Search Results (41)

Background: Sepsis-associated liver injury (SALI) is a severe complication of sepsis that significantly increases the risk of mortality in intensive care unit (ICU) patients. While lactate is recognized as a prognostic biomarker for sepsis, the predictive potential of dynamic lactate trajectories in patients with SALI has not been investigated. This study aims to elucidate the association between serum lactate trajectories and clinical outcomes. Methods: Latent class trajectories of serum lactate dynamics were modeled in 524 patients with SALI from the MIMIC-IV dataset. Serum lactate levels were measured once daily for four consecutive days after ICU admission. Seven distinct trajectory phenotypes were identified, and their prognostic value was assessed using multivariate Cox regression. Results: The seven lactate trajectory phenotypes identified in SALI patients included the Class 1 low-stable, Class 2 moderate-slow decline, Class 3 low-slow decline, Class 4 moderate-slow decline and mild increase, Class 5 moderate-slow decline and rapid increase, Class 6 high-rapid decline, and Class 7 moderate-persistence groups. Fully adjusted multivariate Cox regression indicated significantly elevated mortality risk in Class 5 (HR 2.81, 95% CI 1.67–4.74) and Class 7 (HR 3.44, 95% CI 2.02–5.85) (all p < 0.001), whereas Classes 1–4 and 6 showed no significant differences. The XGBoost classifier achieved a test set AUROC of 0.7098 (training AUROC = 0.9029), indicating limited generalizability due to overfitting. SHAP analysis was used for exploratory purposes to identify potential predictors, with pH, platelets, and alkaline phosphatase emerging as dominant features. Conclusions: Substantial heterogeneity in lactate trajectories was found among patients with SALI, establishing these dynamic patterns as robust predictors of clinical outcomes. Full article

Early identification of sepsis from electronic health records (EHRs) remains challenging because longitudinal laboratory measurements are irregularly sampled, incomplete, and dependent on the observation period. This study presents an interpretable temporal feature-engineering framework integrating Moving Average Convergence Divergence (MACD)-based momentum descriptors with a Signal Correlation Decay Measure (SCDM) representing short-term temporal persistence in longitudinal laboratory trajectories. Using the MIMIC-IV Clinical Database Demo (v2.2), 275 hospital admissions from 100 unique patients were screened. Temporal descriptors were derived from lactate, creatinine, white blood cell count, platelet count, and international normalized ratio. Sepsis status was defined at the hospital-admission level using prespecified ICD-9-CM and ICD-10-CM diagnosis codes, independently of laboratory predictors. Because reliable diagnosis timestamps were unavailable, the task was formulated as admission-level sepsis risk classification rather than prediction of time-stamped sepsis onset. Features were constructed over cumulative 0–12 h, 0–18 h, and 0–24 h observation horizons. Lactate was used exclusively as a predictor. HistGradientBoosting and Logistic Regression were evaluated using repeated patient-grouped cross-validation. Predictive performance varied across observation horizons. Logistic Regression achieved the highest mean AUROC at 24 h (0.711 ± 0.125), while HistGradientBoosting achieved 0.682 ± 0.139. Feature-set ablation indicated that MACD-derived descriptors provided the most consistent incremental contribution relative to conventional features, although their benefit varied by classifier and observation horizon. Permutation importance further demonstrated horizon-dependent feature relevance, with lactate-, INR-, platelet-, and WBC-derived descriptors among the highest-ranked predictors. These findings demonstrate the feasibility of using interpretable momentum, trend, variability, and persistence descriptors to characterize longitudinal laboratory dynamics. The proposed MACD–SCDM framework provides a transparent methodological basis for examining how predictive temporal information evolves as clinical data accumulate. Larger, time-resolved, externally validated multicenter cohorts are required to establish generalizability and clinical utility. Full article

