Time-dependent Operator Research Articles

Abstract P335: Prognostic Cut Point of Fasting Insulin in Apparently Healthy Young Adults for the Development of Future Cardiovascular Disease

Introduction: Early metabolic imbalance (EMI) is insidiously prevalent in the U.S., especially among teens and young adults. It includes markers of insulin resistance, inflammation and oxidative stress, but does not meet the criteria for metabolic syndrome. Individuals with EMI have compensatory hyperinsulinemia, an independent risk factor for CVD. Yet, fasting insulin is an underutilized prognostic marker, partly due to a lack of calibrated cut points for this population. Hypothesis: The prognostic value of insulin for CVD risk is associated with an optimum cut point, which can be calibrated using a time-dependent receiver operator characteristic (timeROC) analysis of CARDIA: Coronary Artery Risk Development in Young Adults. Methods: The parent CARDIA study began in 1985, enrolling 5,114 participants ages 18-30 at baseline, with 35-year follow-up. In our retrospective cohort analysis, the exclusion criteria were hyperglycemia, hypertriglyceridemia, low HDL, pregnancy, diabetes, CVD, or fasting < 8 hours, all at baseline; n=3,292. The primary outcome was time to incident CVD (or censor), defined as fatal/nonfatal MI, coronary revascularization, acute coronary syndrome, CHF, stroke, TIA, carotid or peripheral artery disease. Survival data were analyzed using the ‘timeROC’ package in R v.4.2.1, with/without adjustment for the 2019 ACC/AHA risk factors for CVD. For validation, a conventional ROC (logROC) analysis was performed, with incident CVD as the outcome. For timeROC and logROC, the cut point optimum was determined using minimum distance to the [0, 1] coordinate; predictive accuracy was summarized by area under the curve (AUC). The prognostic value of insulin at its optimum was determined using Cox regression for insulin alone and with risk factors, using Stata v.17.0. Cox results are summarized with hazard ratio (HR) and Harrell’s c-statistic (c). Results: The cut point optimum for baseline fasting insulin was 9.1 mIU/L (60.5 percentile), with AUC 0.583 (95% CI: 53.6, 62.9), sensitivity 54.8% and specificity 61.7%. The results were unchanged with/without covariate adjustment in timeROC, and with logROC. Using the optimum, the unadjusted Cox HR for high vs. low insulin was 1.9 (95% CI 1.4, 2.6, p<0.0001); c=0.580. Cox model 2 included a variable with both high insulin and high waist circumference (WC); HR for both vs. neither condition was 2.6 (95% CI 1.8, 3.8, p<0.0001); c=0.606. Cox model 3 added ACC/AHA risk factors to model 2: HR 2.2 (95% CI 1.5, 3.4, p<0.0001) for high insulin and WC vs. neither; c=0.716. Conclusion: For young adults in CARDIA without metabolic syndrome or prediabetes, the cut point optimum for fasting insulin is near the top tertile. Insulin has a high prognostic value for CVD, especially when combined with WC. Though useful, insulin suffers from modest sensitivity. Better markers of EMI are needed for assessing hidden CVD risk in apparently healthy young adults.

PET/CT standardized uptake value and EGFR expression predicts treatment failure in nasopharyngeal carcinoma

ObjectiveThis study inventively combines epidermal growth factor receptor (EGFR) expression of the primary lesion and standardized uptake value (SUV) of positron emission tomography and computed tomography (PET/CT) to predict the prognosis of nasopharyngeal carcinoma (NPC). This study aimed to evaluate the predictive efficacy of maximum standard uptake value (SUVmax) and EGFR for treatment failure in patients with NPC.MethodsThis retrospective study reviewed the results of EGFR expression and pretreatment 18F-FDG PET/CT of 313 patients with NPC. Time-dependent receiver operator characteristics was used for analyzing results and selecting the optimal cutoff values. Cox regression was used to screen out multiple risk factors. Cumulative survival rate was calculated by Kaplan–Meier.ResultsThe selected cutoff value of SUVmax-T was 8.5. The patients were categorized into four groups according to EGFR expression and SUVmax-T. There were significant differences in the 3-year local recurrence-free survival (LRFS) (p = 0.0083), locoregional relapse-free survival (LRRFS) (p = 0.0077), distant metastasis-free survival (DMFS) (p = 0.013), and progression-free survival (PFS) (p = 0.0018) among the four groups. Patients in the EGFR-positive and SUVmax-T > 8.5 group had the worst survival, while patients in the EGFR-negative and SUVmax-T ≤ 8.5 group had the best prognosis. Subsequently, patients with only positive EGFR expression or high SUVmax-T were classified as the middle-risk group. There were also a significant difference in 3-year overall survival among the three risk groups (p = 0.034). SUVmax-T was associated with regional recurrence-free survival and LRRFS in multivariate analysis, whereas EGFR was an independent prognostic factor for LRRFS, DMFS, and PFS.ConclusionThe combination of SUVmax-T and EGFR expression can refine prognosis and indicate clinical therapy.

