Probe Data Structure Overview

• Probe data structure is a family of probe-conditioned representations that define how instruments or algorithms sample, index, and access data.
• It spans diverse applications such as 4D-STEM imaging, atom probe tomography, and Wi-Fi probe-request analysis with detailed metadata schemas.
• In theoretical computer science, the concept underlies the cell-probe model, shaping lower-bound proofs and complexity measures in dynamic data structures.

Probe data structure is a cross-disciplinary term for representations whose organization is determined by a probe: an instrumental probe that samples a specimen or environment, a network probe request emitted by a device, a software or diagnostic probe whose state must be cataloged, or, in theoretical computer science, a data structure analyzed by the number of memory-cell probes it performs. In the literature summarized here, these representations range from 4D-STEM diffraction tensors and atom-probe point clouds to Wi-Fi probe-request records, tokamak probe metadata tables, adaptive monitoring-probe architectures, and cell-probe formulations of succinct and dynamic data structures (Brown et al., 2018, Bravenec et al., 2023, Weinstein et al., 2016). This suggests that the unifying feature is not a single schema, but the explicit encoding of how a probe interrogates, indexes, or accesses information.

1. Core meanings and canonical record forms

Across these literatures, the “probe” is the mechanism that determines what is observable and how that observable is indexed. In scanning transmission electron microscopy, the data structure is indexed by probe position $\mathbf r$, detector coordinate $\mathbf g$, and defocus $\Delta f$. In Wi-Fi measurement, each record combines receiver timestamp, Radiotap metadata, 802.11 header fields, and Information Elements. In tokamak diagnostics, a probe entry is a metadata row keyed by identity, shot context, geometry, and channel mapping. In the cell-probe model, a data structure is an array of $w$-bit memory cells, and the complexity measure is the number of reads and writes, or probes, rather than arithmetic cost (Brown et al., 2018, Bravenec et al., 2023, Verma et al., 30 Aug 2025, Weinstein et al., 2016).

Domain	Canonical structured object	Role of the probe
4D-STEM	$I_{\mathrm{STEM}}(\mathbf r,\mathbf g,\Delta f)$	Structured incident field and detector-space measurement
Wi-Fi monitoring	$$\{\text{timestamp},\text{Radiotap metadata},\text{802.11 header},\text{Information Elements}\}$$	Management-frame emission captured by a sniffer
Tokamak diagnostics	Excel-backed probe metadata row	Registration of diagnostic geometry and readout mapping
Cell-probe theory	Array of $w$-bit cells with probe budget $t$	Memory-access primitive defining cost

The same term therefore covers both observational data organization and abstract access models. This suggests that “probe data structure” is best understood as a family of probe-conditioned representations, rather than a single discipline-specific format.

2. Probe-generated experimental representations

In atomic-resolution electron microscopy, the central probe-generated structure is the 4D-STEM dataset: a full diffraction pattern is recorded at each probe position in a raster scan and repeated for multiple defocus values. The measured intensity is

$$I_{\mathrm{STEM}}(\mathbf r,\mathbf g,\Delta f)=\left| \sum_{\mathbf h} \mathcal S_{\mathbf g,\mathbf h} \exp\!\left[2\pi i\left(h^2\Delta f\lambda-\mathbf h\cdot\mathbf r\right)\right] \right|^2,$$

with the sum over $\mathbf h$ inside the probe-forming aperture. This organization allows reconstruction of rows of the complex scattering matrix $\mathbf g$0, followed by deterministic inversion of the Bethe multiple-scattering equations to recover the projected electrostatic potential $\mathbf g$1 at atomic resolution, including for a Si [110] specimen about $\mathbf g$2 Å thick (Brown et al., 2018). A central clarification in that work is that the STEM probe is not merely illumination; it supplies a structured basis of incident fields, so the data act like interferometric measurements of the crystal’s response matrix.