We study a class of evolutionary variational inequalities in a Hilbert space that models the long-run balanced-growth equilibrium of a competitive economy with transaction costs, time-dependent production and infrastructure constraints, and exogenous price dynamics. The paper makes four contributions. First, we introduce a parametrized monotonicity functional ${\mu }_{\alpha }(t;F;u,v;p)$ and prove an exact equivalence theorem: the inequality ${\mu }_{\alpha }\ge \beta {∥u-v∥}^2$ holds if and only if the operator F is strongly monotone with the explicitly computed constant $m=\beta -\alpha (1+{∥p∥}_{\infty })$. This turns the growth parameter $\alpha$ and the price level into explicit terms of a single admissibility threshold and, for $\beta <\alpha (1+{∥p∥}_{\infty })$, produces a scale of conditions that covers operators which are not monotone, i.e., economies with a bounded degree of increasing returns. Second, we prove well-posedness: for every admissible initial state there is exactly one Lipschitz equilibrium trajectory $u^{*}(·)$, obtained through Moreau’s catching-up algorithm for the associated perturbed sweeping process, together with the explicit velocity bound $∥{\dot{u}}^{*}∥\le L_K+2C_F$. Third, we derive one comparison estimate from which global exponential stability, the convergence rate $∥u\left(t\right)-u^{*}\left(t\right)∥\le r e^{-mt}+L_p{m}^{-1}\sup ∥\Delta p∥+\epsilon m^{-1}$, and robustness with respect to perturbations of prices and of the operator all follow; we also show that, when the constraint sets stabilize, the trajectory converges to the stationary equilibrium of the limit problem. Fourth, we prove that strong monotonicity implies the c-covering property with $c=m$, so that the shock-absorbing capacity of the economy is governed by the same constant as the speed of convergence. Two examples—a two-resource system and an n-market network with nonlinear transaction costs—are worked out with a complete verification of every hypothesis and with explicit numerical constants. Full article

UAVs increasingly rely on accurate SLAM for aerial mapping and inspection in GPS-denied environments. 3D Gaussian Splatting (3DGS) has opened a new direction for UAV mapping by allowing SLAM systems to build dense, photorealistic, and renderable maps. Yet in 3DGS SLAM the map is optimized from the pose graph, so a false loop closure can deform both the UAV trajectory and the Gaussian map consumed by downstream UAV autonomy. Reliable loop admission is therefore relevant to safe GPS-denied operation because it protects the state and map estimates on which autonomous functions depend. The present work evaluated this upstream estimation-integrity problem; it did not measure closed-loop guidance, control, or navigation-safety outcomes. We address the loop-admission problem that arises after a place-recognition (PR) module proposes a candidate loop and relative-pose seed. GSSeq is a rendered-reference sequential verifier that uses the current Gaussian map as active evidence before inserting a loop factor. It renders RGB-D references with the PR seed, checks LiDAR/rendered-depth consistency and image/rendered-reference consistency over active support, and propagates the seed through a short query trajectory window. A loop is admitted only when this evidence remains geometrically supported and photometrically stable. On fixed LiDAR-PR candidate sets spanning MARS-LVIG, MUN-FRL, and independent NTU-VIRAL aerial sequences together with ground-mobility benchmarks, GSSeq provides a competitive precision-oriented operating point while suppressing false loop admissions. Thresholds calibrated only on NTU-VIRAL spms_01 combine rendered RGB agreement with LiDAR-submap geometry and are then frozen for spms_02. On this held-out sequence, GSSeq rejects all seven false-positive BTC factors while retaining one of three true-positive factors. The trajectory-to-map experiment reduced ATE RMSE from $2.609\mathrm{m}$ to $1.417\mathrm{m}$ and improved selected-view PSNR from $13.80\mathrm{dB}$ to $16.46\mathrm{dB}$. These results show that rendered verification can preserve an aligned, renderable UAV trajectory-map pair before unsupported loop factors reshape the SLAM map. Full article

Many natural and engineered systems evolve under constraints that restrict the set of admissible states. Classical frameworks study invariant sets, viability regions, survival probabilities, and exit-time events, while the explicit treatment of threshold-defined admissible subsets induced by sampled finite-horizon persistence is not usually isolated as a primary state-space object. This paper formulates a finite-horizon framework for Persistence Under Declared Constraints (PSUC). For a fixed constraint set, sampling step, persistence horizon, and tolerance level, the associated survival domain is the set of initial conditions whose sampled trajectories remain inside the declared constraint set with probability of at least $1-\alpha$. Under explicit regularity assumptions, survival domains are closed superlevel sets of the persistence field and form a nested filtration as the persistence horizon increases. This filtration admits a canonical intrinsic representation through a maximal admissible sampled-horizon field whose sampled superlevel sets recover it exactly. The same field also induces a canonical admissibility preorder; after quotienting by horizon-indistinguishability, this yields a partial order and its associated Alexandrov topology, in which the sampled survival filtration is represented as an upper-set filtration. The Alexandrov construction itself is classical; the contribution lies in the canonical order induced by the sampled admissibility-depth field and in the resulting canonical order-theoretic representation of the filtration. A secondary scalar ordering is also obtained for any lower-bounded auxiliary scalar function. Under an additional continuity assumption, the framework further yields boundary localization at the threshold level and an inheritance relation for connected components along the filtration. Finally, the paper shows that sampled survival domains need not coincide with continuous-time survival sets, thereby clarifying the intrinsically protocol-dependent nature of the object studied. The contribution is therefore a restricted but explicit analysis of threshold-defined admissible-state filtrations induced by sampled finite-horizon persistence, together with a canonical order-theoretic representation of the same filtration, formulated in a way that remains compatible with existing work on viability, stochastic survival, and exit-time analysis. Full article