Fc fragment of IgG binding protein is correlated with immune infiltration levels in hepatocellular carcinoma.

The Fc fragment of IgG binding protein (FCGBP) has been confirmed to play an important role in various cancers. However, the specific role of FCGBP in hepatocellular carcinoma (HCC) remains undefined. Thus, in this study, the enrichment analyses (Gene Ontology, Kyoto Encyclopedia of Genes and Genomes, and Gene Set Enrichment Analysis) of FCGBP in HCC and extensive bioinformatic analyses using data of clinicopathologic characteristics, genetic expression and alterations, and immune cell infiltration were perfomed. Quantitative real-time polymerase chain reaction (qRT-PCR) was used to verify the expression of FCGBP in both HCC tissues and cell lines. The subsequent results confirmed thatFCGBP overexpression positively correlated with poor prognosis in patients with HCC. Additionally, FCGBP expression could effectively distinguish tumor tissues from normal tissues, which was verified by qRT-PCR. The result was further confirmed by using HCC cell lines. The time-dependent survival receiver operator characteristic curve exhibited the strong ability of FCGBP to predict survival in patients with HCC. Additionally, we revealed the strong relationship between FCGBP expression and a number of classic regulatory targets and classical oncogenic signaling pathways of tumors. Finally, FCGBP was involved in the regulation of immune infiltration in HCC. Therefore, FCGBP has potential value in the diagnosis, treatment, and prognosis of HCC and may be a potential biomarker or therapeutic target.

Quantum State Tomography in Nonequilibrium Environments

We generalize an approach to studying the quantum state tomography (QST) of open systems in terms of the dynamical map in Kraus representation within the framework of dynamic generation of informationally complete positive operator-valued measures. As applications, we use the generalized approach to theoretically study the QST of qubit systems in the presence of nonequilibrium environments which exhibit nonstationary and non-Markovian random telegraph noise statistical properties. We derive the time-dependent measurement operators for the quantum state reconstruction of the single qubit and two-qubit systems in terms of the polarization operator basis. It is shown that the behavior of the time-dependent measurement operators is closely associated with the dynamical map of the qubit systems.

Assessing temporal differences of baseline body mass index, waist circumference, and waist-height ratio in predicting future diabetes.

Obesity is the prominent modifiable risk factor known to influence the occurrence and progression of diabetes other than age, and the objective of this study was to evaluate and compare the predictive value of three simple baseline anthropometric indicators of obesity, body mass index (BMI), waist circumference (WC), and waist-height ratio (WHtR), for the occurrence of diabetes at different time points in the future. The study subjects were 12,823 individuals with normoglycemic at baseline who underwent health screening and had measurements of BMI, WC, and WHtR. The outcome of interest was new-onset diabetes during follow-up. Time-dependent receiver operator characteristics (ROC) curves of baseline BMI, WC, and WHtR for predicting the risk of diabetes in the next 2 to 12 years were constructed and their area under the ROC curves (AUCs) and corresponding optimal threshold values were calculated for each time point, which were used to compare the accuracy and stability of the above three indicators for predicting the occurrence of diabetes in different future periods. During a median follow-up period of 7.02 years, with a maximum follow-up of 13 years, 320 new-onset diabetes were recorded. After adjusting for confounders and comparing standardized hazard ratios (HRs), WC was shown to be the best simple anthropometric indicator of obesity reflecting diabetes risk in all models, followed by WHtR. Time-dependent ROC analysis showed that WC had the highest AUC in predicting the occurrence of diabetes in the short term (2-5 years), and WHtR had the highest AUC in predicting the occurrence of diabetes in the medium to long term (6-12 years), while in any time point, both WC and WHtR had higher AUC than BMI in predicting future diabetes. In addition, we found relatively larger fluctuations in the thresholds of BMI and WC for predicting diabetes over time, while the thresholds of WHtR consistently remained between 0.47-0.50; comparatively speaking, WHtR may have greater application value in predicting future diabetes. Our analysis sustained that central obesity is a more important predictor of diabetes, and in clinical practice, we proposed measuring WHtR as a useful tool for predicting future diabetes.

