text:
»  Home »  Stata Conferences and Users Group meetings »  Stata Conference Columbus 2018
Columbus 2018
July 19-20

Join Stata users and experts at the 2018 Stata Conference in Columbus on July 19–20.

Experience what happens when new and long-time Stata users from across all disciplines gather to discuss real-world applications of Stata. The Stata Conference provides an unparalleled opportunity for you to collaborate with Stata developers and connect with the inventive and creative user community. Don’t miss this great networking and learning opportunity.

## Program talks include

• Nonlinear mixed-effects regression
Abstract: In many applications, such as biological and agricultural growth processes and pharmacokinetics, the time course of a continuous response for a subject over time may be characterized by a nonlinear function.
Parameters in these subject-specific nonlinear functions often have natural physical interpretations, and observations within the same subject are correlated. Subjects may be nested within higher-level groups, giving rise to nonlinear multilevel models, also known as nonlinear mixed-effects or hierarchical models. The new Stata 15 command menl allows you to fit nonlinear mixed-effects models, in which fixed and random effects may enter the model nonlinearly at different levels of hierarchy. In this talk, I will show you how to fit nonlinear mixed-effects models that contain random intercepts and slopes at different grouping levels with different covariance structures for both the random effects and the within-subject errors. I will also discuss parameter interpretation and highlight postestimation capabilities.
Houssein Assaad, Senior Statistician and Software Developer
StataCorp
• ERMs, simple tools for complicated data
Abstract: While the term "extended regression model" (ERM) may be new, the method is not. ERMs are regression models with continuous outcomes (including censored and tobit outcomes), binary outcomes, and ordered outcomes that
are fit via maximum likelihood and that also account for endogenous covariates, sample selection, and nonrandom treatment assignment. These models can be used when you are worried about bias due to unmeasured confounding, trials with informative dropout, outcomes that are missing not at random, selection on unobservables, and more. ERMs provide a unifying framework for handling these complications individually or in combination. Charles Lindsey will briefly review the types of complications that ERMs can address. He will work through examples that demonstrate several of these complications and show some inferences we can make despite those complications.
Charles Lindsey, Senior Statistician and Software Developer
StataCorp
Abstract: Teaching Markov Chain Monte Carlo Bayesian methods to undergraduates can be challenging because they, for the most part, are not familiar with advanced methodologies such as multilevel models, IRT, or other
analytical methods that are commonly found in Bayesian analyses. However, almost every undergraduate is familiar with the t-test. This presentation will use Stata's bayesmh command to perform a two-sample independent t-test. We will discuss the advantages to using a Bayesian approach to perform t-test type analyses and compare the output or results with the traditional frequentist t-test.
Phil Ender, UCLA (Ret)
• dtalink: Faster probabilistic record linking and deduplication methods in Stata for large data files
Abstract: Stata users often need to link records from two or more data files, or find duplicates within data files. Probabilistic linking methods are often used when the file or files do not have reliable or unique
Keith Kranker, Mathematica Policy Research
• PPMLHDFE: Fast, flexible Poisson estimation with high-dimensional fixed effects
Abstract: This is a Stata package for estimation of Poisson models with high-dimensional fixed effects. It is a joint effort by Sergio Correia (the author of reghdfe), Paulo Guimaraes (the author of poi2hdfe), and
myself (the author of ppml_panel_sg). This new command has several very desirable features that we expect will make it very popular. Like ppml_panel_sg, it is ideally suited for Poison PML estimation of structural gravity models - a workhorse empirical model in economics used to identify spatial frictions. However, like reghdfe, it can be used with any set of fixed effects. Furthermore, like poi2hdfe, it runs on an IRLS loop using the reghdfe architecture to perform each least squares step. This alone makes it very fast. But we have also implemented several additional speed-up tricks for IRLS HDFE estimation that allow for significant further speed gains. In addition, we are working toward a novel way of verifying beforehand that Poisson estimates exist that are robust to the inclusion of high-dimensional fixed effects.
Thomas Zylkin, University of Richmond
• The empirical analysis of core housing need in Canada: Evidence from the survey of household spending
Abstract: In 2011, approximately 12% of Canadian households were in Core Housing Need (CHN), meaning that these households live in housing that requires major repair (adequacy), does not have enough bedrooms for the size of
the household (suitability), costs 30% or more of before-tax income (affordability), or any combination of these three. Moreover, these households would have to spend 30% or more of their income to access local housing that meets the three standards. In 2017, Canada Mortgage and Housing Corporation (CMHC) announces a vision for the National Housing Strategy (NHS), which, among other things, aims to reduce the number of households in CHN. This study exploits rich microdata files from Statistics Canada, the Survey of Household Spending (SHS), and fitted models for the three standards using non-recursive Generalized Structural Equation Model (GSEM) to explain socioeconomic and demographic drivers of CHN. This study also sheds light to policymakers in the development of various policy levers by predicting the impact of housing initiatives on changes in the likelihood of being in CHN.
Duangsuda Sopchokchai, Canada Mortgage and Housing Corporation
• Doing less with Stata Markdown
Abstract: Stata’s new dyndoc and its sister commands provide a rich set of tools for reimagining document writing. An example of this is a document translator, stmd, that converts dynamic documents written with plain
Markdown tags to Stata’s dyndoc format. This allows the user to write documents in the simple, uncluttered Markdown style used with other programming languages and on websites and still use many of dyndoc’s features such as executing code and embedding graphics links.
Doug Hemken, Social Science Computing Cooperative
• Vector-based kernel weighting: A simple estimator for improving precision and bias of average treatment effects in multiple treatment settings
Abstract: Treatment effect estimation must account for endogeneity, in which factors affect treatment assignment and outcomes simultaneously. By ignoring endogeneity, we risk concluding that a helpful treatment is not
beneficial or that a treatment is safe when it is actually harmful. Propensity score (PS) matching or weighting adjusts for observed endogeneity, but matching becomes impracticable with multiple treatments, and weighting methods are sensitive to PS model misspecification in applied analyses. We used Monte Carlo simulations (1,000 replications) to examine sensitivity of multi-valued treatment inferences to PS weighting or matching strategies. We consider four variants of PS adjustment: inverse probability of treatment weights (IPTW), kernel weights, vector matching, and a new hybrid –vector-based kernel weighting (VBKW). VBKW matches observations with similar PS vectors, assigning greater kernel weights to observations with similar probabilities within a given bandwidth. We varied degree of PS model misspecification, sample size, number of treatment groups, and sample distribution across treatment groups. Across simulations, VBKW performed equally or better than the other methods in terms of bias and efficiency. VBKW may be less sensitive to PS model misspecification than other methods used to account for endogeneity in multi-valued treatment analyses.
Jessica Lum, Department of Veterans Affairs
• New data cleaning command: assertlist–improves speed and accuracy of collaborative correction
Abstract: Stata’s handy assert command can certify that a dataset meets a set of user expectations, but when one assertion is violated, it throws an error and does not proceed to check the rest. Identifying problems with
every variable in a large dataset can involve a messy set of ad hoc error traps and LIST commands to learn what unexpected values occur in what dataset rows. Furthermore, code to REPLACE errant values sometimes involves IF syntax with a list of terms connected by Boolean ANDs that identify the row targeted for the fix; when typed by hand, these rows are quite susceptible to typographical errors. This talk describe a new command, assertlist, that can test an entire set of assertions in one run without ad hoc code to drill down or move on. Exceptions are listed either to the screen or a spreadsheet. In situations where problematic values will later be corrected or replaced, assertlist generates spreadsheet columns that wait to receive hand-entered corrected values and other columns that immediately put corrected values into Stata REPLACE commands for easy pasting into downstream .do files. In our experience, assertlist streamlines well-documented data cleaning and guards against errors in correction code.
Dale Rhoda, Biostat Global Consulting
• Organ pipe plots for clustered datasets–visualize disparities in cluster level coverage
Abstract: Leo Tolstoy is famous for his novels and less well known for his ideas on survey data analysis. Concerning estimated proportions, he is said to have written: ͞Covered strata are all alike; every poorly covered
stratum is poorly covered in its own way.͟ I describe a new command to make what we call organ pipe plots to visualize heterogeneity in binary outcomes in clustered data. The plots were conceived for vaccination coverage surveys, but they are helpful in a wide variety of contexts. Imagine a survey where only 50% of sampled children are found to be vaccinated. Different programmatic responses would be appropriate if the vaccinated include all the children in half the clusters versus half the children in all the clusters. These plots have been used to identify neighborhoods that were surreptitiously and intentionally skipped over during vaccination campaigns. The talk will demonstrate the command and discuss similarities with Pareto plots from quality control and a visual connection to the intracluster correlation coefficient (ICC). Note that the ICC shares a connection to anarcho-pacifistic ideas in Tolstoy’s later novels: many students mention them…but few can describe them clearly.
Mary Prier, Biostat Global Consulting
• Even simpler standard errors for two-stage optimization estimators: Mata implementation via the DERIV command
Abstract: Terza (2016a) offers a heretofore unexploited simplification (henceforth referred to as SIMPLE) of the conventional formulation for the standard errors of two-stage optimization estimators (2SOE). In that paper,
SIMPLE was illustrated in the context of two-stage residual inclusion (2SRI) estimation (Terza et al., 2008). Stata/Mata implementations of SIMPLE for 2SRI estimators are detailed in Terza (2017a and b). Terza (2016b) develops a variant of SIMPLE for calculating the standard errors of two-stage marginal effects estimators (2SME). Generally applicable Stata/Mata implementation of SIMPLE for 2SME is detailed in Terza (2017c) and compared with results from the Stata MARGINS command (for the subset of cases in which the MARGINS command is available). Although SIMPLE substantially reduces the analytic and coding burden imposed by the conventional formulation, it still requires the derivation and coding of key partial derivatives that may prove daunting for some model specifications. In this presentation, I detail how such analytic demands and coding requirements are virtually eliminated via the use of the Mata DERIV command. I will discuss illustrations in the 2SRI and 2SME contexts.
Terza, J., A. Basu, and P. Rathouz (2008). Two-stage residual inclusion estimation. Addressing endogeneity in health econometric modeling. Journal of Health Economics 27: 531-543.
Terza, J.V. (2016a). Simpler standard errors for two-stage optimization estimators. Stata Journal 16: 368-385.
Terza, J.V. (2016b). Inference using sample means of parametric nonlinear data transformations. Health Services Research 51: 1109-1113.
Terza, J.V. (2017a). Two-stage residual inclusion estimation: A practitioners guide to Stata implementation. Stata Journal 17: 916-938.
Terza, J.V. (2017b). Two-stage residual inclusion estimation in health services research and health economics. Health Services Research, forthcoming, DOI: 10.1111/1475-6773.12714.
Terza, J.V. (2017c). Causal effect estimation and inference using Stata. Stata Journal 17: 939-961.
Joseph Terza, Department of Economics
Indiana University Purdue University Indianapolis
• Automating exploratory data analysis tasks with eda
Abstract: Several tools currently exist in the Stata ecosystem for document preparation, authoring, and creation, each with their own unique strengths. Similarly, there are many tools available to map data to
visual dimensions for exploratory and expositive purposes. While these tools are powerful on their own, they do not attempt to solve the most significant resource constraint we all face. The eda command is designed to address this time constraint by automating the creation of all the univariate and bivariate data visualizations and summary statistics tables in a data set. Users can specify categorical and continuous variables manually, provide their own rules based on the number of unique values, or allow eda to use its own defaults and eda will apply the necessary logic to graph and describe the data available. The command is designed to produce the maximum amount of output by default, so a single line of code can easily produce a document providing substantial insight into your data.
Billy Buchanan, Fayette County Public Schools
• Output and automatic reporting using putdocx/putpdf
Abstract: Are you tired of copying and pasting tables, titles, figures, paragraphs, and footnotes in Excel into Word or pdf files ? Here is good news: Stata 15 has released a new feature that creates analysis tables,
figures, footnotes, and paragraphs directly in Word or pdf files. The new command, putdocx/putpdf, serves as a one-stop-shop tool for transforming your Stata codes into Word or pdf file. This presentation will show you how to generate analysis tables, figures, and discussion or summary paragraphs directly in Word or pdf format. Plus, instead of manually updating the new numbers in your tables, figures, summary paragraphs, or footnotes when periodic updates are required, all you must do is refresh the dataset and run your existing .do file of putdocx/putpdf, and call it to see the instantly updated results directly in Word/pdf file. This can be done in one click. More specifically, below is a list of formatting and analysis results to be shown out of putdocx/putpdf and output directly in a Word or pdf file: 1. Paragraphs with statistics in them, 2. Figures, 3. Tables - • descriptive summary table • regression table • logistic regression table • survival analysis table, etc. 4. Automation of exporting, and 5. Combination of several .docx files into one summary report.
Dong Hua, Corrona, LLC
• How are population pressures and carbon dioxide emissions linked in Africa?
Abstract: This study uses Stata commands to investigate the relationship between population pressures and carbon dioxide (CO2) emissions in African countries at different income groupings. The Stata commands are
particularly critical when linked with the population-pressures–environment nexus as indicated by the empirical results. Yet, the evidence on the panel-data Stata commands analysis is surprisingly critical, inconclusive, and subject to further investigation. We investigate this issue using descriptive, empirical and rich anthropogenic drivers linked Stata commands population-pressures panel data from 1960–2012. The Stata commands provide efficient descriptive analysis to suggest that the combined CO2 emissions concentration from 1960–2010 indicates an approximate 565%, 1,286%, and 505% increase in emission concentration in upper-income countries in Africa (UICA), lower-middle-income countries in Africa (LMICA), and low-income countries in Africa (LICA), while the total population increased from 1960–2012, accounting for an approximate 221%, 301% and 315% increase in population size, respectively. Furthermore, we provide evidence on the moderating roles of the final consumption expenditure (annual growth), manufacturing sector, and services sector in the linkages between population and CO2 emissions. Stata commands are robust for controlling for contemporaneous correlation, panel heteroskedasticity, and serial correlation. The empirical findings support negative impacts, and suggest the average effect of population growth over CO2 emissions, when the population growth changes across time and, between countries in LICA, LMICA, and UICA rises by 1% and increases CO2 emissions by about 0.38%, 1.08%, and 0.31% respectively, holding all other predictors constant. Overall, the results suggest that particular attention should be devoted to the population size and population growth in ameliorating CO2 emissions, especially countries with high population size such as Nigeria, Egypt, and Ethiopia that all belong to the LIMCA but also support low emission loads in LICA.
Abdulrasaki Saka, Federal Polytechnic Offa, Nigeria
• Assessing the calibration of dichotomous outcome models with the calibration belt
Abstract: The calibration belt is a graphical approach designed to evaluate the goodness of fit of binary outcome models such as logistic regression models. The calibration belt examines the relationship between estimated
probabilities and observed outcome rates. Significant deviations from the perfect calibration can be spotted on the graph. The graphical approach is paired to a statistical test, synthesizing the calibration assessment in a standard hypothesis testing framework. We present the calibrationbelt command, which implements the calibration belt and its associated test in Stata.
Giovanni Nattino, The Ohio State University
• And more.

