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https://www.shaalaa.com/question-bank-solutions/areas-sector-segment-circle-find-area-minor-segment-circle-radius-14-cm-when-its-central-angle-is-60-also-find-area-corresponding-major-segment_1697
Share # Find the area of the minor segment of a circle of radius 14 cm, when its central angle is 60˚. Also find the area of the corresponding major segment. - CBSE Class 10 - Mathematics ConceptAreas of Sector and Segment of a Circle #### Question Find the area of the minor segment of a circle of radius 14 cm, whe...
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https://link.springer.com/chapter/10.1007/978-3-319-39687-3_6
# A Comparison of Performance of Sleep Spindle Classification Methods Using Wavelets • Elena Hernandez-Pereira • Isaac Fernandez-Varela • Vicente Moret-Bonillo Conference paper Part of the Smart Innovation, Systems and Technologies book series (SIST, volume 60) ## Abstract Sleep spindles are transient waveforms and ...
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https://www.physicsforums.com/threads/probability-urn-problem-with-replacement-kinda.616814/
# Homework Help: Probability Urn Problem with Replacement Kinda 1. Jun 26, 2012 ### RaeganW This probabilily summer course I am in is so bizarre; I have no idea where the professor is going during the lecture. Luckily I have awesome notes from another Prob & Stats course, but this problem has me stumped. 1. The pro...
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https://arxiv.org/abs/hep-ph/0012024
# Title:Report of the Working Group on Goldstone Bosons Abstract: An overview is presented of the talks in the working group on Goldstone Bosons. Topics touched on are CP-violation in the Kaon system, rare Kaon decays, $\pi\pi$-scattering, $\phi$-meson decays, scalar mesons, form-factors and polarizabilities, $\eta$-d...
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http://sdss.kias.re.kr/astro/Horizon-Runs/Horizon-Run4.php
## Scientific Purpose The Horizon Run 4 is a cosmological N-body simulation designed for the study of coupled evolution between galaxies and large-scale structures of the Universe, and for the test of galaxy formation models. Using $6300^3$ gravitating particles in a cubic box of $L_\mathrm{box} = 3150 h^{-1}\mathrm{M...
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http://math.stackexchange.com/questions/245165/the-graph-of-a-smooth-real-function-is-a-submanifold?answertab=oldest
# The graph of a smooth real function is a submanifold Given a function $f: \mathbb{R}^n \rightarrow \mathbb{R}^m$ which is smooth, show that $$\operatorname{graph}(f) = \{(x,f(x)) \in \mathbb{R}^{n+m} : x \in \mathbb{R}^n\}$$ is a smooth submanifold of $\mathbb{R}^{n+m}$. I'm honestly completely unsure of where or h...
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http://www.ams.org/joursearch/servlet/DoSearch?f1=msc&v1=65.35&jrnl=one&onejrnl=mcom
# American Mathematical Society My Account · My Cart · Customer Services · FAQ Publications Meetings The Profession Membership Programs Math Samplings Washington Office In the News About the AMS You are here: Home > Publications AMS eContent Search Results Matches for: msc=(65.35) AND publication=(mcom) Sort orde...
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https://hal.archives-ouvertes.fr/hal-01792508
The Infinitesimal Moduli Space of Heterotic G$_{2}$ Systems Abstract : Heterotic string compactifications on integrable G$_{2}$ structure manifolds Y with instanton bundles ${(V,A), (TY,\tilde{\theta})}$ yield supersymmetric three-dimensional vacua that are of interest in physics. In this paper, we define a covariant ...
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https://devel.isa-afp.org/entries/Kleene_Algebra.html
# Kleene Algebra Title: Kleene Algebra Authors: Alasdair Armstrong, Georg Struth and Tjark Weber (tjark /dot/ weber /at/ it /dot/ uu /dot/ se) Submission date: 2013-01-15 Abstract: These files contain a formalisation of variants of Kleene algebras and their most important models as axiomatic type classes in Isabelle/...
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https://brilliant.org/problems/dont-try-to-complicate-it/
# Don't try to complicate it! Algebra Level 3 $\begin{eqnarray} \frac{a^3 + 1}{a^5 - a^4 - a^3 +a^2 } \end{eqnarray}$ Let $$a$$ be one of the roots of the equation $$x^2-x-4=0$$. The value of the expression above is a form of $$\dfrac{m}{n}$$. Submit your answer as $$m+n$$. ×
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https://mathhelpboards.com/threads/locus-in-the-complex-plane.811/
# Locus in the complex plane. #### jacks ##### Well-known member Apr 5, 2012 226 Area of Region Bounded by the locus of $z$ which satisfy the equation $$\displaystyle \arg \left(\frac{z+5i}{z-5i}\right) = \pm \frac{\pi}{4}$$ is #### Mr Fantastic ##### Member Jan 26, 2012 66 Area of Region Bounded by the locus of $z...
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https://www.physicsforums.com/threads/potential-energy-for-magnetic-fields.269770/
# Potential energy for magnetic fields 1. Nov 6, 2008 ### jaejoon89 1. The problem statement, all variables and given/known data A circular 10 turn coil that has a radius of 0.05 m and current of 5A lies in the xy plane with a uniform magnetic field B = 0.05 T i + 0.12 T k (i and k are the unit vectors). What's the...
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https://www.physicsforums.com/threads/actions-and-cross-sections.819049/
Actions and Cross Sections 1. Jun 14, 2015 Cluelessluke Can someone point towards how to derive that the cross section is proportional to the imaginary part of the Action? Also, I thought the Action was a real number? Thanks! 2. Jun 14, 2015 fzero You are probably referring to the Optical Theorem. In that case, ...
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https://www.eurotrib.com/story/2007/6/17/111516/831
Welcome to European Tribune. It's gone a bit quiet around here these days, but it's still going. ## A personal reaction to 9/11 by Jerome a Paris Sun Jun 17th, 2007 at 11:15:16 AM EST The text below was sent to me by a regular reader, who is unable to post himself for professional reasons. I am not endorsing it (see...
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https://ecommons.cornell.edu/browse?type=author&value=Shapiro%2C+Vadim&value_lang=en_US
Now showing items 1-4 of 4 • #### Boundry-Based Separation for B-rep $\rightarrow$ CSG Conversion  (Cornell University, 1991-08) We have shown earlier that one of the most difficult steps in performing b-rep $\rightarrow$ CSG conversion for a curved solid object consists of determining a set of halfspaces that is su...
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https://arxiv.org/abs/0908.3433
nucl-ex (what is this?) # Title: Nuclear physics for geo-neutrino studies Abstract: Geo-neutrino studies are based on theoretical estimates of geo-neutrino spectra. We propose a method for a direct measurement of the energy distribution of antineutrinos from decays of long-lived radioactive isotopes. We present prel...
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https://lautarolobo.xyz/blog/february-of-fortran/
# February of Fortran ## What is Fortran? Fortran is a 63 y.o. programming language developed by IBM for scientific and engineering applications. Its name is an acronym from FORmula TRANslation, and still being in use for that purpose. It’s a general-purpose programming language, but best suited for computationally ...
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https://www.ncbi.nlm.nih.gov/pubmed/17558773
Format Choose Destination # Biogas production from water hyacinth (Eichhornia crassipes (Mart.) Solms) grown under different nitrogen concentrations. ### Author information 1 Department of Civil Engineering, University of Moratuwa, Sri Lanka. mahesh@civil.mrt.ac.lk ### Abstract This paper reports the biogas produ...
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http://cs.nyu.edu/~wanli/dropc/
# Regularization of Neural Networks using DropConnect Li Wan, Matthew Zeiler, Sixin Zhang, Yann LeCun, Rob Fergus Dept. of Computer Science, Courant Institute of Mathematical Science, New York University ### Introduction We introduce DropConnect, a generalization of Hinton's Dropout for regularizing large fully-con...
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http://www.maths.ed.ac.uk/node/348
# Finn Lindgren Stochastic space-time models, non-trivial observation mechanisms, and practical inference Many natural phenomena can be modelled hierarchically, with latent random fields taking the role of unknown quantities for which we may have some idea about smoothness properties and multiscale behaviour. The mec...
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http://www.seas.upenn.edu/~sweirich/types/archive/1997-98/msg00101.html
CFP: WORKSHOP ON PARALLELISM AND IMPLEMENTATION TECHNOLOGY FOR (CONSTRAINT) LOGIC PROGRAMMING LANGUAGES [The Workshop on Parallelism and Implementation Technology for (Constraint) Logic Programming Languages covers all subjects related to the implementation of logic programming systems. The call for papers may be of i...
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http://scikit-learn.org/dev/modules/generated/sklearn.preprocessing.label_binarize.html
# sklearn.preprocessing.label_binarize¶ sklearn.preprocessing.label_binarize(y, classes, neg_label=0, pos_label=1, sparse_output=False)[source] Binarize labels in a one-vs-all fashion Several regression and binary classification algorithms are available in scikit-learn. A simple way to extend these algorithms to the...
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https://miamioh.edu/cec/academics/index.html
For the May 2016 graduates surveyed before graduation, 81% had jobs, were in the military or enrolled in graduate/professional schools. The average salary reported was approximately $63,000 (range$39,000 - \$92,000).
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https://physics.stackexchange.com/questions/435146/energy-of-an-object
Energy of an object When an object goes up we say that it gained potential energy but it is doing positive work on the earth so it should lose energy.Please correct me. • Who's doing the work? – user191954 Oct 17 '18 at 16:02 • The object which is going up is doing the work. – user64348 Oct 18 '18 at 8:27 • @user6434...
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https://st.hujiang.com/topic/161520226797/
# 沪江社团 ## 【爽身粉】英乐随响◆Rather Be conlylam (molly りん) ▼▽ 116 3 2 We're a thousand miles from comfort, we have traveled land and sea But as long as you are with me, there's no place I rather be I would wait forever, exulted in the scene As long as I am with you, my heart continues to beat With every step we take, Kyoto ...
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https://twiki.ace.fordham.edu/bin/rdiff/Sandbox/WebHome?type=history
# Difference: WebHome (1 vs. 6) #### Revision 62013-11-13 - TWikiContributor Line: 1 to 1 %DASHBOARD{ section="banner" image="https://twiki.ace.fordham.edu/pub/TWiki/TWikiDashboardImages/nasa-airfield.jpg" Line: 15 to 15 <--===== TEST TOPICS ============================================--> %DASHBOARD{ section="box_s...
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http://commens.org/dictionary/entry/quote-syllabus-syllabus-course-lectures-lowell-institute-beginning-1903-nov-23-s-33
# The Commens DictionaryQuote from ‘Syllabus: Syllabus of a course of Lectures at the Lowell Institute beginning 1903, Nov. 23. On Some Topics of Logic’ Quote: Separation of Secondness, or Secundal Separation, called Precission, consists in supposing a state of things in which one element is present without the other...
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http://science.sciencemag.org/content/145/3635/932
Reports # Fluoride: Its Effects on Two Parameters of Bone Growth in Organ Culture + See all authors and affiliations Science  28 Aug 1964: Vol. 145, Issue 3635, pp. 932-934 DOI: 10.1126/science.145.3635.932 ## Abstract Bones of the forepaws of young rats were subjected to varying concentrations of fluoride ions in...
