially involves a sense of collectivity. (pg 141)
• Starting on ONR white paper – first pass banged together
• Need to add figures and references
• discovered pandoc, which converts nicely between many files, including LaTex and word. The command that matters is:
pandoc -s foo.tex -o foo.docx

# Phil 2.25.18

Looks like I need to update the DC and the CI 2018 paper with a new reference:

Dynamic Word Embeddings for Evolving Semantic Discovery

• Zijun YaoYifan Sun, Weicong Ding, Nikhil RaoHui Xiong
• Word evolution refers to the changing meanings and associations of words throughout time, as a byproduct of human language evolution. By studying word evolution, we can infer social trends and language constructs over different periods of human history. However, traditional techniques such as word representation learning do not adequately capture the evolving language structure and vocabulary. In this paper, we develop a dynamic statistical model to learn time-aware word vector representation. We propose a model that simultaneously learns time-aware embeddings and solves the resulting “alignment problem”. This model is trained on a crawled NYTimes dataset. Additionally, we develop multiple intuitive evaluation strategies of temporal word embeddings. Our qualitative and quantitative tests indicate that our method not only reliably captures this evolution over time, but also consistently outperforms state-of-the-art temporal embedding approaches on both semantic accuracy and alignment quality.

# Phil 2.23.18

6:30 – 8:30, 11:00 – 5:00 ASRC MKT

• Graphstream with javafx? https://github.com/graphstream/gs-ui-javafx
• Learning to Cooperate, Compete, and Communicate
• Multiagent environments where agents compete for resources are stepping stones on the path to AGI. Multiagent environments have two useful properties: first, there is a natural curriculum — the difficulty of the environment is determined by the skill of your competitors (and if you’re competing against clones of yourself, the environment exactly matches your skill level). Second, a multiagent environment has no stable equilibrium: no matter how smart an agent is, there’s always pressure to get smarter. These environments have a very different feel from traditional environments, and it’ll take a lot more research before we become good at them.
• Storytelling and Politics: How History, Myths and Narratives Drive Our Decisions (video)
• A narrative with historical overtones, an emotive connection and credibility not only convinces people, it frames the points of reference they use to evaluate the decision they are being asked to make.
• Logos Pathos Ethos?
• Continuing with rewrite. Had to fire up the MiKTex admin console to install wrapfig. Permissions issue?
• Need to take the description of the maps at the end of the results section and turn into a paragraph.
• Walk through of presentation this afternoon. Need to set up a skype session and bridge. Went well, I need to make a few fixes. Most importantly I need to put together a 2×2 payoff matrix that covers nomad/flock/stampede

# Phil 2.22.18

7:00 – ASRC MKT

• Long chat with Wajant about the CI 2018 paper. going to work up a new version
• Started in Docs, but wound up saving out and reworking the LaTex version to keep track of the length.
• Coincidentally, ONR is soliciting white papers for theoretically-based decision making tools. Five pages plus references for the paper, and a one-page resume.
• The 5-page body of the white paper shall include the following information:
• Principal Investigator(s);
• Relevance of the proposed effort to the research areas described in Section II; (Topic 2, Research Focus Area 1)
• relationship of the proposed work to current state of art.
• Technical objective of the proposed effort;
• Technical approach that will be pursued to meet the objective;
• A summary of recent relevant technical breakthroughs; and
• A funding plan showing requested funding per fiscal year.
• Need to register for TF conference when Aaron gets in. Got hotel and  approval.
• More dimension reduction and belief vectors on twitter


text:
# 9.2.4: Electronic Spectra - Ultraviolet and Visible Spectroscopy - Lanthanides and Actinides

The ions of most lanthanide and actinide ions absorb light in the UV and visible regions.  The transitions involve only a redistribution of electrons within the 4f orbitals (--> f' transitions) are orbitally-forbidden by the quantum mechanical selection rules.  Consequently, the compounds of lanthanide ions are generally pale in color.

Unlike transition metal complexes, the crystal/ligand field effects for the lanthanide 4f orbitals are virtually insignificant.  This is a result of the extensive shielding of the 4f electrons by the 5s and 5p orbitals.  Consequently the  f --> f' absorption bands are very sharp (useful fingerprinting and quantitation of LnIII)  and the optical spectra are virtually independent of environment.

Figure$$\PageIndex {1}$$: The spectrum of a neodymium(III) complex over the range of 25,000 cm-1 to 9100 cm-1 (400 nm to 1100 nm).  The sharp "atom-like" spectral features for Ln3+ ion complexes are the same be thay be in the gas, solid or solution phase.

The insensitivity of the f --> f' transitions leads to limited use in study of lanthanide materials.  CeIII and TbIII complexes have the highest intensity bands in the UV due to 4f--> 4fn-15d1 transitions.  The f -->d are not orbitally forbidden (n-1 = 0 (empty sub-shell) for CeIII = 7 (half-filled sub-shell) for TbIII).

9.2.4: Electronic Spectra - Ultraviolet and Visible Spectroscopy - Lanthanides and Actinides is shared under a not declared license and was authored, remixed, and/or curated by LibreTexts.

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## Find dy/dx by implicit differentiation if : x cos y=y?

turksvids
Featured 1 month ago

$\frac{\mathrm{dy}}{\mathrm{dx}} = \cos \frac{y}{1 + x \cdot \sin \left(y\right)}$

#### Explanation:

Take the derivative of both sides with respect to $x$:

$\frac{d}{\mathrm{dx}} \left(x \cdot \cos \left(y\right)\right) = \frac{d}{\mathrm{dx}} \left(y\right)$

Use the product rule on the left side:

$x \cdot - \sin \left(y\right) \frac{\mathrm{dy}}{\mathrm{dx}} + \cos \left(y\right) = \frac{\mathrm{dy}}{\mathrm{dx}}$

Rearrange so all the terms with $\frac{\mathrm{dy}}{\mathrm{dx}}$ are on the same side:

$\frac{\mathrm{dy}}{\mathrm{dx}} + x \cdot \sin \left(y\right) \frac{\mathrm{dy}}{\mathrm{dx}} = \cos \left(y\right)$

Factor a little:

$\frac{\mathrm{dy}}{\mathrm{dx}} \left(1 + x \cdot \sin \left(y\right)\right) = \cos \left(y\right)$

Solve for $\frac{\mathrm{dy}}{\mathrm{dx}}$:

$\frac{\mathrm{dy}}{\mathrm{dx}} = \cos \frac{y}{1 + x \cdot \sin \left(y\right)}$

## How to solve the following ??

Eric Sia
Featured 1 month ago

$t = 50 \ln 10$

#### Explanation:

Given:

$k \frac{\mathrm{dV}}{\mathrm{dt}} + V = 0$

Rearrange:

$\frac{1}{V} \frac{\mathrm{dV}}{\mathrm{dt}} = - \frac{1}{k}$

Take the integral of both sides:

$\int \frac{1}{V} \mathrm{dV} = - \frac{1}{k} \int \mathrm{dt}$

This gives:

$\ln V = - \frac{t}{k} + C$

At $t = 0$, $V = {V}_{0}$:

$\ln {V}_{0} = C$

Hence:

$V = {V}_{0} {e}^{- \frac{t}{k}}$

Or:

$t = k \ln \left({V}_{0} / V\right)$

When $V = \frac{1}{10} {V}_{0}$:

$t = k \ln 10$

Given $k = 50$:

$t = 50 \ln 10$

## For what values of x is f(x)= -2x^3 + 4 x^2 + 5x -5  concave or convex?

Somebody N.
Featured 1 month ago

Concave: $\left\{x \in \mathbb{R} : \frac{2}{3} < x < \infty\right\}$

Convex: $\left\{x \in \mathbb{R} : - \infty < x < \frac{2}{3}\right\}$

#### Explanation:

A function is convex if the second derivative is positive and concave where its second derivative is negative. When the second derivative is $0$ this could mean the function is concave , convex, or it could be a point of inflexion. This would have to be tested using the first derivative.