## Scientific committee

Stan Lemeshow (chair)
Ohio State University
Public Health
Timothy R. Sahr (coordinator)
Ohio Colleges of Medicine
Government Resource Center
Kelly Balistreri
Bowling Green State University
Chris Browning
Ohio State University
Sociology
Anand Desai
National Science Foundation
Bo Lu
Ohio State University
Biostatistics
Eric Seiber
Ohio State University
Public Health
Mary Applegate
Ohio Department of Medicaid
Anirudh Ruhil
Ohio University

## Registration

Seats are limited. Choose one of the options below. Lunch and refreshments are included in the registration fee.

Price Student price
Both days
 $195 Register $75 Register
Day 1: Thursday,
July 19, 2018
 $125 Register $50 Register
Day 2: Friday,
July 20, 2018
 $125 Register $50 Register
Dinner (optional)
July 19, 2018

## Venue

Hyatt Regency Columbus
350 North High Street
Columbus, OH 43215

The conference hotel is within steps of the Arena District, Huntington Park, and the popular Short North Arts and Entertainment District. After the Conference, relax and enjoy what Columbus has to offer. From the world-class Columbus Zoo and Aquarium to the Franklin Park Conservatory and Botanical Gardens, you will find much to do during your stay.


text:
# Properties

 Label 490.2.e.h Level $490$ Weight $2$ Character orbit 490.e Analytic conductor $3.913$ Analytic rank $0$ Dimension $2$ CM no Inner twists $2$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$490 = 2 \cdot 5 \cdot 7^{2}$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 490.e (of order $$3$$, degree $$2$$, not minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$3.91266969904$$ Analytic rank: $$0$$ Dimension: $$2$$ Coefficient field: $$\Q(\sqrt{-3})$$ Defining polynomial: $$x^{2} - x + 1$$ Coefficient ring: $$\Z[a_1, a_2]$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 70) Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

## $q$-expansion

Coefficients of the $$q$$-expansion are expressed in terms of a primitive root of unity $$\zeta_{6}$$. We also show the integral $$q$$-expansion of the trace form.

 $$f(q)$$ $$=$$ $$q + \zeta_{6} q^{2} + ( 1 - \zeta_{6} ) q^{3} + ( -1 + \zeta_{6} ) q^{4} -\zeta_{6} q^{5} + q^{6} - q^{8} + 2 \zeta_{6} q^{9} +O(q^{10})$$ $$q + \zeta_{6} q^{2} + ( 1 - \zeta_{6} ) q^{3} + ( -1 + \zeta_{6} ) q^{4} -\zeta_{6} q^{5} + q^{6} - q^{8} + 2 \zeta_{6} q^{9} + ( 1 - \zeta_{6} ) q^{10} + ( 6 - 6 \zeta_{6} ) q^{11} + \zeta_{6} q^{12} + 4 q^{13} - q^{15} -\zeta_{6} q^{16} + ( -2 + 2 \zeta_{6} ) q^{18} + 2 \zeta_{6} q^{19} + q^{20} + 6 q^{22} + 3 \zeta_{6} q^{23} + ( -1 + \zeta_{6} ) q^{24} + ( -1 + \zeta_{6} ) q^{25} + 4 \zeta_{6} q^{26} + 5 q^{27} -3 q^{29} -\zeta_{6} q^{30} + ( 8 - 8 \zeta_{6} ) q^{31} + ( 1 - \zeta_{6} ) q^{32} -6 \zeta_{6} q^{33} -2 q^{36} + 4 \zeta_{6} q^{37} + ( -2 + 2 \zeta_{6} ) q^{38} + ( 4 - 4 \zeta_{6} ) q^{39} + \zeta_{6} q^{40} -9 q^{41} -7 q^{43} + 6 \zeta_{6} q^{44} + ( 2 - 2 \zeta_{6} ) q^{45} + ( -3 + 3 \zeta_{6} ) q^{46} - q^{48} - q^{50} + ( -4 + 4 \zeta_{6} ) q^{52} + ( 6 - 6 \zeta_{6} ) q^{53} + 5 \zeta_{6} q^{54} -6 q^{55} + 2 q^{57} -3 \zeta_{6} q^{58} + ( -6 + 6 \zeta_{6} ) q^{59} + ( 1 - \zeta_{6} ) q^{60} + 5 \zeta_{6} q^{61} + 8 q^{62} + q^{64} -4 \zeta_{6} q^{65} + ( 6 - 6 \zeta_{6} ) q^{66} + ( -5 + 5 \zeta_{6} ) q^{67} + 3 q^{69} -6 q^{71} -2 \zeta_{6} q^{72} + ( -16 + 16 \zeta_{6} ) q^{73} + ( -4 + 4 \zeta_{6} ) q^{74} + \zeta_{6} q^{75} -2 q^{76} + 4 q^{78} -2 \zeta_{6} q^{79} + ( -1 + \zeta_{6} ) q^{80} + ( -1 + \zeta_{6} ) q^{81} -9 \zeta_{6} q^{82} -3 q^{83} -7 \zeta_{6} q^{86} + ( -3 + 3 \zeta_{6} ) q^{87} + ( -6 + 6 \zeta_{6} ) q^{88} -15 \zeta_{6} q^{89} + 2 q^{90} -3 q^{92} -8 \zeta_{6} q^{93} + ( 2 - 2 \zeta_{6} ) q^{95} -\zeta_{6} q^{96} -14 q^{97} + 12 q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$2q + q^{2} + q^{3} - q^{4} - q^{5} + 2q^{6} - 2q^{8} + 2q^{9} + O(q^{10})$$ $$2q + q^{2} + q^{3} - q^{4} - q^{5} + 2q^{6} - 2q^{8} + 2q^{9} + q^{10} + 6q^{11} + q^{12} + 8q^{13} - 2q^{15} - q^{16} - 2q^{18} + 2q^{19} + 2q^{20} + 12q^{22} + 3q^{23} - q^{24} - q^{25} + 4q^{26} + 10q^{27} - 6q^{29} - q^{30} + 8q^{31} + q^{32} - 6q^{33} - 4q^{36} + 4q^{37} - 2q^{38} + 4q^{39} + q^{40} - 18q^{41} - 14q^{43} + 6q^{44} + 2q^{45} - 3q^{46} - 2q^{48} - 2q^{50} - 4q^{52} + 6q^{53} + 5q^{54} - 12q^{55} + 4q^{57} - 3q^{58} - 6q^{59} + q^{60} + 5q^{61} + 16q^{62} + 2q^{64} - 4q^{65} + 6q^{66} - 5q^{67} + 6q^{69} - 12q^{71} - 2q^{72} - 16q^{73} - 4q^{74} + q^{75} - 4q^{76} + 8q^{78} - 2q^{79} - q^{80} - q^{81} - 9q^{82} - 6q^{83} - 7q^{86} - 3q^{87} - 6q^{88} - 15q^{89} + 4q^{90} - 6q^{92} - 8q^{93} + 2q^{95} - q^{96} - 28q^{97} + 24q^{99} + O(q^{100})$$

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/490\mathbb{Z}\right)^\times$$.

 $$n$$ $$101$$ $$197$$ $$\chi(n)$$ $$-\zeta_{6}$$ $$1$$

## Embeddings

For each embedding $$\iota_m$$ of the coefficient field, the values $$\iota_m(a_n)$$ are shown below.