Atom probe tomography uses a different but equally explicit probe-conditioned structure. The primary data object is a 3D point cloud of detected ions, each event carrying a mass-to-charge ratio and a reconstructed 3D position. In the InAs/GaAs quantum-dot study, the dataset contains more than $\mathbf g$3 million detection events, and the point cloud is converted into a voxel grid with $\mathbf g$4 nm and $\mathbf g$5 nm. Local alloy composition is assigned by neighbor search,

$\mathbf g$6

yielding a spatially varying In$\mathbf g$7Ga$\mathbf g$8As composition that is then mapped to a local band structure and inserted into a 3D Schrödinger equation for electrons and heavy holes (Natale et al., 2024). Here the data structure is not only a reconstructed specimen geometry, but an intermediate representation for in situ electronic-structure simulation.

Probe-based data storage treats the physical medium itself as a probe-written data structure. Bits are encoded as local physical changes such as a topographical indentation, a phase state change, a magnetic orientation, a ferroelectric polarization state, or atomic or molecular placement or state. The canonical system architecture is an array of probes, a storage medium, a relative positioning system, and read/write electronics, often with parallel addressing and readout. The review literature presents topographic storage, phase-change storage, magnetic storage, ferroelectric storage, and atomic and molecular storage as variants of the same organizing principle: nanoscale information written and retrieved by localized probe action (Koelmans et al., 2015).

3. Wireless probe requests and compact frame representations

In IEEE 802.11, probe requests are management frames used for network discovery rather than data transfer. Their basic structure has two parts, a header and a set of Information Elements. The header contains fields such as frame control, destination MAC address, source MAC address, and sequence number; for probe requests, the frame control number is $\mathbf g$9, and the destination is often the broadcast address ff:ff:ff:ff:ff:ff. Information Elements may include SSID, supported data rates, HT Capabilities, VHT Capabilities, HE Capabilities, Extended Capabilities, Vendor Specific elements, WPS fields, UUID-E, and WEP Protected status. The packet itself does not carry transmission time; capture time is derived from the receiver’s RTC-based timestamp, and radio metadata such as RSSI, channel, and antenna information are added through Radiotap headers (Bravenec et al., 2023).

The UJI Probes dataset organizes these records as raw packet captures plus a Radio Map of the office environment. A practical summary representation is

$\Delta f$0

The dataset contains $\Delta f$1 collected probe requests from March 2023 in the GEOTEC department office at University Jaume I, Spain, with workdays, weekends, and holidays included. About $\Delta f$2 of captured probe requests used randomized MAC addresses, about $\Delta f$3 contained an SSID, and the dataset contains $\Delta f$4 unique SSIDs. The Radio Map was created on a $\Delta f$5-meter grid and provides a spatial RSSI reference for occupancy and presence analysis (Bravenec et al., 2023). An important design feature is anonymization by SHA512 hashing of only the last $\Delta f$6 bytes of sensitive MAC-related information, which preserves the OUI, the randomized-versus-global MAC structure, and vendor-related analytical signals.

A second line of work replaces full-frame storage by learned compact probe-request fingerprints. After preprocessing, only HT Capabilities, Extended Capabilities, and Vendor Specific Tags are retained, producing a binary vector

$\Delta f$7

corresponding to $\Delta f$8 bytes. Asymmetric Pairwise Boosting then selects from $\Delta f$9 candidate bitmask filters with active lengths $w$0 and four filter types modeled on Haar-like features. The final descriptor is

$w$1

and matching can be reduced to XOR plus Hamming distance when the confidence weights are set to $w$2 (Baccichet et al., 2024). Reported storage reductions are two orders of magnitude relative to IE-based baselines, with compression ratios of $w$3 for a $w$4-bit fingerprint, $w$5 for $w$6 bits, and $w$7 for $w$8 bits.