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https://codegolf.stackexchange.com/questions/118078/appends-or-prepends-depends
# Appends or Prepends? Depends Brain-flak turns one year old tomorrow! In honor of it's birthday, we're having a PPCG style birthday party, where several users post brain-flak related questions! Help us celebrate! :) Brain-flak is an esoteric language I wrote where all of the commands are brackets and all of the brac...
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https://math.stackexchange.com/questions/3235077/find-the-coefficient-of-the-power-series-x31-x-11-2x6
# Find the coefficient of the power series $[x^3](1-x)^{-1}(1-2x)^6$ I need to find $$[x^3](1-x)^{-1}(1-2x)^6$$, where $$[x^3]$$ means the coefficent of the $$[x^3]$$ term. here's what I've done: $$[x^3](1-x)^{-1}(1-2x)^6=[x^3](\sum_{k=0}^6 {6\choose k}(-2x)^k)(\sum_{m=0}^\infty {m\choose 0}x^m)$$ $$= \sum_{k=0}^6 {...
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http://mathoverflow.net/users/22052/aaron-tikuisis?tab=stats
# Aaron Tikuisis less info reputation 514 bio website homepages.abdn.ac.uk/… location Aberdeen, Scotland age 31 member for 2 years seen Mar 6 at 11:28 profile views 464 My research is on the structure of C*-algebras. I am currently a lecturer at the University of Aberdeen. 15 Examples of conjectures that were widely...
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http://tex.stackexchange.com/questions/20096/proper-way-to-use-ensuremath-to-define-a-macro-useable-in-and-out-of-math-mode
Proper way to use \ensuremath to define a macro useable in and out of math mode Based on this solution related to defining a macro I came up with this macro to help me define a macro that I can use either in or outside of math mode. The example as is functions as I want. However, this solution requires me to NOT put ...
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http://en.wikipedia.org/wiki/Adiabatic_lapse_rate
# Lapse rate The lapse rate is defined as the rate at which atmospheric temperature decreases with increase in altitude. [1][2] The terminology arises from the word lapse in the sense of a decrease or decline. While most often applied to Earth's troposphere, the concept can be extended to any gravitationally supported...
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https://ftp.aimsciences.org/article/doi/10.3934/cpaa.2008.7.277
# American Institute of Mathematical Sciences March  2008, 7(2): 277-291. doi: 10.3934/cpaa.2008.7.277 ## Isentropic approximation of the steady Euler system in two space dimensions 1 School of Mathematical Sciences and Institute of Mathematics, Fudan University, Shanghai 200433, China, China Received  March 2007 ...
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http://www.ncbi.nlm.nih.gov/pmc/articles/PMC1609114/?tool=pubmed
BMC Health Serv Res. 2006; 6: 127. Published online 2006 Oct 6. PMCID: PMC1609114 # Priority setting in developing countries health care institutions: the case of a Ugandan hospital ## Abstract ### Background Because the demand for health services outstrips the available resources, priority setting is one of the mo...
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http://www.phy.olemiss.edu/~luca/Topics/p.html
Topics, P p-Adic Number / Structure > s.a. differential equations; knot invariants; Non-Archimedean Structures. * Idea: For each prime number p, the p-adic number system is an extension of the rational numbers different from the real number system. * Motivation, use: Initially motivated by an attempt to use power-seri...
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https://www.shaalaa.com/question-bank-solutions/the-speed-boat-still-water-15-km-hr-it-can-go-30-km-upstream-return-downstream-original-point-4-hours-30-minutes-find-speed-stream-quadratic-equations_27486
Share # The Speed of a Boat in Still Water is 15 Km/Hr. It Can Go 30 Km Upstream and Return Downstream to the Original Point in 4 Hours 30 Minutes. Find the Speed of the Stream. - Mathematics Course #### Question By default showhide Solutions The speed of a boat in still water is 15 km/hr. It can go 30 km upstream ...
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http://mathhelpforum.com/advanced-algebra/78867-torsion-coefficients.html
# Math Help - Torsion coefficients 1. ## Torsion coefficients How would I go about finding the torsion coefficients of Z10 x Z36 x Z14 x Z21? I think the first stage is to write 10, 36, 14 and 31 as products of primes but I'm not sure where to go from there. 2. Originally Posted by d_p_osters How would I go about f...
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https://www.gradesaver.com/textbooks/math/calculus/calculus-3rd-edition/chapter-14-calculus-of-vector-valued-functions-14-1-vector-valued-functions-exercises-page-710/19
Calculus (3rd Edition) Circle in the xz-plane of radius $1$ centered at $(0,0,4)$ We put $$x=\sin t,\quad y=0, \quad z=4+\cos t$$ hence we get $$x^2+(z-4)^2= \sin^2t+\cos^2t=1.$$ Which is a circle in the xz-plane of raduis $1$ centered at $(0,0,4)$.
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http://math.stackexchange.com/users/4447/ondrej-sotolar?tab=summary
Ondrej Sotolar Reputation 203 Next privilege 250 Rep. View close votes Badges 1 6 Newest Impact ~4k people reached • 0 posts edited • 0 helpful flags • 10 votes cast ### Questions (12) 4 Specific ten digit number 3 Trigonometric equality 2 Questions about finite sequences of natural numbers $(a_1, \dots, a_n)$ with...
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https://wusa.ca/about/your-money/funding/student-life-endowment-funding-application-form/
Click or drag files to this area to upload. You can upload up to 4 files. Please ensure that the estimate is a formal one. Include Work Requests and cost estimates from Plant Operations. If you are putting in a request for hard goods (e.g. microwaves, furniture, equipment) you MUST include at least TWO invoices. Withou...
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https://www.physicsforums.com/threads/effective-field-theory-and-wilsons-renormalization-group.587206/
# Effective field theory and Wilson's renormalization group • Start date • #1 188 0 ## Main Question or Discussion Point I have just read my first course on Quantum Field Theory (QFT) and have followed the book by Srednicki. I have peeked a bit in the books by Peskin & Schroeder and Ryder also but mostly Srednicki a...
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https://dash.harvard.edu/handle/1/10445609
# Structural specializations of $$\alpha_4 \beta_7$$, an integrin that mediates rolling adhesion Title: Structural specializations of $$\alpha_4 \beta_7$$, an integrin that mediates rolling adhesion Author: Chen, JianFeng; Yu, Yamei; Zhu, Jianghai; Mi, Li-Zhi; Walz, Thomas; Sun, Hao; Springer, Timothy A. Note: Order ...
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https://www.jask.or.kr/articles/xml/7YPO/
Research Article The Journal of the Acoustical Society of Korea. May 2021. 254-260 # MAIN • I. Introduction • II. Equivalent circuit of the loudspeaker with acoustic terminals • III. Verification through experiment •   3.1 Extract of $Caf$ and $Zar$ •   3.2 Determination of acoustic impedance and sound absorptio...
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http://mathhelpforum.com/advanced-math-topics/161580-fourier-series-addition-cosine-sine-different-frequencies2.html
# Thread: Fourier series - addition of cosine and sine of different frequencies2 1. ## Fourier series - addition of cosine and sine of different frequencies2 I'm trying to find the fourier series of, f(t) = cos(4t) + sin(6t) I know the period is pi and wo = 2. The equation I have been using is an = (2 / pi) * integ...
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https://www.arxiv-vanity.com/papers/1205.6926/
arXiv Vanity renders academic papers from arXiv as responsive web pages so you don’t have to squint at a PDF. Read this paper on arXiv.org. # Indirect Coulomb Energy for Two-Dimensional Atoms Rafael D. Benguria  and  Matěj Tušek Departmento de Física, P. Universidad Católica de Chile, Departmento de Física, P. Univer...
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https://puzzling.stackexchange.com/questions/65800/hey-wake-up-look-at-this-grid-puzzle
# Hey! Wake Up! Look At This Grid Puzzle! The grid is divided into rooms, though some are wibbly-wobbly weird-shaped. Hey, aren't these normally supposed to be blocks? What should the title of this puzzle really be? B S G N I L H I A I O L F F M T R F A R I O R R C J N E S L A T B B I Q C N A T X A R O N O V I F L O ...
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http://tex.stackexchange.com/questions/76152/beamer-definition-list-overlay-uncover-definition-later-than-entry?answertab=active
# beamer definition-list overlay: uncover definition later than entry For educational purposes, I would like to uncover the definitions of my description items only after all the items themselves have been uncovered, like so: \documentclass{beamer} \begin{document} \begin{frame} \begin{overprint} \begin{description} ...
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https://www.gradesaver.com/textbooks/math/algebra/intermediate-algebra-for-college-students-7th-edition/chapter-1-section-1-7-scientific-notation-exercise-set-page-89/42
## Intermediate Algebra for College Students (7th Edition) $6 \times 10^5$ Divide the corresponding parts. Then, put the expression in the form $a*10^n$, where a is a number that is greater than or equal to 1 but less than 10. $=\dfrac{1.2}{2} \times \dfrac{10^4}{10^{-2}} \\=0.6 \times 10^{4-(-2)} \\=0.6 \times 10^{4+...
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https://dml.cz/handle/10338.dmlcz/146752
# Article Full entry | PDF   (0.2 MB) Keywords: Itô functional difference equation; stability of solutions; admissibility of spaces Summary: The admissibility of spaces for Itô functional difference equations is investigated by the method of modeling equations. The problem of space admissibility is closely connected w...
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https://rd.springer.com/article/10.1186/1687-1847-2011-63
, 2011:63 # Stability criteria for linear Hamiltonian dynamic systems on time scales Open Access Research ## Abstract In this article, we establish some stability criteria for the polar linear Hamiltonian dynamic system on time scales by using Floquet theory and Lyapunov-type inequalities. 2000 Mathematics Subjec...
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http://gmatclub.com/forum/a-certain-it-department-of-fewer-than-15-people-hires-coders-137203.html
Find all School-related info fast with the new School-Specific MBA Forum It is currently 27 May 2016, 08:28 ### GMAT Club Daily Prep #### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email. C...
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http://clay6.com/qa/25199/-p-rightarrow-q-is-equivalent-to
# $^{\sim}(p \Rightarrow q)$ is equivalent to $\begin {array} {1 1} (A)\;p \wedge q & \quad (B)\;^{\sim} p V q \\ (C)\;^{\sim} p \wedge ^{\sim}q & \quad (D)\;p \wedge ^{\sim} q \end {array}$ p q $^{\sim}q$ $p \Rightarrow q$ $^{\sim}( p \Rightarrow q)$ $p \wedge ^{\sim}q$ T T F T F F T F T F T T F T F F F F F F T F F...
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http://scott.sherrillmix.com/blog/tag/latex/
## Displaying Code in LaTeX gioby of Bioinfo Blog! (an interesting read by the way) left a comment asking about displaying code in LaTeX documents. I’ve sort of been cludging around using \hspace‘s and \textcolor but I’ve always meant to figure out the right way to do things so this seemed like a good chance to figure...