For more information on an embedded modular form you can click on its label.

Label $$\iota_m(\nu)$$ $$a_{2}$$ $$a_{3}$$ $$a_{4}$$ $$a_{5}$$ $$a_{6}$$ $$a_{7}$$ $$a_{8}$$ $$a_{9}$$ $$a_{10}$$
361.1
 0.5 + 0.866025i 0.5 − 0.866025i
0.500000 + 0.866025i 0.500000 0.866025i −0.500000 + 0.866025i −0.500000 0.866025i 1.00000 0 −1.00000 1.00000 + 1.73205i 0.500000 0.866025i
471.1 0.500000 0.866025i 0.500000 + 0.866025i −0.500000 0.866025i −0.500000 + 0.866025i 1.00000 0 −1.00000 1.00000 1.73205i 0.500000 + 0.866025i
 $$n$$: e.g. 2-40 or 990-1000 Significant digits: Format: Complex embeddings Normalized embeddings Satake parameters Satake angles

## Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
7.c even 3 1 inner

## Twists

By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 490.2.e.h 2
7.b odd 2 1 70.2.e.c 2
7.c even 3 1 490.2.a.b 1
7.c even 3 1 inner 490.2.e.h 2
7.d odd 6 1 70.2.e.c 2
7.d odd 6 1 490.2.a.c 1
21.c even 2 1 630.2.k.b 2
21.g even 6 1 630.2.k.b 2
21.g even 6 1 4410.2.a.bm 1
21.h odd 6 1 4410.2.a.bd 1
28.d even 2 1 560.2.q.g 2
28.f even 6 1 560.2.q.g 2
28.f even 6 1 3920.2.a.p 1
28.g odd 6 1 3920.2.a.bc 1
35.c odd 2 1 350.2.e.e 2
35.f even 4 2 350.2.j.b 4
35.i odd 6 1 350.2.e.e 2
35.i odd 6 1 2450.2.a.w 1
35.j even 6 1 2450.2.a.bc 1
35.k even 12 2 350.2.j.b 4
35.k even 12 2 2450.2.c.g 2
35.l odd 12 2 2450.2.c.l 2

By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
70.2.e.c 2 7.b odd 2 1
70.2.e.c 2 7.d odd 6 1
350.2.e.e 2 35.c odd 2 1
350.2.e.e 2 35.i odd 6 1
350.2.j.b 4 35.f even 4 2
350.2.j.b 4 35.k even 12 2
490.2.a.b 1 7.c even 3 1
490.2.a.c 1 7.d odd 6 1
490.2.e.h 2 1.a even 1 1 trivial
490.2.e.h 2 7.c even 3 1 inner
560.2.q.g 2 28.d even 2 1
560.2.q.g 2 28.f even 6 1
630.2.k.b 2 21.c even 2 1
630.2.k.b 2 21.g even 6 1
2450.2.a.w 1 35.i odd 6 1
2450.2.a.bc 1 35.j even 6 1
2450.2.c.g 2 35.k even 12 2
2450.2.c.l 2 35.l odd 12 2
3920.2.a.p 1 28.f even 6 1
3920.2.a.bc 1 28.g odd 6 1
4410.2.a.bd 1 21.h odd 6 1
4410.2.a.bm 1 21.g even 6 1

## Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on $$S_{2}^{\mathrm{new}}(490, [\chi])$$:

 $$T_{3}^{2} - T_{3} + 1$$ $$T_{11}^{2} - 6 T_{11} + 36$$ $$T_{13} - 4$$

## Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ $$1 - T + T^{2}$$
$3$ $$1 - T + T^{2}$$
$5$ $$1 + T + T^{2}$$
$7$ $$T^{2}$$
$11$ $$36 - 6 T + T^{2}$$
$13$ $$( -4 + T )^{2}$$
$17$ $$T^{2}$$
$19$ $$4 - 2 T + T^{2}$$
$23$ $$9 - 3 T + T^{2}$$
$29$ $$( 3 + T )^{2}$$
$31$ $$64 - 8 T + T^{2}$$
$37$ $$16 - 4 T + T^{2}$$
$41$ $$( 9 + T )^{2}$$
$43$ $$( 7 + T )^{2}$$
$47$ $$T^{2}$$
$53$ $$36 - 6 T + T^{2}$$
$59$ $$36 + 6 T + T^{2}$$
$61$ $$25 - 5 T + T^{2}$$
$67$ $$25 + 5 T + T^{2}$$
$71$ $$( 6 + T )^{2}$$
$73$ $$256 + 16 T + T^{2}$$
$79$ $$4 + 2 T + T^{2}$$
$83$ $$( 3 + T )^{2}$$
$89$ $$225 + 15 T + T^{2}$$
$97$ $$( 14 + T )^{2}$$

format: plain


text:
# Please solve the 8 number. Please do not provide any link. Q.8. In the given figure, AB and CD are two equal chords of a circle, with centre O. If P is the mid-point of chord AB, Q is the mid-point of chord CD and $\angle POQ=150°$, find $\angle APQ$.

• 1
What are you looking for?


text:
SUMMERTIME CHANGES

9 08 2009

Now that the Fish are jumpin’ and the cotton is high: the $\LaTeX$ code renderer this blog was using, is not working in the same way it was.

I´ve discovered today, that some older posts with tables and floor function symbols, are not been displayed properly. As far as I know, the server from http://yourequations.com/ has exceeded its files quota, and they have made some changes that are causing this kind of problems.

So I´ve added a new script that provides very good quality $\LaTeX$ rendering:

http://www.watchmath.com

with the added advantage that the code is easier to be included inside any page.

I´ve also updated my Mathematica´s version from 5.2 to 6.0 with some files I´ve found “somewhere” on the internet.


text:
Home > Standard Error > What Is The Standard Error Of Measurement Definition

What Is The Standard Error Of Measurement Definition

Contents

Learn how MAP helps you prep Learn how Measures of Academic Progress® (MAP®) users can use preliminary Smarter Balanced data to prepare for proficiency shifts. SEM, put in simple terms, is a measure of precision of the assessment—the smaller the SEM, the more precise the measurement capacity of the instrument. The survey with the lower relative standard error can be said to have a more precise measurement, since it has proportionately less sampling variation around the mean. This is usually the case even with finite populations, because most of the time, people are primarily interested in managing the processes that created the existing finite population; this is called http://itechnologysolutionsllc.com/standard-error/what-is-the-standard-error-of-measurement-used-for.php

Stephanie Glen 24,878 views 3:18 Intro Statistics 5 Standard Error - Duration: 6:20. The sample standard deviation s = 10.23 is greater than the true population standard deviation σ = 9.27 years. The researchers report that candidate A is expected to receive 52% of the final vote, with a margin of error of 2%. In fact, an unexpectedly low test score is more likely to be caused by poor conditions or low student motivation than to be explained by a problem with the testing instrument. http://jalt.org/test/PDF/Brown4.pdf

Standard Error Of Measurement Example

BHSChem 7,253 views 15:00 What is a "Standard Deviation?" and where does that formula come from - Duration: 17:26. In this scenario, the 2000 voters are a sample from all the actual voters. The sample proportion of 52% is an estimate of the true proportion who will vote for candidate A in the actual election. Correction for finite population The formula given above for the standard error assumes that the sample size is much smaller than the population size, so that the population can be considered

• It is useful to compare the standard error of the mean for the age of the runners versus the age at first marriage, as in the graph.
• Standard error of mean versus standard deviation In scientific and technical literature, experimental data are often summarized either using the mean and standard deviation or the mean with the standard error.
• For the purpose of hypothesis testing or estimating confidence intervals, the standard error is primarily of use when the sampling distribution is normally distributed, or approximately normally distributed.
• As will be shown, the mean of all possible sample means is equal to the population mean.
• This gives 9.27/sqrt(16) = 2.32.


text:
# Reciprocal Ontological Models Show Indeterminism Comparable to Quantum Theory

@article{Bandyopadhyay2015ReciprocalOM,
title={Reciprocal Ontological Models Show Indeterminism Comparable to Quantum Theory},
author={Somshubhro Bandyopadhyay and Manik Banik and Some Sankar Bhattacharya and Sibasish Ghosh and Guruprasad Kar and Amit Mukherjee and Arup Roy},
journal={Foundations of Physics},
year={2015},
volume={47},
pages={265-273}
}
• Published 10 August 2015
• Philosophy
• Foundations of Physics
We show that within the class of ontological models due to Harrigan and Spekkens, those satisfying preparation-measurement reciprocity must allow indeterminism comparable to that in quantum theory. Our result implies that one can design quantum random number generator, for which it is impossible, even in principle, to construct a reciprocal deterministic model.
3 Citations
Violating the assumption of Measurement Independence in Quantum Foundations
A maximally psi-epistemic model is given which is valid for any dimension of Hilbert space(by violating preparation independence assumption) and a protocol for classical simulation of quantum channels using such a model is developed.
Bell nonlocality and the reality of the quantum wave function
• Philosophy
Physical Review A
• 2021
Status of quantum wavefunction is one of the most debated issues in quantum foundations -- whether it corresponds directly to the reality or just represents knowledge or information about some aspect
Multicopy Adaptive Local Discrimination: Strongest Possible Two-Qubit Nonlocal Bases.
• Mathematics
Physical review letters
• 2021
This Letter provides examples of orthonormal bases in two-qubit Hilbert space whose adaptive discrimination require three copies of the state and comes up with ensembles whose discrimination under an adaptive separable scheme require less numbers of copies than adaptive local schemes.