4. Metadata catalogs and adaptive probe software

Probe data structure can also denote the organizational schema used to register and retrieve instruments rather than the samples they collect. PRISM, a MATLAB App Designer application tested with the ADITYA-U tokamak, uses an Excel .xlsx file on a shared network drive as its backend. Each probe type has a dedicated worksheet, and each record stores fields including probe name, date, shot number, shot duration, channel number, port type, port number, position, $w$9, $I_{\mathrm{STEM}}(\mathbf r,\mathbf g,\Delta f)$0, information type, experiment, and remarks. The effective row-oriented representation is

$I_{\mathrm{STEM}}(\mathbf r,\mathbf g,\Delta f)$1

The workflow separates probe entry and probe retrieval modules, supports validation and duplicate detection, and visualizes retrieved probes in 2D top views, 2D poloidal slices, and 3D tokamak space (Verma et al., 30 Aug 2025). The schema is probe-family-aware rather than fully uniform: some fields are mandatory only for specific probe families, and some values are auto-saved for GLP1–GLP15.

ReProbe treats a probe as a software component that collects raw indicators such as CPU usage, memory consumption, network statistics, or sensor readings, optionally analyzes them locally, and forwards them to downstream services. Its top-level architecture consists of a Publishers Manager, a Collectors Manager, and a Data Manager. A Collector contains a Controller, Metric Samplers, Data Analyzers, and Configuration, with exactly one Metric Sampler and one Data Analyzer active at any given time. Data flow runs from target resource to Metric Sampler to Data Analyzer to Data Manager and then to Publishers; control flow runs through an API that can add or remove plugins, instantiate or destroy them, and reconfigure them at runtime (Alessi et al., 2024). This suggests that, in software monitoring, a probe data structure includes both the payload schema and the control state that governs adaptive collection, local analysis, and multi-sink publication.

5. Probe as an access-cost model in theoretical computer science

In theoretical computer science, “probe” has a formal meaning unrelated to physical instrumentation. In the cell-probe model, a data structure is an array of $I_{\mathrm{STEM}}(\mathbf r,\mathbf g,\Delta f)$2-bit memory cells, with $I_{\mathrm{STEM}}(\mathbf r,\mathbf g,\Delta f)$3 in the dynamic lower-bound literature, and the only charged cost is the number of memory probes. Computation is free. This model is used precisely because it isolates the intrinsic information-theoretic difficulty of a problem from implementation details (Weinstein et al., 2016). In the static linear setting, a query problem is represented by a matrix $I_{\mathrm{STEM}}(\mathbf r,\mathbf g,\Delta f)$4, and a linear data structure factorizes it as

$I_{\mathrm{STEM}}(\mathbf r,\mathbf g,\Delta f)$5

where the preprocessing map is linear, the query map is linear, and each row of $I_{\mathrm{STEM}}(\mathbf r,\mathbf g,\Delta f)$6 has at most $I_{\mathrm{STEM}}(\mathbf r,\mathbf g,\Delta f)$7 nonzeros, meaning that each query probes at most $I_{\mathrm{STEM}}(\mathbf r,\mathbf g,\Delta f)$8 cells (Dvir et al., 2018).

A central example is the succinct rank problem on an $I_{\mathrm{STEM}}(\mathbf r,\mathbf g,\Delta f)$9-bit array $$\{\text{timestamp},\text{Radiotap metadata},\text{802.11 header},\text{Information Elements}\}$$0, with query

$$\{\text{timestamp},\text{Radiotap metadata},\text{802.11 header},\text{Information Elements}\}$$1

The optimal succinct construction uses

$$\{\text{timestamp},\text{Radiotap metadata},\text{802.11 header},\text{Information Elements}\}$$2

bits in the cell-probe model and answers rank queries in $$\{\text{timestamp},\text{Radiotap metadata},\text{802.11 header},\text{Information Elements}\}$$3 time for word size $$\{\text{timestamp},\text{Radiotap metadata},\text{802.11 header},\text{Information Elements}\}$$4. In the standard word-RAM regime, the bound becomes

$$\{\text{timestamp},\text{Radiotap metadata},\text{802.11 header},\text{Information Elements}\}$$5

bits for some constant $$\{\text{timestamp},\text{Radiotap metadata},\text{802.11 header},\text{Information Elements}\}$$6, again with query time $$\{\text{timestamp},\text{Radiotap metadata},\text{802.11 header},\text{Information Elements}\}$$7. The cell-probe result matches the Pătrașcu–Viola lower bound up to constant factors in the exponent (Yu, 2018). The construction is conceptually notable because it reduces succinct data-structure design to approximate nonnegative tensor decomposition.