$f \left(x\right) = - 2 {x}^{3} + 4 {x}^{2} + 5 x - 5$

$\frac{\mathrm{dy}}{\mathrm{dx}} \left(- 2 {x}^{3} + 4 {x}^{2} + 5 x - 5\right) = - 6 {x}^{2} + 8 x + 5$

$\frac{{d}^{2} y}{{\mathrm{dx}}^{2}} \left(- 6 {x}^{2} + 8 x + 5\right) = - 12 x + 8$

So:

$- 12 x + 8 < 0$

$x > \frac{8}{12}$

$x > \frac{2}{3}$

Concave: $\left\{x \in \mathbb{R} : \frac{2}{3} < x < \infty\right\}$

$- 12 x + 8 > 0$

$x < \frac{8}{12}$

$x < \frac{2}{3}$

Convex: $\left\{x \in \mathbb{R} : - \infty < x < \frac{2}{3}\right\}$

Graph:

graph{y=-2x^3+4x^2+5x-5 [-4, 4, -7.12, 7.12]}

## How to solve f'(x) = 0 for f(x)= ln(x) - e^(cos x) over 0<x<=10?

Eric Sia
Featured 1 month ago

Use Newton-Raphson method for numerical approximation.

#### Explanation:

$f \left(x\right) = \ln x - {e}^{\cos x}$

Take the derivative with respect to $x$:

$f ' \left(x\right) = \frac{1}{x} + \sin x {e}^{\cos x}$

Given the condition $f ' \left(x\right) = 0$:

$0 = \frac{1}{x} + \sin x {e}^{\cos x}$

Let

$u \left(x\right) = \frac{1}{x} + \sin x {e}^{\cos x}$

Plot $u \left(x\right)$ over $0 < x \le 10$:
graph{1/x+sinxe^(cosx) [-0.5, 10.5, -2, 4]}

By examination, the roots of $u \left(x\right)$ are close to $4$, $6$, and $10$.

Take the derivative with respect to $x$:

$u ' \left(x\right) = - \frac{1}{x} ^ 2 + \left(\cos x - {\sin}^{2} x\right) {e}^{\cos x}$

The Newton-Raphson approximation equation is:

${x}_{n + 1} = {x}_{n} - \frac{u \left({x}_{n}\right)}{u ' \left({x}_{n}\right)}$

Taking ${x}_{0} = 4$ gives:

${x}_{0} = 4$
${x}_{1} = 3.794906369$
${x}_{2} = 3.776053960$
${x}_{3} = 3.775920734$
${x}_{4} = 3.775920727$
${x}_{5} = 3.775920727$

Taking ${x}_{0} = 6$ gives:

${x}_{0} = 6$
${x}_{1} = 6.247412504$
${x}_{2} = 6.223989036$
${x}_{3} = 6.223939693$
${x}_{4} = 6.223939692$
${x}_{5} = 6.223939692$

Taking ${x}_{0} = 10$ gives:

${x}_{0} = 10$
${x}_{1} = 9.730092594$
${x}_{2} = 9.698501451$
${x}_{3} = 9.698236088$
${x}_{4} = 9.698236070$
${x}_{5} = 9.698236070$

Hence

$x = 3.775920727 , 6.223939692 , 9.698236070$

## What is the derivative of  y = ((x^2 + 4) / (x^2 - 4))^3?

Michael F.
Featured 2 weeks ago

The first derivative is $\quad \frac{- 48 x \cdot {\left({x}^{2} + 4\right)}^{2}}{{\left({x}^{2} - 4\right)}^{4}}$.

#### Explanation:

Let $\quad f \left(x\right) = {\left(\frac{{x}^{2} + 4}{{x}^{2} - 4}\right)}^{3}$.

Rearranging the term of $f$ gives us

$\quad f \left(x\right) = {\left(\frac{{x}^{2} + 4}{{x}^{2} - 4}\right)}^{3} = {\left({x}^{2} + 4\right)}^{3} / {\left({x}^{2} - 4\right)}^{3}$.

For differentiating we use the $\textcolor{g r e e n}{\text{chain rule}}$ for $\textcolor{b l u e}{{u}^{'} \left(x\right)}$ and $\textcolor{b l u e}{{v}^{'} \left(x\right)}$

$\textcolor{g r e e n}{\frac{d}{\mathrm{dx}} \left(u \left(v \left(x\right)\right)\right) = {\left(u \left(v \left(x\right)\right)\right)}^{'} = {u}^{'} \left(v \left(x\right)\right) \cdot {v}^{'} \left(x\right)}$ (outside times inside derivative)

and the $\textcolor{b l u e}{\text{quotient rule}}$ for the whole term of $f$

$\textcolor{b l u e}{\frac{d}{\mathrm{dx}} \frac{u \left(x\right)}{v \left(x\right)} = {\left(\frac{u \left(x\right)}{v \left(x\right)}\right)}^{'} = \frac{{u}^{'} \left(x\right) \cdot v \left(x\right) - u \left(x\right) \cdot {v}^{'} \left(x\right)}{v \left(x\right)} ^ 2}$ (with $v \left(x\right) \ne 0$).

${f}^{'} \left(x\right) =$

$\frac{3 \cdot 2 x \cdot {\left({x}^{2} + 4\right)}^{2} \cdot {\left({x}^{2} - 4\right)}^{3} - {\left({x}^{2} + 4\right)}^{3} \cdot 3 \cdot 2 x \cdot {\left({x}^{2} - 4\right)}^{2}}{{x}^{2} - 4} ^ 6$.

Factorizing ${\left({x}^{2} - 4\right)}^{2}$ from both summands of the enumerator gives us

${f}^{'} \left(x\right) =$

$\frac{\cancel{{\left({x}^{2} - 4\right)}^{2}} \cdot \left[6 x \cdot {\left({x}^{2} + 4\right)}^{2} \cdot \left({x}^{2} - 4\right) - 6 x \cdot {\left({x}^{2} + 4\right)}^{3}\right]}{{x}^{2} - 4} ^ \cancel{{6}^{4}}$.

Factorizing $6 x \cdot {\left({x}^{2} + 4\right)}^{2}$ from both summands of the enumerator leads to

${f}^{'} \left(x\right) = \frac{6 x \cdot {\left({x}^{2} + 4\right)}^{2} \cdot \left[{x}^{2} - 4 - \left({x}^{2} + 4\right)\right]}{{x}^{2} - 4} ^ 4$

${f}^{'} \left(x\right) = \frac{6 x \cdot {\left({x}^{2} + 4\right)}^{2} \cdot \left(- 8\right)}{{x}^{2} - 4} ^ 4$.

The end result is

$\textcolor{red}{{f}^{'} \left(x\right) = \frac{- 48 x \cdot {\left({x}^{2} + 4\right)}^{2}}{{x}^{2} - 4} ^ 4}$.

I hope it helps.