## References

SHOWING 1-10 OF 40 REFERENCES
Ontological models predictively inequivalent to quantum theory.
• Philosophy, Physics
Physical review letters
• 2013
A model is described which violates the statement that no extension of quantum theory can have improved predictive power under a strong assumption of free choice of the experimental settings and validity of quantum mechanics for almost all states of a bipartite two-level system.
Ontological Models in Quantum Mechanics: What do they tell us?
The consequences of the theorems about ontological models are studied. "Maximally $\psi$-epistemic" is shown to be equivalent to the conjunction of two other conditions, each of which can be realized
No-go theorems for ψ-epistemic models based on a continuity assumption.
• Philosophy
Physical review letters
• 2013
This argument is different from the recent proof of Pusey, Barrett, and Rudolph and it already yields a nontrivial constraint on ψ-epistemic models using a single copy of the system in question.
Contextuality for preparations, transformations, and unsharp measurements
The Bell-Kochen-Specker theorem establishes the impossibility of a noncontextual hidden variable model of quantum theory, or equivalently, that quantum theory is contextual. In this paper, an
Einstein, Incompleteness, and the Epistemic View of Quantum States
• Philosophy
• 2007
It is shown that for models wherein the quantum state has the status of something real, the failure of locality can be established through an argument considerably more straightforward than Bell’s theorem.
ψ-epistemic theories: The role of symmetry
• Philosophy
• 2013
Formalizing an old desire of Einstein, “ψ-epistemic theories” try to reproduce the predictions of quantum mechanics, while viewing quantum states as ordinary probability distributions over underlying
A brief note on epistemic interpretations and the Kochen-Specker theorem
One of the recent no-go theorems on \Psi-epistemic interpretations of quantum proves that there are no 'maximally epistemic' interpretations of quantum theory. The proof utilises similar arrangements
The statistical interpretation of quantum mechanics
The Statistical Interpretation of quantum theory is formulated for the purpose of providing a sound interpretation using a minimum of assumptions. Several arguments are advanced in favor of
Distinct quantum states can be compatible with a single state of reality.
• Physics
Physical review letters
• 2012
This work considers models for quantum systems with measurement outcomes determined by an underlying physical state of the system but where several quantum states are consistent with a single underlying state-i.e., probability distributions for distinct quantum states overlap.
Is the Quantum State Real? An Extended Review of -ontology Theorems
The background needed for the novice in this area to understand the current status of the Pusey–Barrett–Rudolph Theorem is provided, and often overlooked subtleties should be of interest to the experts are discussed.


text:
# Why are $\vdash$ and $\vDash$ symbols from metalanguage?

I've read in some textbooks that $\vdash$ and $\vDash$ are symbols present only in metalanguage. From this, I infer that their use in object language is unacceptable.

I would like to know why. Can't we define them as relation symbols in a structure? Or introduce them in statements for the sake of formal proofs?

Consider for example propositional logic

The syntax specifications of the language allows us to build formulae from propositional variables : $p, q, \ldots$ and constants : $\bot, \top$ with the connectives; usually :

$\lnot, \lor, \land, \to$.

Thus, $p \to q$ is a "well-formed" formula, while, e.g. $p+q$ is not.

With the symbol :

$\varphi \vdash \psi$

we mean that the formula $\psi$ can be derived in the calculus from the formula $\varphi$.

Thus, $\vdash$ express a relation between formulae of the calculus but it is not a symbol of the language : it is not present in the syntax specifications above.

The "statements" in the metalanguage express "facts" about the language and the calculus, and thus are not formulae of the language.

This is the reason why the symbols : $\vdash$ and $\vDash$ are only part of the meta-language.

• Yep, exactly. Well-explained. – goblin Apr 3 '15 at 9:39
• Is "+" a symbol from the language of Peano Arithmetic? – Bruno Schiavo Apr 3 '15 at 17:18
• @BrunoSchiavo - yes, it is a symbol of first order arithmetic. – Mauro ALLEGRANZA Apr 4 '15 at 11:55
• Of course, just to confuse the picture, $\vdash$ often is used as an object language symbol in sequent calculus presentations of logics, and then you have to use some other notation for the logical consequence relation. – Rob Arthan Apr 5 '15 at 16:17
• @RobArthan - you are right; this is due to the fact that the sequent calculus can be viewed as a calculus for the derivability relation ... – Mauro ALLEGRANZA Apr 6 '15 at 19:51

I can explain it like this.

Given a set $X$, write $X^*$ for the collection of all finite sequences in $X$, including the empty sequence. Now let $L$ denote an arbitrary set, which we think of as a "language"; so you should be thinking of the elements of $L$ as "formulae". Then:

Definition. An inference relation over $L$ is subset $\vdash$ of $L^* \times L$ subject to certain axioms, like:

1. For all $\Gamma \in L^*$ and all $\varphi \in L$, if $\varphi$ occurs somewhere in $\Gamma$, then $\Gamma \vdash \varphi$.

2. etc.

Note that we write $\Gamma \vdash \varphi$ as a more readable alternative to the more correct $(\Gamma,\varphi) \in \;\vdash$. This notation can be seen in axiom 1, for example.

Now here's where the ambiguity creeps in. Suppose $L$ is the set of all strings featuring the symbols $0,1$, the comma symbol, and the symbol $\vdash$. So a generic element of $L$ looks like:

$$0\vdash 1,,0\vdash,1$$

You can see the issue, right? If we suppose furthermore that $\vdash$ is an inference relation on $L$, then we cannot tell what "$01,1 \vdash 1$" means. It could be an element of $L$. Or, it could be the writer attempting to claim that $(\langle 01,1\rangle,1) \in \;\vdash$. Without further information, we cannot know.

To avoid this kind of ambiguity, we would choose a different symbol for the inference relation, as in:

Suppose furthermore that $\vdash'$ is an inference relation on $L$.

It now becomes clear that $01,1 \vdash 1$ is intended to denote an element of $L$, whereas $01,1 \vdash' 1$ is expressing the proposition that $(\langle 01,1\rangle,1) \in \;\vdash'$.

Make sense?

• That $*$ is the Kleene Star, right? – Luis Orion Mar 14 at 21:12
• @LuisOrion, indeed. "Given a set $X$, write $X^*$ for the collection of all finite sequences in $X$, including the empty sequence." – goblin Mar 15 at 2:06

You can use whatever symbols you want to denote whatever you want. For example, you can use ${\mathfrak w}_\$^7$as a binary function symbol for addition of natural numbers. The utility of that is questionable, though. More seriously, you certainly can introduce them if the structure in question is rich enough to intepret those in a meaningful way: for example, we can certainly interpret$\vdash$and$\vDash$in models of set theory. This is actually how Gödel's incompleteness theorems are proved: by interpreting$\vdash$in a theory of arithmetic. The problem with that is this is merely an interpretation, and depending on the model in which it is considered (which is why the second incompleteness theorem is possible). Those interpretations are distinct from the "true"$\vdash$and$\vDash$(though they will, of course, coincide in case of "true" natural numbers and "true" set-theoretic universe). For an illustration of how such an interpretation can stray from being "true", consider the natural numbers$({\bf N},<)$with standard ordering. This is a nice structure. It is isomorphic to$({\bf N},<_1)$where$n<_1m$iff$m=0$and$n=1$or$n<m$. So now you have an interpretation of$<$which is quite different from the "true"$<$. Worse yet, there are (countable!) structures elementarily equivalent to$({\bf N},<)$with infinite descending chains. In those structures, the interpretation of$<$is (in some ways) very different from the standard interpretation. The same can happen whenever you try to express$\vdash,\vDash\$ in a formal language.


text:
# Capacitive Speakers

#### MarcosKDC

Joined Sep 10, 2021
67
I bought a set of piezoelectric tweeters, I didn't know they were until I found they didn't give continuity at all...
I have 4 XTC PT1, and two bigger conelike XTC PT100.

The bad thing is that I don't really now which is their actual impedance, I searched some information and found this:

" Piezoelectric speakers have a complex electronic equivalent circuit but mainly they can be seen as a capacitive load with values between 10nF and 1µF. The capacitive value of the speaker is an important characteristic for the amplifier circuit of the speaker. “Piezoelectric means capacitive load” Most amplifier IC’s are developed for electrodynamic speakers. They can deliver high current variations and are limited to a voltage level of +/- 10 Vpp. Piezoceramic speakers demand voltage variations. The current consumption is extreme small and the voltage peak to peak level goes up to 60Vpp. "

I wired two XTC PT1 in series, then paralleled with the XTC PT100 , expecting that the little ones will see half the power of the big one, but i'm not sure if that's right..

I guess I don't have to put any capacitor also because of their nature... Somebody told me to put 4ohm resistors in series to protect the amplifier...

#### LowQCab

Joined Nov 6, 2012
2,342
Some Amplifiers are not very stable,
and will not tolerate a direct Capacitive-Load on their Outputs.

Connecting Piezo-Tweeters in series will double the Voltage tolerance,
and reduce their Output by half, just like Electromagnetic Speakers will behave.
This will act like a Resistive-Voltage-Divider,
and they will share the Voltage pretty-close to equally.

The Voltage-Rating of a Piezo-Tweeter is not an absolute value,
neither is it a "guaranteed-performance" number.

Piezo-Tweeters can be "over-heated" by continuous operation at their rated maximum-Voltage.
This heating-effect gets worse as the Frequency gets higher.

If your Amplifier starts getting into some sort of ultra-sonic oscillations,
it will quickly destroy the Piezo-Tweeters "without making a sound", ( that You can hear ).
This is possible even with an Amplifier that can only supply maybe ~10-Volts AC max.
This can be largely mitigated by adding a NON-INDUCTIVE Power-Resistor
of around ~30-Ohms, in series with the Tweeter, ( 4-Ohms is way too low ).
This may also have the effect of smoothing the Frequency-Response of the Tweeter.

The "apparent" Impedance of Piezo-Tweeters gets lower, as the Frequency increases,
and vice-versa,
this is why they don't necessarily require a Crossover.
They can be less than 1-Ohm at Frequencies over 100khz,
but at Audio-Frequencies,
they generally only get down to maybe ~50-Ohms, ( at ~20khz ).

You can also strap an 8-Ohm Resistor across them and then
feed them with any standard Cross-Over-Network,
but it's the Crossover that needs the Resistor, not the Tweeters.

I used to have a Folder with all sorts of tricks for Piezo-Tweeters,
but that was decades ago, and I can't find it now.
Motorola was the original designer and manufacturer of Piezo-Tweeters back in the '60's,
then several other USA manufacturers kinda gave it their shot,
but I think the only manufacturers now are in China,
and most of them are absolute garbage, with very poor quality-control,
but I could be wrong, because I haven't built any Speakers in the last ~10-years or so.
.
.
.

Last edited:

#### Ian0

Joined Aug 7, 2020
5,885
Completely capacitive loads will send some amplifiers unstable, so a series resistor is a good idea.
Putting the two small ones in series will give half the voltage on each. It tends to be overvoltage that kills piezos.
The PT100 is a copy of an old Motorola KSN1025A design, which looks electrically like a 330nF capacitor.
Audio quality is between poor and dreadful as you can see from the frequency response graph. The copies tend to be worse than the originals.
The original KSN1025A had a built-in series resistor to prevent amplifiers from going unstable, but don't for a second believe that the copies might have.

#### MarcosKDC

Joined Sep 10, 2021
67
Thanks a lot for the complete info.

