<?xml version="1.0" encoding="utf-8" standalone="yes"?><rss version="2.0" xmlns:atom="http://www.w3.org/2005/Atom"><channel><title>topology | Math to Power Industry</title><link>https://m2pi.ca/keywords/topology/</link><atom:link href="https://m2pi.ca/keywords/topology/index.xml" rel="self" type="application/rss+xml"/><description>topology</description><generator>Wowchemy (https://wowchemy.com)</generator><language>en-us</language><copyright>© 2025 Pacific Institute for the Mathematical Sciences</copyright><lastBuildDate>Tue, 24 Mar 2026 00:00:00 +0000</lastBuildDate><image><url>https://m2pi.ca/media/logo.svg</url><title>topology</title><link>https://m2pi.ca/keywords/topology/</link></image><item><title>IOTO</title><link>https://m2pi.ca/project/2026/ioto/</link><pubDate>Tue, 24 Mar 2026 00:00:00 +0000</pubDate><guid>https://m2pi.ca/project/2026/ioto/</guid><description>&lt;p>
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&lt;h3 id="overview">Overview&lt;/h3>
&lt;p>We have controlled vocabularies and topic structures that are used to index
and understand large bodies of text. We want to better understand how text is
clustered around known structured topics so that unknown topics can be
identified in texts and added to our controlled vocabularies and topic
structures.&lt;/p>
&lt;h3 id="background">Background&lt;/h3>
&lt;p>Goverlytics&lt;sup>®&lt;/sup> seeks to produce low-dimensional representations of
legislative activity to: 1) make politics accessible to a broader public; and to
2) increase focus on policy goals. The model for Goverlytics&lt;sup>®&lt;/sup> is
sports analytics, which has transformed the way in which sports are understood
and consumed. Goverlytics&lt;sup>®&lt;/sup> analyzes data generated during
legislative sessions: attendance, documents, transcripts, vote tallies, audio
and video recordings.&lt;/p>
&lt;p>Analytics in sports first &lt;a href="https://invention.si.edu/invention-stories/sports-analytics-moneyball" target="_blank" rel="noopener">began with measurement of what could be easily
measured&lt;/a>
– goals (of course!), strokes, hits, etc. By distilling all that goes on during
the activity into a few dimensions that allow for quantification and comparison,
analytics helps to explain and so increase comprehension and engagement.
Increasingly complex measurements are being engineered from ever larger datasets
to enhance predictions and decision-making. Both short-term outcomes and
strategies that may be decided in game, and for long-term considerations such as
player health are at stake.&lt;/p>
&lt;h3 id="challenge">Challenge&lt;/h3>
&lt;p>In some cases, Goverlytics&lt;sup>®&lt;/sup> has to start creating statistics for
legislative sessions from simple audio tracks. Audio is transcribed into words
of a language. Then the language words (and concatenations of them) are binned
into topic discourse, by means language models and &lt;a href="https://www.comparativeagendas.net/datasets_codebooks" target="_blank" rel="noopener">topic
classifications&lt;/a>.
Finally, topic classifications are used to index parts of the legislative
activity that are likely to be interesting for a broader public. This process
is akin to the distillation of a sporting match into a highlights reel or
abbreviated match summary e.g. What topics were discussed the most? Who talked
about those topics? Were there any significant new topics, or was voting and
discussion about previously known topics? Were there significant outliers? Smash
hits?&lt;/p>
&lt;p>Because legislative sessions can go on for hours with very little information of
predictive or decision-making value, it can be costly to process raw data to
reach insight. The challenge is to find shorter paths to interesting bits of
discourse. Can methods from &lt;a href="https://www.mdpi.com/journal/mathematics/special_issues/Mathematical_Methods_Signal_Analysis" target="_blank" rel="noopener">signal
analysis&lt;/a>
or related mathematical fields be used to more efficiently signpost insight into
legislative data? Unsupervised learning techniques may provide some guidance.
