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Energy, industry and public infrastructure
water-scada
water utility control
SCADA
System
Techniques · 19
Primitives · 49
water-scada
Alarm management
embedded · medium: Turn raw process limits into a few actionable operator alarms with delay, deadband, acknowledge and shelving states, plus flood measurement.
›
Hot-standby redundancy
embedded · medium: A second, always-current controller shadows the primary and takes over within a few cycles of silence; epochs stop the old primary from fighting back.
›
Industrial network segmentation
embedded · medium: Zones and conduits (IEC 62443/Purdue) with firewalls and protocol allow-lists for OT
Pipe network hydraulics
embedded · medium: Solve pipe-network flows and heads (Hazen-Williams, gradient method) for water systems
Plc scan cycle
embedded · medium: Cyclic read-inputs, execute-logic, write-outputs execution with IEC 61131-3 programs
Sparse direct solver
numerics · medium: Solve sparse Ax = b exactly by reordering, symbolic analysis, numeric LLᵀ/LU and triangular solves; fill-in, not flops per entry, decides the cost.
›
Mixed-integer programming (branch a…
optimization · medium: Solves LPs with integer variables by solving the LP relaxation, branching on a fractional variable, and pruning subtrees whose LP bound cannot beat the incumbent.
›
Newton root finding
numerics · low: Linearize at the guess and jump to the tangent root; quadratic convergence near a simple root, made robust by brackets (1D) or line search.
›
Swinging door compression
compression · low: Deadband and swinging-door trending compression for process historians
Dnp3 protocol
embedded · low: DNP3 outstation/master protocol: event buffers, unsolicited reporting, time-stamped data
Modbus protocol
embedded · low: Modbus RTU/TCP registers and function codes with polling and CRC
PID controller
robotics · low: Drive a measured value to a setpoint with three terms on the error: proportional, integral, derivative. The default feedback loop for motors, heaters, drones and gimbals.
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Debouncing throttling
systems · low: Coalescing rapid events: debounce (wait for quiet), throttle (max rate), and cancelling stale in-flight requests
Hierarchical state machine
systems · low: Nest states so a substate inherits its parent's reactions and only overrides what differs, with ordered entry and exit actions along the path.
›
Watchdog timer
embedded · low: A hardware down-counter that resets the chip unless software proves, in time and in a plausible pattern, that it is still healthy.
›
Data diode unidirectional transfer
embedded · low: One-way network transfer with FEC and no back channel between safety and IT zones
Deep packet inspection
networking · low: Classify flows by payload/SNI/protocol signatures for application-aware policy
Sparse matrices (CSR)
numerics · low: Compressed sparse row stores only nonzeros as row pointers, column indices and values; SpMV streams them once, so it is memory-bandwidth bound.
›
Fixed-rate control loop
embedded · low: Run a controller at an exact period using absolute deadlines and a fixed dt, so jitter never accumulates and the math stays valid.
›
Real time fieldbus
embedded · low: Deterministic cyclic fieldbuses (EtherCAT, PROFINET IRT): on-the-fly frames, distributed clocks
LU and Cholesky factorization
numerics · low: Factor A = PLU (any square matrix, partial pivoting) or A = LLᵀ (SPD) once in O(n³), then solve each right-hand side in O(n²).
›
d-ary heap
data-structures · low: Array heap with d children per node (d = 4 typical): half the binary heap's depth, siblings in one cache line, faster priority queues.
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Simplex method
optimization · low: Solves linear programs by walking along the edges of the feasible polytope from vertex to vertex, one basis swap (pivot) at a time; the workhorse behind MIP solvers.
›
+ 12 more techniques
+ 33 more primitives
System
Techniques · 19
Primitives · 49
water-scada
Alarm management
embedded · medium: Turn raw process limits into a few actionable operator alarms with delay, deadband, acknowledge and shelving states, plus flood measurement.
›
Hot-standby redundancy
embedded · medium: A second, always-current controller shadows the primary and takes over within a few cycles of silence; epochs stop the old primary from fighting back.
›
Industrial network segmentation
embedded · medium: Zones and conduits (IEC 62443/Purdue) with firewalls and protocol allow-lists for OT
Pipe network hydraulics
embedded · medium: Solve pipe-network flows and heads (Hazen-Williams, gradient method) for water systems
Plc scan cycle
embedded · medium: Cyclic read-inputs, execute-logic, write-outputs execution with IEC 61131-3 programs
Sparse direct solver
numerics · medium: Solve sparse Ax = b exactly by reordering, symbolic analysis, numeric LLᵀ/LU and triangular solves; fill-in, not flops per entry, decides the cost.
›
Mixed-integer programming (branch a…
optimization · medium: Solves LPs with integer variables by solving the LP relaxation, branching on a fractional variable, and pruning subtrees whose LP bound cannot beat the incumbent.