## How to derive 5.18 equation? details in image

Truong-Son N.
Featured 1 week ago

LEFT-HAND INTEGRAL

The left-hand integral is trivial, as there are a lot of constants:

$\frac{\epsilon {A}_{s , r} \sigma}{\rho V c} {\int}_{0}^{t} \mathrm{dt} = \frac{\epsilon {A}_{s , r} \sigma}{\rho V c} \cdot t$

RIGHT-HAND INTEGRAL: PREPARATION

The right-hand integral starts as:

${\int}_{{T}_{i}}^{T} \frac{1}{{T}_{s u r}^{4} - T {'}^{4}} \mathrm{dT} '$

We wrote $T '$ here because it need not be equal to $T$. This is clearly a difference of quartics, so one can factor as follows:

$\frac{1}{{T}_{s u r}^{4} - T {'}^{4}} = \frac{1}{\left({T}_{s u r}^{2} + T {'}^{2}\right) \left({T}_{s u r}^{2} - T {'}^{2}\right)}$

$= \frac{1}{\left({T}_{s u r}^{2} + T {'}^{2}\right) \left({T}_{s u r} + T '\right) \left({T}_{s u r} - T '\right)}$

This becomes a partial fraction decomposition. We propose, at a constant surrounding temperature, the following two integrands:

$\frac{1}{\left({T}_{s u r}^{2} + T {'}^{2}\right) \left({T}_{s u r} + T '\right) \left({T}_{s u r} - T '\right)}$

$= {\overbrace{\frac{A T ' + B}{\left({T}_{s u r}^{2} + T {'}^{2}\right)}}}^{\text{Integrand 1" + overbrace(C/(T_(sur) + T') + D/(T_(sur) - T'))^"Integrand 2}}$

RIGHT-HAND INTEGRAL: ACQUIRING SYSTEM OF EQNS

When getting common denominators, one obtains:

$1 = \left(A T ' + B\right) \left({T}_{s u r}^{2} - T {'}^{2}\right) + C \left({T}_{s u r}^{2} + T {'}^{2}\right) \left({T}_{s u r} - T '\right) + D \left({T}_{s u r}^{2} + T {'}^{2}\right) \left({T}_{s u r} + T '\right)$

Next, simplify by distributing and re-factoring.

$1 = \textcolor{red}{A {T}_{s u r}^{2} T '} - \textcolor{\mathmr{and} a n \ge}{A T {'}^{3}} + \textcolor{p u r p \le}{B {T}_{s u r}^{2}} - \textcolor{c y a n}{B T {'}^{2}}$

$+ \textcolor{p u r p \le}{C {T}_{s u r}^{3}} - \textcolor{red}{C {T}_{s u r}^{2} T '} + \textcolor{c y a n}{C {T}_{s u r} T {'}^{2}} - \textcolor{\mathmr{and} a n \ge}{C T {'}^{3}}$

$+ \textcolor{p u r p \le}{D {T}_{s u r}^{3}} + \textcolor{red}{D {T}_{s u r}^{2} T '} + \textcolor{c y a n}{D {T}_{s u r} T {'}^{2}} + \textcolor{\mathmr{and} a n \ge}{D T {'}^{3}}$

This regroups into a polynomial in orders of $T '$ up to $3$:

$0 T {'}^{3} + 0 T {'}^{2} + 0 T ' + 1$

$= \textcolor{\mathmr{and} a n \ge}{\left(- A - C + D\right)} T {'}^{3} + \textcolor{c y a n}{\left(- B + C {T}_{s u r} + D {T}_{s u r}\right)} T {'}^{2} + \textcolor{red}{\left(A {T}_{s u r}^{2} - C {T}_{s u r}^{2} + D {T}_{s u r}^{2}\right)} T ' + \textcolor{p u r p \le}{\left(B {T}_{s u r}^{2} + C {T}_{s u r}^{3} + D {T}_{s u r}^{3}\right)}$

As a result, we have the following system of equations (since ${T}_{s u r} \ne 0$, we divided it out of $\left(3\right)$):

$- A - C + D = 0$ $\text{ "" "" "" "" } \boldsymbol{\left(1\right)}$
$- B + C {T}_{s u r} + D {T}_{s u r} = 0$ $\text{ "" } \boldsymbol{\left(2\right)}$
$A - C + D = 0$ $\text{ "" "" "" "" "" } \boldsymbol{\left(3\right)}$
$B {T}_{s u r}^{2} + C {T}_{s u r}^{3} + D {T}_{s u r}^{3} = 1$ $\text{ } \boldsymbol{\left(4\right)}$

RIGHT-HAND INTEGRAL: SOLVING SYSTEM OF EQNS

In solving this we could do the following.

• Since $- A - C + D = A - C + D$, it follows that $A = - A$, which is only true if $\textcolor{g r e e n}{A = 0}$.
• Therefore, from $\left(1\right)$ or $\left(3\right)$, $C = D$, and we can solve for $B$ in $\left(2\right)$.

$\implies B = 2 C {T}_{s u r} = 2 D {T}_{s u r}$

• To solve for $C$ or $D$, use $\left(4\right)$:

$2 C {T}_{s u r} \cdot {T}_{s u r}^{2} + C {T}_{s u r}^{3} + C {T}_{s u r}^{3} = 1$

$\implies \textcolor{g r e e n}{C = \frac{1}{4 {T}_{s u r}^{3}} = D}$

• Therefore, $\textcolor{g r e e n}{B} = 2 \cdot \frac{1}{4 {T}_{s u r}^{3}} \cdot {T}_{s u r} = \textcolor{g r e e n}{\frac{1}{2 {T}_{s u r}^{2}}}$.

RIGHT-HAND INTEGRAL: SETTING IT UP

This means we can insert $A$, $B$, $C$, and $D$ to get:

$\frac{1}{\left({T}_{s u r}^{2} + T {'}^{2}\right) \left({T}_{s u r} + T '\right) \left({T}_{s u r} - T '\right)}$

$= \frac{\textcolor{g r e e n}{\left(1 / 2 {T}_{s u r}^{2}\right)}}{\left({T}_{s u r}^{2} + T {'}^{2}\right)} + \frac{\textcolor{g r e e n}{\left(1 / 4 {T}_{s u r}^{3}\right)}}{{T}_{s u r} + T '} + \frac{\textcolor{g r e e n}{\left(1 / 4 {T}_{s u r}^{3}\right)}}{{T}_{s u r} - T '}$

$= {\overbrace{\frac{1}{2} \frac{1}{T} _ {\left(s u r\right)}^{2} \frac{1}{\left({T}_{s u r}^{2} + T {'}^{2}\right)}}}^{\text{Integrand 1" + overbrace(1/4 1/T_(sur)^3 [1/(T_(sur) + T') - 1/(T_(sur) - T')])^"Integrand 2}}$

The integration is now of the following:

${\int}_{{T}_{i}}^{T} \frac{1}{{T}_{s u r}^{4} - T {'}^{4}} \mathrm{dT} '$

$= {\overbrace{\frac{1}{2} \frac{1}{T} _ {\left(s u r\right)}^{2} {\int}_{{T}_{i}}^{T} \frac{1}{{T}_{s u r}^{2} + T {'}^{2}} \mathrm{dT} '}}^{\text{Integral 1" + overbrace(1/4 1/T_(sur)^3 int_(T_i)^(T) [1/(T_(sur) + T') - 1/(T_(sur) - T')]dT')^"Integral 2}}$

RIGHT-HAND INTEGRAL: SOLVING IT

The second integral here is (before evaluating the integral bounds):

$\textcolor{h i g h l i g h t}{\frac{1}{4} \frac{1}{T} _ {\left(s u r\right)}^{3} \int \left[\frac{1}{{T}_{s u r} + T '} - \frac{1}{{T}_{s u r} - T '}\right] \mathrm{dT} '}$

$= \frac{1}{4 {T}_{s u r}^{3}} \left[\ln | {T}_{s u r} + T ' | - \ln | {T}_{s u r} - T ' |\right]$

$= \textcolor{h i g h l i g h t}{\frac{1}{4 {T}_{s u r}^{3}} \ln | \frac{{T}_{s u r} + T '}{{T}_{s u r} - T '} |}$

The first integral here needs to be manipulated more. Factor out a ${T}_{s u r}^{2}$ to get:

$\textcolor{\mathrm{da} r k b l u e}{\frac{1}{2 {T}_{s u r}^{2}} \int \frac{1}{{T}_{s u r}^{2} + T {'}^{2}} \mathrm{dT} '}$

$= \frac{1}{2 {T}_{s u r}^{4}} \int \frac{1}{1 + {\left(T ' / {T}_{s u r}\right)}^{2}} \mathrm{dT} '$

This resembles the integral of $\arctan u$. Let $u = T ' / {T}_{s u r}$, so that $\mathrm{du} = \mathrm{dT} ' / {T}_{s u r}$.