Objective: To compare disability-inclusion strategies and programmes in higher education institutions in Mexico and Colombia and identify organisational conditions associated with gaps between policy intentions and implementation. Methods: A qualitative comparative multi-case design used a documentary corpus of 15 materials and eight semi-structured interviews with adult professional key informants, one per case university. A criterion-based purposive sample of eight universities (four per country) balanced public and private institutions and prioritised cases with disability-support units or inclusive education programmes. Data were analysed through grounded theory-informed axial and selective coding, with triangulation across documents and interviews; informed consent was obtained. Results: Five categories structured the findings: inclusive cultures, inclusive policies, inclusive practices, educational trajectories and progress/challenges. Within this case set, Mexican universities showed stronger institutionalisation through protocols, structured support routes and more visible technological accessibility. Colombian universities showed more fragmented implementation, often dependent on local initiatives, with persistent attitudinal barriers and weaker systematisation. In both contexts, misalignment between normative discourse and implementation capacity constrained staff training and impact evaluation. Conclusions: Sustainable inclusion was most evident where institutional culture, policy and practice were aligned. Monitoring mechanisms, stable resourcing and longitudinal support pathways are needed to secure equitable student trajectories from admission to graduation. Full article

(1) Background: The digital traces of unmanned aerial vehicles (UAVs) are becoming increasingly important in criminal incidents, the violation of airspace and in military operations, thus making the reconstruction of the digital traces a critical task. But, current tools like DatCon, Autopsy and GRYPHON cannot recover telemetry when the flight logs are logically damaged, fragmented or partially deleted and don’t offer any quantitative measurement of the confidence of the recovered information. (2) Methods: A unified hardware-software complex, including a forensic workstation, a hardware write-blocker and SD/microSD/eMMC adapters; a set of software modules for extracting artifacts from files, structural parsing of DAT/BIN/CSV log, neural network reconstruction of missing telemetry using a two-layer LSTM architecture; a multi-source correlation module that combines flight logs, telemetry, media metadata and controller artifacts; a module, Confidence Score (CS), that computes a reliability measure in $[0,1]$; and a visualization module to generate a reconstructed trajectory on an electronic map. (3) Results: The complex has been tested on 105 flights on 10 different UAVs, 492 flight logs were gathered, 10,435 were the media item files and 624 GB was the amount of storage during acquisition. The carving stage recovers 98.7% of artifacts across the eight signature classes, the LSTM module recovers all five telemetry parameters with $R^2>0.99$ and a single-step horizontal position error of 6.8 m, which is reduced to 4.7 m after multi-source correlation (below the 5 m operational target consistent with consumer-GNSS precision); the dependence on gap length is described by the empirical growth law ${\epsilon }_{\mathrm{horiz}}\approx 4.84·G^{1.44}$ m; 46.8% of recovered records fall within the high-confidence band of $\mathrm{CS}\ge 0.8$; and the complex outperforms DatCon, Autopsy + DJI Analyzer and GRYPHON by 22–35 percentage points in end-to-end record recovery and by a factor of ∼2.6 in mean horizontal error (4.7 m vs. 12.4–18.7 m). (4) Conclusions: The combined write-blocked hardware acquisition, neural reconstruction of telemetry, and quantitative confidence index provides a forensically structured pipeline that fills an existing gap in UAV digital forensics; we note that technical reconstruction accuracy does not by itself confer legal admissibility, which remains a function of jurisdiction-specific evidentiary standards discussed in the Conclusions. Full article