›
Model predictive control
robotics · medium: Each tick, solve a small optimization over a predicted horizon, apply only the first input, repeat. Handles constraints and multiple inputs that a PID loop cannot.
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Time-series anomaly detection
statistics · medium: Predict the expected value from a seasonal baseline, scale the residual by a robust spread (MAD), threshold at a chosen false-alarm rate, then merge flags into incidents.
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Time-series forecasting (baselines,…
statistics · medium: The end-to-end recipe: fix horizon and uncertainty, beat naive baselines, choose a model family, and validate with rolling-origin backtests and scale-free metrics.
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Primary-backup replication
distributed · medium: One node orders all writes and ships them to standbys; the acknowledgement rule (none, one, all) sets what a crash loses, and an external arbiter decides who takes over.
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Packet classification
networking · medium: Multi-field rule matching (tuple space search, decision trees) and flow caches
Fill-reducing ordering
numerics · medium: Permute a sparse symmetric matrix before Cholesky/LU so the factor has few new nonzeros; minimum degree, nested dissection and RCM trade quality, speed and parallelism.
›
Cutting planes
optimization · medium: Valid inequalities added to an LP relaxation to cut off its fractional optimum without removing any integer point; the engine of branch-and-cut MIP solvers.
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Presolve reductions
optimization · medium: Cheap, provably safe reductions run before the solver (fix variables, drop rows, tighten bounds and coefficients) so LP and MIP solves start from a smaller, tighter model.
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Quadratic programming
optimization · medium: Convex QP solvers (active-set, interior-point, ADMM) for constrained optimization
Arima
statistics · medium: ARIMA/SARIMA forecasting: differencing, AR and MA terms, order selection, maximum-likelihood fit
Graph partitioning
graphs · medium: Split a graph into k balanced parts with few edges between them; multilevel coarsen-partition-refine (METIS, KaHIP) for quality, streaming heuristics (LDG, Fennel) for one-pass scale.
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Interior-point method (primal-dual,…
optimization · medium: Follows the central path with Newton steps on the perturbed KKT system, one sparse Cholesky per iteration; Mehrotra's predictor-corrector makes it fast.
›
Newton root finding
numerics · low: Linearize at the guess and jump to the tangent root; quadratic convergence near a simple root, made robust by brackets (1D) or line search.
›
Swinging door compression
compression · low: Deadband and swinging-door trending compression for process historians
Dnp3 protocol
embedded · low: DNP3 outstation/master protocol: event buffers, unsolicited reporting, time-stamped data
Modbus protocol
embedded · low: Modbus RTU/TCP registers and function codes with polling and CRC
PID controller
robotics · low: Drive a measured value to a setpoint with three terms on the error: proportional, integral, derivative. The default feedback loop for motors, heaters, drones and gimbals.
›
Debouncing throttling
systems · low: Coalescing rapid events: debounce (wait for quiet), throttle (max rate), and cancelling stale in-flight requests
Hierarchical state machine
systems · low: Nest states so a substate inherits its parent's reactions and only overrides what differs, with ordered entry and exit actions along the path.
›
Watchdog timer
embedded · low: A hardware down-counter that resets the chip unless software proves, in time and in a plausible pattern, that it is still healthy.
›
Data diode unidirectional transfer
embedded · low: One-way network transfer with FEC and no back channel between safety and IT zones
Deep packet inspection
networking · low: Classify flows by payload/SNI/protocol signatures for application-aware policy
Sparse matrices (CSR)
numerics · low: Compressed sparse row stores only nonzeros as row pointers, column indices and values; SpMV streams them once, so it is memory-bandwidth bound.
›
Fixed-rate control loop
embedded · low: Run a controller at an exact period using absolute deadlines and a fixed dt, so jitter never accumulates and the math stays valid.
›
Real time fieldbus
embedded · low: Deterministic cyclic fieldbuses (EtherCAT, PROFINET IRT): on-the-fly frames, distributed clocks
LU and Cholesky factorization
numerics · low: Factor A = PLU (any square matrix, partial pivoting) or A = LLᵀ (SPD) once in O(n³), then solve each right-hand side in O(n²).
›
d-ary heap
data-structures · low: Array heap with d children per node (d = 4 typical): half the binary heap's depth, siblings in one cache line, faster priority queues.
›
Simplex method
optimization · low: Solves linear programs by walking along the edges of the feasible polytope from vertex to vertex, one basis swap (pivot) at a time; the workhorse behind MIP solvers.
›
Runge-Kutta 4
numerics · low: The classic four-stage, fourth-order ODE step; error drops 16× when the step halves, with no derivatives or past steps needed.
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Kalman filter
robotics · low: Optimal recursive estimator for a linear system with Gaussian noise: fuses a motion model with noisy measurements into a state estimate plus its covariance.
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Isolation forest
machine-learning · low: Score each record by how few random axis-aligned splits it takes to isolate it in a small forest of random trees; anomalies are few and different, so they isolate fast.