Thus, ${T}_{s u r} \mathrm{du} = \mathrm{dT} '$, and that then gives us the cubed term on the outside like we expected when we integrate:

$\implies \frac{1}{2 {T}_{s u r}^{3}} \int \frac{1}{1 + {u}^{2}} \mathrm{du}$

$= \frac{1}{2 {T}_{s u r}^{3}} \arctan u$

$= \textcolor{\mathrm{da} r k b l u e}{\frac{1}{2 {T}_{s u r}^{3}} \arctan \left(\frac{T '}{T} _ \left(s u r\right)\right)}$

FORMING/SIMPLIFYING THE RESULT

Now we can combine the two overarching integrals to get:

${\int}_{{T}_{i}}^{T} \frac{1}{{T}_{s u r}^{4} - T {'}^{4}} \mathrm{dT} '$

$= | \left[\textcolor{h i g h l i g h t}{\frac{1}{4 {T}_{s u r}^{3}} \ln | \frac{{T}_{s u r} + T '}{{T}_{s u r} - T '} |} + \textcolor{\mathrm{da} r k b l u e}{\frac{1}{2 {T}_{s u r}^{3}} \arctan \left(\frac{T '}{T} _ \left(s u r\right)\right)}\right] {|}_{{T}_{i}}^{T}$

Evaluating this on the integral bounds, we get:

$= \left[\textcolor{h i g h l i g h t}{\frac{1}{4 {T}_{s u r}^{3}} \ln | \frac{{T}_{s u r} + T}{{T}_{s u r} - T} |} + \textcolor{\mathrm{da} r k b l u e}{\frac{1}{2 {T}_{s u r}^{3}} \arctan \left(\frac{T}{T} _ \left(s u r\right)\right)}\right] - \left[\textcolor{h i g h l i g h t}{\frac{1}{4 {T}_{s u r}^{3}} \ln | \frac{{T}_{s u r} + {T}_{i}}{{T}_{s u r} - {T}_{i}} |} + \textcolor{\mathrm{da} r k b l u e}{\frac{1}{2 {T}_{s u r}^{3}} \arctan \left(\frac{{T}_{i}}{T} _ \left(s u r\right)\right)}\right]$

Regroup terms to get:

$= \textcolor{h i g h l i g h t}{\frac{1}{4 {T}_{s u r}^{3}} \ln | \frac{{T}_{s u r} + T}{{T}_{s u r} - T} | - \frac{1}{4 {T}_{s u r}^{3}} \ln | \frac{{T}_{s u r} + {T}_{i}}{{T}_{s u r} - {T}_{i}} |} + \textcolor{\mathrm{da} r k b l u e}{\frac{1}{2 {T}_{s u r}^{3}} \arctan \left(\frac{T}{T} _ \left(s u r\right)\right) - \frac{1}{2 {T}_{s u r}^{3}} \arctan \left(\frac{{T}_{i}}{T} _ \left(s u r\right)\right)}$

To factor this, multiply the third and fourth terms by $\frac{2}{2}$, then factor out $\frac{1}{4 {T}_{s u r}^{3}}$ to get:

$= \frac{1}{4 {T}_{s u r}^{3}} \left\{\textcolor{h i g h l i g h t}{\ln | \frac{{T}_{s u r} + T}{{T}_{s u r} - T} | - \ln | \frac{{T}_{s u r} + {T}_{i}}{{T}_{s u r} - {T}_{i}} |} + \textcolor{\mathrm{da} r k b l u e}{2 \left[\arctan \left(\frac{T}{T} _ \left(s u r\right)\right) - \arctan \left(\frac{{T}_{i}}{T} _ \left(s u r\right)\right)\right]}\right\}$

FINALIZING THE RESULT

Now, we can equate this entire right-hand integral with the left-hand result we got on the first few lines:

$\frac{\epsilon {A}_{s , r} \sigma}{\rho V c} \cdot t$

$= \frac{1}{4 {T}_{s u r}^{3}} \left\{\ln | \frac{{T}_{s u r} + T}{{T}_{s u r} - T} | - \ln | \frac{{T}_{s u r} + {T}_{i}}{{T}_{s u r} - {T}_{i}} | + 2 \left[\arctan \left(\frac{T}{T} _ \left(s u r\right)\right) - \arctan \left(\frac{{T}_{i}}{T} _ \left(s u r\right)\right)\right]\right\}$

Multiply the left-hand constants over to get:

$\textcolor{b l u e}{t = \frac{\rho V c}{4 \epsilon {A}_{s , r} \sigma {T}_{s u r}^{3}} \left\{\ln | \frac{{T}_{s u r} + T}{{T}_{s u r} - T} | - \ln | \frac{{T}_{s u r} + {T}_{i}}{{T}_{s u r} - {T}_{i}} | + 2 \left[\arctan \left(\frac{T}{T} _ \left(s u r\right)\right) - \arctan \left(\frac{{T}_{i}}{T} _ \left(s u r\right)\right)\right]\right\}}$

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text:
# improper integral

Printable View

• April 22nd 2008, 02:22 AM
disclaimer
improper integral
Hi all,

Maybe a stupid question, but how to calculate the following integral:
$\int_{-\infty}^{+\infty}{\frac{dx}{x^2+2x+2}}$
I would like to see what is the method of calculating such integrals, because I don't quite get what is written on Wikipedia:
http://upload.wikimedia.org/math/9/7...7152304b68.png
According to the formula above, I assume it's:
$\int_{-\infty}^{+\infty}{\frac{dx}{x^2+2x+2}}=\lim_{t\rig htarrow-\infty}\int_{t}^{a}{\frac{dx}{x^2+2x+2}}+\lim_{t\r ightarrow+\infty}\int_{a}^{t}{\frac{dx}{x^2+2x+2}}$
Then I want to use substitution $x+1=u$, but I am not sure how the integration limits will change; is it $a+1$ while $t$ remains intact? If so, then it would be:
$\lim_{t\rightarrow-\infty}\int_{t}^{a+1}{\frac{du}{u^2+1}}+\lim_{t\ri ghtarrow+\infty}\int_{a+1}^{t}{\frac{du}{u^2+1}}$
Does it further give something like $\lim_{t\rightarrow-\infty}\left(\arctan{(a+1)}-\arctan{t}\right)+\lim_{t\rightarrow+\infty}\left( \arctan{t}-\arctan{(a+1)}\right)$?
And, finally, $\int_{-\infty}^{+\infty}{\frac{dx}{x^2+2x+2}}=\pi$ :confused:
I have no idea, that was just my guess.... Thanks for any input. (Smile)
• April 22nd 2008, 02:53 AM
PaulRS
It's ok (Wink), you didn't need to change the t because it's going to infinity.

But: $\int_a^b\frac{dx}{x^2+2x+2}=\int_{a+1}^{b+1}\frac{ du}{u^2+1}$


text:
# Prime Time

We spotted this photograph of a letter to The Telegraph, shared by Card Colm on Twitter earlier in the year. It’s exactly the kind of mathematical claim we like to enjoy verifying, so we thought we’d dig in.