Nonequilibrium spectral moment sum rules of the Holstein–Hubbard model

We derive a general procedure for evaluating the nth derivative of a time-dependent operator in the Heisenberg representation and employ this approach to calculate the zeroth to third spectral moment sum rules of the retarded electronic Green’s function and self-energy for a system described by the Holstein–Hubbard model allowing for arbitrary spatial and time variation of all parameters (including spatially homogeneous electric fields and parameter quenches). For a translationally invariant (but time-dependent) Hamiltonian, we also provide sum rules in momentum space. The sum rules can be applied to various different phenomena like time-resolved angle-resolved photoemission spectroscopy and benchmarking the accuracy of numerical many-body calculations. This work also corrects some errors found in earlier work on simpler models.

A novel pyroptosis scoring model was associated with the prognosis and immune microenvironment of esophageal squamous cell carcinoma.

The phenotype of pyroptosis has been extensively studied in a variety of tumors, but the relationship between pyroptosis and esophageal squamous cell carcinoma (ESCC) remains unclear. Here, 22 pyroptosis genes were downloaded from the website of Gene Set Enrichment Analysis (GSEA), 79 esophageal squamous cell carcinoma samples and GSE53625 containing 179 pairs of esophageal squamous cell carcinoma samples were collected from the Cancer Genome Atlas (TCGA) and the Gene Expression Omnibus (GEO), respectively. Then, pyroptosis subtypes of esophageal squamous cell carcinoma were obtained by cluster analysis according to the expression difference of pyroptosis genes, and a pyroptosis scoring model was constructed by the pyroptosis-related genes screened from different pyroptosis subtypes. Time-dependent receiver operator characteristic (timeROC) curves and the area under the curve (AUC) values were used to evaluate the prognostic predictive accuracy of the pyroptosis scoring model. Kaplan-Meier method with log-rank test were conducted to analyze the impact of the pyroptosis scoring model on overall survival (OS) of patients with esophageal squamous cell carcinoma. Nomogram models and calibration curves were used to further confirm the effect of the pyroptosis scoring model on prognosis. Meanwhile, CIBERSORTx and ESTIMATE algorithm were applied to calculate the influence of the pyroptosis scoring model on esophageal squamous cell carcinoma immune microenvironment. Our findings revealed that the pyroptosis scoring model established by the pyroptosis-related genes was associated with the prognosis and immune microenvironment of esophageal squamous cell carcinoma, which can be used as a biomarker to predict the prognosis and act as a potential target for the treatment of esophageal squamous cell carcinoma.

Second-order problems involving time-dependent subdifferential operators and application to control

<p style='text-indent:20px;'>The paper provides a new result concerning the existence of solutions for second-order evolution problems associated with time-dependent subdifferential operators involving both single-valued and mixed semi-continuous set-valued perturbations. Optimal control problems corresponding to such differential inclusions using relaxation theorems with Young measures are investigated. The existence of solutions for a coupled system governed by a second-order differential equation with an evolution problem is also addressed.</p>

Functional differential inclusions with maximal monotone operators and nonconvex perturbations

In this paper, we study the existence of solutions for functional differential inclusions governed by time-dependent maximal monotone operators with nonconvex perturbations depending on all the variables.

Development of a novel transcription factor signature for accurate cervical cancer prognosis

Cervical cancer (CC) is a leading cause of cancer-related deaths in women. During tumor development, transcriptional factors regulate the transcription of proto-oncogenes and tumor suppressor genes. We examined the possibility of using transcription factors as prognostic biomarkers for patients with cervical cancer. Single-cell RNA-sequencing data were downloaded from the Gene Expression Omnibus database to identify specific activated transcription factors in different types of cells from CC. Publicly available bulk RNA-sequencing and clinical data of CC were obtained to identify associated prognostic transcription factors using survival analysis and the random survival forest methods. Accuracy and effectiveness of the established transcription factor-related predictive random survival forest model were verified using training and test datasets. We identified specific activated transcription factors in tissue cells of cervical cancer. A 3-transcription factors (PBX4 (PBX Homeobox 4), EBF2 (EBF Transcription Factor 2) and ZNF696 (Zinc Finger Protein 696)) prognostic signature for patients with cervical cancer was constructed showing good survival prediction. Gene function enrichment analysis indicated a correlation between the prognostic characteristics and different signaling pathways associated with cancer. Using the random survival forest model based on the 3-transcription factor signature, patients with cervical cancer were stratified into low- and high-risk groups with significant variations in overall survival (p < 0.001). The area under the curve of the time-dependent receiver operator characteristic revealed a strong predictive accuracy for training and test datasets of the corresponding signature. CC has cellular heterogeneity of transcriptional activation. Our analyses provide a novel transcription factor-associated prognostic model for CC. These transcription factors could be used as effective prognostic biomarkers and potential therapeutic targets for patients with cervical cancer.