I will be mainly using car amplifiers, I'm not expecting to have more than 25V rms...

I did the series combination because I think I've read that the little ones would handle less power than the big one maybe I'm wrong...

I don't really know about the quality, I've heard about the motorola thing but I don't think these ones are original...

I'm just hoping them to give some more highs... Now I have two pionner 6x9 and a sub all enclosed in their respective boxes, and it sounds too bassy...

Ungratefully I'm a newbie in the audio thing... I'm basically tryna start with the electronics then move to acoustics... But missing the basics of speaker design and that makes it quite difficult to get what I want at first try :')

#### Ya’akov

Joined Jan 27, 2019
6,275
From a reproduction standpoint piezo tweeters are really crappy. That is, if you care about the original concept of “high fidelity”. Wthi electronic, studio produced music the “hifi” reproduction is going to be based on what the artist mixed using whatever monitors they used.

A long time ago when I was involved in the recording studio business, the stated of the art for a serious (rock/pop) studio were Yamaha NS-10Ms for the near field and UREI coaxial monitors for high level playback.

NS-10M Pro and UREI Coaxial Monitor

So, unlike the BBC using an orchestra and a tape to A/B test the LS35A designs, the test today is one set of speakers against another. But almost no one cares about such comparisons. Instead a smooth power response over the reproduction range with low distortion at high volume is considered “high fidelity” as far as anyone cares.

Before this narrative grabs a hold of my brain and takes it on a long journey requiring thousands of words to complete, I will get to my point:

Even given the relativistic nature of what is considered good reproduction in the current non-acoustic music environment, piezo tweeter stink on ice delivering shrill highs with a noticeable discontinuity from the mids to the highs in most cases. The distortion produced by a piezo tweeter is very unpleasant as well but can be very subtle since it can occur at frequencies at the edge of perception of even in the audible range as interference.

I would expect that if you can do, ditching those piezos in favor of dome or electrodynamic horn tweeters would make you listening life a happier thing.

#### Ian0

Joined Aug 7, 2020
5,885
From a reproduction standpoint piezo tweeters are really crappy.
I did come across something potentially worse. It was an automotive tweeter, which consisted of a piezo transducer attached to an autotransformer, wound on an open bobbin of the kind used for DC inductors, or it may even have been air-cored.
Needless to say, I didn’t do any measurements to find out just how bad it was.

#### MisterBill2

Joined Jan 23, 2018
12,704
First question is if the piezo tweeters are the only load for the amplifier or not. That matters because the amp sees the combined load.
The comments about the very peaky response ignore the type of stuff being played through the system, some of it is improved by high distortion, (over 10%THD).
The rap played on the multi-thousand watt car systems is much better when the distortion is at least 50%, in my opinion. At higher percentages it becomes no worse than a simple loud exhaust sound.

#### LowQCab

Joined Nov 6, 2012
2,342
Interesting side note ............
The ( Old ), ( Motorola or CTS ), 2X6 Piezo-Tweeters were
far superior to the 3X3 "Super-Tweeters".
When used in a Line-Array of ~6 or more they would smooth out nicely,
and legitimately cover 2khz to 20khz with excellent Fidelity.
.
.
.

#### MarcosKDC

Joined Sep 10, 2021
67
I don't understand most of what you've said, but yes, this speakers were cheap, so I guess they're not gonna sound amazing.. But well, I'm just tryna learn a bit with cheap equipment before getting broke xD

#### Audioguru again

Joined Oct 21, 2019
4,945
.....most of them are absolute garbage, with very poor quality-control.
I agree.
All piezo tweeters I have heard sound awful. I have always used Name Brand coil and magnet dome tweeters that sound wonderful.


text:
## Related calculators

If you find any bug or need any improvements in solution report it here

$$\displaylines{---}$$
$$\displaylines{ \mathbf{\color{Green}{Let's\;call\;All\;possible\;states\;as\;}} \begin{bmatrix} 1 & 2 & \end{bmatrix} \\ \\ \mathbf{\color{Green}{First\;we\;have\;to\;create\;Stochastic\;matrix}} \\ \\ Stochastic\;matrix\;=\;P= \begin{bmatrix} * & 1 & 2 & \\ \\ 1 & 0.5 & 0.5 & \\ \\ 2 & 0.8 & 0.2 & \end{bmatrix} \\ \\ \\ \\ \mathbf{\color{Green}{For\;steady\;state.\;We\;have\;to\;solve\;these\;equation}} \\ \\ X*P=X \\ \\ and\; x_{1}+x_{2} =1 \\ \\ Where\;X\;=\; \begin{bmatrix} x_{1} & x_{2} & \end{bmatrix} \\ \\ P= \begin{bmatrix} 0.5 & 0.5 & \\ \\ 0.8 & 0.2 & \end{bmatrix} \\ \\ \mathbf{\color{Green}{That\;is\;}} \\ \\ \Rightarrow \begin{bmatrix} x_{1} & x_{2} & \end{bmatrix} \begin{bmatrix} 0.5 & 0.5 & \\ \\ 0.8 & 0.2 & \end{bmatrix} = \begin{bmatrix} x_{1} & x_{2} & \end{bmatrix} \\ \\ and\; x_{1}+x_{2} =1 \\ \\ \mathbf{\color{Green}{Simplifying\;that\;will\;give}} \\ \\ x_{1}*(0.5)+x_{2}*(0.8)=x_{1} \\ \\ x_{1}*(0.5)+x_{2}*(0.2)=x_{2} \\ \\ x_{1}+x_{2} =1 \\ \\ \mathbf{\color{Green}{Simplifying\;again\;will\;give}} \\ \\ x_{1}*(-0.5)+x_{2}*(0.8)=0 \\ \\ x_{1}*(0.5)+x_{2}*(-0.8)=0 \\ \\ x_{1}+x_{2} =1 \\ \\ \mathbf{\color{Green}{Solving\;those\;will\;give\;below\;result...}} \\ \\ \begin{bmatrix} x_{1} & x_{2} & \end{bmatrix} = \begin{bmatrix} 0.615385 & 0.384615 & \end{bmatrix} }$$


text:
Previous issue ·  Next issue ·  Most recent issue · All issues

# Journal of Operator Theory

Volume 53, Issue 1, Winter 2005  pp. 91-117.

The Fine Structure of the Kasparov Groups. III: Relative Quasidiagonality

Authors Claude L. Schochet
Author institution: Mathematics Department, Wayne State University, Detroit, MI 48202, USA

Summary:  In this paper we identify $QD(A,B)$, the quasidiagonal classes in $KK_1(A,B)$, in terms of $K_*(A)$ and $K_*(B)$, and we use these results in various applications. Here is our central result: Let $\widetilde{\mathcal N}$ denote the category of separable nuclear $C^*$-algebras which satisfy the Universal Coefficient Theorem. Suppose that $A \in \widetilde{\mathcal N}$ and $A$ is quasidiagonal relative to $B$. Then there is a natural isomorphism \begin{equation*} QD(A,B) \,\cong\, \mathrm{Pext}_{\mathbb Z}^1( {K_*(A)},{K_*(B)}) _{0} .\end{equation*} Thus, for $A \in \widetilde{\mathcal N}$ quasidiagonality of $KK$-classes is indeed a topological invariant.

Contents    Full-Text PDF


text:
# Chapter 11 - Section 11.4 - Introduction to Derrivatives - Exercise Set - Page 1177: 83

The height of the tower is approximately $190\ \text{feet}$.

#### Work Step by Step

Consider the distance of the point on the level ground from base of the tower which is $145\ \text{feet}$ and the angle of elevation of ${{52.6}^{\circ }}$. Suppose the height of the tower is x feet. Since the above figure is right-angled, take the tangent of the angle of elevation. $\tan {{52.6}^{\circ }}=\frac{x}{145}$ Substitute the value $\tan {{52.6}^{\circ }}=1.307$ and solve for x. \begin{align} & 1.307=\frac{x}{145} \\ & x=1.307\times 145 \\ & =189.515 \\ & \approx 190 \end{align} Therefore, to the nearest foot, the height of the tower is approximately $190\ \text{feet}$.

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.


text:
# Tag Info

3

As far as I know, the sigmoid is often used as the activation function of the output layer mainly because it is a convenient way of producing an output $p \in [0, 1]$, which can be interpreted as a probability, although that can be misleading or even wrong (if you interpret it as an uncertainty too). You may require the output of the neural network to be a ...

0

It's a very simplified explantion. I am just talking about the core idea. A neural network is a combination of many layers. A neural network (Multiple Layer Perceptron: Regular neural network ): It does a linear combination (a mathematical operation) between the previous layer's output and the current layer's weights(vectors) and then it passes data to ...

1

If you think about it, it is already happening. Thousands of drivers work for Uber Intelligence. There are many applications that dictate the rules and define what the seller and the end user need to do This idea is called Singularity or Technological Singularity, it would be possible with a Superintelligence. However, the possibility of this happening is ...

1

It is called Singularity. A point in future where AI will surpass Human Knowledge and become Omniscient. AI will be able to operate on an order manifolds time to that of a human brain thus developing and designing itself without any assistance.

0

A feedforward network with its full linkage, is the super set of a 2 level feedforward translationally invarient network.

24

If I'm not mistaken you're looking for Roko's Basilisk, in which an otherwise benevolent future AI system tortures simulations of those who did not work to bring the system into existence

6

The likely expression you are looking for is AI takeover, which is a common topic in science fiction movies, such as 2001: A Space Odyssey and The Matrix, and popular culture. Although the AI takeover is an unlikely scenario in the next years, certain scientists, such as Stephen Hawking, have expressed concerns about it and some philosophers, especially Nick ...

10

I believe the term you are looking for is "(technological) singularity". https://en.wikipedia.org/wiki/Technological_singularity

Top 50 recent answers are included


text:
# At Mikefest

I’m at a conference this week of a very particular type: a birthday conference. When folks in my field turn 60, their students and friends organize a special conference for them, celebrating their research legacy. With COVID restrictions just loosening, my advisor Michael Douglas is getting a last-minute conference. And as one of the last couple students he graduated at Stony Brook, I naturally showed up.

The conference, Mikefest, is at the Institut des Hautes Études Scientifiques, just outside of Paris. Mike was a big supporter of the IHES, putting in a lot of fundraising work for them. Another big supporter, James Simons, was Mike’s employer for a little while after his time at Stony Brook. The conference center we’re meeting in is named for him.

I wasn’t involved in organizing the conference, so it was interesting seeing differences between this and other birthday conferences. Other conferences focus on the birthday prof’s “family tree”: their advisor, their students, and some of their postdocs. We’ve had several talks from Mike’s postdocs, and one from his advisor, but only one from a student. Including him and me, three of Mike’s students are here: another two have had their work mentioned but aren’t speaking or attending.