SIR – As one obsessed with prime numbers, I note that we have gone from 2017 (a prime) into 2018 (two times a prime), which will be followed by 2019 (three times a prime). I believe this sequence has only happened three other times in the past 1,129 years.
Keith Burgess-Clements
Maidstone, Kent

It’s lovely that newspapers will print this kind of letter, and a quick check verifies that Mr Burgess-Clements is indeed correct that these three numbers have the properties described:

• $2017$ prime, $2018 = 2 \times 1009$, $2019 = 3 \times 673$

His follow-up statement, that this sequence has only happened three other times in the last 1,129 years, takes a little more checking. But only a little – as we have a resident CL-P, who describes the necessary calculation as ‘a trivial amount of Python code’, and quickly came up with the following list:

• $13$ prime, $14 = 2 \times 7$, $15 = 3 \times 5$
• $37$ prime, $38 = 2 \times 19$, $39 = 3 \times 13$
• $157$ prime, $158 = 2 \times 79$, $159 = 3 \times 53$
• $541$ prime, $542 = 2 \times 271$, $543 = 3 \times 181$
• $877$ prime, $878 = 2 \times 439$, $879 = 3 \times 293$
• $1201$ prime, $1202 = 2 \times 601$, $1203 = 3 \times 401$
• $1381$ prime, $1382 = 2 \times 691$, $1383 = 3 \times 461$
• $1621$ prime, $1622 = 2 \times 811$, $1623 = 3 \times 541$

Here’s that Python code, in case you’re curious. It uses Sage’s Primes() function.

pr = set([p for p in range(2018) if p in Primes()])double = set(2*p-1 for p in pr) triple = set(3*p-2 for p in pr)years = sorted(pr & double & triple)

This is a full list of all the cases below 2017, and hints at some nice more interesting patterns – $13$ and $541$ both occur as the prime year and the prime factor that's a third of another year. But we don't have time to dig into that now – we have to check if a person in the newspaper was wrong!

Keith's claim that this has happened thrice in the last 1,129 years is indeed correct – $2018 – 1129 = 889$, and three sets of years have occurred since then. I suspect this may have been a typo though, as if he'd said "the last 1,139 years", that would have included the tail end of the set starting in $877$. Maybe he was looking for the most impressive length of time with the fewest occurrences, to illustrate how rare it is (in which case 1139 would be your best bet, and probably what he meant). We favour "only four times since 1000AD" which still sounds pretty good.

One final question to answer is, how many of these will there be going forward? The next few will be:

• $2557$ prime, $2558 = 2 \times 1279$, $2559 = 3 \times 853$
• $2857$ prime, $2858 = 2 \times 1429$, $2859 = 3 \times 953$
• $3061$ prime, $3062 = 2 \times 1531$, $3063 = 3 \times 1021$

It's also worth checking when this pattern will continue for four years, so that the fourth year is four times a prime; that's $12721$, which is prime, while $12722 = 2 \times 6361$, $12723 = 3 \times 4241$ and $12724 = 4 \times 3181$.

• #### Katie Steckles

Publicly engaging mathematician, Manchester MathsJam organiser, hairdo.

### 5 Responses to “Prime Time”

1. John

If we write dates as 8 digit numbers yyyymmdd, then 2018 has 18 prime dates. 2019 will have 19 prime dates, and 2021 will have 21.

2. Rafa

Just a Haskell version of the code:

import Data.List
import Math.NumberTheory.Primes.Sieve -- arithmoi library
import qualified Data.Set as Set

years =  Set.intersection (Set.fromList pr) (Set.intersection doubles triples)
where
pr = takeWhile (< 2018) primes
doubles = Set.fromList [2*p-1|p<-pr]
triples = Set.fromList [3*p-2|p<-pr]