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http://www.wantedvibes.co.uk/nse9p/doctor-crossword-clue-6db064
the bond angles of this is 109.5 and that is is the bond angles . Three Dee is confusing that with the total … the shape is bent. Log in. Welcome; Our Menu; Contact Us; facebook; 0 ฿ 0.00 View Cart; Checkout Since there are two lone pairs on chlorine, the electron pair repulsion will result in a bond angle that is ...
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http://edoc.mpg.de/display.epl?mode=doc&id=715988&col=61&grp=3972
Home News About Us Contact Contributors Disclaimer Privacy Policy Help FAQ Home Search Quick Search Advanced Fulltext Browse Collections Persons My eDoc Session History Login Name: Password: Documentation Help Support Wiki Direct access to document ID: Institute: MPI für Physik     Collection: YB 2016     Display D...
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https://homework.cpm.org/category/CON_FOUND/textbook/mc1/chapter/7/lesson/7.1.2/problem/7-21
### Home > MC1 > Chapter 7 > Lesson 7.1.2 > Problem7-21 7-21. Use a Giant One to change each of the following fractions to a number written as a fraction over $100$. Then write each portion as a percent. 1.  $\frac { 3 } { 20 }$ $20\left(5\right) = 100$ 1.  $\frac { 3 } { 40 }$ What do you multiply by $40$ to get...
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https://asmedigitalcollection.asme.org/fluidsengineering/article-abstract/132/1/011303/467228/Liquid-Sheet-Breakup-in-Gas-Centered-Swirl-Coaxial?redirectedFrom=fulltext
The study deals with the breakup behavior of swirling liquid sheets discharging from gas-centered swirl coaxial atomizers with attention focused toward the understanding of the role of central gas jet on the liquid sheet breakup. Cold flow experiments on the liquid sheet breakup were carried out by employing custom fab...
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https://proofwiki.org/wiki/Completion_of_Normed_Division_Ring
# Completion of Normed Division Ring ## Theorem Let $\struct {R, \norm {\, \cdot \,} }$ be a normed division ring. Then: $\struct {R, \norm {\, \cdot \,} }$ has a normed division ring completion $\struct {R', \norm {\, \cdot \,}' }$ ## Proof Let $d$ be the metric induced by $\struct {R, \norm {\, \cdot \,} }$. L...
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http://spark.apache.org/docs/latest/mllib-decision-tree.html
# Decision Trees - RDD-based API Decision trees and their ensembles are popular methods for the machine learning tasks of classification and regression. Decision trees are widely used since they are easy to interpret, handle categorical features, extend to the multiclass classification setting, do not require feature ...
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https://cs.stackexchange.com/questions/41154/can-a-probabilistic-turing-machine-compute-an-uncomputable-number
# Can a probabilistic Turing Machine compute an uncomputable number? Can a probabilistic Turing Machine compute an uncomputable number? My question probably does not make sense, but, that being the case, is there a reasonably simple formal explanation for it. I should add that I am pretty much ignorant of probabilist...
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http://users.umiacs.umd.edu/~hal/HBC/hbc_v0_1.html
HBC: Hierarchical Bayes Compiler Pre-release version 0.1 HBC is a toolkit for implementing hierarchical Bayesian models. HBC created because I felt like I spend too much time writing boilerplate code for inference problems in Bayesian models. There are several goals of HBC: 1. Allow a natural implementation of hierarc...
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https://www.semanticscholar.org/paper/The-Weight-Distribution-of-Quasi-quadratic-Residue-Boston-Hao/e3239244301b92eb8a3187c783dc979426368806
# The Weight Distribution of Quasi-quadratic Residue Codes @article{Boston2017TheWD, title={The Weight Distribution of Quasi-quadratic Residue Codes}, author={Nigel Boston and Jing Hao}, year={2017}, volume={12}, pages={363-385} } • Published 18 May 2017 • Computer Science We investigate a family of codes called quasi...
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https://www.gamedev.net/forums/topic/336304-how-would-i-rotate-around-a-center-point/
# How would I rotate around a center point? ## Recommended Posts Say I want to rotate the other points around the center point, and I don't have opengl to push, rotate, and pop... how can I do it? [Edited by - ScottC on August 2, 2005 4:52:12 AM] ##### Share on other sites You could use matrices like the APIs but ju...
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https://www.bartleby.com/solution-answer/chapter-17-problem-8ps-chemistry-and-chemical-reactivity-10th-edition/9781337399074/10bdb30a-a2ce-11e8-9bb5-0ece094302b6
Question Chapter 17, Problem 8PS a) Interpretation Introduction ## Interpretation:Calculate the pH of the resulting buffer solution formed by adding 2.75 g of NaCH3CHOHCO2, sodium lactate, to 5.00×102 ml of 0.100 M lactic acid.Concept introduction:The Henderson-Hasselbalch equation relates pH of a buffer to pKa of a...
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https://quant.stackexchange.com/questions/27763/why-does-jump-process-has-to-be-cadlag-and-not-the-other-way-around/27764
# Why does jump process has to be Cadlag and not the other way around In all books and references that I have been exposed to, the jump processes have been defined to be Cadlag(right continuous with left limits). But no one has explained why this is the preferable case, why can't it be Caglad? I suspect it has someth...
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http://star-www.rl.ac.uk/star/docs/sc4.htx/sc4se12.html
### 12 Dealing with Files #### 12.1 Extracting parts of filenames Occasionally you’ll want to work with parts of a filename, such as the path or the file type. The C-shell provides filename modifiers that select the various portions. A couple are shown in the example below. set type = $1:e set name =$1:r if ( $type ...
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https://geoenergymath.com/2014/07/
# Correlation of time series [mathjax]The Southern Oscillation embedded with the ENSO behavior is what is called a dipole [1], or in other vernacular, a standing wave.  Whenever the atmospheric pressure at Tahiti is high, the pressure at Darwin is low, and vice-versa.  Of course the standing wave is not perfect and fa...
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http://www.gamedev.net/page/resources/_/technical/artificial-intelligence/pathfinding-with-the-c4-game-engine-r2420?st=210
• Create Account $5 Categories (See All) Like 0Likes Dislike Pathfinding With the C4 Game Engine By Jon Watte | Published Oct 09 2007 09:37 PM in Artificial Intelligence navmesh code navpoint level point controller path node function If you find this article contains errors or problems rendering it unreadable (missin...
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http://libros.duhnnae.com/2017/sep/150524545559-Trispectrum-estimator-in-equilateral-type-non-Gaussian-models-High-Energy-Physics-Theory.php
# Trispectrum estimator in equilateral type non-Gaussian models - High Energy Physics - Theory Trispectrum estimator in equilateral type non-Gaussian models - High Energy Physics - Theory - Descarga este documento en PDF. Documentación en PDF para descargar gratis. Disponible también para leer online. Abstract: We in...
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https://www.kitronik.co.uk/blog/how-a-thermistor-works
### My Cart: 0 item(s) - \$0.00 You have no items in your shopping cart. # How A Thermistor Works ## Introduction A thermistor is a component that has a resistance that changes with temperature. There are two types of thermistor. Those with a resistance that increase with temperature (Positive Temperature Coefficie...
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https://economics.stackexchange.com/questions/25043/augmented-gravity-model
# Augmented Gravity Model I am currently using the gravity model for my dissertation on migration flows. Do gravity models need to be augmented by dummy variables only or can other explanatory variables (such as the unemployment rate in the destination/ origin country) be included please? All your feedback is greatly...
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https://lo.calho.st/posts/ndnsim-custom-fields/
The recommended way to build something on top of ndnSIM is to fork its scenario template repository and work inside there. You still need to download and compile the actual framework, however you will simply install it into /usr/local and link to it instead of actually working inside the main repository. It turns out ...
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https://pdglive.lbl.gov/DataBlock.action?node=S048M&home=BXXX040
# ${{\boldsymbol \Xi}_{{c}}^{0}}$ MASS INSPIRE search The fit uses the ${{\mathit \Xi}_{{c}}^{0}}$ and ${{\mathit \Xi}_{{c}}^{+}}$ mass and mass-difference measurements. VALUE (MeV) EVTS DOCUMENT ID TECN  COMMENT $\bf{ 2470.90 {}^{+0.22}_{-0.29}}$ OUR FIT $\bf{ 2470.99 {}^{+0.30}_{-0.50}}$ OUR AVERAGE $2470.85$ $\pm0....
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https://www.physicsforums.com/threads/convolution-of-a-dirac-delta-function.222873/
# Convolution of a dirac delta function 1. Mar 19, 2008 ### pka Alright...so I've got a question about the convolution of a dirac delta function (or unit step). So, I know what my final answer is supposed to be but I cannot understand how to solve the last portion of it which involves the convolution of a dirac/unit...
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http://autoplot.org/Test_dataset_urls
# Test dataset urls This is an old set of URIs for testing, back when this was done by hand when making a release. Autoplot is tested now automatically and continuously, see http://jfaden.net/hudson/. See also http://autoplot.org//developer.listOfUris . This is tested with http://jfaden.net:8080/hudson/job/autoplot-te...
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https://link.springer.com/article/10.1007%2Fs11661-011-1045-9
Metallurgical and Materials Transactions A , Volume 43, Issue 6, pp 1845–1860 # Prediction of Inhomogeneous Distribution of Microalloy Precipitates in Continuous-Cast High-Strength, Low-Alloy Steel Slab • Suparna Roy • Sudipta Patra • S. Neogy • A. Laik • S. K. Choudhary • Debalay Chakrabarti Article DOI: 10.1007/s...
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http://lesprobabilitesdedemain.fr/edition2017/programme.html
## Programme de la journée 2017 8h30 -- 9h00 Café d'accueil. 9h00 -- 9h20 Présentation de la journée par les organisateurs. 9h20 -- 10h20 Dmitry Chelkak 2D Ising model: combinatorics, CFT/CLE description at criticality and beyond 10h20 -- 10h40 Pause café. 10h40 -- 11h00 Paul Melotti Récurrence spatiales, modèles ass...
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https://chem.libretexts.org/Under_Construction/Purgatory/Core_Construction/Chemistry_30/Electrochemistry/2.6_Batteries
# 2.6 Batteries Electrochemical cells used for power generation are called batteries. Although batteries come in many different shapes and sizes there are a few basic types. You won't be required to remember details of the batteries, but some general information and features of each type is presented here. ## 1. Prim...
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https://classes.areteem.org/mod/forum/discuss.php?d=299&parent=642
## Online Course Discussion Forum ### MC2A Help 1 Re: Thanks Hey David. The hints I put in there had the wrong numbers, but were for the problems you were asking (it said 16 instead of 15 and 17 instead of 16, but it is fixed now).
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https://www.physicsforums.com/threads/kinetic-theory.559123/
# Kinetic Theory 1. Dec 11, 2011 ### luigihs Can someone explain me this theory ? and how to use the equation please I have this in my notes but I dont understand :( Average (translational) Kinetic Energy per molecule is E= 3/2kT The same, per mole, is U = 3/2 * R* T 2. Dec 11, 2011 ### sophiecentaur Hi The b...
