2DS Dataset: Multi-domain Insights

• 2DS dataset is a multifaceted term defined across fields such as energy thresholds in superconductors, large-scale CT imaging, and robust graph domination in distributed algorithms.
• Methodologies include precise spectral mapping, advanced preprocessing using Beer–Lambert transformations, and asynchronous ELLSS algorithms ensuring rapid convergence in graph settings.
• Datasets also enable detailed characterization of 2D semiconductors and momentum-resolved quantum responses, bridging experimental diagnostics with theoretical modeling.

The term "2DS dataset" possesses domain-specific meanings contingent on context, including superconductivity (where it denotes energy thresholds for spin excitations), computational imaging (e.g., large-scale 2D CT datasets), distributed algorithmics (as the target structure for self-stabilizing graph algorithms), semiconducting device physics (monolayer two-dimensional semiconductors), and momentum-resolved nonlinear spectroscopy (where it refers to multidimensional maps of quantum field responses). Expert usage reflects diversity across these fields. The following sections survey representative definitions, properties, and research significance across areas directly addressed in the literature.

1. Spin Excitation Spectra in Iron-Based Superconductors

Within the context of iron-based superconductors, "2DS" designates the energy threshold $2\Delta_s$, where $\Delta_s$ is the superconducting gap. In the spin fluctuation (spin-exciton) model, magnetic neutron scattering enhancements—spin resonances—occur only for excitation energies $E_{\mathrm{res}} < 2\Delta_s$ (Lee et al., 2016). The canonical value is $2\Delta_s = 7.5 k_B T_c$, correlating resonance energy scales with the critical temperature. Empirical studies reveal:

Doping Regime	Resonance Location	Spectral Weight
Optimal ($x = 0.50$)	$E_{\mathrm{res}} \approx 15$ meV, $< 2\Delta_s$	Sharply peaked below $2\Delta_s$
Overdoped ($x = 0.84$)	$E_{\mathrm{res}} > 2\Delta_s$, $\sim 3\Delta_s$	Suppressed below $2\Delta_s$, redistributed to higher energies

Significance: The presence or absence of low-energy resonance below $2\Delta_s$ constrains pairing mechanisms—favoring spin-fluctuation models in optimal doping, but pointing to orbital fluctuation or alternate models in overdoped regimes. The 2DS dataset in this context should encode detailed energy-resolved spectral maps versus doping, permitting discrimination among competing superconductivity theories.

2. Large-Scale 2D Computed Tomography Datasets

In computational imaging and ML-driven CT reconstruction, the 2DS dataset refers to large collections of experimentally acquired 2D fan-beam CT data (Kiss et al., 2023). The 2DeteCT dataset exemplifies this paradigm:

• Composition: 5,000 standard slices of heterogeneous samples (dried fruits, nuts, stones) plus 750 out-of-distribution slices with sample/beam variations; each simulates tissue contrasts encountered in clinical CT.
• Acquisition Modes: High-fidelity (optimized filtering), low-dose (increased noise, lower tube current), beam-hardening-inflicted (unfiltered beam).
• Resolution: 3,601 projections per slice (0.1° angular steps, ~60 µm spatial resolution).

Acquisition Mode	Tube Power	Filtered	Artifact Profile
High-fidelity	90 W	Yes	Low noise, artifact-minimized
Low-dose	3 W	Yes	High noise
Beam-hardening	60 kV	No	Pronounced beam hardening

Each dataset instance includes raw sinograms, reference reconstructions (NNLS via Nesterov’s accelerated GD), 4-class segmentations, and calibration images. Preprocessing employs Beer–Lambert law transformation:

$y = -\log \left( \frac{S - D}{F - D} \right)$

where $S$ is the measured sinogram, $D$ the dark-field, $F$ the flat-field.

Significance: The dataset supports development and benchmarking of ML/AI-based CT reconstruction algorithms. Its diversity enables robust testing of artifact removal, denoising, super-resolution, segmentation, and sparse-angular schemes. Open-source pipelines leveraging CUDA and ASTRA Toolbox are provided for reproducible research.

3. Self-Stabilizing Algorithms for 2-Dominating Set Problems

In distributed algorithmics, "2DS" conventionally denotes the 2-dominating set problem, where the solution $\mathcal{D} \subseteq V(G)$ not only dominates the graph but is robust against swaps: no outside node can replace two in-set nodes while preserving domination (Gupta et al., 2023).

Formal predicates:

• $\mathcal{P}'_{d}(\mathcal{D})$: $$\forall i, i \in \mathcal{D} \vee (\exists j \in \text{Adj}_i : j \in \mathcal{D})$$
• $\mathcal{P}_{d}(\mathcal{D})$: minimality w.r.t. domination
• $\mathcal{P}_{2d}(\mathcal{D})$: swap robustness, i.e.,

$$\neg(\exists i \in V \setminus \mathcal{D} : (\exists j, k \in \text{Adj}_i \cap \mathcal{D} : \mathcal{P}'_{d} (\mathcal{D} \cup \{i\} \setminus \{j, k\})))$$

The eventually lattice-linear self-stabilizing (ELLSS) algorithm proceeds in two phases:

1. Feasibility: Addable nodes join the set until at least minimal domination is achieved.
2. Lattice-linear optimization: Nodes use local predicates (Removable-2DS, Two-Addable-2DS, Impedensable-2DS) to asynchronously remove/substitute nodes, converging to a minimal robust 2-domination.