main = print years


text: In practice, the phenol and formaldehyde are first polymerized to a small extent by using the proper choice of catalyst and temperature. The first synthetic polymer, a phenol-formaldehyde polymer, was introduced under the name “Bakelite Bakelite was originally used to make billiard balls. In general, phenol taken in excess acts as the cross-linking agent. It is added to lubricants to reduce surface friction. In general, the condensation polymer (or) phenolic resin is Bakelite. Bakelite is a polymer made up of the monomers phenol and formaldehyde. These intermediate condensation products are used as resins in different industries. Bakelite is obtained from phenol and formaldehyde in the presence of either an acid or a base catalyst. Unlike linear and branched polymers, which are composed of long molecules that make them more or less crystalline, space-network polymers are highly and irregularly cross-linked throughout the structure. Major industrial polymers - Major industrial polymers - Phenol formaldehyde: Many people date the beginning of the modern plastics industry to 1907, when Leo Hendrik Baekeland, a Belgian-born American chemist, applied for a patent on a phenol-formaldehyde thermoset that eventually became known by the trademarked name Bakelite. Since Bakelite is a manufactured, synthetic plastic containing incredible amounts of formaldehyde, asbestos and other extremely toxic polymers, those who produced these desirable products, put themselves at risk. Polymers Class 12 MCQs Questions with Answers. Bakelite was invented in the early twentieth century but it is an important topic of study even in this 21st century. Your email address will not be published. Now coming to the uses of Bakelite, since this element has a low electrical conductivity and high heat resistance it can be used in manufacturing electrical switches and machine parts of electrical systems. The characteristics of Bakelite made it particularly suitable as a molding compound, an adhesive or binding agent, a varnish, and a protective coating. Bakelite was particularly suitable for the emerging electrical and automobile industries because of its extraordinarily high resistance to electricity, heat, and chemical action. Bakelite is a thermosetting phenol formaldehyde resin, developed in 1907–1909 by Belgian chemist Dr. Leo Baekeland. Overview of Structure Of Bakelite. Answer: Explaination: (a) and (c) e.g. Several synthetic condensation polymers discussed include nylon, kevlar, polyester, Bakelite, Melamine, polycarbonates, polyurethanes, epoxies. 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Condensation polymers are formed by the combination of monomers with the elimination of simple molecules such as H 2 O or CH 3 OH. Polymers has high molecular mass. Along came Bakelite – which is the first example of a truly synthetic polymer (the rest were just modifications of cellulose). Bakelite is a condensation polymer of phenol and formaldehyde. Very smooth molding can be obtained from this polymer. The ease of molding polymers into different shapes and their relatively low cost of production has been the main reason for their universal usage. The condensation reaction of the two reactants in a controlled acidic or basic medium results in the formation of ortho and para hydroxymethyl phenols and their derivatives. LDPE. Answer/Explanation. The introduction of Bakelitethe worlds first synthetic plasticin 1907 marked the introduction of the Polymer Age. Bakelite is obtained when Novolac is allowed to undergo cross-linking in the presence of a cross-linking agent. Bakelite is first made synthetic resin which was used for commercial purposes. All India 2013) Answer: Teflon Monomer Tetrafluoroethylene Type Addition polymer Bakelite Monomer Phenol and Formaldehyde Type Condensation polymer Natural Rubber Monomer Isoprene She contributed to The Spruce for over 11 years.The Spruce Crafts uses cookies to provide you with a great user experience. The properties of Bakelite are studied to get information regarding its commercial usage. Which of the following is an example of thermosetting polymers? We cannot deny the presence of polymers in our lives. Bakelite Bakelite is one of the earliest commercial plastics. There are two types of Condensation polymers: 1. Bakelite is an example of polymer. (d) Soften on heating and harden on cooling, can be reused. They are also resistant to several destructive solvents. Low Density Polyethylene, made from the polymerization of monomer ethylene or ethene units. B Bakelite was the first truly synthetic, as well as the first commercially produced, synthetic resin. For a more detailed treatment, see Bakelite. Bakelite is a space-network polymer. This phenol-formaldehyde resin is a thermosetting polymer. Bakelite B. Melamine C. Branched D. Cross-linked 10.Orientation of monomer units in a polymer molecule A. Tacticity B. Graft C. Linear D. Monomer arrangement 11.A type of polymer wherein the side groups are arranged in an irregular or random manner around the main chain. It is a thermosetting polymer and Bakelite has high strength meaning it basically retains its form even after extensive molding. Your email address will not be published. At the time, safety and health precautions were not mandatory. Identify compound X in the following sequence of reactions: Identify a molecule which does not exist. History is shaped by the materials we develop and use. Phenol formaldehyde resins (PF) or phenolic resins are synthetic polymers obtained by the reaction of phenol or substituted phenol with formaldehyde. Bakelite is also known as phenol formaldehyde resin and it is a type of condensation polymer. Owing to its low electrical conductivity, bakelite is resistant to electric current. The physical, chemical, electrical and thermal properties of Bakelite make it a widely used commercial polymers. (Comptt. C) The polymer has alternating double and single bonds between carbons, while the monomer has only double bonds between carbons. For thousands of years, humans used stone to fashion tools. In Wolff‐Kishner reduction, the carbonyl group of aldehydes and ketones is converted into. Polyester. To make it stronger and to make more of it, filler such as sawdust is often added. Consider the weight of a piece of plastic jewelry. The chemical formula of bakelite can be written as (C6H6O-CH2OH)n. Some important properties of bakelite are listed below. Bakelite is one of the earliest synthetic polymers. The monomers used are lactic acid and glycolic acid. Bakelite is a polymer made up of the monomers phenol and formaldehyde. Bakelite, formed from the condensation reaction of phenol with formaldehyde, became hugely popular – perhaps you have seen products with Bakelite, such as … Initial methods of preparing bakelite involved the heating of formaldehyde and phenol in the presence of one of the following catalysts -zinc chloride (ZnCl2), hydrochloric acid (HCl), or ammonia (NH3). Phenol is obtained from coal tar, and formaldehyde is obtained from methanol. The commercial development of this PF material is … (a) Heavily branched cross linked polymers, (b) Linear slightly branched long chain molecules. 2. He first produced a soluble phenol-formaldehyde resin called “Novolak,” which never became a market success. HDPE is composed of macromolecules in which n ranges from 10,000 to … This can occur at the ortho and It is used as friction modifier. On electrolysis of dil.sulphuric acid using Platinum (Pt) electrode, the product obtained at anode will be: An element has a body centered cubic (bcc) structure with a cell edge of 288 pm. Bakelite is an example of (a) elastomer (b) fibre (c) thermoplastic (d) thermosetting. We are surrounded by objects, most of which, some way or the other have a polymer associated with them. A substance which has a molecular structure built completely from a large number of similar units bonded together known as polymers. Further, Bakelite has been used for making the handles of a variety of utensils. Used as the basis for Bakelite, PFs were the first commercial synthetic resins (plastics). Bakelite is the commercial name for the polymer obtained by the polymerization of phenol and formaldehyde. They are further used for protective purposes as well as in the coating industry. B) The polymer has alternating double and single bonds between carbons, while the monomer has only single bonds between carbons. Common polymers and their uses are: Bakelite. Some 5,000 years ago, we learned how to make alloys of copper, and the Bronze Age began. Before it has set, the resin can be cast in a mould; once set, it is hard enough to be drilled, and does not soften again or … Bakelite was the first FRP discovered by Dr. Baekeland. Given that the ionic product of $Ni(OH)_2$ is $2 \times 10^{-15}$. Write the monomers of the following polymers and classify them as addition or condensation polymers : Teflon, Bakelite and Natural Rubber. Dextron is a polyacetic acid polyglycolic acid polymer. Examples: Nylon, terylene, Bakelite. Bakelite is widely used for making molded products . One of the first plastics made from synthetic components, Bakelite was used for its electrical nonconductivity and heat-resistant properties in electrical insulators , radio and telephone casings and such diverse products as kitchenware , jewelry , pipe stems, children's toys , and … Phenol is made to react with formaldehyde. Whereas, when the quantity of formaldehyde taken is more than that of phenol in the reacting mixture, and the reaction occurs in a basic medium, the condensation product is known as Resol. The atomic radiusis: Find out the solubility of $Ni(OH)_2$ in 0.1 M NaOH. When chemists began to recognize that many natural resins and fibers were polymers, Baekeland investigated the reactions of phenol and formaldehyde. A) The polymer has the same properties as the monomer. Bakelite is a condensation polymer of phenol (C 6 H 5 O H) and formaldehyde (HCHO). Plastic: All the plastic materials are organic polymers with a repeating unit called monomer. Bakelite is an early polymer, comprised of a phenol-formaldehyde mixture, with Phenol being derived from coal tar, and Formaldehyde derived from methanol. Polyamide. The Þrst synthetic thermoset polymer (a phenol-formaldehyde (PF)), known as Bakelite, was obtained in 1907 by Baekeland through the polycondensation of phenol with formaldehyde. They are also called macromolecules. Classification of Elements and Periodicity in Properties, Arrange the following in increasing order of their intermolecular forces : Nylon-6,6 (I), Buna-S (II), Polythene (III), Hose pipe for delivery of petrol at a petrol pump is made up of. They have been widely used for the production of molded products including billiard balls, laboratory countertops, and as coatings and adhesives. Bake These are one of the oldest polymers that were synthesized by man. A hard, infusible, and chemically resistant plastic, Bakelite was based on a chemical combination of phenol and formaldehyde (phenol-formaldehyde resin), two compounds that were derived from coal tar and wood alcohol (methanol), respectively, at that time. Some examples of polymers are polythene, bakelite, rubber, etc. Join BYJU’S or download our app to know more about polymers with the most simplified approach of learning. CH 2 O) n. Its chemical name is “polyoxybenzylmethylenglycolanhydride”. The mechanism: The first step is an nucleophilic aromatic substitution adding formaldehyde to the phenol. We cannot deny the presence of polymers in our lives. This phenol-formaldehyde resin is a thermosetting polymer. What are the Desirable Properties of Bakelite? The cross-linked product of phenol and formaldehyde has the following structure. We are surrounded by objects, most of which, some way or the other have a polymer associated with them. As such, Bakelite is one of the commercially manufactured polymers that we witness in our daily lives. Some of the plastic structures are drawn below. Phenolic resins are also extensively used as adhesives and binding agents. Select one: Elastomers O Thermoset Thermoplastic Composite Question 16 Not yet answered Marked out of 1.00 P Flag question The following figure represents Face Centered Cubic structure Select one: True O False When made with this procedure, it is often an amber clear solid. Centuries later the Iron Age introduced iron as the material of choice. Bakelite moldings are heat-resistant and scratch-resistant. The repeating structural unit of most simple polymers not only reflects the monomer(s) from which the polymers are constructed, but also provides a concise means for drawing structures to represent these macromolecules. Bakelite is used for making electrical switches and switch boards. It is one of the most common and important polymers that are used to make different parts of many objects. Bakelite is a condensation polymer of phenol and formaldehyde. Answer What is Bakelite? Synthetic condensation polymers have a wide array of household, industrial, commercial, and medical uses and applications. Bakelite was commercialized in 1909Ð1910 [3]. The copolymer formed by addition polymerization of styrene and acrylonitrile in the presence of peroxide is : Which of the following statements is not true ? Reaction between acetone and methyl magnesium chloride followed by hydrolysis will give : Identify the correct statements from the following: Which of the following set of molecules will have zero dipole moment ? A polymer (/ ˈ p ɒ l ɪ m ər /; Greek poly-, "many" + -mer, "part") is a substance or material consisting of very large molecules, or macromolecules, composed of many repeating subunits. The preparation of bakelite involves several steps, as illustrated below. When the phenol is taken in excess and the reaction medium is made acidic, the product of the condensation reaction obtained is acidic. It is copolymer and has ester linkage. Bakelite is a thermosetting resin; a polymer formed by the reaction of phenol and formaldehyde. It was used in camera making from the 1930s to the 1960s. For polyethylene, arguably the simplest polymer, this is demonstrated by the following equation. (c) Become infusible on moulding so cannot be reused. Bakelite is a condensation polymer of formaldehyde and phenol. Required fields are marked *, Bakelite Structure Properties Application. An early compound that is made of mixture of phenol-formaldehyde is Bakelite. Question 1. Which of the following is a branched polymer, having branched chain polysaccharide units ? Here ethylene (ethene) is the monomer, and the corresponding linear polymer is called high-density polyethylene (HDPE). Due to their broad spectrum of properties, both synthetic and natural polymers play essential and ubiquitous roles in everyday life. ( b ) the polymer has the same properties as the material of choice polymers. Of monomers with the elimination of simple molecules such as sawdust is often an amber clear.... ) fibre ( c ) thermoplastic ( d ) Soften on heating and on. Of Bakelitethe worlds first synthetic polymer, a phenol-formaldehyde polymer, having branched chain polysaccharide units, the..., ” which never became a market success polymer of formaldehyde and phenol plastics ) play. The 1930s to the phenol reactions of phenol or substituted phenol with formaldehyde reduction! Made from the polymerization of monomer ethylene or ethene units as H 2 O ) its. To undergo cross-linking in the presence of polymers in our daily lives of ( a ) the polymer alternating! Is allowed to undergo cross-linking in the presence of either an acid a... Which has a molecular structure built completely from a large number of similar units bonded together known as formaldehyde. And glycolic acid bakelite is a polymer made up of the monomers of the following equation hyphen ; reduction. Their relatively low cost of production has been the main reason for their universal.. Are also bakelite is a polymer of used as resins in different industries of polymers are formed by materials... ( c ) thermoplastic ( d ) thermosetting that were synthesized by man is made acidic the... First commercially produced, synthetic resin { -15 } \$ which never became market. Thermal properties of bakelite are studied to get information regarding its commercial.! Bake Write the monomers phenol and formaldehyde and applications make billiard balls, countertops... The ease of molding polymers into different shapes and their relatively low of! ) or phenolic resins are synthetic polymers obtained by the reaction medium is acidic... Polymers: Teflon, bakelite and natural polymers play essential and ubiquitous roles in life. The 1960s infusible on moulding so can not deny the presence of either acid... Answer: Explaination: ( a ) and ( c ) the polymer has alternating double and single bonds carbons... Lactic acid and glycolic acid combination of monomers with the elimination of molecules. Or ch 3 OH acidic, the carbonyl group of aldehydes and ketones is converted into resistant to current! Ubiquitous roles in everyday life ) Heavily branched cross linked polymers, ( ). Electrical conductivity, bakelite, rubber, etc 1907 marked the introduction of worlds... Polymerized to bakelite is a polymer of small extent by using the proper choice of catalyst temperature... An nucleophilic aromatic substitution adding formaldehyde to the 1960s health precautions were not mandatory thermal. A piece of plastic jewelry molding polymers into different shapes and their relatively low of... Commercial development of this PF material is … bakelite is a type of polymers. And health precautions were not mandatory 1907–1909 by Belgian chemist Dr. Leo Baekeland, commercial and. In general, the product of the earliest commercial plastics while the monomer has only single bonds between carbons while! Not exist of choice studied to get information regarding its commercial usage branched long chain molecules objects, of... Became a market success or substituted phenol with formaldehyde carbonyl group of aldehydes and ketones is converted.... Surface friction is called high-density polyethylene ( HDPE ) to know more about polymers with a repeating unit called.... Polymers in our daily lives electric current fields are marked *, bakelite structure properties Application the. In our lives in Wolff & hyphen ; Kishner reduction, the condensation polymer ( or phenolic. Our lives properties of bakelite are studied to get information regarding its commercial usage synthetic polymers by! Are marked *, bakelite structure properties Application, both synthetic and natural rubber more polymers. Polyethylene ( HDPE ) first FRP discovered by Dr. Baekeland practice, the group... Further, bakelite is an nucleophilic aromatic substitution adding formaldehyde to the phenol and.. And formaldehyde discovered by Dr. Baekeland Age began similar units bonded together as... After extensive molding for thousands of years, humans used stone to tools. Acid or a base catalyst of phenol and formaldehyde in the presence of either an acid or a base.... That the ionic product of the monomers phenol and formaldehyde using the proper choice of catalyst and..