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https://codegolf.stackexchange.com/questions/86880/hofstadter-q-sequence/88644
# Definition 1. a(1) = 1 2. a(2) = 1 3. a(n) = a(n-a(n-1)) + a(n-a(n-2)) for n > 2 where n is an integer Given positive integer n, generate a(n). # Testcases n a(n) 1 1 2 1 3 2 4 3 5 3 6 4 7 5 8 5 9 6 10 6 11 6 12 8 13 8 14 8 15 10 16 9 17 10 18 11 19 11 20 12 # Reference • – Leaky Nun Jul 29 '16 at 15...
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http://math.stackexchange.com/questions/390393/finding-the-base-of-a-triangle?answertab=active
# finding the base of a triangle In A triangle ABC ,AB=AC.D is a point inside the triangle such that AD=DC.Median on AC from D meets median on BC from A at the centroid of the triangle.If the area of the triangle ABC equals to $4\sqrt 3$ .Find the base i.e. BC. The method that i have used to solve this problem works b...
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http://quant.stackexchange.com/questions/8478/close-form-for-stochastic-integral?answertab=active
# close form for stochastic integral I am new to stochastic calculus. Can I know how to compute the close-form solution for $$\int_0^t \exp(\alpha s - \sigma W_s) \; ds$$ and $$\int_0^t \exp(\alpha s - \sigma W_s) \; dW_s.$$ I encounter that when trying to solve for the following SDE $$dX_t = \theta(\mu - X_t)\; dt + ...
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http://bitfunnel.org/strangeloop/
BitFunnel performance estimation · BitFunnel # BitFunnel performance estimation Hi! I’m going to talk about two things today. First, I’m going to talk about one way to think about performance. That is, one way you can reason about performance. Second, I’m going to talk about search. We’re going to look at search as...
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http://math.poly.edu/news/seminars.phtml
Colloquia COMING COLLOQUIA Thursday, March 13, 2014: Colloquium Vertical versus horizontal Poincare inequalities Assaf Naor, Courant Institute of Mathematical Sciences New York University4:35-5:20 PM, Rogers Hall 302 Thursday, March 20, 2014: No Coloquium, Spring Break Thursday, April 03, 2014: Remarks on the conject...
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https://wiki.melvoridle.com/index.php?title=Combat&oldid=60633
# Combat (diff) ← Older revision | Latest revision (diff) | Newer revision → (diff) Combat Combat page. Farmlands combat area selected. Fighting a Chicken. Death screen. Combat involves fighting various monsters throughout the combat areas, slayer areas, and dungeons of Melvor. Food and Equipment cannot be changed wh...
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https://www.elastic.co/blog/index-type-parent-child-join-now-future-in-elasticsearch
Tech Topics # Indices, types, and parent / child: current status and upcoming changes in Elasticsearch A year and a few months ago, we blogged about the differences of types and indices, including "when to pick which."  If you don't wish to read the full history, I'll give you the TL;DR: the conclusion was something ...
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https://www.physicsforums.com/threads/2x2-matrix-a-has-only-one-eigenvalue-l-with-eigenvector-v.374163/
# 2x2 matrix A has only one eigenvalue λ with eigenvector v 1. Jan 31, 2010 ### nlews This is a revision problem I have come across, I have completed the first few parts of it, but this is the last section and it seems entirely unrelated to the rest of the problem, and I can't get my head around it! Suppose that t...
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http://math.stackexchange.com/questions/11601/proof-that-a-combination-is-an-integer
# Proof that a Combination is an integer From its definition a combination $(^n_k)$, is the number of distinct subsets of size k from a set of n elements. This is clearly an integer, however I was curious as to why the equation $\frac{n!}{k!(n-k)!}$ always evaluates to an integer. So far I figured: $n!$, is clearl...
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http://debraborkovitz.com/author/dborkovitz/page/3/
Trigonometry Yoga posted in: Trigonometry | Which is bigger, the sine of 40$$^{\circ}$$ or the sine of 50$$^{\circ}$$? This is a great trigonometry assessment question.   Unfortunately, virtually none of my college students who haven’t used trig for a while can answer it (without a calculator).   For … Read More The...
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http://cms.math.ca/cmb/kw/Polarized%20manifold
On the nonemptiness of the adjoint linear system of polarized manifold Let $(X,L)$ be a polarized manifold over the complex number field with $\dim X=n$. In this paper, we consider a conjecture of M.~C.~Beltrametti and A.~J.~Sommese and we obtain that this conjecture is true if $n=3$ and $h^{0}(L)\geq 2$, or $\dim \Bs ...
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https://scattered-thoughts.net/blog/2017/12/12/notes-on-psycgd02-principles-of-cognition/
ERROR: type should be string, got "https://www.ucl.ac.uk/lifesciences-faculty-php/courses/viewcourse.php?coursecode=PSYCGD02\n\nThis module outlines general theoretical principles that underlie cognitive processes across many domains, ranging from perception to language, to reasoning and decision making. The focus will be on general, quantitative regularities, and the degree to which theories focusing on specific cognitive scientific topics can be constrained by such principles. There will be an introduction on general methods and approaches in cognitive science and some of the problems related to them. Later in the course, some computational approaches in cognitive science will be discussed. There will be particular emphasis on understanding cognitive principles that are relevant to theories of decision making.\n\n## What is Cognitive Science?\n\nBrief history.\n\nNotable that the narrative revolves around several key conferences where prominent figures from different fields became aligned.\n\n## Bridging Levels of Analysis for Probabilistic Models of Cognition\n\nLevels of models:\n\n• Computational - problem and declarative solution eg Bayesian inference\n• Algorithmic - representation and constructive solution eg message passing\n• Implementation - physical processes eg neurons\n\nPopular research method is to look at where people diverge from ideal solutions, to figure out what algorithms their mind is using to approximate the solution. But.. .\n\n• Vulnerable to misidentifying the computational problem being solved.\n• eg strategies for iterated PD look irrational in single PD\n• Requires understanding how levels constrain each other\n• eg are probalistic models fundamentally incompatible with connectionist models or can we implement one on top of the other?\n\nRational process models - identify algorithm for approximating probabilistic inference under time/space limits, compare to what we know about mind and behavior.\n\n• Bridges computational and algorithmic levels.\n• Constrains possible algorithms to those that produce ideal behavior in limit.\n• Explains many cases where individuals deviate but average behavior is close to ideal.\n\nExample - Monte Carlo with small number of samples is tractable. Consistent with:\n\n• Averaging multiple guesses from one person increases accuracy (ie contains some independent error)\n• Recall similar events ~= importance sampling. Predicts availability bias? Incorrect re-weighting?\n• Order effects (order of information incorrectly affects results of update) ~= particle filter.\n• Perceptual bistability ~= random walk.\n\nSome progress in bridging to implementation level eg neural models of importance sampling.\n\n## Lecture 1\n\nCognitive science as reverse engineering - understand how the mind works by trying to build one and see what differs.\n\nBrief history:\n\n• Structuralism\n• Building blocks are qualia\n• Learning via systematic introspection\n• Controlled, replicable experiments\n• But different labs struggled to replicate each others results\n• Difficult to relate conscious experiences which don’t match qualia (eg non-visual mental models)\n• Vulnerable to observer effects, confirmation, priming, retroactive justification\n• Introspection actually = retrospection\n• eg visual illusions, choice blindness\n• Behaviorism\n• Only talk about observable stimulus and response\n• Mostly experiments with animal learning\n• eg classic conditioning (event -> event -> response => event -> … -> response)\n• eg operant conditioning (action -> +/- => +/- action)\n• Reinforcement machines, not reasoning machines\n• Doesn’t allow internal state/structure\n• Doesn’t explain how stimulus/response are categorized - theoryless learning\n• But language has infinite structure => can’t be learned from stimulus/response without hyperpriors\n• Rats choose shorted route available, rather than most reinforced route\n• Cognitive science\n• Thought as computation / information processing - data + algorithms\n• We needed to invent computation first to be able to have this idea!\n\nMethods:\n\n• Behavioral studies\n• Lesion studies\n• Single-cell recordings\n• fMRI\n• Neural activity -> blood de-oxygenation -> magnetic interaction changes -> measure with big magnets\n• Spatial resolution ~1mm\n• Temporal resolution ~seconds\n• EEG\n• Neural activity -> electromagnetic field -> measure with electrodes on scalp\n• Can only measure large fields\n• Spatial resolution ~poor\n• Temporal resolution ~1ms\n• MEG\n• Neural activity -> electromagnetic field -> measure with ?\n• Spatial resolution ~better\n• Temporal resolution ~1ms\n• tDCS\n\n## Automaticity of Social Behavior: Direct Effects of Trait Construct and Stereotype Activation on Action\n\n(Paired with the more recent failed replication.)\n\nArguing that non-conscious priming can strongly affect behavior.\n\nExperiment 1:\n\n• Use scrambled sentence test with words that prime rude/polite/neutral\n• All experimenters blinded\n• Sent to another room for next test, where waiting confederate is asking experimenter questions\n• Time how long it takes them to interrupt\n• Huge effect sizes: almost 2x mean time, <20% vs >60% interruptions within 10min cutoff\n• No significant differences in reported perceptions of experimenters politeness\n• Should we trust reports of politeness? It’s a bad idea to call your professor rude!\n• Effect sizes are enormous. If a few words can double impatience, what could listening to angry music on the journey do? If we’re so strongly susceptible to small influences, how is there room for personality? How do we have any resistance to marketing?\n\nExperiment 2:\n\n• Two successful iterations!\n• Same setup, but priming elderly/neutral (without priming slow)\n• Timed how long subjects took to walk to the next room\n• Much smaller effect size - mean 7.30s -> 8.28s\n• Near identical results in both iterations!\n• Elderly -> slow? I get thinking about rudeness making me rude, but thinking about elderly making me slow seems a much bigger stretch. Thinking about predators makes me want to eat meat? Being chased by a tiger and stop for a steak sandwich?\n• Followup experiment with 19 undergrads found only 1 noticed the elderly priming\n\n• Do elderly priming, then Affect-Arousal Scale\n• Primed group were in slightly more positive mood, but not significantly\n• Uses this to defend against the idea that they walked slower because sad, but seems bizarre that they are affected so much that they move differently but not so much that they feel differently.\n\nExperiment 3:\n\n• Flash either African-American or Caucasian face before each trial.\n• On 130th claim error and say they have to start again. Experimenter explains error, but is blinded.\n• Facial expression caught by camera and rated by blinded experimenter.\n• Only two subjects reported seeing the faces when asked and couldn’t identify which they saw\n• Both experimenter in room and raters of pictures gave near-identical results!\n• But no difference in self-reported racial prejudice.\n\nArgues that this works where subliminal adverts for pepsi don’t because they directly activate traits which contain behavior whereas pepsi just activates the pepsi representation. So elderly -> walk slow but pepsi -/> drink pepsi? Also because there is some activation energy to get up and buy coke, whereas they setup situations where the action was already required and the only difference was in accessibility. So priming for hostility will make people more likely to react to an annoying trigger but not to be randomly hostile.\n\nNote that results for behavior here are stronger than their previous results for judgments, but would assume that judgments mediate behavior. But in ex1 there was no effect on perception of the experimenter. And little evidence so far for judgment mediating behavior.