Most of the speakers have collaborated with Mike, but only for a few papers each. All of them emphasized a broader debt though, for discussions and inspiration outside of direct collaboration. The message, again and again, is that Mike’s work has been broad enough to touch a wide range of people. He’s worked on branes and the landscape of different string theory universes, pure mathematics and computation, neuroscience and recently even machine learning. The talks generally begin with a few anecdotes about Mike, before pivoting into research talks on the speakers’ recent work. The recent-ness of the work is perhaps another difference from some birthday conferences: as one speaker said, this wasn’t just a celebration of Mike’s past, but a “welcome back” after his return from the finance world.

One thing I don’t know is how much this conference might have been limited by coming together on short notice. For other birthday conferences impacted by COVID (and I’m thinking of one in particular), it might be nice to have enough time to have most of the birthday prof’s friends and “academic family” there in person. As-is, though, Mike seems to be having fun regardless.

Happy Birthday Mike!

# Things Which Are Fluids

For overambitious apes like us, adding integers is the easiest thing in the world. Take one berry, add another, and you have two. Each remains separate, you can lay them in a row and count them one by one, each distinct thing adding up to a group of distinct things.

Other things in math are less like berries. Add two real numbers, like pi and the square root of two, and you get another real number, bigger than the first two, something you can write in an infinite messy decimal. You know in principle you can separate it out again (subtract pi, get the square root of two), but you can’t just stare at it and see the parts. This is less like adding berries, and more like adding fluids. Pour some water in to some other water, and you certainly have more water. You don’t have “two waters”, though, and you can’t tell which part started as which.

Some things in math look like berries, but are really like fluids. Take a polynomial, say $5 x^2 + 6 x + 8$. It looks like three types of things, like three berries: five $x^2$, six $x$, and eight $1$. Add another polynomial, and the illusion continues: add $x^2 + 3 x + 2$ and you get $6 x^2+9 x+10$. You’ve just added more $x^2$, more $x$, more $1$, like adding more strawberries, blueberries, and raspberries.

But those berries were a choice you made, and not the only one. You can rewrite that first polynomial, for example saying $5(x^2+2x+1) - 4 (x+1) + 7$. That’s the same thing, you can check. But now it looks like five $x^2+2x+1$, negative four $x+1$, and seven $1$. It’s different numbers of different things, blackberries or gooseberries or something. And you can do this in many ways, infinitely many in fact. The polynomial isn’t really a collection of berries, for all it looked like one. It’s much more like a fluid, a big sloshing mess you can pour into buckets of different sizes. (Technically, it’s a vector space. Your berries were a basis.)

Even smart, advanced students can get tripped up on this. You can be used to treating polynomials as a fluid, and forget that directions in space are a fluid, one you can rotate as you please. If you’re used to directions in space, you’ll get tripped up by something else. You’ll find that types of particles can be more fluid than berry, the question of which quark is which not as simple as how many strawberries and blueberries you have. The laws of physics themselves are much more like a fluid, which should make sense if you take a moment, because they are made of equations, and equations are like a fluid.

So my fellow overambitious apes, do be careful. Not many things are like berries in the end. A whole lot are like fluids.

# W is for Why???

Have you heard the news about the W boson?

The W boson is a fundamental particle, part of the Standard Model of particle physics. It is what we call a “force-carrying boson”, a particle related to the weak nuclear force in the same way photons are related to electromagnetism. Unlike photons, W bosons are “heavy”: they have a mass. We can’t usually predict masses of particles, but the W boson is a bit different, because its mass comes from the Higgs boson in a special way, one that ties it to the masses of other particles like the Z boson. The upshot is that if you know the mass of a few other particles, you can predict the mass of the W.

And according to a recent publication, that prediction is wrong. A team analyzed results from an old experiment called the Tevatron, the biggest predecessor of today’s Large Hadron Collider. They treated the data with groundbreaking care, mindbogglingly even taking into account the shape of the machine’s wires. And after all that analysis, they found that the W bosons detected by the Tevatron had a different mass than the mass predicted by the Standard Model.

How different? Here’s where precision comes in. In physics, we decide whether to trust a measurement with a statistical tool. We calculate how likely the measurement would be, if it was an accident. In this case: how likely it would be that, if the Standard Model was correct, the measurement would still come out this way? To discover a new particle, we require this chance to be about one in 3.5 million, or in our jargon, five sigma. That was the requirement for discovering the Higgs boson. This super-precise measurement of the W boson doesn’t have five sigma…it has seven sigma. That means, if we trust the analysis team, then a measurement like this could come accidentally out of the Standard Model only about one in a trillion times.

Ok, should we trust the analysis team?

If you want to know that, I’m the wrong physicist to ask. The right physicists are experimental particle physicists. They do analyses like that one, and they know what can go wrong. Everyone I’ve heard from in that field emphasized that this was a very careful group, who did a lot of things impressively right…but there is still room for mistakes. One pointed out that the new measurement isn’t just inconsistent with the Standard Model, but with many previous measurements too. Those measurements are less precise, but still precise enough that we should be a bit skeptical. Another went into more detail about specific clues as to what might have gone wrong.

If you can’t find an particle experimentalist, the next best choice is a particle phenomenologist. These are the people who try to make predictions for new experiments, who use theoretical physics to propose new models that future experiments can test. Here’s one giving a first impression, and discussing some ways to edit the Standard Model to agree with the new measurement. Here’s another discussing what to me is an even more interesting question: if we take these measurements seriously, both the new one and the old ones, then what do we believe?

I’m not an experimentalist or a phenomenologist. I’m an “amplitudeologist”. I work not on the data, or the predictions, but the calculational tools used to make those predictions, called “scattering amplitudes”. And that gives me a different view on the situation.

See in my field, precision is one of our biggest selling-points. If you want theoretical predictions to match precise experiments, you need our tricks to compute them. We believe (and argue to grant agencies) that this precision will be important: if a precise experiment and a precise prediction disagree, it could be the first clue to something truly new. New solid evidence of something beyond the Standard Model would revitalize all of particle physics, giving us a concrete goal and killing fruitless speculation.

This result shakes my faith in that a little. Probably, the analysis team got something wrong. Possibly, all previous analyses got something wrong. Either way, a lot of very careful smart people tried to estimate their precision, got very confident…and got it wrong.

(There’s one more alternative: maybe million-to-one chances really do crop up nine times out of ten.)

If some future analysis digs down deep in precision, and finds another deviation from the Standard Model, should we trust it? What if it’s measuring something new, and we don’t have the prior experiments to compare to?

(This would happen if we build a new even higher-energy collider. There are things the collider could measure, like the chance one Higgs boson splits into two, that we could not measure with any earlier machine. If we measured that, we couldn’t compare it to the Tevatron or the LHC, we’d have only the new collider to go on.)

Statistics are supposed to tell us whether to trust a result. Here, they’re not doing their job. And that creates the scary possibility that some anomaly shows up, some real deviation deep in the sigmas that hints at a whole new path for the field…and we just end up bickering about who screwed it up. Or the equally scary possibility that we find a seven-sigma signal of some amazing new physics, build decades of new theories on it…and it isn’t actually real.

We don’t just trust statistics. We also trust the things normal people trust. Do other teams find the same result? (I hope that they’re trying to get to this same precision here, and see what went wrong!) Does the result match other experiments? Does it make predictions, which then get tested in future experiments?

All of those are heuristics of course. Nothing can guarantee that we measure the truth. Each trick just corrects for some of our biases, some of the ways we make mistakes. We have to hope that’s good enough, that if there’s something to see we’ll see it, and if there’s nothing to see we won’t. Precision, my field’s raison d’être, can’t be enough to convince us by itself. But it can help.

# The Undefinable

If I can teach one lesson to all of you, it’s this: be precise. In physics, we try to state what we mean as precisely as we can. If we can’t state something precisely, that’s a clue: maybe what we’re trying to state doesn’t actually make sense.

Someone recently reached out to me with a question about black holes. He was confused about how they were described, about what would happen when you fall in to one versus what we could see from outside. Part of his confusion boiled down to a question: “is the center really an infinitely small point?”

I remembered a commenter a while back who had something interesting to say about this. Trying to remind myself of the details, I dug up this question on Physics Stack Exchange. user4552 has a detailed, well-referenced answer, with subtleties of General Relativity that go significantly beyond what I learned in grad school.

According to user4552, the reason this question is confusing is that the usual setup of general relativity cannot answer it. In general relativity, singularities like the singularity in the middle of a black hole aren’t treated as points, or collections of points: they’re not part of space-time at all. So you can’t count their dimensions, you can’t see whether they’re “really” infinitely small points, or surfaces, or lines…

This might surprise people (like me) who have experience with simpler equations for these things, like the Schwarzchild metric. The Schwarzchild metric describes space-time around a black hole, and in the usual coordinates it sure looks like the singularity is at a single point where r=0, just like the point where r=0 is a single point in polar coordinates in flat space. The thing is, though, that’s just one sort of coordinates. You can re-write a metric in many different sorts of coordinates, and the singularity in the center of a black hole might look very different in those coordinates. In general relativity, you need to stick to things you can say independent of coordinates.

Ok, you might say, so the usual mathematics can’t answer the question. Can we use more unusual mathematics? If our definition of dimensions doesn’t tell us whether the singularity is a point, maybe we just need a new definition!

According to user4552, people have tried this…and it only sort of works. There are several different ways you could define the dimension of a singularity. They all seem reasonable in one way or another. But they give different answers! Some say they’re points, some say they’re three-dimensional. And crucially, there’s no obvious reason why one definition is “right”. The question we started with, “is the center really an infinitely small point?”, looked like a perfectly reasonable question, but it actually wasn’t: the question wasn’t precise enough.

This is the real problem. The problem isn’t that our question was undefined, after all, we can always add new definitions. The problem was that our question didn’t specify well enough the definitions we needed. That is why the question doesn’t have an answer.

Once you understand the difference, you see these kinds of questions everywhere. If you’re baffled by how mass could have come out of the Big Bang, or how black holes could radiate particles in Hawking radiation, maybe you’ve heard a physicist say that energy isn’t always conserved. Energy conservation is a consequence of symmetry, specifically, symmetry in time. If your space-time itself isn’t symmetric (the expanding universe making the past different from the future, a collapsing star making a black hole), then you shouldn’t expect energy to be conserved.

I sometimes hear people object to this. They ask, is it really true that energy isn’t conserved when space-time isn’t symmetric? Shouldn’t we just say that space-time itself contains energy?

And well yes, you can say that, if you want. It isn’t part of the usual definition, but you can make a new definition, one that gives energy to space-time. In fact, you can make more than one new definition…and like the situation with the singularity, these definitions don’t always agree! Once again, you asked a question you thought was sensible, but it wasn’t precise enough to have a definite answer.

Keep your eye out for these kinds of questions. If scientists seem to avoid answering the question you want, and keep answering a different question instead…it might be their question is the only one with a precise answer. You can define a method to answer your question, sure…but it won’t be the only way. You need to ask precise enough questions to get good answers.