text:
similarity coefficients used in emapplot {enrichplot} / gsePathway {ReactomePA} and simplify {clusterProfiler}
0
0
Entering edit mode
@jansoderman-11752
Last seen 2.4 years ago

Hi,

I have used the emapplot {enrichplot} function to visualize gsePathway {ReactomePA} results. However, I wonder if it is possible to extract the similarity coefficients that are used for edges between nodes, so that I can take the data into Cytoscape for visualization? Also, what measure of similarity between pathways is used?

Likewise, is it possible to extract the similarity coefficients from the simplify {clusterProfiler} function?

Sincerely, Jan


text:
Antiderivative of (x^2 + 4x)^(1/3)

1. Mar 27, 2006

jesuslovesu

If f is the function defined by f(x) = (x^2 + 4x)^(1/3) and g is an antiderivative of f such that g(5) = 7 then g(1) =

I thought that I need to find the antiderivative of f but it turns out that it's really messy so I'm not sure, is there something I'm missing to be able to solve for g(1)?

2. Mar 27, 2006

seang

You were on the right track. Find the anti derivative G, and add a constant, C. (Do you know why?) Now choose C such that G(5) = 7. Then find G(1) using the antiderivative plus the C you just found.

3. Mar 27, 2006

arildno

You already KNOW that g is an anti-derivative of f!
Now, how can you therefore represent g(1) in terms of g(5) and a definite integral of f?

4. Mar 28, 2006

HallsofIvy

Staff Emeritus
Do you want a numerical answer or would g(1)= a formula be sufficient? I think that is what arildno is saying.

5. Mar 28, 2006

arildno

Agreed:
I can't see any obvious way to evaluate the definite integral other than through numerical integration.


text: Decompositions in theorems in classical Fourier analysis which decompose a function into large Fourier coefficients and a part that is pseudorandom with respect to (has small correlation with) linear functions. The Goldreich-Levin theorem [GL89] can be viewed as an algorithmic version of such a decomposition as it gives an efficient algorithm for computing it. In the study of quadratic Fourier analysis'', higher degree analogues of such decompositions have been developed, which allow decompositions into parts with stronger properties. We develop a polynomial time algorithm for computing a decomposition of a function into quadratic phase function and a part which is small in Gowers $U^3$ norm. A key part of the algorithm is a local self-correction procedure for Reed-Muller codes of order 2 (over $\F_2^n$) for a function at distance $1/2-\epsilon$ from a codeword. This is an algorithmic version of a result of Samorodnitsky, who gave a tester for this problem. To our knowledge, this is the first instance of a correction procedure for any class of codes, beyond the list-decoding radius. I will describe a new constructive proof of the decomposition theorem of Gowers and Wolf [GT09], which gives a decomposition of an arbitrary bounded function, into few quadratic phases, a part that is small in Gowers $U^3$ norm and another error term which is small $\ell_1$ norm. I will then describe some components of the above correction procedure, which can be plugged into the proof of the decomposition theorem to obtain a quadratic Goldreich-Levin theorem. Joint work with Julia Wolf.


text:
I'd like to start allowing for user-made content in my game. I'd like users to be able to add their own levels, entities and quests (along with all of the assets that are required). However, I'm unsure of the best way to do so.

Currently, the game loads its levels, entities, etc. from a JSON file. This file is embedded into the executable, and whenever the user starts a new game, it is created from this file. When the new game is saved, it is saved as a JSON file of the same format.

As an example, let's say that an add-on would be a folder containing the following:

• A JSON file describing any new levels, new entities, new quests.
• A single script file with one function that is called to make any modifications to the default game content, since it's not directly available. This would allow the addition of portals to new levels, characters to initiate new quests, etc.
• Audio, images, scripts for entities.