\n\n## Behavioral Priming: It’s all in the Mind, but Whose Mind?\n\nFailed replication of previous paper.\n\nReasons to doubt original:\n\n• Only two indirect replications.\n• Small sample sizes.\n• Evidence from neuroscience suggests that top-down attention and bottom-up saliency are both required for the spreading activations that are used to explain priming.\n• Experimenter who administered the task was not blinded enough - authors found that it was easy to accidentally glimpse the task sheet (original describes them as being in a closed envelope?)\n• Measuring time with a stopwatch is susceptible to bias\n• Not clear exactly what participants where asked afterwards - aware of stimulus vs aware of response vs aware of link.\n\nExperiment 1:\n\n• Task sheets in a closed envelope, opened by subjects\n• Experimenters assigned to subjects are random\n• Experimenters follow a strict script\n• Walking speed recorded by infrared beam\n• No significant difference in walking times\n• Four students reported being aware of the elderly-ness\n• Primed group chose pictures of old people significantly more often in forced choice test\n• No experimenters reported having any specific expectations about subject behavior\n\nExperiment 2:\n\n• 50 subjects, 10 experimenters\n• Half of experimenters told that primed participants will walk slower, other half told faster\n• Experimenters were unblinded\n• First subject for each experimenter was a confederate who behaved to confirm this expectation\n• Experimenters measured with stopwatch\n• For stopwatch times, fast+prime went faster and slow+prime went slower.\n• For infrared times, slow+prime went slightly slower and fast+prime was same as fast+control.\n\nMost subjects were aware of the prime (but it said 6%…) and are in psych course so might be expected to be suspicious.\n\nPriming via social cues is way more believable to me than priming via word choice. Clear selective pressure for understanding and reacting to social cues.\n\n## Lecture 2\n\nScientific reasoning. Psi hypothesis as running example.\n\nBase-rate fallacy vs significance testing.\n\nSuccessful replication could just mean replicating the mistakes of the original.\n\nIn a replication aim to improve on original methods or test some new factor - more likely to be received in good faith and more likely to generate new insight beyond back-and-forth.\n\nA good successfully replication can falsify a hypothesis by more accurately identifying the mechanism behind the effect eg previous paper replicated slow walking, but showed that the effect disappeared under proper blinding.\n\nDefenses of priming:\n\n• Hidden moderators\n• Experienced researchers\n\nBut:\n\n• Then the original effect is less powerful/robust than claimed\n• Post-hoc reasoning - just a hypothesis until tested\n• Administering questionnaires is not that hard\n• Most of the legwork is done by grad students anyway\n\nTry to structure experiments with multiple competing hypotheses where any given result would support some hypothesis and weaken the others.\n\n## The Cognitive Neuroscience of Human Memory Since H.M.\n\nIntro:\n\n• Current categories used in memory took time to establish - non-obvious.\n• Specific impairments from lesions rather than general degradation shows that brain is structured and specialized.\n\nHippocampus:\n\n• Hippocampal volume reduction of ~40% is common in memory-impaired patients - may be maximum cell loss ie 60% remaining is just dead tissue.\n• Damage to other regions can also impair memory.\n\nHM:\n\n• Learned a motor skill => memory not one single unit\n• Reasoning and perception intact => memory not required for reasoning/perception\n• Could sustain attention and had short-term recall => damaged ares not required for working memory\n• Had memories from before surgery => long-term storage not in damaged areas\n\nOther patients:\n\n• Perceptual priming still works\n• Can learn in Bayesian fashion, but not explicit memorization\n• Learned skills are rigid, fail if task is modified\n\nDeclarative: facts, representations, conscious recall, compare/contrast memories Non-declarative memory: unconscious performance, black box\n\nVisual perception:\n\n• Initially thought to require memory in some cases, but…\n• Tests accidentally benefit from memory\n• Often damage to adjacent vision-processing areas\n• Requires better imaging/locating of lesions to clear up confusion\n\nImmediate and working memory:\n\n• HM limited to 6 digit recall, but could maintain memory for 15 mins\n• => Immediate memory not time-limited, but maintenance-limited\n• Demonstrated in other patients - they do fine on tasks where distractions impair healthy subjects (working memory) but fail on tasks where distractions are fine for healthy subjects (long-term memory)\n• Open question - are there tasks that can be handled by working memory but are still impaired by hippocampus damage\n• Debate around path integration - unclear whether subjects are each using same process and representation\n\nRemote memory:\n\n• HM initially had autobiographical memory\n• (Later in life was limited to factual recall, but later MRIs also showed changes since initial event)\n• Many other patients also have autobiographical memory.\n• In patients without, often unclear how far damage extends and whether it might affect other areas\n\nWorking theory of long-term memory::\n\n• Medial temporal lobes deal with creating and maintaining declarative memories\n• Sensory memories stored in same area that initially processed them\n• Supported by many individual patients eg ‘colorblind painter’ - after damage that removed color perception, could no longer remember colors except declaratively\n• Recall consists of tying all of these together\n• Supported by various fMRI studies\n• Initially requires hippocampus, but over years memories reorganized, stored more permanently by changes across neocortex that tie these areas together\n\nStructure::\n\n• Working theory - organized by semantic categories\n• eg JBR lost memory of things identified by attributes but not things identified by function\n• Recollection = what was in specific memory?\n• Familiarity = was prompt in any memory?\n• Hippocampus damaged patients are impaired on both old/new task (familiarity + some recollection) and free recall (recollection)\n• Combine old/new with recall of which source - patients have less instances of familiarity without recall => damage is not recall only\n\nGroup studies average out individual variation - allows studying less obvious effects\n\n## Finding the engram\n\nEngram def=\n\n• Persistance - persistent physical change in brain resulting from specific experience\n• Ecphory - automatic retrieval in presence of cue\n• Content - reflects what happened and what can be retrived\n• Dormancy - exists (but dormant) even when encoding and retrieval not active\n\nThe hunt:\n\n• Moving target eg reconsolidation\n• Many learning-related changes observed in brain eg synaptic, chemical, epigenetic.\n• Different persistence periods.\n• Not clear if related to engrams.\n• Often don’t predict retrieval success.\n• Dominant theory - stronger connections between neurons that are active during encoding - neuronal ensemble\n\nSharp-wave ripple events in hippocampus:\n\n• Multi-unit recordings in rodents, fMRI in humans\n• Replay observed during tasks, resting and sleeping\n• Strength of replay correlates with later retrieval performance\n• Disrupting waves impairs subsequent expression\n• Some progress on correlating content\n• Related sensory cues may trigger replay\n• Hard to observe dormancy\n\nTracking:\n\n• Non-specific lesions only caused retrieval failure when wide areas damaged => memories are distributed\n• But overtrained rats => resilient memories\n• But may have accidentally damaged hippocampus with large lesions\n• Would like to lesion specific ensembles\n• Tagging shows that some same neurons active during both encoding and retrieval (~10%, >chance, possibly collateral tagging during encoding)\n• Neurons with higher levels of CREB are more often recruited into ensemble\n• Neurons with virally over-expressed CREB are more often recruited into ensemble\n• More CREB -> more excitable\n• Increasing excitability via various other methods also has same effect\n• Allocate-and-erase - ablating (killing?) artificially excitable neurons reduces retrieval performance without affecting future learning\n• Even if only one brain region is targeted => some parts of ensemble have key roles\n• Tag-and-erase - tag active neurons, apply inhibitors (how are these targeted?), same effect\n• Worries about collateral tagging resolved:\n• Tag 1st experience\n• Silence during 2nd\n• 2nd still learned but 1st is gone => not enough collateral tagging to interfere with 2nd task\n\nActivating:\n\n• Uncontrolled experiments with focal electrical stimulation during surgery\n• Tag-and-manipulate / allocate-and-manipulate - re-triggers learned behavior even in unrelated contexts\n• In both cases, activation seems to spread from initial site to entire ensemble\n• Can create false associations:\n• Tag ensemble in context 1\n• Activate in context 2 and shock mice\n• Learned fear response in context 1\n• No fear response in context 2\n• Even indirectly\n• Tag ensemble in context 1\n• Tag ensemble during shock\n• Repeatedly active both in context 2\n• Learned fear response in context 2\n• No fear response in context 1\n• Artificial activation paired with chemical that inhibits reconsolidation removes association\n• So far stimuli limited to fear/reward and response limited to freeze/approach/avoid - need more complex tasks to test episodic memory\n\n## Memory, navigation and theta rhythm in the hippocampal-entorhinal system\n\nHaving a lot of trouble with this paper. Needs much more time and depth.\n\n• Allocentric / map-based navigation - static representation, navigate by external landmarks\n• Egocentric navigation / path integration - track motion, estimate path from origin\n• Hippocampus and entorhinal cortex support both declarative memory and navigation\n• Semantic memory (data independent of temporal context) ~ allocentric navigation\n• Episodic memory (first-person experiences in context) ~ egocentric navigation\n• Semantic memory abstracts repeated patterns in episodic memory ~ allocentric maps abstract repeated paths and observations\n\nImplementation possibilities:\n\n• Place cells in hippocampus - fire at specific locations in space - possibly encode position or distance?\n• Grid cells in medial entorhinal cortex - fire in repeating hexagonal pattern in space - different scales - possibly coordinate system?\n• Head direction cells - ?\n• Border cells - ?\n• This is too complicated to skim\n• Firing patterns are not simple - small changes in environment can result in large change in firing patterns - provides high-dimensional code for storing many different envs?\n\n• Insects manage to navigate with much simpler circuits / less storage.\n• Massive excess capacity in mammals might be related to reuse for different kinds of memory.\n• Might also enable ‘maps’ of semantic knowledge\n• cf spatial metaphors in language\n• Recognition and recall associated with unique firing patterns in that area for each object/event\n\n• If episodic memories are stored similarly to paths through environment, might explain time-asymmetry and temporal contiguity (recalling one events makes it easier to recall other events that are nearby in time)\n\n• Neuronal assembly sequences:\n\n• Patterns of activation in time?\n• Generated continuously even when environment and body signals are kept constant\n• Can predict correct/incorrect moves in maze seconds before motor event\n• Maybe used to organize episodic memory\n• Are chunked, just like paths and memory\n• Limits error in long sequences\n• Is chunking like a hash tree?\n\nSome complex ideas about implementation in theta waves that I can’t follow, but apparently explains:\n\n• Fine resolution near recalled event/location, coarse structure elsewhere\n• Limited number of concurrently recalled events/locations\n• Long-distance jumps between events/locations (related to chunking?)\n• Compressed recall eg episodic recall tends to focus around highlights/lowlights rather than being linear in time\n• Why episodic recall plays out in real-time - tied to same mechanism that implements subjective time tracking\n\nMaybe this explains why word-vec works? Are we just reverse-engineering the minds spatial relationships?\n\nQuestions:\n\n• Encoding/meaning of firing patterns\n• Other animals have similar cells but that are not theta modulated - do they have some substitute system?\n• What does the representation space look like (size, layout)?\n• How does the cell layout vary between rodents and primates? Do some areas grow out of proportion?