# Of Snowmass and SAGEX

arXiv-watchers might have noticed an avalanche of papers with the word Snowmass in the title. (I contributed to one of them.)

Snowmass is a place, an area in Colorado known for its skiing. It’s also an event in that place, the Snowmass Community Planning Exercise for the American Physical Society’s Division of Particles and Fields. In plain terms, it’s what happens when particle physicists from across the US get together in a ski resort to plan their future.

Usually someone like me wouldn’t be involved in that. (And not because it’s a ski resort.) In the past, these meetings focused on plans for new colliders and detectors. They got contributions from experimentalists, and a few theorists heavily focused on their work, but not the more “formal” theorists beyond.

This Snowmass is different. It’s different because of Corona, which changed it from a big meeting in a resort to a spread-out series of meetings and online activities. It’s also different because they invited theorists to contribute, and not just those interested in particle colliders. The theorists involved study everything from black holes and quantum gravity to supersymmetry and the mathematics of quantum field theory. Groups focused on each topic submit “white papers” summarizing the state of their area. These white papers in turn get organized and summarized into a few subfields, which in turn contribute to the planning exercise. No-one I’ve talked to is entirely clear on how this works, how much the white papers will actually be taken into account or by whom. But it seems like a good chance to influence US funding agencies, like the Department of Energy, and see if we can get them to prioritize our type of research.

Europe has something similar to Snowmass, called the European Strategy for Particle Physics. It also has smaller-scale groups, with their own purposes, goals, and funding sources. One such group is called SAGEX: Scattering Amplitudes: from Geometry to EXperiment. SAGEX is an Innovative Training Network, an organization funded by the EU to train young researchers, in this case in scattering amplitudes. Its fifteen students are finishing their PhDs and ready to take the field by storm. Along the way, they spent a little time in industry internships (mostly at Maple and Mathematica), and quite a bit of time working on outreach.

They have now summed up that outreach work in an online exhibition. I’ve had fun exploring it over the last couple days. They’ve got a lot of good content there, from basic explanations of relativity and quantum mechanics, to detailed games involving Feynman diagrams and associahedra, to a section that uses solitons as a gentle introduction to integrability. If you’re in the target audience, you should check it out!

# Duality and Emergence: When Is Spacetime Not Spacetime?

Spacetime is doomed! At least, so say some physicists. They don’t mean this as a warning, like some comic-book universe-destroying disaster, but rather as a research plan. These physicists believe that what we think of as space and time aren’t the full story, but that they emerge from something more fundamental, so that an ultimate theory of nature might not use space or time at all. Other, grumpier physicists are skeptical. Joined by a few philosophers, they think the “spacetime is doomed” crowd are over-excited and exaggerating the implications of their discoveries. At the heart of the argument is the distinction between two related concepts: duality and emergence.

In physics, sometimes we find that two theories are actually dual: despite seeming different, the patterns of observations they predict are the same. Some of the more popular examples are what we call holographic theories. In these situations, a theory of quantum gravity in some space-time is dual to a theory without gravity describing the edges of that space-time, sort of like how a hologram is a 2D image that looks 3D when you move it. For any question you can ask about the gravitational “bulk” space, there is a matching question on the “boundary”. No matter what you observe, neither description will fail.

If theories with gravity can be described by theories without gravity, does that mean gravity doesn’t really exist? If you’re asking that question, you’re asking whether gravity is emergent. An emergent theory is one that isn’t really fundamental, but instead a result of the interaction of more fundamental parts. For example, hydrodynamics, the theory of fluids like water, emerges from more fundamental theories that describe the motion of atoms and molecules.

(For the experts: I, like most physicists, am talking about “weak emergence” here, not “strong emergence”.)

The “spacetime is doomed” crowd think that not just gravity, but space-time itself is emergent. They expect that distances and times aren’t really fundamental, but a result of relationships that will turn out to be more fundamental, like entanglement between different parts of quantum fields. As evidence, they like to bring up dualities where the dual theories have different concepts of gravity, number of dimensions, or space-time. Using those theories, they argue that space and time might “break down”, and not be really fundamental.

The skeptics, though, bring up an important point. If two theories are really dual, then no observation can distinguish them: they make exactly the same predictions. In that case, say the skeptics, what right do you have to call one theory more fundamental than the other? You can say that gravity emerges from a boundary theory without gravity, but you could just as easily say that the boundary theory emerges from the gravity theory. The whole point of duality is that no theory is “more true” than the other: one might be more or less convenient, but both describe the same world. If you want to really argue for emergence, then your “more fundamental” theory needs to do something extra: to predict something that your emergent theory doesn’t predict.

Sometimes this is a fair objection. There are members of the “spacetime is doomed” crowd who are genuinely reckless about this, who’ll tell a journalist about emergence when they really mean duality. But many of these people are more careful, and have thought more deeply about the question. They tend to have some mix of these two perspectives:

First, if two descriptions give the same results, then do the descriptions matter? As physicists, we have a history of treating theories as the same if they make the same predictions. Space-time itself is a result of this policy: in the theory of relativity, two people might disagree on which one of two events happened first or second, but they will agree on the overall distance in space-time between the two. From this perspective, a duality between a bulk theory and a boundary theory isn’t evidence that the bulk theory emerges from the boundary, but it is evidence that both the bulk and boundary theories should be replaced by an “overall theory”, one that treats bulk and boundary as irrelevant descriptions of the same physical reality. This perspective is similar to an old philosophical theory called positivism: that statements are meaningless if they cannot be derived from something measurable. That theory wasn’t very useful for philosophers, which is probably part of why some philosophers are skeptics of “space-time is doomed”. The perspective has been quite useful to physicists, though, so we’re likely to stick with it.

Second, some will say that it’s true that a dual theory is not an emergent theory…but it can be the first step to discover one. In this perspective, dualities are suggestive evidence that a deeper theory is waiting in the wings. The idea would be that one would first discover a duality, then discover situations that break that duality: examples on one side that don’t correspond to anything sensible on the other. Maybe some patterns of quantum entanglement are dual to a picture of space-time, but some are not. (Closer to my sub-field, maybe there’s an object like the amplituhedron that doesn’t respect locality or unitarity.) If you’re lucky, maybe there are situations, or even experiments, that go from one to the other: where the space-time description works until a certain point, then stops working, and only the dual description survives. Some of the models of emergent space-time people study are genuinely of this type, where a dimension emerges in a theory that previously didn’t have one. (For those of you having a hard time imagining this, read my old post about “bubbles of nothing”, then think of one happening in reverse.)

It’s premature to say space-time is doomed, at least as a definite statement. But it is looking like, one way or another, space-time won’t be the right picture for fundamental physics. Maybe that’s because it’s equivalent to another description, redundant embellishment on an essential theoretical core. Maybe instead it breaks down, and a more fundamental theory could describe more situations. We don’t know yet. But physicists are trying to figure it out.

# The Unpublishable Dirty Tricks of Theoretical Physics

As the saying goes, it is better not to see laws or sausages being made. You’d prefer to see the clean package on the outside than the mess behind the scenes.

The same is true of science. A good paper tells a nice, clean story: a logical argument from beginning to end, with no extra baggage to slow it down. That story isn’t a lie: for any decent paper in theoretical physics, the conclusions will follow from the premises. Most of the time, though, it isn’t how the physicist actually did it.

The way we actually make discoveries is messy. It involves looking for inspiration in all the wrong places: pieces of old computer code and old problems, trying to reproduce this or that calculation with this or that method. In the end, once we find something interesting enough, we can reconstruct a clearer, cleaner, story, something actually fit to publish. We hide the original mess partly for career reasons (easier to get hired if you tell a clean, heroic story), partly to be understood (a paper that embraced the mess of discovery would be a mess to read), and partly just due to that deep human instinct to not let others see us that way.

The trouble is, some of that “mess” is useful, even essential. And because it’s never published or put into textbooks, the only way to learn it is word of mouth.

A lot of these messy tricks involve numerics. Many theoretical physics papers derive things analytically, writing out equations in symbols. It’s easy to make a mistake in that kind of calculation, either writing something wrong on paper or as a bug in computer code. To correct mistakes, many things are checked numerically: we plug in numbers to make sure everything still works. Sometimes this means using an approximation, trying to make sure two things cancel to some large enough number of decimal places. Sometimes instead it’s exact: we plug in prime numbers, and can much more easily see if two things are equal, or if something is rational or contains a square root. Sometimes numerics aren’t just used to check something, but to find a solution: exploring many options in an easier numerical calculation, finding one that works, and doing it again analytically.

“Ansatze” are also common: our fancy word for an educated guess. These we sometimes admit, when they’re at the core of a new scientific idea. But the more minor examples go un-mentioned. If a paper shows a nice clean formula and proves it’s correct, but doesn’t explain how the authors got it…probably, they used an ansatz. This trick can go hand-in-hand with numerics as well: make a guess, check it matches the right numbers, then try to see why it’s true.

The messy tricks can also involve the code itself. In my field we often use “computer algebra” systems, programs to do our calculations for us. These systems are programming languages in their own right, and we need to write computer code for them. That code gets passed around informally, but almost never standardized. Mathematical concepts that come up again and again can be implemented very differently by different people, some much more efficiently than others.

I don’t think it’s unreasonable that we leave “the mess” out of our papers. They would certainly be hard to understand otherwise! But it’s a shame we don’t publish our dirty tricks somewhere, even in special “dirty tricks” papers. Students often start out assuming everything is done the clean way, and start doubting themselves when they notice it’s much too slow to make progress. Learning the tricks is a big part of learning to be a physicist. We should find a better way to teach them.

# The arXiv SciComm Challenge

Fellow science communicators, think you can explain everything that goes on in your field? If so, I have a challenge for you. Pick a day, and go through all the new papers on arXiv.org in a single area. For each one, try to give a general-audience explanation of what the paper is about. To make it easier, you can ignore cross-listed papers. If your field doesn’t use arXiv, consider if you can do the challenge with another appropriate site.

I’ll start. I’m looking at papers in the “High Energy Physics – Theory” area, announced 6 Jan, 2022. I’ll warn you in advance that I haven’t read these papers, just their abstracts, so apologies if I get your paper wrong!

arXiv:2201.01303 : Holographic State Complexity from Group Cohomology

This paper says it is a contribution to a Proceedings. That means it is based on a talk given at a conference. In my field, a talk like this usually won’t be presenting new results, but instead summarizes results in a previous paper. So keep that in mind.