A coupled problem described by time-dependent subdifferential operator and non-convex perturbed sweeping process

The aim of the present paper is to state the well-posedness of a new dynamical system driven by a differential inclusion involving time-dependent subdifferential operators with integral perturbation and a non-convex perturbed sweeping process. The current study is motivated by recent works on integro-differential sweeping processes and dynamical systems coupled by differential inclusions (involving sweeping processes and maximal monotone operators). In our development, we proceed using a discretization method, combining tools of first-order evolution problems of subdifferential type and those governed by the normal cone of $ r $-prox regular moving sets. We establish a new existence result to the class of dynamical systems under consideration, in the context of infinite dimensional Hilbert setting. This allows us to deal with a Bolza-type problem in optimal control theory.

Competitive Risk Model Nomogram to Predict Prognosis in Patients Aged Over 65 Years with nonmetastatic Cervical Cancer: A SEER Population-Based Study.

Objective: The prognostic factors for elderly patients with cervical cancer differ from those of younger patients. Competitive risk events could cause biases in the Cox proportional hazards (PH) model. This study aimed to construct a competitive risk model (CRM) nomogram for patients aged > 65 years with nonmetastatic cervical cancer. Methods: We retrospectively analyzed data extracted from the Surveillance, Epidemiology, and End Results (SEER) database and a total of 1856 patients from 18 cancer registries across the United States diagnosed between 2010 and 2015 were included. Kaplan-Meier analysis and log-rank tests were used to compare intergroup survival. Univariate and multivariate Cox proportional regression analyses were performed to identify independent prognostic factors. The cumulative incidence function (CIF) and Fine and Gray's test were used to determine the impact of competitive risk events on prognosis. The CRM nomogram was internally and externally validated using time-dependent receiver operator characteristic (ROC) curve (time-AUC), Brier scores, Harrell's concordance index (C-index), calibration curve, and decision curve analysis (DCA). Results: Analyses revealed that histology, age, the International Federation of Gynaecologists and Obstetricians (FIGO) stage, number of in situ malignancies, chemotherapy, radiotherapy (RT), and surgery were independent prognostic factors. The CRM nomogram accurately predicted 1-year, 3-year, and 5-year disease-specific survival (DSS). The C-indexes and Brier scores of the CRM nomogram were 0.641 and 0.094, respectively, at the 1-year cut-off in the training set. The time-AUC of the CRM nomogram at the 1-year, 3-year, and 5-year intervals in the training set were 77.6%, 77.3%, and 74.5%, respectively. The calibration curve demonstrated a favorable concordance. DCA suggested that the nomogram had a good net benefit. Therefore, the Cox model underestimated the weight of risk factors compared to CRM. Conclusions: This study presents the CRM nomogram to predict DSS in patients aged > 65 years with nonmetastatic cervical cancer. It can help clinicians implement more accurate personalized diagnostic and treatment modalities for elderly patients with cervical cancer.

Identification of a Two-Gene Signature and Establishment of a Prognostic Nomogram Predicting Overall Survival in Diffuse-Type Gastric Cancer.

It is widely acknowledged that the molecular biological characteristics of diffuse-type gastric cancer are different from intestinal-type gastric cancer. Notwithstanding that significant progress in high-throughput sequencing technology has been made, there is a paucity of effective prognostic biomarkers for diffuse gastric cancer for clinical practice. We downloaded four GEO datasets (GSE22377, GSE38749, GSE47007 and GSE62254) to establish and validate a prognostic two-gene signature for diffuse gastric cancer. The TGCA-STAD dataset was used for external validation. The optimal gene signature was established by using Cox regression analysis. Receiver operating characteristic (ROC) methodology was used to find the best prognostic model. Gene set enrichment analysis was used to analyze the possible signaling pathways of the two genes (MEF2C and TRIM15). A total of four differently expressed genes (DEGs) (two upregulated and two downregulated) were identified. After a comprehensive analysis, two DEGs (MEF2C and TRIM15) were utilized to construct a prognostic model. A prognostic prediction model was constructed according to T stage, N stage, M stage and the expression of MEF2C and TRIM15. The area under the time-dependent receiver operator characteristic was used to evaluate the performance of the prognosis model in the GSE62254 dataset. We demonstrated that MEF2C and TRIM15 might be key genes. We also established a prognostic nomogram based on the two-gene signature that yielded a good performance for predicting overall survival in diffuse-type gastric cancer.