\n• ?\n• Does awareness of recollections require only the prefontal cortex, or also interaction with the rest of the cerebral cortex.\n\n## The role of the hippocampus in navigation is memory\n\nPlace cells, grid cells etc seem to imply that the hippocampus provides navigation. Paper argues that the evidence actually shows that it provides general cognitive maps and that navigation is just one usecase.\n\n• Search\n• No active goal orientation\n• Just movement and goal recognition\n• Target approaching\n• Orienting towards observable goal\n• Guidance\n• Towards pre-calculated goal location\n• eg defined by relationship between multiple landmarks\n• Requires some spatial computation, and thereafter is just target approaching\n• Wayfinding\n• Recognizing and approaching landmarks\n• Joining landmarks into route\n• Joining routes together into topological map\n• Embed known routes/maps into common frame of reference\n• Supports novel routes, detours, shortcuts\n\nRats with hippocampal lesions:\n\n• Can handle route navigation (eg turn left a T) - presumably recognition-triggered\n• Can handle alternating routes - again presumably recognition-triggered - but not if delays are inserted\n• Can handle guidance navigation with single route (eg water maze task - memorizing location of invisible platform relative to objects on wall - same starting point)\n• Can’t handle guidance navigation with multiple routes (eg water maze task with different starting points)\n• Can’t handle survey navigation (eg maze rotated after learning)\n• May or may not be able to handle path integration\n• (and both rats and humans suck at it anyway)\n• In one experiment, humans could but rats couldn’t\n• In another, rats were impaired even when visual cues existed => maybe the problem is forgetting where the goal is\n• Recording studies haven’t found compelling evidence of hippocampal neurons involved in path integration\n• Grid cell firing patterns degrade in the dark => they don’t work well with path integration alone\n\nHumans with hippocampal lesions:\n\n• Can navigate by reading a map\n• Can handle guidance navigation and path integration, so long as fits in working memory\n• Can describe routes in areas they knew before damage\n\nWorking theory:\n\n• Hippocampus is required for survey navigation.\n• But survey navigation is sometimes used even when lower-level strategies would suffice, explaining failures on simpler tasks\n• eg when foraging for food in open field, see firing patterns in grid cells et al, see place cells fire in sequence when navigating to regular food drops, seee map updates when goal locations change\n• eg when disoriented animals reorient, they use local geometry even if prominent landmark is available\n• Hippocampus probably not required for path integration, except to remember starting point and goal\n\nEvidence that different spatial mappings are used for different tasks within the same environment.\n\nHippocampus maps abstract spaces:\n\n• Rats with lesions can learn direct SR but not transitive\n• Humans with lesions have higher deficits for order of events than for direct recall\n• Rats with lesions can recognize odors but not recall order in which they were presented\n• Interesting signals in human brains when presented with social or associative problems\n• Similarly to in spatial tasks, some memory tasks engage hippocampal relational processing even when not required (this paragraph seems to contradict itself?)\n\nImaging suggests that hippocampus is not continuously involved when using cognitive maps in navigation, but only when learning or when planning/altering routes.\n\nSpeculation that hippocampus originally evolved for navigation but was co-opted for abstract relationships. (How does hippocampus size vary across species?).\n\n## Lecture 3\n\nDivide into declarative vs non-declarative memory no longer seems to be carving at the joints:\n\n• HM couldn’t learn maze routes but could learn mirror drawing.\n• House task - recall vs recognition of complex spatial arrangements (front doors and porches). Suddenly recall tanks for patients.\n• Patients impaired at statistical learning of relationships and associations.\n• Mountain task - normal when matching color/time-of-day but impaired when matching arrangement/rotation.\n• Lesioned rats can detect novel objects and novel placements but can’t pair placement with background context.\n\nPattern separator vs pattern completer.\n\n• Old people struggle at pattern separation (old vs similar).\n• CA1 responds to any difference, CA3/DG responds to degree of difference.\n\nPatients learn facts at school, have high IQ and get good grades.\n\nUse fMRI to detect 60% periodicity in humans when navigating => grid cells. Periodicity correlates with success on spatial memory task.\n\nExperiment suggesting that periodicity can be observed even for abstract spaces, by pairing a coordinate system with bird pictures of varying neck and leg length.\n\nSomething analogous to space cells for time observed in rats.\n\n## Uniting the Tribes of Fluency to Form a Metacognitive Nation\n\nTheory: the difficulty of a cognitive task (from fluent to non-fluent) is used as a meta-cognitive cue that feeds into other judgments via ‘naive theories’ aka heuristics.\n\nFluency:\n\n• Perceptual\n• Physical eg illegible text, varying contrast\n• Temporal eg briefly flashed images\n• Memory\n• Retrieval eg availability heuristic\n• Encoding eg memorization techniques\n• Embodied (not connected to judgments by the references here)\n• Facial expressions eg smiling in math class\n• Body feedback eg mirror writing\n• Linguistic\n• Phonological eg pronounceable vs unpronounceable letter strings\n• Lexical eg familiar vs unfamiliar synonyms\n• Syntactic eg sentence tree structure\n• Orthographic eg using other alphabets, 12% vs twelve percent (reading latex?)\n• Conceptual eg priming with structurally similar explanations, semantic coherence\n• Spatial reasoning eg rotating shapes (not connected to judgments by the references here)\n• Imagery eg imagining hypothetical scenarios\n• Decision eg jam choices\n\nJudgments:\n\n• Truth\n• Liking\n• Confidence\n\nDiscounting - if fluency is recognized, subject corrects and may even over-correct.\n\nSeems like discounting provides a lot of adjustment room in this theory. How to falsify? Could try varying eg legibility over a wide scale and looking for a discounting effect.\n\n## Lecture 4\n\nFluency can induce:\n\n• familiarity\n• likability\n• dis-likability (but not replicated).\n• perception of light or darker image (but not replicated)\n• judgments of fame (abolished by eating popcorn)\n• judgments of danger (abolished by eating popcorn)\n• volume of background noise\n\nFamiliarity seems like a reasonable heuristic - exposure => fluency, so assume fluency => exposure.\n\nExplanation for the popcorn is that it prevents subvocalisation so can’t judge pronunciation fluency of words.\n\nOthers make less sense to me.\n\nNotable that the class was typically split when asked to predict outcome of experiments ie proposed mechanism is so vague that either outcome is plausible.\n\nOther ‘constructs’:\n\n• Subjects reconstruct past to create useful narratives\n• Subjects claim even under strong pressure to remember seeing events that only their partner saw\n• Subjects remember seeing words when only related words were present\n\nNot worth reviewing, not confident in results.\n\n## Understanding face recognition\n\nBroad view of facial recognition, including processes like retrieving information about the faces owner.\n\nWhat information might components of facial recognition produce?\n\n• Pictorial - when viewing static photo, reconstruct some 3d representation after correcting for lighting, grain etc\n• Structural - angle/lighting/expression -invariant model of face shape/structure usable for recognition\n• Identifiable from low-res photos and caricatures\n• Pictorial vs structural - recognition of photos of strangers faces is impaired by changing angle/lighting => structural representation takes time to build up.\n• Recognition of familiar faces is less impaired by changes to external features => over long-term representation picks up on more unchangeable details eg feature arrangement vs hair color\n• Recognition from restricted (eg just eyes) and occluded (eg wearing sunglasses) views => heavy redundancy in structural code\n• Visually-derived semantic eg age, gender, similar faces\n• Identity-specific semantic eg occupation, friends\n• Slower than recognition alone\n• Name\n• Separated from identity-specific because it is sometimes uniquely effected by injury\n• Often get familiarity without identity, or identity without name. But name without identity would be surprising.\n• Usually try to get name by searching for further identity details, suggests it’s attached to identity rather than directly to structural info.\n• Slower than identity-specific semantic alone\n• Expression\n• Facial speech - everyone lip-reads a little.\n• Separated from recognition by injury in both directions\n\nOpen questions:\n\n• Finer-grained breakdown of cognitive processes involved.\n• Do we decide that something is a face and then apply facial recognition or vice versa?\n• How is contextual information included? eg not recognizing someone because you didn’t expect to see them in that place\n\n## Are faces special?\n\nAre there dedicated cognitive process for facial processing, or do we just reuse generic object recognition?\n\nMain arguments:\n\n• Face-directed activity in infants => innate\n• Holistic recognition only occurs for faces, not other objects\n• There are face-specific neural representations\n\nMain challenges\n\n• Most experiments test within-class discrimination for faces vs between-class discrimination for objects - may be different processes\n• Expertise hypothesis - maybe similar results for any class that is well practiced eg dog judge recognizing different dogs\n\nInnate:\n\n• Newborn babies can distinguish similar faces even after changing hair and viewpoint\n• Same for young monkeys with no previous exposure to faces\n• But only for upright faces\n• Perceptual narrowing to faces of familiar races occurs\n\nHolistic/configural processing vs within-class discrimination:\n\n• Inversion effects much stronger for faces than within other classes\n• Inversion effects occur for ambiguous patterns that are primed as faces, but not if primed as characters\n• Part-whole effect - much better recognition for face parts when presented in a face vs alone, not for objects\n• Composite effect - much worse recognition for top half with non-matching bottom half than top half alone, not for objects\n• Inversion effects for objects disappear with repeated trials, but not for faces.\n\nNeural:\n\n• Monkeys and humans show face-selective cells in large clusters\n• Can be disrupted with TMS\n• Face and object discrimination can be separated by injury\n• FFA is strongly activated by face tasks but (usually) not by object tasks\n\nExpertise:\n\n• No holistic effects found in object experts (eg radiologists, ornithologists)\n\nArgument that too many studies rely on significant vs not-significant, rather than testing interactions.\n\n## Lecture 5\n\nAre faces special?\n\n• Functional specificity - specialized mechanisms\n• Neural specificity - implemented in face-selective areas/neurons/cells\n• Holistic - face is not represented as collection of parts, but as single object. (Tricky to pin down - makes more sense relative to later experiments.)\n• Configural - face representation depends on spatial configuration of features, not just features alone\n\nFace recognition could be:\n\n• Domain-general object recognition (item-level hypothesis)\n• Domain-specific object recognition (eg expertise hypothesis)\n• Face-specific (face-specificity hypothesis)\n• Some mixture of the above\n\nBehavioral experiments:\n\n• Have to separate ‘face’ from ‘low-level details that happen to occur in faces’ - inverted faces are good control\n• Face inversion effect - face recognition impaired much more by inversion than other expert objects\n• But much more expert in faces than anything else\n• Experiments testing correlation between degree of expertise and inversion effect have mixed results - still unsettled\n• Face-composite effect - easier to tell if top halves of faces are different when bottom halves are misaligned\n• Part-whole effect - easier to discriminate features in context of whole face, rather than alone\n• (Face-composite and part-whole seem directly opposed?)