Previous research has shown sector-conditional asymmetry in implied volatility levels and in option returns. However, no prior work has parameterised that asymmetry at the effective-theta layer in a form that fires a non-discretionary rule trigger. This study supplies the parameterisation, its formulation, the first observation, and the data evidence. An effective theta is defined as ${\Theta }_e=\alpha \left(s,r\right)\cdot {\Theta }_{BS}$, where ${\Theta }_{BS}$ is the standard Black–Scholes (BS) theta and $\alpha \left(s,r\right)$ is a sector- and regime-conditional scaling factor. A SIMDEC decomposition is used to filter the input space and to determine the corner where $\alpha$ matters most. The framework is a bounded retrieval-and-deterministic compute system. The instruments are retrieved from cached market data and the learned layer’s outputs are constrained to that admissible set. Therefore, by construction, it cannot confabulate a fictitious or out-of-bounds instrument and the generative-class hallucination failure mode cannot occur. This concerns the groundedness and bounds of every output and is distinct from the accuracy of the regime and quality labels. SIMDEC supplies the joint-state filtering partition and, together with the Sobol variance decomposition, an explainability and attribution layer in which every position-level evaluation maps to an interpretable joint-state bin and a variance-share attribution. A “first observation” arising from a three-position long-call cohort traversing terminal decay is deployed using eight intraday states tracked on the trajectory at primary-source resolution and illustrates the relationship of the $\alpha$ parameterisation to existing market conditions. To examine the effectiveness of the approach, a SIMDEC dataset from the same deployment supplies population-level support across 12 sectors and a three-tier quality stratification. The dataset is the output of the THETA AI/ML pipeline—a multi-architecture deep-learning inference system that treats SIMDEC joint-state partitioning and Sobol variance decomposition as complementary interpretability inputs, with the regime classifier carrying the labels and the composite quality scorer carrying the stratification. The PC-based, token-free analytical procedure for regulated decision-making settings, together with an illustrative example of the asymmetry in the effective-theta provide a “next level” contribution to traditional option methodology. Full article

Volcanic gas and isotope time series are indirect observables of coupled magmatic and hydrothermal dynamics. We formulate a reduced integer–fractional model in which ordinary differential equations describe deep recharge, pressure, gas-phase volatile inventory, and source mixing, whereas Caputo equations describe shallow hydrothermal pressure, thermal excess, gas pathway effectiveness, permeability, and scrubbing. Under explicit local regularity and admissibility assumptions, the mixed-order Volterra problem is locally well-posed and the physically admissible state set is positively invariant. We derive componentwise dissipative estimates and state conditions for global continuation under bounded trajectories and analyze finite-interval consistency with the integer-order limit and local stability of a frozen commensurate hydrothermal linearization. Conservative observation equations link hidden states to gas ratios, fluxes, and isotope ratios. The inverse problem is treated diagnostically; global identifiability is not claimed. Local sensitivity screening, Fisher information concepts, and scalar recovery tests are used only as preliminary local diagnostics of information content under known or misspecified forcing. Synthetic demonstrations and a reference forward solver illustrate how hydrothermal memory and sulfur scrubbing can reshape carbon dioxide/sulfur dioxide (CO₂/SO₂) anomalies before site-specific calibration. Full article