A second canonical problem is systematic succinct Boolean matrix-vector multiplication. Here the input matrix is stored in read-only memory, and only side information is charged. The upper bound stores

$$\{\text{timestamp},\text{Radiotap metadata},\text{802.11 header},\text{Information Elements}\}$$8

additional bits and answers each query in

$$\{\text{timestamp},\text{Radiotap metadata},\text{802.11 header},\text{Information Elements}\}$$9

cell probes with success probability at least $w$0. The matching lower bound states that any structure with side space $w$1 and query time $w$2 must satisfy

$w$3

and

$w$4

thereby essentially settling the cell-probe complexity up to polylogarithmic factors (Chakraborty et al., 2017).

For dynamic data structures, the strongest example in the material is two-dimensional weighted orthogonal range counting. Using the $w$5 randomized nondeterministic four-party communication model, the lower-bound result shows that any dynamic data structure in the regime of $w$6 updates and $w$7 queries must use

$w$8

probes in total, even if it succeeds with probability as small as $w$9. The lower bound is asymptotically tight, producing what is described as a “sharp threshold” phenomenon for dynamic data structures (Weinstein et al., 2016).

6. Structural limits, confounding, and interpretation

Probe-conditioned representations are powerful precisely because they preserve acquisition or access structure, but that same structure can limit inference. In 4D-STEM inversion, the principal resolution limits are finite probe-forming aperture, spatial incoherence, and residual aberrations. The aperture truncates the measurable reciprocal-space extent of the $t$0-matrix; increasing from $t$1 mrad to $t$2 mrad improves reconstruction fidelity. Experimental agreement required modeling incoherence by a Gaussian blur with $t$3 Å, followed by Lucy–Richardson deconvolution, although deconvolution cannot recover frequencies suppressed below the noise floor (Brown et al., 2018). The data structure is therefore informative enough to invert multiple scattering, but only within the transfer limits imposed by the probe and the instrument.

Wireless probe-request records exhibit a different kind of structural limitation. Since timestamps and Radiotap metadata are receiver-side additions rather than official 802.11 frame fields, the record format already entangles transmitted content with capture context. The UJI dataset explicitly addresses this by preserving radio metadata and by anonymizing only the last three bytes of sensitive MAC-related information, thereby protecting privacy while keeping analytical features such as vendor-related structure and randomized-MAC detection (Bravenec et al., 2023). This suggests that provenance fields are not incidental embellishments but part of the operational data structure.

A related methodological caution appears in probe-based analysis of LLMs. Under a controlled $t$4 design separating context from prompt format, linear logistic-regression probes trained on frozen residual-stream activations of Llama-3.1-8B-Instruct do not generalize as abstract detectors of “evaluation awareness.” In the standard confounded training regime, Layer 24 results classify Bench-Eval as $t$5 Evaluation, Casual-Eval as $t$6, Casual-Deploy as $t$7, and Bench-Deploy as $t$8 Evaluation; with decorrelated paired training, Bench-Deploy falls to $t$9 and Casual-Eval rises to $$I_{\mathrm{STEM}}(\mathbf r,\mathbf g,\Delta f)=\left| \sum_{\mathbf h} \mathcal S_{\mathbf g,\mathbf h} \exp\!\left[2\pi i\left(h^2\Delta f\lambda-\mathbf h\cdot\mathbf r\right)\right] \right|^2,$$0 (Devbunova, 19 Mar 2026). The central conclusion is that standard probe-based methodologies do not reliably disentangle evaluation context from structural artifacts when benchmark format and context are correlated.

Taken together, these cases show that probe data structure is inseparable from the constraints of acquisition, representation, and access. Whether the probe is an electron beam, an atom probe, a Wi-Fi sniffer, a software collector, or a cell-probe abstraction, the structure imposed by the probe determines both what can be recovered and what can be mistaken for signal.