\n• Both effects much stronger for faces vs objects of expertise\n• Measures of degree of holistic processing? Comparing strengths of effects within subjects:\n• Inversion ~ part-whole = 0.28\n• Inversion ~ composite = -0.03\n• Part-whole ~ composite = 0.05\n• Inversion ~ face recognition = 0.42\n• Part-whole ~ face recognition = 0.25\n• Composite ~ face recognition = 0.04\n• Would expect strong correlations all round\n\nNeural experiments:\n\n• In FMRI, FFA reacts more strongly to faces vs objects\n• Low-level features? Faces vs scrambled faces.\n• Item-level recognition? Faces vs houses/porches.\n• Animate objects? Faces vs hands.\n• But stronger response for inverted faces.\n• More processing for triggered-but-failed recognition?\n• Similar results for other objects categories in other areas - indicates other specificities?\n• Places\n• Visual words\n• Bodies\n• Other peoples thoughts\n• Similar results for single-cell recordings in monkeys\n• Can find cells which react linearly to continuous changes in several of many face features\n• Deep brain stimulation results in mis-recognition\n• Face space (Chang & Tsao 2017)\n• Use PCA to choose vectors in face space\n• Found faces cells that react only to single vectors\n• Can reconstruct faces from cell responses\n\nMedical cases:\n\n• Prosopagnosia (developmental in ~2% of population)\n• Module defect or the tail of a bell curve?\n• Most visible symptom of general object agnosia? Some prosopagnosiacs have normal object recognition\n• Impairment of item-level recognition? Some prosopagnosiacs have normal item-level recognition\n• Impaired recognition of visually similar forms? Some prosopagnosiacs score normally on differentiation of morphed objects, as long as they are not faces\n• Impaired recognition of objects-of-expertise? WJ learned to recognize sheep at expert levels after injury.\n• Some subjects with object agnosia can recognize faces made out of vegetables, but can’t recognize the vegetables => independent mechanisms, not superset\n\nInnate:\n\n• Babies orient more towards face-like arrangements\n• Subject with upside-down head shows normal recognition accuracy on inverted faces, and > inverted accuracy on normal faces\n• (Surprised by interpretation. Also, maybe vision is flipped upstream?)\n\n## Lecture 6\n\nSkipped the reading this week :S\n\nSocial cognition - ‘the psychological processes that result from inferring the actual, imagined, or implied mental state of another’\n\nAffect is creeping back into models of decision-making.\n\nMoving away from 2-process model because of neuro evidence - clearly many systems involved.\n\nWhat makes a process automatic? Not requiring:\n\n• Intent\n• Capacity\n• Effort\n• Awareness\n\nRare for any given process to hit all 4.\n\nIllusion of agency - maybe intent does not exist.\n\nDebate over value of heuristics vs rationality.\n\nMentalizing:\n\n• inferring intentions, goals, desires of other mind (or own mind?)\n• typically care about intent and capability (eg warmth, competence etc)\n\nWhen do we attribute responsibility to an agent for an action?\n\n• Jones says single behavior => specific intent when:\n• given choice\n• has capability\n• departs from behavior of other agents\n• behaves differently in other contents / with other targets\n• Kelley says behavior over time => disposition when:\n• departs from behavior of other agents\n• behaves differently in other contents / with other targets\n• consistently behaves in this way in this context\n\nJohn laughs at the comedian. No one else laughs at the comedian. John laughs at every comedian. John laughs at the comedian every time. => Behavior is attributable to John, not to comedian\n\nExperimentally, seems to be less sensitive to consensus than other two.\n\nAttribute agency to objects similarly, but not moral status eg ‘computer said no’ but don’t feel bad for throwing the computer away. How do we tell the difference?\n\nEmotions hard to define.\n\n• Facial expressions are interpreted in context - changing context changes perception\n• No 1-1 mapping from face muscles to emotions - complex signal\n• Much disagreement on mapping emotions to brain regions\n• Anxious reappraisal\n• Self-reported eg happiness easily influenced by context, but discounted if made aware\n• Ability to mimic faces is innate, so universality of expressions could be from cultural transmission\n• Subjects with amygdala lesions can be fear-conditioned but are not aware of being afraid\n• Awareness of own heart rate predicts differing emotional reactions\n\nDominant theory - emotion as cognitive interpretation of physiological signals . Behavior change:\n\n• motivation + capacity\n• very resistant eg anti-smoking ads\n• changing environment almost always easier than changing the person\n\nDefault mode = social cognition applied to self?\n\n## Lecture 7\n\nExamples of theories that try to unify multiple phenomena:\n\n• Scale invariance\n• Decision by sampling\n• A theory of magnitude\n\nScale invariance:\n\n• $y \\propto x^\\alpha$\n• Examples in cogsci:\n• Weber’s law - smallest perceptable change : magnitude of stimulus\n• Fechner’s law - subjective intensity : physical intensity\n• Exponent varies by sense\n• Fitt’s law - time to hit target : log (target distance / target width)\n• Forgetting - recollection probability(?) : time\n• Surprising - exponential decay is a much more natural model\n• Practice - task reaction time : practice time\n• Recall - number of items recalled : time spent recalling\n• Seems not to depend at all on period covered by recall\n• Luce’s choice rule and Herrnstein’s matching law - probability of choosing item : attractiveness/payoff\n• Most examples cover a few ranges of magnitude but fall down at extremes\n• Causes?\n• Tends to be null hypothesis since it turns up so often\n• Violations, switching points are interesting\n\nDecision by sampling:\n\n• Need to be able to trade-off between utility of different outcomes, subjective probability, time\n• Well-calibrated\n• eg prospect theory matches up with empirical distribution of credits/debits into bank accounts, supermarket prices\n• eg temporal discounting matches up with number of google hits / newspaper entries for different durations\n• eg subjective risk evaluation matches up with probability judgments of probabilistic phrases + distribution of phrases in British National Corpus\n• How to explain this calibration?\n• Could be caused in other direction - subjective curves => behavior - but hard to see why it would affect distribution in this way.\n• Plausible algorithm - no numerical scale, just sample several similar elements and compare to get a rough ranking\n• How does sampling work? How is the reference class decided?\n• From memory - choose a reference class - explains framing\n• From context - explains anchoring and effect of irrelevant options\n• From exploration\n• How do we translate between reference scales eg trade off time vs money?\n• Poorly, usually.\n• CFAR’s ‘units of exchange’ provides anchors / exchange rate?\n• Picoeconomics claims willpower problems caused by hyperbolic discounting. Can we change the discounting curve by changing sampling process?\n\nA theory of magnitude:\n\n• Walsh 2003\n• Proposes that time, space and number are represented by same mechanism\n• Poorly supported, lecturer expects it to be wrong but useful as research direction\n• Time and space usually need to processed together eg for motor action, predicting movement\n• Plausible that number sense piggybacks on same system\n• Number vs space (well supported):\n• Quicker to distinguish numbers that have larger differences (ie further apart on number line)\n• SNARC effect - quicker response to small numbers on left side of vision, large numbers on right side of vision\n• Attention bias effect - quicker to notice stimuli in left when fixated on small number, right when fixated on large number\n• Line bisection effect - left/right bias when picking middle of string depending on number word in string eg “twotwotwotwo”\n• Asymmetric deficits on number tasks in neglect patients / TMS subjects\n• Some subjects describe weird number lines and also deviate from these patterns\n• Time vs number (poorly supported):\n• Number tasks and time estimation impair each other\n• Time vs space (poorly supported):\n• Subjects imaging 30m activity in scale model take longer for larger models\n• Neglect patients show asymmetric deficits when estimating duration of stimulus in neglected side of field\n\n## Scale-invariance as a unifying psychological principle\n\nScale invariance common in nature. Psych processes adapted to reflect this?\n\nClear examples in perception:\n\n• Luminance between sunlight and shade can be 10000x but brightness and color of an object is perceived same in both - visual system processes ratios, not absolute magnitudes\n• Similarly for hearing frequency - absolute pitch is rare but relative pitch is common\n• Weber’s law - difficulty of distinguishing perceptions proportional to ratio of magnitude, not absolute difference\n• But power varies across scale, so not totally clear\n• Steven’s law - in >30 perceptual/motor dimensions mapping to numerical scale is power law\n• When making judgments on numerical scale, does anchoring a point in the middle shift judgements in a scale-invariant fashion?\n\nCan’t be purely scale-invariant, because it is possible to judge magnitudes, but usually poorly.\n\nNot true at all for eg color perception.\n\nPerhaps reflects that the systems themselves are implemented physically.\n\n## A theory of magnitude: common cortical metrics of time, space and quantity\n\nArgues that:\n\n• Hemispheric asymmetry is because numerical calculation tied to language\n• Number-selective neurons located in same space as space-selective neurons, and some circumstantial evidence of temporal-sensitive neurons in same area\n\nExplaining interference in terms of attention is way too unconstrained. Sounds like single theory but close reading of literature shows that wide variety of proposed effects and causal mechanisms.\n\nPredicts SNARC should work for any space/action -coded magnitude.\n\n## Decision by sampling\n\nTypical theories of decision-making take utility functions as given. How do we build/calibrate a utility function given basic psychological operations?\n\nTo relate this back to previous two papers, how do we get an absolute judgment of utility out of brain systems that are only good at relative, scale-invariant judgments?\n\nMany examples of utility functions (in aggregate) matching cumulative distribution of events in the real world.\n\nProposes that we sample several items from memory and use these to estimate percentile on empirical distribution.\n\nMany other examples of similar processes:\n\n• Norm theory - judge normality by similarity to sampled events\n• Decision field theory - compare alternative by weighted sampling of advantages on random walk\n• Support theory - subjective probability depends on alternative hypotheses sampled\n• MINERVA-DM - subjective probability/plausibility based on similarity to sampled events\n• Stochastic difference model - ?\n\nAssumes that sampling from memory is a good approximation of sampling from reality. Some evidence for this eg Anderson & Schooler 1991.\n\nHas anyone tested the predicted binomial noise?\n\nTweaks:\n\n• Temporal discount rate decreases with magnitude of gain. Explained by assuming that time and magnitude are sampled together, not independently.\n• Temporal discount rate is higher for gains than losses. Explained by curvature of gain/loss utility interacting with base discount rate - discount applies to utility, not gain/loss directly.\n• Working-memory load increases discounting of delayed vs immediate gains. Explained by failing to sample enough large delays - biases score upwards.\n\n## Lecture 8\n\nLanguage is hard to define:\n\n• Clark & Clark 1977\n• Arbitrary - mapping from words to meanings\n• Structured - mapping from sentence to meaning\n• Generative - not limited to fixed set of meanings\n• Dynamic - words and structure change over time\n• Hocket 1963 - 13 features, of which 10-13 are claimed to only exist in humans\n• Displacement - refer to things removed in time and space\n• Productivity - create novel utterances/meanings which are nevertheless understood by others\n• Cultural transmission\n• Duality of patterning - generative\n• (But many of these arguably displayed in animals eg Alex the parrot)\n\nLevels of analysis:\n\n• Phonology - phonemes, speech perception, spectrograms\n• Semantics - words, semantic priming\n• Grammar - hierarchical structure, formal grammars\n\n• Broca’s area = speech production\n• Wernicke’s area = speech comprehension\n• Connected by arcuate fasciculus\n• Concentrated in left hemisphere:\n• Wada test - inject sodium amital into artery to sedate one hemisphere\n• Anatomical asymmetry in related areas\n• Asymmetry in PET and fMRI on language tasks\n• Differences in neuron shape between hemispheres\n• But hugely confounded by motor control which is also asymmetric\n\nProblems with model:\n\n• No clear causal relation between lesions and defects (including patients recovering from defects over time)\n• No consistent correlation established by functional imaging\n• Voxel-based lesion-symptom mapping identifies different areas\n• Evidence for multiple networks for language comprehension\n• Right hemisphere dominant for many complex language tasks\n• Word-specific activation distributed throughout brain, seemingly paralleling organization of sensory and motor systems eg action words in the motor system\n\nSpeech perception is ambiguous - requires top-down processing. Illusion of speech units.