Assessing the longitudinal association between the GGT/HDL-C ratio and NAFLD: a cohort study in a non-obese Chinese population

BackgroundA cross-sectional association between the combination indicator of high-density lipoprotein cholesterol (HDL-C) and gamma-glutamyl transferase (GGT) and fatty liver has been described in several recent studies, and this study aims to further evaluate the longitudinal relationship between the ratio of GGT to HDL-C (GGT/HDL-C ratio) and nonalcoholic fatty liver disease (NAFLD).MethodsThis cohort study included 12,126 individuals without NAFLD at baseline, followed prospectively for 5 years, and the endpoint of interest was new-onset NAFLD. The relationship of the GGT/HDL-C ratio with new-onset NAFLD and the shape of the association was assessed by Cox regression models and restricted cubic spline (RCS) regression, respectively. Time-dependent receiver operator characteristics (ROC) curves were constructed to evaluate the predictive value of GGT, HDL-C, GGT/HDL-C ratio and BMI for the occurrence of NAFLD at different time points in the future.ResultsThe prevalence of NAFLD was 72.46/1000 person-years during the 5-year follow-up period. Results of multivariate Cox regression analysis showed a positive association of the GGT/HDL-C ratio with new-onset NAFLD after adequate adjustment of the related confounding factors, and the degree of correlation was slightly higher than that of GGT, and further subgroup analysis found that this association was more significant in the population with elevated systolic blood pressure (SBP). In addition, we also found a nonlinear relationship of the GGT/HDL-C ratio with the risk of new-onset NAFLD using the RCS regression, where the saturation threshold was about 31.79 U/mmol. Time-dependent ROC analysis results showed that the GGT/HDL-C ratio was increasingly valuable in predicting NAFLD over time, and was better than HDL-C in predicting NAFLD in the early stage (1–3 years), but was not superior to BMI and GGT.ConclusionsIn this large longitudinal cohort study based on a Chinese population, our results supported that the GGT/HDL-C ratio was positively and nonlinearly associated with the risk of new-onset NAFLD in a non-obese population. In the assessment of future NAFLD risk, the GGT/HDL-C ratio was slightly better than GGT alone; However, the GGT/HDL-C ratio did not appear to have a significant advantage over GGT and BMI alone in predicting NAFLD.

Data-driven reduced-order modeling for nonautonomous dynamical systems in multiscale media

In this article, we present data-driven reduced-order modeling for nonautonomous dynamical systems in multiscale media. The Koopman operator has received extensive attention as an effective data-driven technique, which can transform the nonlinear dynamical systems into linear systems through acting on observation function spaces. Different from the case of autonomous dynamical systems, the Koopman operator family of nonautonomous dynamical systems significantly depend on a time pair. In order to effectively estimate the time-dependent Koopman operators, a moving time window is used to decompose the snapshot data, and the extended dynamic mode decomposition method is applied to computing the Koopman operators in each local temporal domain. Many physical properties in multiscale media often vary in very different scales. In order to capture multiscale information well, the dimension of collected data may be high. To accurately construct the models of dynamical systems in multiscale media, we use high spatial dimension of observation data. It is challenging to compute the Koopman operators using the very high dimensional data. Thus, the strategy of reduced-order modeling is proposed to treat the difficulty. The proposed reduced-order modeling includes two stages: offline stage and online stage. In offline stage, a block-wise low rank decomposition is used to reduce the spatial dimension of initial snapshot data. For the nonautonomous dynamical systems, real-time observation data may be required to update the Koopman operators. The online reduced-order modeling is proposed to correct the offline reduced-order modeling. Three methods are developed for the online reduced-order modeling: fully online, semi-online and adaptive online. The adaptive online method automatically selects the fully online or semi-online and can achieve a good trade-off between modeling accuracy and efficiency. A few numerical examples are presented to illustrate the performance of the different reduced-order modeling methods.