However, a successful solution will reveal what in the legislative activity is
deserving of attention from a policy point of view, ether by connecting with a
known policy ontology (such as &lt;a href="https://www.comparativeagendas.net/pages/master-codebook" target="_blank" rel="noopener">comparative agendas
codebook&lt;/a>, or by
surfacing issues that should be connected to a known ontology.&lt;/p>
&lt;h3 id="data">Data&lt;/h3>
&lt;p>At a minimum, APIs covering topic data for various legislative leagues (Canada,
BC, Alberta, etc.) will be made available to the M2PI team. These APIs reliably
serve data concerning legislative &amp;lsquo;players&amp;rsquo; and their topic-related interventions
over a number of legislative sessions. Corresponding audio will also be supplied.&lt;/p>
&lt;p>Further datasets concerning elections, voting, and financial data may be made
available – depending time available, which legislative leagues the M2PI team
elects to study, and how they choose to analyse.&lt;/p>
&lt;ul>
&lt;li>Finance data are available from
&lt;a href="https://data.oecd.org/gga/general-government-spending.htm" target="_blank" rel="noopener">OECD&lt;/a>, &lt;a href="https://www150.statcan.gc.ca/n1/en/type/data" target="_blank" rel="noopener">Statistics
Canada&lt;/a>, and &lt;a href="https://www2.gov.bc.ca/gov/content/data/statistics/economy/bc-economic-accounts-gdp" target="_blank" rel="noopener">legislative
&amp;rsquo;leagues&amp;rsquo;
themselves&lt;/a>.&lt;/li>
&lt;li>Topics are standardized along &lt;a href="https://www.comparativeagendas.net/pages/master-codebook" target="_blank" rel="noopener">Comparative Agendas Project (CAP)
lines&lt;/a>&lt;/li>
&lt;li>Charts of
&lt;a href="https://www.tpsgc-pwgsc.gc.ca/recgen/pceaf-gwcoa/2324/tdm-toc-eng.html" target="_blank" rel="noopener">accounts&lt;/a>
for
&lt;a href="https://www.oecd-ilibrary.org/sites/df28fbde-en/index.html?itemId=/content/component/df28fbde-en#:~:text=Governments%27%20expenditures%20by%20function%20reveal,and%20public%20order%20and%20safety" target="_blank" rel="noopener">finance&lt;/a>
overlap topic categories, but do not correspond exactly.&lt;/li>
&lt;li>Voting data for bills and motions may be available for &lt;a href="https://www.ourcommons.ca/members/en/votes" target="_blank" rel="noopener">certain
legislatures&lt;/a>.&lt;/li>
&lt;li>Audio files are available for whatever legislative level is chosen for study
by the M2PI team.&lt;/li>
&lt;/ul></description></item><item><title>University of Victoria</title><link>https://m2pi.ca/project/2026/uvic/</link><pubDate>Tue, 24 Mar 2026 00:00:00 +0000</pubDate><guid>https://m2pi.ca/project/2026/uvic/</guid><description>&lt;h3 id="overview">Overview&lt;/h3>
&lt;p>The goal of this project is to develop an interface between quantum and classical (binary) computing systems for climate modeling.&lt;/p>
&lt;p>Climate models are large, complex computer programs made up of multiple components that represent different parts of the Earth system, such as the atmosphere, oceans, cryosphere, and vegetation. Each component is typically developed as a separate code, and many of these are further divided into sub-modules.&lt;/p>
&lt;p>For example, atmospheric models usually include a dynamics module—often called the dynamical core—and one or more physics modules. The dynamical core is based on systematic discretization methods (such as finite differences, finite volumes, or spectral methods) to solve the equations of motion. In contrast, the physics modules represent processes that are not explicitly resolved by the dynamical core. These processes occur at spatial or temporal scales smaller than the model’s grid resolution and include phenomena such as radiation, phase changes of water and associated latent heat transfer, turbulence, and convection.&lt;/p>
&lt;p>Because resolving these small-scale processes directly is computationally expensive, they are typically approximated using heuristic models based on ad hoc closure assumptions.&lt;/p>
&lt;p>Although quantum computing is advancing rapidly, it is not yet practical to implement all components of climate models on quantum systems. Moreover, existing classical codes for dynamical cores are well established and highly reliable. However, if a quantum algorithm can be developed for specific sub-grid processes that is both efficient and accurate, it could be integrated with a classical dynamical core to create a hybrid quantum–classical modeling framework.&lt;/p>
&lt;p>As a proof of concept, this project proposes to couple a simple convection model with a toy climate model developed by Khouider et al. (2010). The convection model, known as the Stochastic Multicloud Model (SMCM), is a Markov model that describes the area fractions of three cloud types.&lt;/p>
&lt;p>In &lt;a href="#ref2">Khouider et al. (2010)&lt;/a>, the SMCM is coupled with a set of ordinary differential equations (ODEs) that describe the vertical profiles of temperature and moisture, assuming horizontal homogeneity (i.e., no spatial derivatives). More recently, Ueno and Miura (2025) developed a quantum implementation of the SMCM component alone.&lt;/p>
&lt;p>This project aims to integrate the quantum SMCM code of &lt;a href="#ref1">Ueno and Miura (2025)&lt;/a> with the ODE-based system used in Khouider et al. (2010), which serves as a simplified dynamical core. This integration will act as a demonstration of a hybrid quantum–classical climate modeling approach.&lt;/p>
&lt;p>As a possible extension, the quantum SMCM code could also be applied to machine learning tasks. For example, it could be used to generate sample paths for a synthetic likelihood algorithm to calibrate the SMCM using radar data (Sevilla and Khouider, unpublished work).&lt;/p>
&lt;h2 id="references">References&lt;/h2>
&lt;ol>
&lt;li>&lt;a name="ref1">&lt;/a>Kazumasa Ueno, Hiroaki Miura, Quantum Algorithm for a Stochastic
Multicloud Model, SOLA, 2025, Vol. 21, pp. 43-50, Publication Date
2025/01/22, [Early Release] Publication Date 2024/12/11, Online ISSN
1349-6476, &lt;a href="https://doi.org/10.2151/sola.2025-006" target="_blank" rel="noopener">https://doi.org/10.2151/sola.2025-006&lt;/a>.&lt;/li>
&lt;li>&lt;a name="ref2">&lt;/a> Khouider, B., J. Biello, and A. J. Majda, 2010: &lt;a href="https://projecteuclid.org/journals/communications-in-mathematical-sciences/volume-8/issue-1/A-stochastic-multicloud-model-for-tropical-convection/cms/1266935019.full" target="_blank" rel="noopener">A stochastic multicloud
model for tropical
convection&lt;/a>. Commun. Math. Sci., 8, 187–216.&lt;/li>
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