There is an idea in physics called holography, where two theories are secretly the same even though they describe the world with different numbers of dimensions. Usually this involves a gravitational theory in a “box”, and a theory without gravity that describes the sides of the box. The sides turn out to fully describe the inside of the box, much like a hologram looks 3D but can be printed on a flat sheet of paper. Using this idea, physicists have connected some properties of gravity to properties of the theory on the sides of the box. One of those properties is complexity: the complexity of the theory on the sides of the box says something about gravity inside the box, in particular about the size of wormholes. The trouble is, “complexity” is a bit subjective: it’s not clear how to give a good definition for it for this type of theory. In this paper, the author studies a theory with a precise mathematical definition, called a topological theory. This theory turns out to have mathematical properties that suggest a well-defined notion of complexity for it.

arXiv:2201.01393 : Nonrelativistic effective field theories with enhanced symmetries and soft behavior

We sometimes describe quantum field theory as quantum mechanics plus relativity. That’s not quite true though, because it is possible to define a quantum field theory that doesn’t obey special relativity, a non-relativistic theory. Physicists do this if they want to describe a system moving much slower than the speed of light: it gets used sometimes for nuclear physics, and sometimes for modeling colliding black holes.

In particle physics, a “soft” particle is one with almost no momentum. We can classify theories based on how they behave when a particle becomes more and more soft. In normal quantum field theories, if they have special behavior when a particle becomes soft it’s often due to a symmetry of the theory, where the theory looks the same even if something changes. This paper shows that this is not true for non-relativistic theories: they have more requirements to have special soft behavior, not just symmetry. They “bootstrap” a few theories, using some general restrictions to find them without first knowing how they work (“pulling them up by their own bootstraps”), and show that the theories they find are in a certain sense unique, the only theories of that kind.

arXiv:2201.01552 : Transmutation operators and expansions for 1-loop Feynman integrands

In recent years, physicists in my sub-field have found new ways to calculate the probability that particles collide. One of these methods describes ordinary particles in a way resembling string theory, and from this discovered a whole “web” of theories that were linked together by small modifications of the method. This method originally worked only for the simplest Feynman diagrams, the “tree” diagrams that correspond to classical physics, but was extended to the next-simplest diagrams, diagrams with one “loop” that start incorporating quantum effects.

This paper concerns a particular spinoff of this method, that can find relationships between certain one-loop calculations in a particularly efficient way. It lets you express calculations of particle collisions in a variety of theories in terms of collisions in a very simple theory. Unlike the original method, it doesn’t rely on any particular picture of how these collisions work, either Feynman diagrams or strings.

arXiv:2201.01624 : Moduli and Hidden Matter in Heterotic M-Theory with an Anomalous U(1) Hidden Sector

In string theory (and its more sophisticated cousin M theory), our four-dimensional world is described as a world with more dimensions, where the extra dimensions are twisted up so that they cannot be detected. The shape of the extra dimensions influences the kinds of particles we can observe in our world. That shape is described by variables called “moduli”. If those moduli are stable, then the properties of particles we observe would be fixed, otherwise they would not be. In general it is a challenge in string theory to stabilize these moduli and get a world like what we observe.

This paper discusses shapes that give rise to a “hidden sector”, a set of particles that are disconnected from the particles we know so that they are hard to observe. Such particles are often proposed as a possible explanation for dark matter. This paper calculates, for a particular kind of shape, what the masses of different particles are, as well as how different kinds of particles can decay into each other. For example, a particle that causes inflation (the accelerating expansion of the universe) can decay into effects on the moduli and dark matter. The paper also shows how some of the moduli are made stable in this picture.

arXiv:2201.01630 : Chaos in Celestial CFT

One variant of the holography idea I mentioned earlier is called “celestial” holography. In this picture, the sides of the box are an infinite distance away: a “celestial sphere” depicting the angles particles go after they collide, in the same way a star chart depicts the angles between stars. Recent work has shown that there is something like a sensible theory that describes physics on this celestial sphere, that contains all the information about what happens inside.

This paper shows that the celestial theory has a property called quantum chaos. In physics, a theory is said to be chaotic if it depends very precisely on its initial conditions, so that even a small change will result in a large change later (the usual metaphor is a butterfly flapping its wings and causing a hurricane). This kind of behavior appears to be present in this theory.

arXiv:2201.01657 : Calculations of Delbrück scattering to all orders in αZ

Delbrück scattering is an effect where the nuclei of heavy elements like lead can deflect high-energy photons, as a consequence of quantum field theory. This effect is apparently tricky to calculate, and previous calculations have involved approximations. This paper finds a way to calculate the effect without those approximations, which should let it match better with experiments.

(As an aside, I’m a little confused by the claim that they’re going to all orders in αZ when it looks like they just consider one-loop diagrams…but this is probably just my ignorance, this is a corner of the field quite distant from my own.)

arXiv:2201.01674 : On Unfolded Approach To Off-Shell Supersymmetric Models

Supersymmetry is a relationship between two types of particles: fermions, which typically make up matter, and bosons, which are usually associated with forces. In realistic theories this relationship is “broken” and the two types of particles have different properties, but theoretical physicists often study models where supersymmetry is “unbroken” and the two types of particles have the same mass and charge. This paper finds a new way of describing some theories of this kind that reorganizes them in an interesting way, using an “unfolded” approach in which aspects of the particles that would normally be combined are given their own separate variables.

(This is another one I don’t know much about, this is the first time I’d heard of the unfolded approach.)

arXiv:2201.01679 : Geometric Flow of Bubbles

String theorists have conjectured that only some types of theories can be consistently combined with a full theory of quantum gravity, others live in a “swampland” of non-viable theories. One set of conjectures characterizes this swampland in terms of “flows” in which theories with different geometry can flow in to each other. The properties of these flows are supposed to be related to which theories are or are not in the swampland.

This paper writes down equations describing these flows, and applies them to some toy model “bubble” universes.

arXiv:2201.01697 : Graviton scattering amplitudes in first quantisation

This paper is a pedagogical one, introducing graduate students to a topic rather than presenting new research.

Usually in quantum field theory we do something called “second quantization”, thinking about the world not in terms of particles but in terms of fields that fill all of space and time. However, sometimes one can instead use “first quantization”, which is much more similar to ordinary quantum mechanics. There you think of a single particle traveling along a “world-line”, and calculate the probability it interacts with other particles in particular ways. This approach has recently been used to calculate interactions of gravitons, particles related to the gravitational field in the same way photons are related to the electromagnetic field. The approach has some advantages in terms of simplifying the results, which are described in this paper.

Merry Newtonmas, Everyone!

In past years, I’ve compared science to a gift: the ideal gift for the puzzle-fan, one that keeps giving new puzzles. I think people might not appreciate the scale of that gift, though.

Maybe you’ve heard the old joke that studying for a PhD means learning more and more about less and less until you know absolutely everything about nothing at all. This joke is overstating things: even when you’ve specialized down to nothing at all, you still won’t know everything.

If you read the history of science, it might feel like there are only a few important things going on at a time. You notice the simultaneous discoveries, like calculus from Newton and Liebniz and natural selection from Darwin and Wallace. You can get the impression that everyone was working on a few things, the things that would make it into the textbooks. In fact, though, there was always a lot to research, always many interesting things going on at once. As a scientist, you can’t escape this. Even if you focus on your own little area, on a few topics you care about, even in a small field, there will always be more going on than you can keep up with.

This is especially clear around the holiday season. As everyone tries to get results out before leaving on vacation, there is a tidal wave of new content. I have five papers open on my laptop right now (after closing four or so), and some recorded talks I keep meaning to watch. Two of the papers are the kind of simultaneous discovery I mentioned: two different groups noticing that what might seem like an obvious fact – that in classical physics, unlike in quantum, one can have zero uncertainty – has unexpected implications for our kind of calculations. (A third group got there too, but hasn’t published yet.) It’s a link I would never have expected, and with three groups coming at it independently you’d think it would be the only thing to pay attention to: but even in the same sub-sub-sub-field, there are other things going on that are just as cool! It’s wild, and it’s not some special quirk of my area: that’s science, for all us scientists. No matter how much you expect it to give you, you’ll get more, lifetimes and lifetimes worth. That’s a Newtonmas gift to satisfy anyone.

# Calculations of the Past

Last week was a birthday conference for one of the pioneers of my sub-field, Ettore Remiddi. I wasn’t there, but someone who was pointed me to some of the slides, including a talk by Stefano Laporta. For those of you who didn’t see my post a few weeks back, Laporta was one of Remiddi’s students, who developed one of the most important methods in our field and then vanished, spending ten years on an amazingly detailed calculation. Laporta’s talk covers more of the story, about what it was like to do precision calculations in that era.

“That era”, the 90’s through 2000’s, witnessed an enormous speedup in computers, and a corresponding speedup in what was possible. Laporta worked with Remiddi on the three-loop electron anomalous magnetic moment, something Remiddi had been working on since 1969. When Laporta joined in 1989, twenty-one of the seventy-two diagrams needed had still not been computed. They would polish them off over the next seven years, before Laporta dove in to four loops. Twenty years later, he had that four-loop result to over a thousand digits.

One fascinating part of the talk is seeing how the computational techniques change over time, as language replaces language and computer clusters get involved. As a student, Laporta learns a lesson we all often need: that to avoid mistakes, we need to do as little by hand as possible, even for something as simple as copying a one-line formula. Looking at his review of others’ calculations, it’s remarkable how many theoretical results had to be dramatically corrected a few years down the line, and how much still might depend on theoretical precision.

Another theme was one of Remiddi suggesting something and Laporta doing something entirely different, and often much more productive. Whether it was using the arithmetic-geometric mean for an elliptic integral instead of Gaussian quadrature, or coming up with his namesake method, Laporta spent a lot of time going his own way, and Remiddi quickly learned to trust him.

There’s a lot more in the slides that’s worth reading, including a mention of one of this year’s Physics Nobelists. The whole thing is an interesting look at what it takes to press precision to the utmost, and dedicate years to getting something right.


text:
# Standard deviation as a percent?

1. Oct 9, 2014

### zeromodz

Say if I have a sample space 2,3, and 5. I want to find by what percent points deviate from the mean. So I would take the standard deviation as follows.

2+3+5 / 3 = 3.33

(2-3.33)^2 + (3-3.33)^2 + (5-3.33)^2 / 3 = 1.55

(1.55)^(1/2) = 0.775

So we get a standard deviation of 0.775. So how do I turn the standard deviation into a plus or minus percentage?

2. Oct 9, 2014

### mathman

Step 1: √1.55555 = 1.25
Step 2: 100(1.25/3.33)

3. Oct 9, 2014

### FactChecker

It's important that you say that the three points, 2, 3, and 5 are equally likely results. That is implied by your calculation of the mean = (2+3+5)/3, where the three points each have probability 1/3 of occurring.

As @mathman points out, your calculation of the standard deviation is wrong. You divided by 2 instead of taking the square root. The correct value is 1.24722.

You want to know what percentage of a sample will be within 1 standard deviation of the mean. That is between 3.33333 - 1.24722 and 3.33333 + 1.24722. (between 2.086 and 4.581. Only the results X=3 are in that range. That probability is 1/3 = 33.3%

Last edited: Oct 9, 2014