Non-Hermitian Hamiltonian beyond PT symmetry for time-dependent [formula omitted] and [formula omitted] systems — Exact solution and geometric phase in pseudo-invariant theory

In this paper we investigate time-dependent non-Hermitian Hamiltonians, which consist of SU(1,1) and SU(2) generators. The former Hamiltonian is PT symmetric but the latter one is not. A time-dependent non-unitary operator is proposed to construct the non-Hermitian invariant, which is verified as pseudo-Hermitian with real eigenvalues. The exact solutions are obtained in terms of the eigenstates of the pseudo-Hermitian invariant operator for both the SU(1,1) and SU(2) systems in a unified manner. Then, we derive the Lewis–Riesenfeld (LR) phase, which can be separated into the dynamic and the geometrical phases. The analytical results are well consistent with those of the corresponding Hermitian Hamiltonians reported in the literature.

Unitary evolution for a two-level quantum system in fractional-time scenario.

The time-evolution operator obtained from the fractional-time Schrödinger equation(FTSE) is said to be nonunitary since it does not preserve the norm of the vector state in time. As done in the time-dependent non-Hermitian quantum formalism, for a traceless non-Hermitian two-level quantum system, we demonstrate that it is possible to map the nonunitary time-evolution operator in a unitary one. It is done by considering a dynamical Hilbert space with a time-dependent metric operator, constructed from a Hermitian time-dependent Dyson map, in respect to which the system evolves in a unitary way, and the standard quantum mechanics interpretation can be made properly. To elucidate our approach, we consider three examples of Hamiltonian operators and their corresponding unitary dynamics obtained from the solutions of FTSE, and the respective Dyson maps.

Impact response of a viscoelastic plate made of a material with negative Poisson’s ratio1

In this article, the problem on impact response of a viscoelastic plate, made of viscoelastic auxetic with fractional viscosity, has been formulated for the case, when the shear operator is governed by the fractional derivative model, resulting in auxetic’s Poisson’s ratio as a time-dependent operator changing its values from negative to positive magnitudes with time. The proposed mathematical model and numerical calculations based on the obtained asymptotic solutions of the stated problem have verified existing experimental results, which demonstrate enhancing indentation and impact resistance in auxetic materials.

Reduced-quaternionic Mathieu functions, time-dependent Moisil-Teodorescu operators, and the imaginary-time wave equation

We construct a one-parameter family of generalized Mathieu functions, which are reduced quaternion-valued functions of a pair of real variables lying in an ellipse, and which we call λ-reduced quaternionic Mathieu functions. We prove that the λ-RQM functions, which are in the kernel of the Moisil-Teodorescu operator D+λ (D is the Dirac operator and λ∈R∖{0}), form a complete orthogonal system in the Hilbert space of square-integrable λ-metamonogenic functions with respect to the L2-norm over confocal ellipses. Further, we introduce the zero-boundary λ-RQM-functions, which are λ-RQM functions whose scalar part vanishes on the boundary of the ellipse. The limiting values of the λ-RQM functions as the eccentricity of the ellipse tends to zero are expressed in terms of Bessel functions of the first kind and form a complete orthogonal system for λ-metamonogenic functions with respect to the L2-norm on the unit disk. A connection between the λ-RQM functions and the time-dependent solutions of the imaginary-time wave equation in the elliptical coordinate system is shown.

Bounds on quantum evolution complexity via lattice cryptography

We address the difference between integrable and chaotic motion in quantum theory as manifested by the complexity of the corresponding evolution operators. Complexity is understood here as the shortest geodesic distance between the time-dependent evolution operator and the origin within the group of unitaries. (An appropriate 'complexity metric' must be used that takes into account the relative difficulty of performing 'nonlocal’ operations that act on many degrees of freedom at once.) While simply formulated and geometrically attractive, this notion of complexity is numerically intractable save for toy models with Hilbert spaces of very low dimensions. To bypass this difficulty, we trade the exact definition in terms of geodesics for an upper bound on complexity, obtained by minimizing the distance over an explicitly prescribed infinite set of curves, rather than over all possible curves. Identifying this upper bound turns out equivalent to the closest vector problem (CVP) previously studied in integer optimization theory, in particular, in relation to lattice-based cryptography. Effective approximate algorithms are hence provided by the existing mathematical considerations, and they can be utilized in our analysis of the upper bounds on quantum evolution complexity. The resulting algorithmically implemented complexity bound systematically assigns lower values to integrable than to chaotic systems, as we demonstrate by explicit numerical work for Hilbert spaces of dimensions up to \sim 10^4∼104.