›
Exponential smoothing (ETS, Holt-Wi…
statistics · low: Forecast by keeping a few running states (level, trend, seasonal) updated by a fraction of each forecast error; O(1) memory per series and a strong baseline.
›
Robust statistics
statistics · low: Location and scale estimates (median, MAD, trimmed mean, Huber M-estimator) that stay correct when a minority of the data is garbage.
›
STL decomposition (seasonal-trend w…
statistics · low: Split a series into trend, seasonal and remainder with iterated loess smoothing; the seasonal shape may drift and robust weights keep outliers out of it.
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Croston method
statistics · low: Forecasting intermittent demand by separately smoothing demand sizes and intervals (Croston, SBA, TSB)
Time-series cross-validation (rolli…
statistics · low: Estimate forecast error by repeatedly training on the past and testing on the next h steps, moving the origin forward; never trains on the future.
›
Leases
distributed · low: A lock that expires on its own: bounded-time ownership that survives crashes and partitions, given bounded clock drift and fencing tokens on writes.
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Write-ahead log
storage · low: Append each change to a checksummed sequential log and fsync it before touching data pages; the basis of crash durability in nearly every database.
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Health checking
systems · low: Decide per backend whether to route to it using probes and real-traffic errors, with consecutive-count hysteresis, capped ejection and a panic fallback.
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Interval tree
data-structures · low: Index of ranges that answers "which intervals overlap this point or range?" in O(log n + k); static sorted-array form is the compact, cache-friendly choice.
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Swiss table
data-structures · low: Open-addressing hash table that filters 8-16 slots at once with 1-byte hash tags and SIMD, giving fast lookups at 87.5 % load.
›
Packet header parsing
networking · low: Parse graph state machines for Ethernet, IP, TCP and UDP headers in hardware and software
Tcam ternary matching
networking · low: TCAM ternary match tables: priorities, range expansion, power and capacity trade-offs
LRU and CLOCK
systems · low: LRU evicts the least recently used entry via hash map plus linked list; CLOCK approximates it with a reference bit, so hits take no lock.
›
Floating-point error
numerics · low: How IEEE 754 rounding error accumulates and how to contain it: compensated (Kahan/Neumaier) and pairwise summation, error-free transformations with FMA, ULP comparisons.
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Fast hash functions
data-structures · low: Non-cryptographic hashes built from 64×64→128-bit multiplies and xor-shifts; pick by key size, trust level and whether the hash is persisted.
›
Interval arithmetic
numerics · low: Rigorous bounds with outward rounding; root isolation and robust geometric tests
Finite differences
numerics · low: Replace derivatives with weighted differences of grid values; simple stencils plus a stability condition (CFL) turn PDEs like heat, advection and waves into array loops.
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L-BFGS
numerics · low: Quasi-Newton minimizer that approximates the inverse Hessian from the last m gradient differences via the two-loop recursion; O(m·n) memory and work per step.
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PRNGs (PCG, xoshiro)
numerics · low: Small, fast, statistically strong non-cryptographic generators: PCG32 and xoshiro256**, with seeding, parallel streams and unbiased ranges.
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Fencing tokens
distributed · low: A number that grows with every lock grant and is checked by the protected resource, so a paused ex-holder's late write is rejected.
›
Dma transfers
embedded · low: DMA controllers: descriptors, circular buffers, cache coherence for zero-CPU data movement
PWM generation
embedded · low: A timer's counter, period and compare registers draw the pulse train; preload, dead time and DMA make duty changes glitch-free, shoot-through-free and cheap.
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CRC32C checksums
hardware-os · low: The Castagnoli CRC-32 with dedicated instructions on x86 (SSE4.2) and ARMv8. It is the standard fast integrity check for storage blocks, logs and network frames.
›
fsync, O_DSYNC and O_DIRECT
hardware-os · low: What fsync, fdatasync, O_DSYNC, O_DIRECT and F_FULLFSYNC really guarantee on Linux and macOS, and the exact call sequences for crash-safe files.
›
SIMD programming
hardware-os · low: Process 4-16 lanes per instruction with AVX2, AVX-512 or NEON via Rust std::arch, with runtime dispatch and a portable fallback.
›
Evaluation metrics
machine-learning · low: Precision, recall, ROC AUC, average precision, log loss, NDCG and pass@k computed correctly, plus paired confidence intervals for comparing models.
›
Loss functions
machine-learning · low: The scalar a model minimizes: cross-entropy for classes and tokens, MSE or Huber for values, each with a stable form and simple gradient.
›
Explicit Euler
numerics · low: Step an ODE forward by its current slope, y += h·f(t, y); first-order, one evaluation per step, the baseline every other integrator is measured against.
›
Thomas tridiagonal solver
numerics · low: O(n) tridiagonal linear solve used in implicit finite-difference and spline schemes
Bootstrap confidence intervals
statistics · low: Resampling-based confidence intervals for arbitrary statistics
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