Find research datasets worth reusing
Search datasets from major research repositories and use ShareScore to quickly assess how well each record supports discovery, access, and reuse.
3
datasets available to search
ShareScore release 0.9.0
Dataset results
3 results for “sum of squares”
Approximate sum of squares decompositions for Adj₅ + k·Op₅ - λΔ₅ ∈ ISAut(F₅)
<p>This is the dataset accompanying <em>On property (T) for Aut(Fₙ) and SLₙ(</em>ℤ<em>) </em>paper (https://arxiv.org/abs/1812.03456). See the appendix thereof and Section 4 of (<a href="https://arxiv.org/abs/1712.07167">Aut(F₅) has property (T)</a>) for more details.</p> <p><strong>Content</strong></p> <ol> <li><code>1812.03456-cf6dee7.zip</code> contains a julia environment specification (<code>Project.toml</code> and <code>Manifest.toml</code>) as well as <code>1812.03456.jl</code> script used for automatic certification and jupyter noteboks in <code>./notebooks</code> directory.</li> <li><code>SAutF5_r2.tar.xz</code> contains the precomputed solutions for expressing <code>Adj₅+2·Op₅-0.28Δ₅</code> and <code>Adj₅+3·Op₅-1.4Δ₅</code> as sum of (hermitian) squares in the group ring of <code>SAut(F₅)</code>. The contents of this archive must be placed inside `<code>1812.03456`</code>directory from the <code>zip</code> file.</li> </ol> <p><strong>Preparation</strong></p> <p>The code needs to be run with <code>julia-1.4.0</code> or higher (tested versions include also versions <code>julia-1.5</code>). In principle any version in <code>[1.4-2.0)</code> should work due to the promise of forward compatibility.</p> <p>While located in the main directory (<code>1812.03456</code>) you should run the following code in <code>julia</code>s <code>REPL</code> console to instantiate the environment for computations:</p> <pre><code class="language-julia">using Pkg Pkg.activate(".") Pkg.instantiate()</code></pre> <p>(this needs to be done once per installation). Then the directory <code>SAutF5_r2</code> (from the <code>SAutF5_r2.tar.xz</code> archive) needs to be placed in <code>1812.03456</code>.</p> <p><strong>Replication: Jupyter notebook</strong></p> <p>A jupyter server may be launched then within the directory <code>1812.03456</code> by issuing from julia command-line (<code>REPL</code>) the following commands.</p> <pre><code>using Pkg Pkg.activate(".") using IJulia notebook(dir=".")</code></pre> <p>During the first run the user may be asked for installation of <code>Jupyter</code> program (a server for running this notebook) within <code>miniconda</code> environment, which will happen automatically after confirmation. To execute the commands in the notebook, one needs to navigate to <code>notebooks</code> subdirectory of <code>1812.03456</code> and click either of the notebooks.</p> <p>One can replicate the main computational results of the paper by executing all the cells in the <code>Positivity of Adj_n + kOp_n in ISAut(F_n)</code> notebook.</p> <p><strong>Replication: script</strong></p> <p>To verify that <em>(Adj₅ + 3.0·Op₅) - 1.4·Δ₅</em> admits an approximate sum of squares decomposition run in <code>1812.03456</code> directory</p> <blockquote> <p><code>julia --project=. --color=yes 1812.03456.jl -n 5 -k 3 -l 1.4</code></p> </blockquote> <p>On a modern laptop computer this should finish in less than 2h.</p> <p>At the end of computations you will see lines such as:</p> <blockquote> <p>┌ Info: λ is certified to be ><br> └ λ_cert.lo = 1.3701131733828074<br> [ Info: i.e Adj_5 + 3.0·Op_5 - (1.3701131733828074)·Δ_5 ∈ Σ²₂ ISAut(F_5)</p> </blockquote> <p>This means that <em>Adj₅ + 3.0·Op₅ - λΔ₅</em> is a sum of Hermitian squares of elements from <em>ISAut(F₅)</em> for every <code>λ < 1.370....</code></p> <p>A similar verification for <em>Adj₅ + 2.0·Op₅ - 0.28·Δ₅</em> can be run by executing</p> <blockquote> <p><code>julia --project=. --color=yes 1812.03456.jl -n 5 -k 2 -l 0.28</code></p> </blockquote> <p><strong>Generating the provided files</strong></p> <p>If you wish to produce the whole certificate on your own (including the generation of group ring and its multiplication table), delete all <code>*.jld</code> files from the <code>SAutF5_r2</code> folder and run one of the above commands with the same (or different) parameters again. Note: To do this you need at least 16GB of RAM and spare 24h of your CPU.</p> <p>This research was supported in part by National Science Center, Poland, grant 2017/26/D/ST1/00103.</p>
Autoconfig: Balanced Minimum sum-of-squares clustering case
<p>Autoconfig: Balanced Minimum Sum-of-Squares Clustering</p> <p>See https://github.com/rmartinsanta/ac-BMSSC for full details.</p> <p> </p> <p>Authors of the original paper: <br>Alberto (Herrán González)<br>José Manuel (Colmenar Verdugo)<br>Abraham (Duarte Muñoz)</p>
SWISS MADE: Standardized WithIn class Sum of Squares to evaluate Methodologies And Dataset Elements
GEO Series GSE20234. Homo sapiens. 8 samples. Type: Expression profiling by array.
ScienceDex guides
Understand access before you commit
These curated guides explain access requirements, typical timelines, costs, and reuse considerations for widely used research datasets.
Allen Brain Atlas
Allen Brain Atlas is an Allen Institute collection of brain map atlases, datasets, APIs, and analysis tools covering mouse, human, and non-human primate brain resources.
Annotated Behaviour and Observability Dataset (ABODe)
ABODe is a University of Edinburgh DataShare dataset for behavior classification in group-housed mice using home-cage video, identities, bounding boxes, ground-plate positions, and annotator labels.
DANDI Archive for NWB datasets
DANDI is a BRAIN Initiative archive for publishing and sharing neurophysiology data, including electrophysiology, optophysiology, and behavioral data packaged as NWB and related standards.
International Brain Laboratory public data
The International Brain Laboratory public data releases expose standardized mouse decision-making experiments, including Neuropixels recordings, widefield calcium imaging, behavior, and session metadata accessed through the ONE API.
OpenNeuro
OpenNeuro is a free, open platform for sharing neuroimaging datasets, with public search, dataset pages, and download paths for web, S3, DataLad, and the OpenNeuro CLI.