In recent years, artificial intelligence (AI) has been increasingly used in criminal justice systems across the world. To achieve objectives set out through Sustainable Development Goals (SDGs), adoption of technology is inevitable and undeniable. The press release dated 25 February 2025 from India’s Ministry of Law and Justice, quoting Prime Minister of India Narendra Modi to make a “justice system that will be fully future-ready”, confirmed that the Indian law enforcement agencies are integrating AI into policing and law enforcement to enhance crime detection, criminal investigation, etc. It is intended to enhance their capabilities in solving criminal cases and delivering justice speedily and more efficiently. However, the usage of AI tools in such contexts presents a double-edged sword, as evidenced by their application in a number of cases across the world like Christopher Gatlin, Nijeer Parks, the Harm Assessment Risk Tool (HART), and in India during the 2020 Delhi riots cases. As reported by the Washington Post, in Christopher Gatlin’s case it was found that the police arrested him on the basis of the facial recognition programme matching his face with the captured video footage. He spent 17 months in jail before his release by the court, observing that the police failed to conduct fair investigation. A similar incident was reported by NJ.com and CNN Business. In the investigations following the 2020 Delhi riots, Delhi Police effected over 1900 arrests in 758 riot-related cases, relying predominantly on AI-driven facial recognition matches. Subsequent court scrutiny in decided cases raised questions about reliability, leading to widespread acquittals and discharges of the accused in 82% of decided cases as of early 2025. In certain cases, AI-driven solutions have failed, leading to criminal prosecutions of innocent people based on AI-generated evidence. This study examines the reliability, validity, and ethics of AI technology in the criminal justice system in India’s unique socio-legal and political environment. The researchers analyse three interrelated axes. First, a comprehensive review of the international algorithmic policing literature to identify successes and failures. In addition, cases of AI-assisted investigations during the Delhi riots show how facial recognition systems and other AI techniques were used for inquiry. Finally, stakeholders’ perspectives, including a preliminary survey of 27 legal experts showing strong consensus on classifying AI-FRT outputs strictly as corroborative evidence and highlighting BSA insufficiencies for addressing opacity and explainability, help identify practical, procedural, and normative fault lines. Researchers noted that while AI has the potential to revolutionise resource-constrained investigative agencies, its unquestioning and uncritical adoption risks amplify pre-existing biases, undermine presumptions of innocence, and shift the burden of refuting algorithmic inference onto the accused. Independent algorithmic audits, transparent documentation of error rates and confidence thresholds, statutory guidelines on AI tool use and admissibility, and sustained capacity-building throughout the justice delivery chain are needed to integrate it into the Indian criminal justice system. Without such measures, the very tools designed and introduced to enhance accuracy threaten to undermine the fundamental norms of the criminal justice system such as fairness and due process. This fills a gap in doctrinal analysis of AI-specific evidentiary admissibility in non-Western contexts like India. This study aims to propose policy reforms, enhance judicial discourse, and promote a more circumspect trajectory for AI adoption in Indian law enforcement by mapping the potential and risks of algorithmic evidence in a non-Western legal order. Full article

This paper proposes a methodology for designing full-order and reduced-order interval observers for Linear Time-Invariant (LTI) systems, in both continuous and discrete-time settings, in the presence of uncertainties, disturbances, and measurement noise. The class of systems considered requires that the number of independent measured outputs be greater than or equal to the number of unmeasured states. The proposed approach enables the constructive assignment of the state matrix of the estimation error dynamics over the admissible Metzler–Hurwitz class compatible with the observer structure through an appropriate selection of the observer gains, ensuring both stability and cooperativity conditions without requiring the solution of Linear Matrix Inequalities. This flexibility facilitates the design of full and reduced-order interval observers for both continuous and discrete-time cases, generating upper and lower estimates that enclose the true state trajectory. Numerical examples are presented to illustrate the effectiveness of the proposed interval observer design methodology. Full article

Artificial intelligence systems deployed in safety-critical and regulated environments require not only predictive performance, but also strict adherence to operational constraints, auditability, and reproducibility. However, in most contemporary architectures, governance is treated as an external or post hoc mechanism, limiting the ability to ensure consistent and verifiable decision execution. This paper introduces Controlled Agentic AI Systems (CAIS), a formal architectural framework in which governance is embedded directly into the decision pipeline as a deterministic operator. The proposed formulation integrates a decision model, a constraint specification, and a governance operator that transforms proposed actions into admissible executed actions. The framework further defines audit trace semantics and replayability conditions, enabling deterministic reconstruction of decision trajectories. Theoretical analysis demonstrates that, under standard regularity assumptions, governance can be modeled as a non-expansive projection that enforces constraint-aware decision transformation while inducing bounded decision drift. This provides formal guarantees that governance does not destabilize system dynamics under perturbations. To evaluate these properties, we implement a reference CAIS architecture and conduct controlled experiments in multi-agent and federated simulation environments. The results show that embedding governance significantly reduces the frequency and severity of constraint violations across a range of scenarios. Projection-based repair consistently outperforms approval-only strategies, achieving near-complete compliance in structured regimes while maintaining bounded intervention costs. Importantly, governance does not degrade stability or convergence in federated settings and, in some cases, reduces action-level variance induced by distributed training. While strict feasibility cannot be guaranteed in all practical settings due to approximation and solver limitations, the empirical findings confirm that governance acts as a stabilizing transformation that consistently improves compliance without introducing destabilizing effects. The CAIS framework establishes governance as a first-class architectural component of agentic AI systems, providing a unified foundation for designing constraint-aware, auditable, and reproducible decision pipelines in regulated environments. Full article