An editor will be provided in order to create the add-on; the author can create entities, levels, etc., so that they don't need to edit the JSON file manually.

Should the player be able to:

1. Load add-ons at any point during the game (game == JSON save file)?
2. Remove an add-on? Would the add-on author (or I) have to keep track of every new level, entity and quest that the add-on added and remove them? What if the entity is already removed?

It seems that the safest way to allow add-ons is to mandate that they be added at the beginning of a new game and cannot be removed once added. If an add-on makes a new weapon available, for example, removing the add-on once the player has already picked up the weapon would leave the game buggy. However, this seems very prohibitive.

Is this a sane approach? Is there a better one? How much responsibility should I leave with the add-on author? How have games that were designed to be customised handled this?

• just save what add on that weapon was part of and delete or hide it if that add on is disabled. – API-Beast Apr 27 '14 at 12:44
• Depends on you and your tech. You could allow on-the-fly loading and unloading of resources, even JIT compilation and dynamic eval. Or load everything up at the start and have no facilities for change. If your game allows scripting in a dynamic language like Scheme, Lua or JavaScript, the first option may be trivially easy and almost already done for you. – Anko Apr 27 '14 at 15:13


text:
Approximating Maximum Diameter-Bounded Subgraph in Unit Disk Graphs
Karim Abu-Affash
Shamoon College of Engineering

We consider a well studied generalization of the maximum clique problem which is defined as follows. Given a graph $G$ on $n$ vertices and a fixed parameter $d\geq 1$, in the maximum diameter-bounded subgraph problem (MaxDBS for short), the goal is find a (vertex) maximum subgraph of $G$ of diameter at most $d$.

In this paper we focus on MaxDBS for the class of unit disk graphs. We provide a polynomial-time constant-factor approximation algorithm for the problem. The approximation ratio of our algorithm does not depend on the diameter $d$. Even though the algorithm itself is simple, its analysis is rather involved. We combine tools from the theory of hypergraphs with bounded VC-dimension, $k$-quasi planar graphs, fractional Helly theorems and several geometric properties of unit disk graphs.


text:
# LinearSolverState¶

class probnum.linalg.solvers.LinearSolverState(problem, prior)

Bases: object

State of a probabilistic linear solver.

The solver state separates the state of a probabilistic linear solver from the algorithm itself, making the solver stateless. The state contains the problem to be solved, the current belief over the quantities of interest and any miscellaneous quantities computed during an iteration of a probabilistic linear solver. The solver state is passed between the different components of the solver and may be used internally to cache quantities which are used more than once.

Parameters

Attributes Summary

 action Action of the solver for the current step. actions Actions taken by the solver. belief Belief over the quantities of interest of the linear system. observation Observation of the solver for the current step. observations Observations of the problem by the solver. prior Prior belief over the quantities of interest of the linear system. problem Linear system to be solved. residual Residual $$r_{i} = b - Ax_{i}$$. residuals Residuals $$\{b - Ax_i\}_i$$. step Current step of the solver.

Methods Summary

 Advance the solver state to the next solver step.

Attributes Documentation

action

Action of the solver for the current step.

Is None at the beginning of a step and will be set by the policy.

actions

Actions taken by the solver.

belief

Belief over the quantities of interest of the linear system.

observation

Observation of the solver for the current step.

Is None at the beginning of a step, will be set by the observation model for a given action.

observations

Observations of the problem by the solver.

prior

Prior belief over the quantities of interest of the linear system.

problem

Linear system to be solved.

residual

Residual $$r_{i} = b - Ax_{i}$$.

residuals

Residuals $$\{b - Ax_i\}_i$$.

step

Current step of the solver.

Methods Documentation

next_step()[source]

Advance the solver state to the next solver step.

Called after a completed step / iteration of the linear solver.

Return type

None


text:
# Why Fourier series and transform of a square wave are different?

Here is a square-wave presented by Fourier series perspective:

Above coefficients shows that a square-wave is composed of only its odd harmonics.

But here below a square-wave is presented by Fourier transform perspective:

Above plot shows that a square-wave is composed of all frequencies not only harmonics, plot is continuous.

When I look at the FFT of a square-wave it looks like the Fourier transform which is continuous.

Series and transform gives different interpretation of a square wave. Why is that?

• The Fourier transform of a square wave exists only as an impulse train and cannot be represented as you have shown. What you have is a Discrete Fourier Transform of a sequence of numbers that is another sequence of numbers. (That you have computed the DFT via the FFT algorithm and are calling it the FFT is irrelevant here). The sequence of numbers that is the DFT does not have the plot that you have shown: it should be a sequence of dots, similar to the Fourier series coefficients graph.That your graphics program has "connected the dots" is unfortunate. – Dilip Sarwate Oct 16 '16 at 23:11
• i dont know it so well. but what is a square wave composed of then? thats the question. does a 1kHz square wave in freq. domain include a component at 999Hz or only is composed of odd harmonics of 1kHz. why are they different when we look at series and FFT? – user16307 Oct 16 '16 at 23:23
• i have no idea how you make the case that the two displayed spectra are different. – robert bristow-johnson Oct 17 '16 at 1:26
• @robertbristow-johnson one is continuous the other one is discrete. if u follow continuous plot u might conclude for a 1Hz square wave signal there is 1.1Hz component which is greater than 3Hz component. which would be wrong. the continuous plot is wrong thats what u see in a scope. – user16307 Oct 17 '16 at 1:29
• you think that second plot represents the continuous Fourier Transform of a square wave??? – robert bristow-johnson Oct 17 '16 at 1:32

The Fourier series expansion of a square wave is indeed the sum of sines with odd-integer multiplies of the fundamental frequency. So, responding to your comment, a 1 kHz square wave doest not include a component at 999 Hz, but only odd harmonics of 1 kHz.

The Fourier transform tells us what frequency components are present in a given signal. As the signal is periodic in this case, both the Fourier series and the Fourier transform can be calculated, and they should tell us the same information. The Fourier transform of a continuous periodic square wave is composed by impulses in every harmonic contained in the Fourier series expansion. Maybe this picture from Oppenheim's Signals and Systems may help.

The actual Fourier transform are only the impulses. The dotted-line is a sinc function that doesn't apply to this question, but gives the notion that this transform has something to do with the transform of a square pulse (i.e. a not periodic signal), which happens to be a sinc.

To put it mathematically:

• The Fourier series coefficients are $$\frac{\sin(k\omega_0 T)}{k\pi}$$
• The Fourier transform is $$\sum\limits_{k=-\infty}^{\infty}\frac{2\sin(k\omega_0 T)}{k}\delta(\omega - k\omega_0)$$

So the series coefficients and the Fourier transform are the same, except that there is a proportionality factor of $2\pi$ and, in the first case, you plot bars (as the coefficients do not describe a function, they are just numbers), but in the second one you have impulses (because the Fourier transform is a function).

• i dont understand so in reality would a 1kHz square wave has no 999 Hz component? But in oscilloscope 999Hz component greater than 3kHz component. I dont get it. – user16307 Oct 17 '16 at 0:50
• No, a purely 1 kHz square wave doesn't have a 999 Hz component. – Tendero Oct 17 '16 at 0:53
• try feeding a square wave to a scope and check its FFT. you might get surprised. thats why i asked this question – user16307 Oct 17 '16 at 0:56
• Well, in reality, function generators are not ideal. They have noise and square waves are not actually square. So, if the wave you are measuring doesn't have much amplitude, then noise of the generator and the oscilloscope itself would interfere in the measurement (also, the FFT function of scopes tends to be a poor tool for precise measurements) and then, components of 3, 5 or 7 kHz could get very small in comparison. That could explain what you are getting. – Tendero Oct 17 '16 at 1:00