\n\n• At phonology level:\n• Segmentation problem - cannot find word/syllable boundaries in spectrogram\n• ‘Lack of invariance’ problem - phonemes do no have consistent representation in spectrogram\n• Speaking rate eg careful pronunciation vs normal conversation produce different spectrograms\n• Huge variation between accents\n• At word level:\n• Homonyms\n• Polysemy eg ‘the door fell off its hinge’ vs ‘the child ran through the door’\n• At syntax level:\n• Ambiguous binding\n• Combined eg ‘Mary made her dress correctly’\n• Correct interpretation improved by access to mouth movements, body movements (co-speech), conversational context\n\nReally no reason to continue teaching Wernicke-Geschwind model.\n\n## The free-energy principle: a unified brain theory?\n\nSummary of Surfing Uncertainty\n\nSummary of The Predictive Mind\n\nWikipedia on free-energy principle\n\nVariational Bayes:\n\n• Posterior $P(Z \\vert X)$ is hard to calculate exactly, so instead we approximate it by some family of distributions $Q_\\theta(Z)$\n• Want to minimize $D_{\\mathrm{KL}}(Q(Z) \\Vert P(Z \\vert X))$, because we have to minimize something and this is both reasonable and tractable.\n• Related - $P_\\mathrm{new}(\\theta, X) = \\mathrm{argmin}_Q D_{KL}(Q(\\theta, X) \\Vert P_\\mathrm{old}(\\theta, X)) \\text{ subject to } \\sum_\\theta Q(\\theta, X=x) = 1 \\text{ and } \\sum_\\theta Q(\\theta, X \\neq x) = 0$. Is minimizing distance to posterior equivalent to minimizing distance to prior subject to constraints?\n• Implications for forward vs reverse KL\n• Can rewrite as $D_{\\mathrm{KL}}(Q \\Vert P) = \\mathrm{constant} -H(Q) -E_Q[\\log{P(Z,X)}]$. Last term (last two terms?) is called ‘variational free energy’. Because thermodynamics?\n• If $Q$ has some factorization over $Z$ can use calculus of variations (somehow) to produce a set of recursive equations that describe the minimum and which converge under iteration.\n\nFree energy principle\n\n• $P$ is joint distribution of world model (‘causes’) and sensory input. Bayesian update on this model predicts future sensory inputs from past sensory inputs, via inferring underlying causes.\n• $Q$ is referred to as recognition density. (Why?)\n• Express free energy $F$ wrt energy and entropy:\n• $F = -E_Q[\\log{P(\\text{sense}, \\text{cause})}] -H(Q(\\text{cause}) = \\text{energy} - \\text{entropy} = \\text{expected surprise} - \\text{complexity of model}$\n• Shows that free energy can be evaluated using information that the agent has\n• Rewrite free energy $F$ wrt action:\n• IE how much we had to mess with the model vs how much predictive accuracy we gained for the recent sensation\n• The action that minimizes free energy is the one that minimizes surprise about the resulting sensations => act to confirm predictions\n• Hard to interpret. Eg changing point of view to disambiguate optical illusion?\n• Active inference\n• Rewrite free energy $F$ wrt sensation:\n• As approximation -> model, $F$ -> surprise\n• Choosing actions and models to minimize $F$ places an upper bound on surprise\n• Perceptions feed into online update of $Q$ to more accurately model causes and hence future perceptions.\n\nBut we like surprising things? Presumably this is to be explained. Or are actions chosen to minimize $F$ in general, rather than for this specific action?\n\nRelation to infomax principle (maximizing mutual information between sense and model subject to constraints on complexity of model). Complexity term in 1st formulation penalizes more complex models - regularization/shrinking.\n\nThe fact that these models predict empirically observed receptive fields so well suggests that we are endowed with (or acquire) prior expectations that the causes of our sensations are largely independent and sparse.\n\nArranged hierarchically, so each model passes prediction error up and passes predictions down. Precision parameter models noise at each level. High noise => more trust in priors / predictions from above. Low noise => more trust in sensory data from below.\n\nStates ‘value is inverse proportional to surprise’. (In a particular simple model) if we perform gradient ascent on value, then the long-term proportion of time spent in a state is proportional to value, so surprise is inversely proportional to value. Since we act to minimize free energy, priors can encode values. But does acting to minimize free energy lead to gradient ascent on value? Seems like the argument is backwards.\n\nStarting to get flashes of picoeconomics here - recursive relation between model of the future and model of own decision making.\n\nMany references to more general connections between minimizing free energy and defying thermodynamics over lifetime of agent, which I don’t follow at all.\n\n## Active Inference, Curiosity and Insight\n\nVarious activities can be explained as acting to reduce uncertainty:\n\n• Hidden states -> perceptual inference\n• Future states -> information-seeking behavior, intrinsic motivation\n• Future outcomes -> goal-seeking behavior, extrinsic motivation\n• World model / parameters -> novelty-seeking behavior, curiosity\n\nTo infer expected free energy, we need priors on our own behavior.\n\n• Minimizing free energy == avoiding surprise\n• Minimizing expected free energy == acting to resolve uncertainty\n• Need prior on our own behavior to calculate expected free energy. Active inference == prior that we will minimize free energy.\n\nUsing example of learning complex rules by active inference. Use prior beliefs about own behavior to encode rules of task, in a way that I don’t understand.\n\nNon-REM sleep. In absence of new sensory input, minimizing free energy => minimizing model complexity vs accuracy. Pruning as regularization.\n\nREM sleep. After pruning parameters, need to reevaluate posterior. Can do this by re-simulating observed evidence.\n\nSuperstition as premature pruning.\n\nOpen confusions: choice of action vs expected free energy, encoding values as priors, explore vs exploit, precision. Suspect that many of these would be resolved by implementing one of the examples\n\n## Lecture 9\n\nValue of actions can depend on order eg find food then eat vs eat then find food. So have to evaluate policies, not individual actions.\n\n$\\sigma$ is softmax.\n\nPenalizes divergence between $Q$ and $P_\\text{prior}$, can set prior on future state to encode value. Not clear how to encode non-bounded tasks.\n\nBear in mind that we are summing log-probabilities == multiplying probabilities. So states that have 0 on any of the decompositions are still worthless overall.\n\nDepression, self-destructive behavior etc explained as malformed priors.\n\nFrom discussion afterwards:\n\n• Example models don’t show precision. When used, it’s often to fixed to a constant unless they are trying to model dopamine.\n• Policies are pure function of Q - so not timeless but not directly depending on time either - allows controlling how much memory the model has by controlling what Q remembers of the past.\n• In examples path integral is trivial, but in more complex models use time slicing?\n\n## Lecture 10\n\nEmbodied cognition - cognitive processes rooted in perception and action, knowledge not stored as abstract symbolic representation but derived on the fly from perception (past or present) and action.\n\nDoesn’t seem to pin down a clear hypothesis, makes it difficult to figure out which experiments support which version of the theory.\n\nEg language\n\n• Some support for abstract representation\n• eg mix up phonemes sometimes => phonemes are a unit at some level of processing\n• But how is abstract representation connected to the world?\n• Embodied metaphors eg future is in front, past is behind.\n\nUsually attempt to demonstrate embodiment by demonstrating interaction between cognition and perception/action.\n\nClassic experiments which failed to replicate:\n\n• Hold pen in mouth to create frown or smile, affects humor rating of cartoons\n• Adverts which suggest an action matching the viewers handedness are preferred, reversed when hand is already occupied\n• Parsing action sentences as valid/invalid is quicker when the correct option is presented in a location that matches the action direction\n• Hearing words associated with body parts activates same brain region as moving those body parts\n\nPresented several other experiments which have yet to be replicated. Effect sizes are typically <1%\n\nThink of embodiment as a spectrum from purely symbolic/logical to fully embodied. Claim evidence does not strongly support either end of the spectrum.\n\nModels of embodiment underspecified. Any effect of the body on thought taken as evidence for embodiment without understanding of how embodiment works. We should be able to explain the pattern of results, not just whether embodiment is there or not."
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http://math.stackexchange.com/users/52694/mike-battaglia
# Mike Battaglia less info reputation 117 bio website location age member for 1 year, 11 months seen Sep 3 at 4:03 profile views 99 # 19 Questions 14 Integer sequences which quickly become unimaginably large, then shrink down to “normal” size again? 14 Elements in $\hat{\mathbb{Z}}$, the profinite completion of the...
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http://www.talkstats.com/threads/log-rank-or-other-test-for-difference-between-survival-curves.25008/
# log-rank (or other) test for difference between survival curves #### @nthRo ##### New Member Hi, all. I have co-opted some R code that estimates parameters for a Gompertz-Makeham mortality model. The data to which the model is fit is interval censored, with counts of individuals in each age-range category. For exa...
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http://www2.macaulay2.com/Macaulay2/doc/Macaulay2-1.19/share/doc/Macaulay2/Polyhedra/html/_is__Pointed.html
# isPointed -- checks if a Cone or Fan is pointed ## Synopsis • Usage: b = isPointed C b = isPointed F • Inputs: • F, an instance of the type Fan • Outputs: • b, , true if the Cone or the Fan is pointed, false otherwise ## Description Tests if a Cone is pointed, i.e. the lineality space is 0. A Fan is pointed if on...
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https://www.clutchprep.com/chemistry/practice-problems/103744/carbon-disulfide-a-poisonous-flammable-liquid-is-an-excellent-solvent-for-phosph-1
# Problem: Carbon disulfide, a poisonous, flammable liquid, is an excellent solvent for phosphorus, sulfur, and some other nonmetals. A kinetic study of its gaseous decomposition gave these data:Calculate the average value of the rate constant. ⚠️Our tutors found the solution shown to be helpful for the problem you're...
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http://nrich.maths.org/public/leg.php?code=-99&cl=2&cldcmpid=1235
# Search by Topic #### Resources tagged with Working systematically similar to Estimating Angles: Filter by: Content type: Stage: Challenge level: ### There are 325 results Broad Topics > Using, Applying and Reasoning about Mathematics > Working systematically ### First Connect Three ##### Stage: 2 and 3 Challeng...
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https://www.usgs.gov/media/images/another-look-margin-kahauale-a-2-flow-small-vegetat
# Another look at the margin of the Kahauale‘a 2 flow. Small vegetat... ## Detailed Description Another look at the margin of the Kahauale‘a 2 flow. Small vegetation fires triggered by the active lava spread a short distance out from the flow margin. ## Details Image Dimensions: 4608 x 3456 Date Taken:
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https://chem.libretexts.org/Under_Construction/Purgatory/Book%3A_Analytical_Chemistry_2.0_(Harvey)/12_Chromatographic_and_Electrophoretic_Methods/12.7%3A_Electrophoresis
# 12.7: Electrophoresis Electrophoresis is a class of separation techniques in which we separate analytes by their ability to move through a conductive medium—usually an aqueous buffer—in response to an applied electric field. In the absence of other effects, cations migrate toward the electric field’s negatively char...
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