Background: The optimal method of starting maintenance haemodialysis (HD) in patients with kidney failure is not known. We have compared early treatment characteristics, blood pressure trajectories, and selected dialysis-related safety events in patients who started HD using a stepped and phased approach, with those who received conventional care. Method: A single-centre cohort feasibility study was conducted. Participants with kidney failure, about to start maintenance HD, were enrolled prospectively (intervention arm). They started treatment on a novel regime comprising four pre-specified incremental steps (Phases 1 to 4) over 14 weeks. They were matched using propensity scores with historical controls: patients who had previously started HD on a three-times weekly basis from the outset (control arm). Results: The final cohort comprised 15 and 29 participants in the intervention and control arms respectively (1:2 ratio; one control excluded after matching). Intervention group participants were slightly older with a higher proportion of men. The rate of decline in blood pressure was slower in the intervention group. There were also signals for fewer events of intra-dialytic hypotension (211 vs. 379 per 100 person-year), infections not requiring admission (56 vs. 114 per 100 person-year) and loss of vascular access (56 vs. 79 per 100 person-year) in intervention group. There was a signal for higher incidence of severe hypertension (systolic BP ≥ 180 or diastolic BP ≥ 110 mmHg) in the intervention group. Hospitalisation rates were similar; there were no deaths and one non-fatal major cardiac event (MACE) in the intervention group, and one death and no MACE in the control group. Conclusions: Implementing a short transitional regime of incremental HD may be possible in clinical settings, potentially helping to reduce the gradient of physiological change and burden of early treatment. The findings of this feasibility study are exploratory, and fully powered randomised controlled trials are needed to establish the efficacy and safety of such a programme. Full article

Lithium-ion batteries in hybrid solar-grid systems experience complex electro-thermal dynamics and stochastic mode switching that threshold-based battery management systems fail to capture. This paper proposes a hybrid deviation detection framework that treats anomaly detection as a trajectory-consistency problem over a power-feasible Markov jump nonlinear system. A disturbance-robust invariant operating region is first established under explicit current bounds. A reachable-set equivalence is then derived, linking residual consistency to disturbance-augmented trajectory membership. Building on this structure, Isolation Forest empirically estimates the support of admissible electro-thermal trajectories, capturing nonlinear and mode-dependent behaviors not fully described by the analytical disturbance model. A unified sequential detection rule integrates structural constraint violations, model-based residual deviations, and empirical support inconsistencies into a coherent real-time monitor. The framework is validated on a hybrid solar-grid platform with a 6 W photovoltaic panel, a 3.7 V 1820 mAh lithium-ion battery, and a Raspberry Pi, collecting 3976 samples over four days. Results demonstrate early detection of depletion events and mode-transition anomalies before hard threshold violations, with zero false alarms during steady operation and an overall deviation rate of 4.8%, aligning with the configured contamination level. Early warning was observed at 20% state of charge, providing a 10% margin before the hardware threshold of 10%, while 88% of detected anomalies occurred in sequences, validating the persistence rule. Real-time inference required 47 ms per cycle with a 156 MB memory footprint, confirming edge deployment feasibility. Full article

Rigid-body chain following on piecewise analytic paths is a fundamental subroutine in motion planning and multibody simulation. The problem is nontrivial when only the leader trajectory of the first node is available: enforcing fixed inter-node distances reduces to circle–curve intersection, which is generally multi-valued and becomes particularly challenging near non-smooth junctions. We present a Dichotomy Geometric Path Search (DGPS) framework that converts each constraint into a one-dimensional root-finding task and resolves the branch selection through no-backtracking ordering: at every time step, the admissible solution for the current node is the nearest feasible root in the past relative to its immediately preceding node. DGPS combines backward bracketing with bisection, achieving robust convergence. Compared with the inverse Jacobian method, which maps end-effector velocities to joint velocities via explicit inversion, the proposed approach avoids Jacobian inversion and globally coupled nonlinear solves. We further characterize the local structure of the zero set and establish monotonicity/uniqueness conditions that justify stable root selection across piecewise junctions. Extensive tests on representative piecewise trajectories (line–arc–line, polylines with corners, piecewise sinusoids, and time reparameterization) show that DGPS enforces distance constraints to near machine precision, produces interpretable speed/acceleration transients around non-smooth events, and exhibits computational costs consistent with iteration difficulty. The results support DGPS as a general, efficient solver requiring only the prescribed leader trajectory. Full article