Performance:

• Provable convergence in $1$ round plus $2n$ moves, i.e., within $3n$ moves for $n$ nodes.
• Asynchronicity tolerated: threads read stale values, yet monotonic progress is guaranteed.
• Empirical findings (primarily in MIS but applicable to 2DS) show superior wall-clock convergence compared to synchronous algorithms.

Significance: The 2DS dataset here refers to graph-structured data encoding node states and transitions during distributed self-organization. Algorithms using ELLSS paradigms ensure rapid, low-synchronization convergence in large-scale graph settings.

4. 2D Semiconductor Nanoribbons and Device Metrics

In semiconductor device physics, "2DS" denotes two-dimensional semiconductors, especially monolayer transition metal dichalcogenides (TMDs) such as MoS$_2$, WS$_2$, and WSe$_2$ (Peña et al., 12 Sep 2025). Recent work demonstrates top-down fabrication of nanoribbon transistors with aggressive width ($W_\text{ch}$ down to 25 nm) and length ($L_\text{ch}$ down to 50 nm) scaling using multi-patterning LELE processes.

Key device metrics:

• On-state currents: MoS$_2$ ($\sim$560 $\mu$A/$\mu$m), WS$_2$ ($\sim$420 $\mu$A/$\mu$m), WSe$_2$ (p-type, $\sim$130 $\mu$A/$\mu$m) at $V_\text{DS}=1$ V.
• Contact resistance: $R_\text{c} < 560\,\Omega \cdot \mu$m.
• Mobility: $\mu_\text{FE}$ typically 30–60 cm$^2$/Vs.

Fundamental equation (linear regime):

$$I_D = \mu_\text{FE} \cdot C_\text{ox} \cdot \frac{W}{L} \cdot (V_\text{GS} - V_T) \cdot V_\text{DS}$$

Characterization using Raman spectroscopy and tip-enhanced photoluminescence demonstrates minimal edge-induced disorder; transmission electron microscopy (TEM/STEM) confirms crystallinity at nanoribbon edges.

Significance: This benchmark 2DS dataset combines electrical, geometric, and spectroscopic parameters, critical for modeling and designing next-generation gate-all-around nanosheet transistors. Record current densities and robust nanoscale imaging herald integration feasibility with CMOS processes.

5. Momentum-Resolved Two-Dimensional Spectroscopy Datasets

In quantum optics and strongly correlated matter, the "2DS dataset" refers to momentum-resolved two-dimensional spectral maps of nonlinear system responses (Santis et al., 29 Sep 2025). The framework utilizes double-pulse spectroscopy on ultracold atomic systems, mapping quantum sine-Gordon model excitations:

• Each dataset instance is a two-dimensional map, $\mathcal{D}_k^\mathrm{nl}(\omega_1, \omega_2)$, constructed via double Fourier transformation of time-delayed response functions at fixed momentum $k$.
• Signatures include
  • Diagonal peaks: two-particle continuum ($B_1$ breather pairs)
  • Off-diagonal asymmetric cross-peaks: mixing between discrete ($B_2$) and continuum ($B_1$) excitations

Mathematical representation:

$$H_0 = \frac{1}{2} \int dx \left[ (\partial_x \phi)^2 + \Pi^2 - \Delta_0 \cos(\beta \phi) \right]$$

The nonlinear response is encoded as

$$\mathcal{D}_k^\mathrm{nl}(t_1, t_2) = \mathcal{D}_k^\mathrm{AB}(t_1, t_2) - \mathcal{D}_k^\mathrm{A}(t_1, t_2) - \mathcal{D}_k^\mathrm{B}(t_1, t_2)$$

Significance: The resulting dataset offers detailed fingerprints of many-body quantum field dynamics, pivotal for diagnosing integrability, anharmonicity, and disorder in tunable quantum simulators. Such maps facilitate direct, model-sensitive comparisons between theory and experimental atom-chip platforms.

6. Interdisciplinary Implications and Research Directions

The diversity of meanings attached to "2DS dataset" across physical sciences, imaging, algorithmic graph theory, and quantum measurement exemplifies the importance of domain-precise definitions. Application-dependent datasets harness high-resolution experimental acquisition, sophisticated algorithmic characterization, and nuanced physical modeling. The datasets facilitate comparative theory-experiment studies, robust algorithm benchmarking, model parameter estimation, and device design optimization.

Researchers should attend to contextual definitions when constructing, analyzing, or referencing a "2DS dataset," document measurement modes and data provenance rigorously, and leverage provided open-source toolchains for reproducibility. The cross-disciplinary nature of the term reinforces its role as an essential but contextually polymorphic construct for advancing data-driven scientific inquiry.